The exact values for the intersection point is (20/9, -107/9)
Given the system of equation expressed as;
y = −13x + 17;
y = 5x - 23
Since they are both y-values, we will equate both expressions to have:
-13x + 17 = 5x - 23
-13x - 5x = -23 - 17
-18x = -40
x = 40/18
x = 20/9
Substitute x = 20/9 into equation 2:
y = 5x - 23
y = 5(20/9) - 23
y = 100/9 - 23
y = -107/9
Hence the exact values for the intersection point is (20/9, -107/9)
Learn more on solution to equations here: https://brainly.com/question/13729904
Answer:
The answer is 7.5 and 14.5
( 7.5 , 14.5 )
Step-by-step explanation:
Find the missing segment in the attached image
Answer:
? = 78
Step-by-step explanation:
Use similar triangles.
26/12 = (26 + ?)/48
13/6 = (26 + ?)/48
6(26 + ?) = 13 * 48
156 + 6? = 624
6? = 468
? = 78
Answer:
The missing segment is equal to 78
Step-by-step explanation:
Using the similarity of triangles:
[tex]x=?[/tex]
[tex]$\frac{x+26}{48}=\frac{26}{12} $[/tex]
[tex]12(x+26)=48 \cdot 26[/tex]
[tex]12x+312=1248[/tex]
[tex]12x+312=1248[/tex]
[tex]12x=936[/tex]
[tex]x=78[/tex]
A freight train is carrying goods across the country. The number of gallons of fuel it has used varies directly with the distance it has traveled. See the graph
below.
Answer:
0.125 miles per gallon.
Step-by-step explanation:
After 200 gallons used the freight train has traveled 25 miles. This means that we need to divide both sides by 200 to get a singular gallon's worth of miles traveled. 200/200 is 1, and 25/200 is 0.125.
---------------------
Extra
---------------------
IF it were how many gallons per mile, you would divide both answers by 25 resulting in 8 gallons per mile.
PLEASE!!! HELP!!! Question: If you have points on a graph that plot (1,7), (2,8), (3,5) and (4,6) what would be the slope?
Answer:
1
Step-by-step explanation:
You only need two points to find the slope.
Let's use (1,7) and (2,8).
The formula for slope is (y2-y1)/(x2-x1)
Let's plug the values in:
(8-7)/(2-1) = 1.
So, the slope is 1.
Using this coin and a number cube, which simulation would help you answer this question? A professor found that her students pass the final exam about 50% of the time. She gives the exam during the fall, spring, and summer terms. If she has 30 students during each term and you choose a student at random, what are the chances that the student passed the exam during the fall term.
Answer:
didnt understand the quedtion clearly
Find the volume of a right circular cone that has a height of 18.8 in and a base with a
diameter of 14.3 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
The volume of the cone is 1006.9in³
Step-by-step explanation:
Given
[tex]Height = 18.8\ in[/tex]
[tex]Diameter = 14.3\ in[/tex]
Required
Calculate the volume;
The volume of a cone is calculated as thus;
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Where V represents volume; r represents radius; and h represents height
The radius is calculated as thus;
[tex]r = \frac{1}{2}Diameter[/tex]
[tex]r = \frac{1}{2} * 14.3[/tex]
[tex]r = 7.15[/tex]
Substitute [tex]r = 7.15[/tex]; [tex]h = 18.8[/tex] and [tex]\pi = \frac{22}{7}[/tex]
[tex]V = \frac{1}{3} \pi r^2h[/tex] becomes
[tex]V = \frac{1}{3} * \frac{22}{7} * 7.15^2 * 18.8[/tex]
[tex]V = \frac{1}{3} * \frac{22}{7} * 51.1225 * 18.8[/tex]
[tex]V = \frac{22* 51.1225 * 18.8}{3 * 7}[/tex]
[tex]V = \frac{21144.266}{21}[/tex]
[tex]V = 1006.86980952[/tex]
[tex]V = 1006.9\ in^3[/tex] (Approximated)
Hence, the approximated volume of the cone is 1006.9in³
Answer:1006.5
Step-by-step explanation:
how would a bank represent a withdrawal of 19.43 dollars?
