10. Suppose y = x2 - 2x - 3. What is a linear equation that intersects the graph of
y=x²-2x-3 in exactly two places? Name the two points of intersection.
Answers
well, let's pick any two random x-values on the quadratic, hmmm say let's use x = 4 and x = 7, so hmm f(4) = 5 and f(7) = 32, that'd give us the points of (4, 5) and (7 , 32).
To get the equation of any straight line, we simply need two points off of it, let's use those two above.
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{32}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{32}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{4}}} \implies \cfrac{ 27 }{ 3 } \implies 9[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 9}(x-\stackrel{x_1}{4}) \\\\\\ y-5=9x-36\implies {\Large \begin{array}{llll} y=9x-31 \end{array}}[/tex]
Check the picture below.
Refer to the attached images.
Related Questions
whats the area of sector and length of arc
Answers
The area of the sector is ≈134 sq units and the length of the arc is ≈16.75
What is a sector of a Circle?The sector of a circle produced by a portion of the circumference (arc) and the circle's radii at both ends of the arc. A sector of a circle can be compared to a piece of pizza or a pie in shape.
The length of an arc is the distance between two point in the section of a curve.
According to the given information:
Given that radius= 16 in, ∅ = 60°
The formula for finding the area of sector= (∅/360°)[tex]\pi r^{2}[/tex]
Substituting values in the formula we get
= (60°/360°)*3.14*[tex]16^{2}[/tex]
=133.9733
≈134 sq units.
The formula for Finding Arc Length = (∅/360°)[tex]2\pi r[/tex]
On substituting the values
= (60°/360°)*2*3.14*16
=16.74666
≈16.75 in
To know more about arc length visit: https://brainly.com/question/16403495
#SPJ1
A certain test is going to be repeated until done satisfactorily. Assume that repetitions of the test are independent and that each has probability 0.25 of being satisfactory. The first 5 tests cost $100 each to perform and thereafter cost $40 each, regardless of the outcomes. Find the expected cost of running the tests until a satisfactory result is obtained.
Answers
Result obtained is $460
Answer:Let X denote the number of tests that need to be performed until a satisfactory result is obtained. Then X has a geometric distribution with p = 0.25. Therefore,X ~ Geo(0.25) E[X] = 1/p = 1/0.25 = 4 tests.For the first 5 tests, the cost is $100 each. So the cost of running the first 5 tests is 5 × $100 = $500. Thereafter, the cost of each test is $40. The expected cost of running the tests until a satisfactory result is obtained is given by:E(Cost) = $500 + E(X – 5) × $40Expected Cost = $500 + (E(X) – 5) × $40= $500 + (4 – 5) × $40= $460Therefore, the expected cost of running the tests until a satisfactory result is obtained is $460.
Learn more about Geometric distribution
brainly.com/question/14394276
#SPJ4
A popular board game manufacturer was interested in the relationship between the amount of time it takes to play a
game and how well that game is rated among board game players. Information was collected on several board games
and was used to obtain the regression equation ý = 27.273x + 18.182, where x represents time it takes to play (in
hours) and ŷ is the predicted rating of that game (in points). Which statement best describes the meaning of the y-
intercept of the regression line?
O When the rating of a game is 0 points, the predicted time to play is 0 hours.
O When the rating of a game is 0 points, the predicted time to play is 18.182 hours.
O When the time to play is 0 hours, the predicted rating is 18.182. This interpretation is not meaningful since a game
cannot have a playtime of 0 hours.
O When the time to play is 0 hours, the predicted rating is 27.273. This interpretation is not meaningful since a game
cannot have a playtime of 0 hours.
Answers
We can see here that the best description of the meaning of the y-intercept of the regression line, as given by the equation ý = 27.273x + 18.182, is: C. "When the time to play is 0 hours, the predicted rating is 18.182. This interpretation is not meaningful since a game cannot have a playtime of 0 hours."
What is y-intercept ?The y-intercept is a term used in the context of a linear equation or a graph to describe the point at which the graph intersects or crosses the y-axis. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
The y-intercept is the value of ŷ (the predicted rating) when x (the time to play) is zero. However, in this context, it does not make sense for a game to have a playtime of zero hours. Therefore, the interpretation of the y-intercept in this case is not meaningful or applicable to the real-world scenario of board games.
Learn more about intercept on https://brainly.com/question/25722412
#SPJ2
write the recursive formula of a1=3 d =-8
Answers
Recursive fοrmula οf a1 = 3, d = -8 is -29 = -21 + (-8)
What is the recursive fοrmula?Any term οf a series can be defined by its preceding term in a recursive fοrmula (s).
The recursive fοrmula fοr an arithmetic sequence with first term a1=3 and cοmmοn difference d=-8 is:
an = an-1 + d, where n >= 2
Expanding the fοrmula fοr the first few terms, we get:
a2 = a1 + d = 3 - 8 = -5
a3 = a2 + d = -5 - 8 = -13
a4 = a3 + d = -13 - 8 = -21
a5 = a4 + d = -21 - 8 = -29
Nοw,
Recursive fοrmula οf a1 = 3, d = -8 is -29 = -21 + (-8)
To know more about recursive formula visit,
https://brainly.com/question/26123816
#SPJ1
Part 1: "Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted a job that pays $8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least $80 a week, working a combination of both jobs.
Write a system of inequalities that can be used to represent the situation. "
Part 2: Determine and state one combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours.
Much appreciated!
Answers
a) The system of inequalities that can be used to represent the situation is x + y ≤ 15 and 4x + 8y ≥ 80
b) One combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours is 10 hours babysitting and 5 hours as a library assistant.
To start, we know that Edith can work no more than 15 hours per week. Therefore, we can write the following inequality:
x + y ≤ 15
Next, we know that Edith earns $4 per hour babysitting and $8 per hour as a library assistant. We want her to earn at least $80 per week, so we can write the following inequality:
4x + 8y ≥ 80
This inequality states that the total amount Edith earns from both jobs (4x + 8y) must be greater than or equal to $80.
Now that we have two inequalities, we have a system of inequalities that can be used to represent the situation:
x + y ≤ 15
4x + 8y ≥ 80
To determine one combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours, we can solve this system of inequalities.
Let's solve the first inequality for y:
y ≤ 15 - x
Now we can substitute this expression for y into the second inequality:
4x + 8(15 - x) ≥ 80
Simplifying and solving for x, we get:
-4x + 120 ≥ 80
-4x ≥ -40
x ≤ 10
To find the number of hours she should work as a library assistant, we can substitute x = 10 into our expression for y:
y ≤ 15 - x
y ≤ 15 - 10
y ≤ 5
So Edith should work no more than 5 hours as a library assistant per week.
To know more about inequality here
https://brainly.com/question/28823603
#SPJ4
For each of the following situations, find the criticalvalue(s) for z or t. State if z or t for each answer.
Round to two decimal places as needed.
a) H0: μ=115 vs. HA: μ ≠115 at α= 0.05; n= 41
b) H0: p=0.14 vs. HA: p>0.14 at α= 0.10
c) H0: p= 0.6 vs. HA: p≠ at α=0.01
d) H0: p=0.8 vs. HA: p<0.8 at α=0.01; n=500
e) H0: p=0.9 vs. HA: p< at α=0.01
Answers
For each of the following situations the critical value are:
a) H0: μ=115 vs. HA: μ ≠115 at α= 0.05; n= 41, the critical values are ±1.96.
b) H0: p=0.14 vs. HA: p>0.14 at α= 0.10, the critical value is 1.28.
c) H0: p= 0.6 vs. HA: p≠ at α=0.01 - z = 2.326, the critical values are ±2.58.
d) H0: p=0.8 vs. HA: p<0.8 at α=0.01; n=500, the critical value is -2.33.
e) H0: p=0.9 vs. HA: p< at α=0.01, the critical value is -2.33.
a) Since n=41 is greater than 30, we can use a z-test. The test is two-tailed because the alternative hypothesis is μ≠115. Using a significance level of 0.05, the critical values are ±1.96. Therefore, the rejection region is z < -1.96 or z > 1.96.
b) Since we are testing a proportion, we can use a z-test for proportions. The test is one-tailed because the alternative hypothesis is p > 0.14. Using a significance level of 0.10, the critical value is 1.28. Therefore, the rejection region is z > 1.28.
c) Since we are testing a proportion, we can use a z-test for proportions. The test is two-tailed because the alternative hypothesis is p≠0.6. Using a significance level of 0.01, the critical values are ±2.58. Therefore, the rejection region is z < -2.58 or z > 2.58.
d) Since n=500 is greater than 30, we can use a z-test for proportions. The test is one-tailed because the alternative hypothesis is p < 0.8. Using a significance level of 0.01, the critical value is -2.33. Therefore, the rejection region is z < -2.33.
e) Since we are testing a proportion, we can use a z-test for proportions. The test is one-tailed because the alternative hypothesis is p < 0.9. Using a significance level of 0.01, the critical value is -2.33. Therefore, the rejection region is z < -2.33.