Answer:
-19.43
Step-by-step explanation:
Withdrawals are negative
How many distinct triangles can be drawn using three of the dots below as vertices?
Answer:
The number of distinct triangles that can be drawn using the dots = 6
Step-by-step explanation:
The parameters given are;
Two rows of three evenly spaced dots
To form a triangle, two dots will be selected from 1 row while the third dot will be selected from the other row
The number of ways of selecting the dots are therefore;
₃C₂ × ₃C₁ = 3 × 3 = 9 triangles
The same procedure can be done from the top row to give another 9 triangles
Which gives the total number of triangles = 18 triangles
The number of distinct triangles are found as follows;
Given that triangles obtained from the top row are similar to those of the bottom row, we reduce the range from which the distinct triangles can be found to 19 - 9 = 9 triangles
Of the 9 triangles formed by one dot on top and two dots on the bottom, the two adjacent dots of the three dots which are on the left and on the right of the lower row of dots, form the same three triangles with the three dots on the top row
Therefore, since there are 3 sets of two dots forming 9 triangles, each pair of dots can form 3 triangles, and as mentioned, 2 pairs of dots of the 3 pairs form the same triangles making the distinct triangle = 9 - 3 = 6.
Sorry the question before didnt make sense.heres the full pic .
Answer:
No
Step-by-step explanation:
The question is:
Are 3/5 and 6/25 equivalent fractions?
Multiply the first fraction by 5/5:
3/5 * 5/5 = 15/25
3/5 is equivalent to 15/25
15/25 is not equal to 6/25.
Answer: No
2. Company A packages roofing nails in boxes that are normally distributed with a mean of 276 nails and a standard deviation of 5.8 nails. Company B packages roofing nails in boxes that are normally distributed with a mean of 252 nails and a standard deviation of 3.4 nails. Which company is more likely to produce a box of 260 roofing nails? Explain your answer using z-scores.
Answer:
Company B
Step-by-step explanation:
We would use z score formula
z = (x - μ) / σ
x = raw score
μ = mean
σ = Standard deviation
let x = 260 with the mean μ1 = 276 and standard deviation σ = 5.8
let x = 260 with the mean μ2 = 252 and standard deviation σ = 3.4
z1 = (x- μ1) / σ = (260- 276) / 5.8 = -2.7586206897
z2 = (x2 - μ) / σ = (260 -252) / 3.4= 2.3529411765
Comparing the two z scores, we can see that company B has the probability of producing 260 nails because it has a positive z score of approximately 2.35 compared to company A with a z score of -2.76.
Elijah created the scatterplot to show the relationship between the temperature in degrees Fahrenheit and the number of visitors to a zoo. A graph titled Temperature versus Zoo Visitors has Degrees Fahrenheit on the x-axis, and Visitors on the y-axis. Points are at (70, 100), (77, 96), (90, 75), (93, 73), (98, 60). Which is true regarding the data in his scatterplot? As the temperature increases, the number of visitors decreases. As the temperature increases, the number of visitors increases. As the temperature increases, the number of visitors remains the same. As the temperature increases, the number of visitors increases then decreases.
Answer:
A
Step-by-step explanation:
it right on edge
Answer:
A.
Step-by-step explanation:
Did the unit test in edge and got 100
simplify this please 41 =12d-741=12d−7
Answer:
Simplifying
41 = 12d + -7
Reorder the terms:
41 = -7 + 12d
Solving
41 = -7 + 12d
Solving for variable 'd'.
Move all terms containing d to the left, all other terms to the right.
Add '-12d' to each side of the equation.
41 + -12d = -7 + 12d + -12d
Combine like terms: 12d + -12d = 0
41 + -12d = -7 + 0
41 + -12d = -7
Add '-41' to each side of the equation.
41 + -41 + -12d = -7 + -41
Combine like terms: 41 + -41 = 0
0 + -12d = -7 + -41
-12d = -7 + -41
Combine like terms: -7 + -41 = -48
-12d = -48
Divide each side by '-12'.
d = 4
Simplifying
d = 4
The graph of the function F(x) = 2x^2-8 is changed. The new graph can be
represented by the function F(X)= -2x^2-4.