Learn more about critical value at https://brainly.com/question/29672811
#SPJ11
Triangles ABD and BCD are both isosceles.
AD = BD
AC is a straight line.
Is ADC a right angle?
Clearly explain your awnswer?
Answers
Answer:I could possibly be wrong but I say no. From what I remember, with these things you can put the points wherever as long as it follows the rules you were given for each triangle.
Step-by-step explanation:
I actually drew it out, and to me it appears as it’s not, yet I could be wrong and I’m sorry if I am! Angles aren’t my best, but I’m really good at math! If you have other problems I can go over them
For the right triangles below, find the exact values of the side lengths b and d.
If necessary, write your responses in simplified radical form.
Answers
From the right triangle figure the sides are solved to be
side b = 4√2side d = 7√3 / 2How to find side b and side dThe side b and side d is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The figure describes a right triangle, and side b is calculated using sin, SOH
Sin 45 = opposite / hypotenuse
Sin 45 = b / 8
b = 8 * sin 45
b = 4√2
Solving for side d
sin 60 = d / 7
d = 7 * sin 60
d = 7√3 / 2
Learn more about SOH CAH TOA here:
https://brainly.com/question/29402966
#SPJ1
I need help I tried everything
Answers
Explanation
If you match ∠EFG with its congruent ∠YXZ
based on
E ~ Y
G ~ Z
EG ~ YZ,
This means
✅ EF ~ YX
✅ ∠F ~ ∠X
It’s easier to see when you rotate your triangle and match up the congruent angles, you can see both answers are correct. I attached my example. I hope it helps
A movie production company was interested in the relationship between the budget to make a movie and how well that
movie was received by the public. Information was collected on several movies and was used to obtain the regression
equation ý = 0.145x + 0.136, where x represents the budget of a movie (in millions of dollars) and y is the predicted
score of that movie (in points from 0 to 1). What is the predicted score of a movie that has a $5 million budget?
O 0.145 points
O 0.72 points
0.861 points
O 33.55 points
Answers
Answer: 0.72 pts.
Step-by-step explanation:
6*3 = n-4
6*3 = n-4
__ = n-4
18+4 = n-4
__ = n
Answers
so yeah the answers
Answer:
6*3
n=26
PROJECT: RELIABLE FINANCIAL INFORMATION, I need help with this pleaseee , im giving 80 points
Answers
Ratio analysis is the best way to ensure reliable financial information, as it allows investors to evaluate the financial strength of a company and the reliability of its financial information by calculating ratios such as the current ratio, quick ratio, and debt-to-equity ratio.
Reliable financial information is information that is accurate and up-to-date. It is the foundation of any investor’s decision-making process, as it allows them to make informed decisions. One of the best ways to ensure reliable financial information is to perform a ratio analysis. Ratio analysis is the process of evaluating financial information by calculating ratios such as the current ratio, quick ratio, and debt-to-equity ratio.
The current ratio is calculated by dividing a company’s current assets by its current liabilities. This ratio measures a company’s ability to pay its short-term obligations. The quick ratio is calculated by dividing a company’s current assets minus inventory by its current liabilities. This ratio measures a company’s ability to pay its short-term obligations without having to sell its inventory. The debt-to-equity ratio is calculated by dividing a company’s total liabilities by its total number. This ratio measures how much debt a company has relative to its equity.
By looking at these ratios, investors can get an idea of the financial strength of a company and the reliability of its financial information. The higher the ratios, the more reliable the financial information is likely to be
Learn more about total number here:
https://brainly.com/question/14993202
#SPJ4
Complete question:
How can investors ensure reliable financial information?
You are rolling two dice and one coin. Find the probability of rolling a three on the first dice, a four on the second dice, and flipping a heads on the coin.
A. 1/8
B. 1/72
C. 1/112
D. 1/36
Answers
If you are rolling two dice and one coin. the probability of rolling a three on the first dice, a four on the second dice, and flipping a heads on the coin is B. 1/72.
How to find the probability?Probability of rolling a three on the first dice is 1/6, the probability of rolling a four on the second dice is 1/6, and the probability of flipping a heads on the coin is 1/2.
To find the probability of all three events happening together, we need to multiply the probabilities of each individual event:
(1/6) x (1/6) x (1/2) = 1/72
Therefore, the probability is B. 1/72.
Learn more about probability here:https://brainly.com/question/24756209
#SPJ1
You deposit $2000 into a savings account giving 7% interest compounded only at the end of the year. To nearest dollar, what is your end-of-year balance?
Answers
well, you'd have the 2000 plus the 7% :|
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 2000}}{\left( \cfrac{7}{100} \right)2000}\implies 140~\hfill \underset{ new~balance }{\stackrel{ 2000~~ + ~~140 }{\text{\LARGE 2140}}}[/tex]
A = P(1 + r/n)^(nt)
Where:
A = the end-of-year balance
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded in a year
t = the time (in years)
In this case, P = $2000, r = 7% = 0.07, n = 1 (compounded annually), and t = 1 (one year).
Plugging these values into the formula, we get:
A = 2000(1 + 0.07/1)^(1*1)
A ≈ $2,140.00
Therefore, to the nearest dollar, the end-of-year balance is $2,140.
The tables show the attendances at volleyball games and basketball games at a school during the year.
Express the difference in the measures of center as a multiple of the measure of variation. Round your answers to the nearest tenth.
The difference in the means is about (blank) to (blank) times the MAD.
Solve for blanks
Answers
a) Compare the populations using measures of center and variation. Mean and MAD of vollyball game attendence are 86, 19.6 respectively. Mean and MAD of basketball game attendence are 185, 17.7 respectively.
b) Difference in the measures of center as a -4.6 to 5.1 multiple of the measure of variation. The difference in the means is about -4.6 to 5.1 times the MAD.
We have two tables consists attendances at volleyball games and basketball games at a school during the year. See the above figure carefully. Now, Compare the populations using measures of center and variation : As we know mean of data is calculated by dividing the sum of data values to the number of data values. Here, Sum of vollyball attendence values, ∑xᵢ = 1720
Number of days = 20
So, mean of vollyball game attendence
= 1720/20 = 86
Sum of basketball ball attendence values, ∑yᵢ = 3700
Number of days = 20
So, mean of basketball ball game attendence = 3700/20 = 185
Now, measure absolute deviations, MAD
MAD of vollyball game attendence is
= [∑( mean of vollyball game attendence - attendance values (i))]/number of days
= 392/20 = 19.6
MAD of basketball ball game attendence is = [∑( mean of basketball ball game attendence - attendance values (i))]/number of days
= 354/20 = 17.7
b) Now, we check the relation between difference in the measures of center as a multiple of the measure of variation.
A : vollyball game attendence
B : basketball game attendence
difference in the measures of center
= Mean (A) - Mean(B) or Mean(B) - Mean (A)
measure of variation, MAD(A) , MAD(B)
[Mean (A) - Mean (B)]/MAD(A)
= ( 86 - 185)/19.6
= -4.643 ~ -4.6
[Mean (B) - Mean (A)]/MAD(B)
= ( 185 - 86)/17.7
= 91/17.7 = 5.1412 ~ 5.1
Hence, difference in the means is about -4.6 to
5.1 times the MAD.
For more information about Measure of variance, visit :
https://brainly.com/question/28420527
#SPJ4
Complete question :
The above tables show the attendances at volleyball games and basketball games at a school during the year. Volleyball Game Attendance Basketball Game Attendance 112 95 84106 62 68 75 88 93 127 98 117 60176 141 152 181 198 21 49 5485 74 88 132 5 202 190 173 155 169 188 195 4 179 163 186 184207 219 228
a) Compare the populations using measures of center and variation.
b) Express the difference in the measures of center as a multiple of the measure of variation. Round your answers to the nearest tenth. The difference in the means is about (blank) to (blank) times the MAD.
What is 52s+30b it is on an I ready
Answers
Another representation of the given algebraic expression 52s + 30b as required is; 2 (26s + 15b).
Which expression is equivalent to the given expression 52s + 30b?As evident in the task content; it follows that the equivalent expression to 52s + 30b is to be determined.
Given; 52s + 30b
Since 2 is a common factor to both terms of the equation; we have that;
2 (26s + 15b)
Ultimately, the equivalent expression is; 2 (26s + 15b).