Which of the following describes the changes made to the graph of the
original function?
Answer:
The graph now opens in the opposite direction. The y intercept is shifted up 4.
Step-by-step explanation:
F(x) = 2x^2-8
F(X)= -2x^2-4
We know that the graph is reflected over the y-intercept becuase of the negative sign in the second equation ( F(X)= -2x^2-4)
We know that the intercept is shifted up four, because the number decreased from 8 to 4, and the graph is reflected.
Attacthed is both of the equations graphed to help you visualize this shift!
Choose the single logarithmic expression that is equivalent to the one shown.
log2 6 + log2 2 − log2 8
Answer:
C. log2 3/2.
Step-by-step explanation:
When you are adding two logs with the same base, you multiply.
So, log2 6 + log2 2 = log2 6 * 2 = log2 12
When you subtract two logs with the same base, you divide.
So, log2 12 - log2 8 = log2 12 / 8 = log2 3/2
The answer is C. log2 3/2.
Hope this helps!!
MATH— Please help me answer this question. Hopefully you can see the picture
Find the missing length indicated.
Answer:
Step-by-step explanation:
x=✓64*36=✓8^2*6^2
x=8*6
x=48
PLEASE ANSWER! FIRST CORRECT ANSWER GETS BRAINLIEST!
Answer:
The answer should be 20.
Step-by-step explanation:
First, you need to understand the abbreviated list: PEMDAS. I'm not sure if you guys learned this or not, but it helps to know when solving problems like this.
So, if you don't know: PEMDAS is a list of what order you would need to start with when solving a problem. The order is Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
With that in mind, we'll start by looking at the numbers in the numerator of this fraction. (Doesn't matter if you start with the numerator or denominator first.)
You want to start with the numbers in the parentheses as that is the first letter in the PEMDAS phrase.
[tex](7-6.35) = 0.65[/tex]
Now, we have division and an addition sign next. According to PEMDAS, you want to start with Division before you Add. So, you will end up having a 10 in the numerator. (I'm assuming you can use a calculator for this, so I'm not showing how to divide the decimals.)
[tex]\frac{(0.65)}{6.5}+9.9=0.1+9.9 =10[/tex]
Save that number somewhere for now since we will have to come back to it later. For the denominator, we have a set of parentheses that the problem wants us to focus on so, ignore the [tex]7\frac{1}{24}[/tex] for now.
Start with the first set of numbers that have the division sign in between.
[tex]\frac{1.2}{36} =0.03333[/tex]
Don't add just yet after getting this number. You want to divide the 1.2 and [tex]\frac{1}{4}[/tex] since Division needs to be done first before Adding or Subtracting.
[tex]\frac{1.2}{\frac{1}{4} }=4.8[/tex]
The resulting numbers in the parentheses should look like this now (we're still ignoring the [tex]7\frac{1}{24}[/tex] at the end after the parentheses):
[tex](0.03333+4.8-1\frac{5}{16})=3.520833333[/tex]
This expression is also the same as this if you wanted to change the fraction at the end of the parentheses:
[tex](0.03333+4.8-\frac{21}{16})=3.520833333[/tex]
Now you can finally take this number and divide it by [tex]7\frac{1}{24}[/tex] or [tex]\frac{169}{24}[/tex].
[tex]\frac{3.520833333}{\frac{169}{24} }=0.5[/tex]
These are really big numbers when you are dividing so hopefully you don't have to solve this all out in your head or by paper. Now, remember that 10 we got from the numerator earlier? We can finally use that here where we have that as our numerator and 0.5 as our denominator.
[tex]\frac{10}{0.5} =20[/tex]
This gives you the final answer of 20.
The graph of F(x) shown below resembles the graph of G(x) = x ^ 2 but it has been changed somewhat. Which of the following could be the equation of F(x)
Answer:
Option (A)
Step-by-step explanation:
Parent function of the function graphed is,
G(x) = x²
Graph shows the vertex of the given parabola is at (3, 3).