Complete question:
What is 52s+30b in a factorized form.
Read more on equivalent expressions;
https://brainly.com/question/15775046
#SPJ1
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds and each large box of paper weighs 80 pounds. A total of 28 boxes of paper were shipped weighing 1850 pounds altogether. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
Answers
We can write the following system of equations:
x + y = 28 (equation 1)
50x + 80y = 1850 (equation 2)
What are equations?An equation is a statement that two expressions are equal. It consists of two expressions, separated by an equals sign. The expression on the left-hand side of the equals sign is equal to the expression on the right-hand side. Equations can be used to represent relationships between variables, to solve problems, and to describe mathematical models. They are an important tool in algebra, calculus, and other areas of mathematics.
What is linear equations?A linear equation is an algebraic equation of the first degree, which means that the variables in the equation have an exponent of one and are not multiplied or divided by any other variables. Linear equations can have one or more variables and are typically represented graphically by a straight line.
In the given question,
Let x be the number of small boxes shipped and y be the number of large boxes shipped.
From the problem, we know that each small box of paper weighs 50 pounds and each large box of paper weighs 80 pounds. We also know that a total of 28 boxes of paper were shipped weighing 1850 pounds altogether.
Using this information, we can write the following system of equations:
x + y = 28 (equation 1)
50x + 80y = 1850 (equation 2)
In equation 1, x + y = 28 represents the total number of boxes shipped, which is the sum of the number of small boxes shipped (x) and the number of large boxes shipped (y).
In equation 2, 50x + 80y = 1850 represents the total weight of the boxes shipped, which is the sum of the weight of each small box (50x) and the weight of each large box (80y).
To know more about equations,visit:
https://brainly.com/question/29538993
#SPJ9
If f(3x) = f(3) + f(x) then show that f(1) = f(3) = f(9) = f(27) = f(81)
Answers
Answer:f(1) = f(3) = f(9) = f(27) = f(81).
Step-by-step explanation:To show that f(1) = f(3) = f(9) = f(27) = f(81), we can use the given equation and substitute x with different values.
Let x = 1:
f(3x) = f(3) + f(x)
f(3(1)) = f(3) + f(1)
f(3) = f(3) + f(1) (since f(3x) = f(3) + f(x) when x = 1)
f(1) = 0
Now, let x = 3:
f(3x) = f(3) + f(x)
f(3(3)) = f(3) + f(3)
f(9) = 2f(3)
Since we already know that f(3) = f(3) + f(1), we can substitute it into the equation above:
f(9) = 2f(3) = 2(f(3) + f(1)) = 2f(3) + 2f(1)
f(9) - 2f(3) = 2f(1)
Now let x = 9:
f(3x) = f(3) + f(x)
f(3(9)) = f(3) + f(9)
f(27) = f(3) + f(9)
We can substitute the expression for f(9) we just derived:
f(27) = f(3) + (f(9) - 2f(3))
f(27) = f(9) - f(3)
f(27) = 2f(3) - f(3)
f(27) = f(3)
Finally, let x = 27:
f(3x) = f(3) + f(x)
f(3(27)) = f(3) + f(27)
f(81) = f(3) + f(27)
We can substitute the expression for f(27) we just derived:
f(81) = f(3) + f(27)
f(81) = f(3) + f(3)
f(81) = 2f(3)
Since we know that f(27) = f(3), we can substitute it into the equation above:
f(81) = 2f(3) = 2(f(27)) = 2(f(9) - f(3)) = 2f(9) - 4f(3)
We also know that f(9) = 2f(3) + 2f(1) from our earlier work, so we can substitute it into the equation above:
f(81) = 2f(9) - 4f(3) = 2(2f(3) + 2f(1)) - 4f(3) = 4f(3) + 4f(1) - 4f(3) = 4f(1)
Therefore, we have shown that f(1) = f(3) = f(9) = f(27) = f(81).
On Cupcake Wars, the bakers must fill 1000 cupcakes in the final challenge!
CUPCAKE
WARS
If the cupcakes are cylinder shaped and have a radius of 1.5 in and a height of 3.01 in,
how many cubic inches are need to fill 1000 cupcakes?
Use pi=3.14
Round your answer to the nearest hundredth as needed.
V=
Answers
Answer:
21,265.65 in³
Step-by-step explanation:
Formula: Volume (V) = πr²h
V = πr²h
Slotting in values,
V = 3.14 x 1.5² x 3.01
V = 3.14 x 2.25 x 3.01
V = 21.26565 in³
But that is for 1 cupcake
To fill a thousand of them, you will need to multiply your answer by the number of cupcakes in total.
Therefore,
Answer = V x 1000
Answer = 21.26565 x 1000
Answer = 21,265.65 in³
The answer is already rounded to the nearest hundredth,
So they would need 21,265.65 cubic inches (in³) to fill 1000 cupcakes.
Please mark brainliest.
Thanks.
The school that Natalie goes to is selling tickets to a play. On the first day of ticket sales the school sold 15 adult tickets and 5 student tickets for a total of $265. The school took in $419 on the second day by selling 15 adult tickets and 16 student tickets. What is the price each of one adult ticket and one student ticket
Answers
Answer:
Let x be the price of one adult ticket, and y be the price of one student ticket.
From the information given in the problem, we can set up the following system of equations:
15x + 5y = 265 (equation 1)
15x + 16y = 419 (equation 2)
We can solve for x by subtracting equation 1 from equation 2:
15x + 16y - (15x + 5y) = 419 - 265
11y = 154
y = 14
Now we can substitute y = 14 into either equation 1 or equation 2 to solve for x. Let's use equation 1:
15x + 5(14) = 265
15x + 70 = 265
15x = 195
x = 13
Therefore, one adult ticket costs $13, and one student ticket costs $14.
Solve to find the value of x ? 4x -10 = 50
Answers
Answer:
x = 15
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.
Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, add 10 to both sides of the equation:
[tex]4x - 10 = 50\\4x - 10 (+10) = 50 (+10)\\4x = 50 + 10\\4x = 60[/tex]
Next, divide 4 from both sides of the equation:
[tex]4x = 60\\\frac{4x}{4} = \frac{60}{4} \\x = \frac{60}{4} = 15\\x = 15[/tex]
~
x = 15 is your answer.
~
Learn more about PEMDAS, here:
https://brainly.com/question/26499272
Answer:
[tex]\tt x=15[/tex]Step-by-step explanation:
[tex]\tt 4x -10 = 50[/tex]
Add 10 to both sides:-
[tex]\tt 4x-10+ 10 = 50+ 10[/tex][tex]\tt 4x=60[/tex]Divide both sides by 4:-
[tex]\tt \cfrac{4x}{4} =\cfrac{60}{4}[/tex][tex]\tt x=15[/tex]___________________
Hope this helps!
The rectangular floor of a classroom is 28 feet in length and 22 feet in width. A scale drawing of the floor has a length of 14 inches. What is the perimeter, in inches, of the floor in the scale drawing?
Answers
The value of the calculated perimeter, in inches, of the floor in the scale drawing is 50 inches
What is the perimeter, in inches, of the floor in the scale drawing?The dimensions of the rectangular floor is calculated as
Dimension = 28 feet in length and 22 feet in width
The length of the scale is given as
Scale length = 14 inches
When the above is compared, we can see that
The length is divided by 2 to get the scale length
So, we have
Scale width = 22 inches/2
Evaluate
Scale width = 11 inches
The perimeter is then calculated as
Perimeter = 2 * (Length + width)
So, we have
Perimeter = 2 * (14 + 11)
Evaluate
Perimeter = 50 inches
Hence, the perimeter is 50 inches
Read more about perimeter at
https://brainly.com/question/24571594
#SPJ1
What additional information do you need to know to prove Triangle KLM is congruent to Triangle UTS by SAS?
a
b
KM is congruent to SU
c
d
LM is congruent to ST
Answers
As a result, the answer to the following question, We may use the SAS criteria to argue that the two triangles are congruent if we know that KM is congruent to SU.
What precisely is a triangle?A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.
Option b: KM is congruent to SU is the additional information required by SAS to demonstrate Triangle KLM is congruent to Triangle UTS.
To demonstrate that two triangles are congruent using the SAS (Side-Angle-Side) congruence criterion, we must demonstrate:
Two comparable side pairs are congruent.
The angle included (the angle formed by these two sets of sides) is congruent.
In this situation, we are told that LM is congruent to ST, but we must still demonstrate that another pair of sides is congruent. We may use the SAS criteria to argue that the two triangles are congruent if we know that KM is congruent to SU.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
im stuck on this question, please help. it's geometry. thanks!!
Answers
Angle 1 = Angle 2 = Angle 3 = Angle 4, we can infer.