Vertex form of a parabola is,
F(x) = a(x - h)² + k
where (h, k) is the vertex.
By substituting the coordinates of the vertex in the equation,
F(x) = a(x - 3)² + 3
Since the given parabola is opening upwards, value of 'a' will be positive.
So the equation will be,
F(x) = 2(x - 3)² + 3
Therefore, from the given options, equation given in Option (A) matches the answer.
Answer:
A is the correct answer.
Step-by-step explanation:
Laura’s overall monthly living expenses are $1,600. How much money does she have at the end of the month to put into savings?
Step-by-step explanation:
The question has missing details nevertheless we can make head way with the information on ground.
Given that Laura's overall monthly living expenses are $1,600
in order to calculate her savings for the month we need to know her income for the month, that is the overall sum she has at hand before incurring any expenses(this is the missing detail).
Say this overall amount is "x"
her saving for the month = [tex](x- 1600)[/tex]
Find the missing segment in the attached image
Answer:
The length of the missing segment is 36
Step-by-step explanation:
Given
The figure above
Required
Determine the missing segment
Let the missing segment be represented with x
Given that, there exist parallel lines between the two triangles;
The relationship between the sides of the triangles is as follows;
[tex]\frac{20}{24} = \frac{30+20}{24+x}[/tex]
[tex]\frac{20}{24} = \frac{50}{24+x}[/tex]
Cross Multiply
[tex]20 * (24 + x) = 24 * 50[/tex]
[tex]20 * (24 + x) = 1200[/tex]
Divide both sides by 20
[tex]\frac{20 * (24 + x)}{20} = \frac{1200}{20}[/tex]
[tex](24 + x)= \frac{1200}{20}[/tex]
[tex]24 + x= 60[/tex]
Subtract 24 from both sides
[tex]24 - 24 + x = 60 - 24[/tex]
[tex]x = 60 - 24[/tex]
[tex]x = 36[/tex]
Hence, the length of the missing segment is 36
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1m to catch rainwater off his roof. He has a full 2 litres tin of paint in his store and decides to paint the tank (not the base). If he uses 250 ml to cover 1 , will he have enough paint to cover the tank with one layer of paint? [take π=3.142]
Answer:
Yes, he will have enough paint to cover the tank with one layer of paint.
Step-by-step explanation:
We are given that Tublu buys a cylindrical water tank of height 1.4 m and diameter 1.1 m to catch rainwater off his roof. He has a full 2 liters tin of paint in his store and decides to paint the tank (not the base).
He uses 250 ml to cover 1 [tex]\text{m}^{2}[/tex].
From the question, it is clear the area of the tank which needs to be painted is the lateral surface area (because the base is not included).
The lateral surface area of the cylinder = [tex]2\pi rh[/tex]
where, r = radius of the cylinder = [tex]\frac{\text{Diameter}}{2}[/tex] = [tex]\frac{1.1 }{2}[/tex] = 0.55 m
h = height of the cylinder = 1.4 m
[tex]\pi[/tex] = 3.142 (given)
So, the lateral surface area of a cylindrical water tank = [tex]2 \times 3.142 \times 0.55 \times 1.4[/tex]
= 4.84 [tex]\text{m}^{2}[/tex].
Now, it is given in the question that; Tublu uses 250 ml to cover 1 [tex]\text{m}^{2}[/tex] area, this means that;
To cover 4.84 [tex]\text{m}^{2}[/tex] area, he will use paint = [tex]4.84 \times 250[/tex] = 1210 ml
Since he has a full 2 liters tin of paint in his store which is equal to 2000 ml but he need only 1210 ml of paint.
This means that yes, he will have enough paint to cover the tank with one layer of paint.
I need help with this question
Answer:
It's the first option.
Step-by-step explanation:
The line which rises to the right has a slope of 1 and a y-intercept of -6.
It's equation is y = x - 6.
The one which rises to the left has slope -1 and y-intercept -2.
It's equation is y = -x - 2 or x + y = -2.
The solution is at the point where the 2 lines cross - that is (2, -4).