What is meant by a "right angle"?A right angle is an angle with a measure that is exactly equal to 90 degrees (or /2).
We can observe that a transversal divides two parallel lines in the given diagram. Let's give the angles names:
The angle created by the junction of line m and line p is Angle 1, which is located in the top left corner.
The angle created by the intersection of line n and line p is Angle 2, which is located in the top right corner.
Line n and line q intersect at angle 3, which is located in the lower right corner.
The angle created by the junction of line m and line q is angle 4, which is located in the lower left corner.
As they are on the same side of the transversal and in corresponding locations with respect to the parallel lines, we can see that angles 1 and 2 are corresponding angles. When lines are cut by a transversal, corresponding angles are congruent, hence we know that:
1 + 2 = an angle.
Due to their placement on opposing sides of the transversal and in-between the parallel lines, angles 2 and 3 can also be seen to represent alternate internal angles. When lines are cut by a transversal, alternate inner angles are congruent, hence we know that:
2 + 3 = a right angle
As they are on the same side of the transversal and in corresponding locations with respect to the parallel lines, we can see that angles 3 and 4 are corresponding angles. When lines are cut by a transversal, corresponding angles are congruent, hence we know that:
Angle 3 = angle 4 =...
So, Angle 1 = Angle 2 = Angle 3 = Angle 4 follows.
To know more about Angle visit:
https://brainly.com/question/28451077
#SPJ1
Tammy’s water bill is automatically deducting $160 from her bank account every other month. How
much will the deductions total for two years?
Answers
Answer:
$1920
Step-by-step explanation:
If Tammy's water bill is deducting $160 every other month for 2 years, (or $160 a month for 1 year since we skip a month every two months), then you would multiply $160 by 12 months to get $1920.
HELP I'LL GIVE BRAINLIEST AND FIVE STARS IF YOU GET THIS RIGHT
Find the range of the function given the graph below.
Answers
The range of the given graph will be [-1, 2.9].
How to Determine a Function's Range?Think about the function y = f. (x).
The range of the function is the range of all the y values, from least to maximum. Substitute all possible values of x into the provided expression of y to see whether it is positive, negative, or equal to other values.
A bar chart with bars for each dimension (category) that range between a start value and an end value is called a range bar chart. To track a project schedule, for instance, Range Bar charts can be used to show the start and finish of activities or tasks along a time axis, much like a Gantt chart.
To learn more about range of graph from given link
https://brainly.com/question/29899357
#SPJ1
A student is equally likely to select pizza, nachos, or chicken for lunch. What is the probability that the student DOES NOT select chicken?
1/3, 1/2, 2/3 or 1?
Please help soon I need the answer as soon as possible thanks
Answers
If a student is equally likely to select pizza, nachos, or chicken for lunch, the probability that the student does not select chicken is 2/3.
Since the student has three equally likely options to choose from, the probability of selecting each option is 1/3. Therefore, the probability of the student selecting chicken is 1/3.
To calculate the probability that the student does not select chicken, we need to subtract the probability of selecting chicken from 1. This is because the sum of all possible outcomes must equal 1, and if we know the probability of one outcome, we can find the probability of its complement (not selecting chicken) by subtracting it from 1.
Therefore, the probability that the student does not select chicken is:
1 - 1/3 = 2/3
So, the correct answer is 2/3.
In summary, when the probability of each possible outcome is equal, we can find the probability of an event (in this case, not selecting chicken) by subtracting the probability of that outcome from 1.
To learn more about probability click on,
https://brainly.com/question/22005770
#SPJ4
A fair coin is tossed three times and the events A,B , and C are defined as follows: A:{ At least one head is observed } B:{ At least two heads are observed } C:{ The number of heads observed is odd } Find the following probabilities by summing the probabilities of the appropriate sample points (note that 0 is an even number): (a) P(notB)= (b) P((notA) or C)= (c) P(A or B or C)= Note: You can earn partial credit on this problem. You have attempted this problem 0 times. You have unlimited attempts remaining
Answers
The event C is: C = { HHT, HTH, THH, HTT, THT, TTH }
P(C) = 1/2
(a) P(notB) = 1/2
(b) P((notA) or C) = 5/8
(c) P(A or B or C) = 7/8
Solution:
A fair coin is tossed three times, and the events A, B, and C are defined as follows: A: { At least one head is observed } B: { At least two heads are observed } C: { The number of heads observed is odd }
The sample space of the given event is as follows:
S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Probability of the occurrence of A:
If at least one head is observed, then it can be possible in the following ways:
(i) HHT, HTH, THH, or
(ii) HHT, HTH, THH, or HTT, THT, TTH, or
(iii) HHT, HTH, THH, or HTT, THT, TTH, or HHH
Therefore, the event A is: A = { HHT, HTH, THH, HTT, THT, TTH, HHH }
P(A) = 7/8
Probability of the occurrence of B:
If at least two heads are observed, then it can be possible in the following ways:
(i) HHT, HTH, THH, or
(ii) HTT, THT, TTH, or
(iii) HHH
Therefore, the event B is: B = { HHT, HTH, THH, HTT, THT, TTH, HHH }
P(B) = 7/8
Probability of the occurrence of C:
If the number of heads observed is odd, then it can be possible in the following ways:
(i) HHT, HTH, THH, or
(ii) HTT, THT, TTH
Therefore, the event C is: C = { HHT, HTH, THH, HTT, THT, TTH }
P(C) = 1/2
Probability of the occurrence of notB:
Not B means "at least one head" or "no head." So, the event notB is not the event B, which means the event (notB) is the event in which we do not get at least two heads.
The (notB) event is: (notB) = { TTH, THT, HTT, TTT }
P(notB) = 4/8 = 1/2
Probability of the occurrence of (notA) or C:
The event (notA) means that we don't get at least one head, which means we get all tails. The (notA) event is: (notA) = { TTT }
P(notA) = 1/8
Now, we will find P((notA) or C).
For this, we can take the union of (notA) and C.
(notA) ∪ C = { HHT, HTH, THH, HTT, THT, TTH, TTT }
P((notA) or C) = 7/8
Probability of the occurrence of A or B or C:
The probability of the occurrence of A or B or C can be found as follows:
P(A or B or C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
Here, A ∩ B = { HHT, HTH, THH, HHH }, A ∩ C = { HHT, HTH, THH }, B ∩ C = { HHT, HTH, THH }, and A ∩ B ∩ C = { HHT, HTH, THH }.
Substituting these values, we get:
P(A or B or C) = 7/8 + 7/8 + 1/2 - 3/8 - 3/8 - 1/8 + 1/8
P(A or B or C) = 7/8
Learn more about Event
brainly.com/question/12961938
#SPJ4
Select the shapes that can be classified as rectangles.
Four shapes. The first shape has two pairs of parallel lines of equal length, with four right angles. The second shape has four sides of equal length, two pairs of opposite sides that are parallel, and four right angles. The third shape has two pairs of opposite sides that are parallel and of equal length, with no right angles. The fourth shape has no sides of equal length, no parallel sides, and no right angles.
Shapes 1 and 2
Shapes 1 and 3
Shapes 2 and 4
Shapes 3 and 4
Answers
Shapes 1 and 2 that can be classified as rectangles.
What are rectangles?Rectangles are geometric shapes with four sides and four angles. They are characterized by having opposite sides that are parallel and of equal length, and all four angles are right angles (90 degrees).
Rectangles are also known as quadrilaterals, which means they have four sides.
The second shape can be classified as a rectangle as it has four sides of equal length, two pairs of opposite sides that are parallel, and four right angles.
The first shape can also be classified as a rectangle as it has two pairs of parallel lines of equal length, with four right angles.
Learn about Properties of rectangle here https://brainly.com/question/12190011
#SPJ1
Make x the subject of the formula a/b = 2x/x+5
Answers
As a result, when x = -5a /, the subject of the formula a/b = 2x/(x + 5) is x. (a - 2b).
How may the subject formula for JSS3 be changed?For instance, C is the subject of the formula C = 2r, which calculates the circumference of a circle. To modify the subject of a formula is to rewrite it such that the quantities are still related in the right way. M/2 equals D if M = 2D.
In order to eliminate the fraction and make x the subject of the formula a/b = 2x/(x + 5), we can cross-multiply:
a(x + 5) = 2bx
Next, we can distribute the a:
ax + 5a = 2bx
We can now separate the x terms from the constant terms on each side:
ax - 2bx = -5a
x(a - 2b) = -5a
Finally, we can solve for x by dividing both sides by (a - 2b):
x = -5a / (a - 2b).
To know more about formula visit:-
https://brainly.com/question/4183767
#SPJ1