What's the standard equation of the circle with the general equation x2 + y2 + 4x – 2y – 20 = 0? answers: 1) (x + 2)2 + (y – 1)2 = 5 2) (x – 2)2 + (y + 1)2 = 25 3) (x + 1)2 + (y – 2)2 = 5 4) (x + 2)2 + (y – 1)2 = 25
Answer:
4). (x + 2)^2 + (y - 1)^2 = 25.
Step-by-step explanation:
x^2 + y^2 + 4x - 2y - 20 = 0
x^2 + 4x + y^2 - 2y = 20
Completing the square on the x and y terms:
(x + 2)^2 - 4 + (y - 1)^2 - 1 = 20
(x + 2)^2 + (y - 1)^2 = 20 + 4 + 1
(x + 2)^2 + (y - 1)^2 = 25.
The standard equation of the circle with the given equation is (x+2)²+(y-1)²=25. Therefore, option 4 is the correct answer.
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²
The given circle equation is x²+ y²+4x-2y-20=0.
Here, x²+ y²+4x-2y=20
By completing the square on the x and y terms:
Now, add 4 on both the sides of an equation, we get
x²+ y²+4x-2y+4=20+4
x²+4x+4+y²-2y=24
Add 1 on both the sides of an equation, we get
(x+2)²+y²-2y+1=24+1
(x+2)²+(y-1)²=25
The standard equation of the circle with the given equation is (x+2)²+(y-1)²=25. Therefore, option 4 is the correct answer.
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https://brainly.com/question/23799314.
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What is the value of Fraction 1 over 2x3 + 3.4y when x = 2 and y = 5?
18
20
21
37
Answer:
[tex]C. \[/tex] [tex]\frac{1}{2}x^3 + 3.4y = 21[/tex]
Step-by-step explanation:
Given
[tex]x = 2[/tex]
[tex]y = 5[/tex]
Required
[tex]\frac{1}{2}x^3 + 3.4y[/tex]
Substitute 2 for x and 5 for y;
The expression becomes
[tex]=\ \frac{1}{2} * 2^3 + 3.4 * 5[/tex]
Multiply 3.4 by 5
[tex]=\ \frac{1}{2} * 2^3 + 17[/tex]
---------------------------
[tex]2^3 = 2 * 2 * 2 = 8[/tex]
--------------------------
[tex]=\ \frac{1}{2} * 8 + 17[/tex]
[tex]=\ \frac{8}{2} + 17[/tex]
[tex]=\ 4 + 17[/tex]
[tex]=\ 21[/tex]
Hence;
[tex]\frac{1}{2}x^3 + 3.4y = 21[/tex]
A restaurant offers 6 choices of appetizer, 8 choices of main meal and 5 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses. Assuming all choices are available, how many different possible meals does the restaurant offer?
Answer:
377 choices
Step-by-step explanation:
The following values were given in the question:
The restaurant offered
6 choices of appetizer
8 choices of main meal
5 choices of dessert.
We are also told in the question that the customer can choose to eat just one course, or two different courses, or all three courses.
Let us represent each choice by :
A = Appetizer = 6
B = Main meal = 8
C = Dessert = 5
a) The 3 choices together
ABC=6 × 8 × 5=240 choices
b) AB= Appetizer and Main meal
= 6 × 8 = 48 choices
c) AC= Appetizer and Dessert
= 6 × 5 = 30 choices
d) BC = Main meal × Dessert
= 8 × 5 = 40 choices
e) A,B,C = the customer having each of the choices only
Appetizer + Main meal + Dessert
= 6 + 8 + 5
= 19 choices
The number of possible meals is calculated as:
240 choices + 48 choices + 30 choices + 40 choices + 19 choices
= 377 choices
Find the missing side to the triangle in the attached image. Thanks.
Answer:
Let's use Pythagorean Theorem which states:
6² + 10² = x²
36 + 100 = x²
136 = x²
x = ± 2√34
Since the side lengths of a triangle cannot be negative, x = -2√34 is an extraneous solution which means that x = 2√34.
Answer:Answer:
Let's use Pythagorean Theorem which states:
6² + 10² = x²
36 + 100 = x²
136 = x²
x = ± 2√34
Since the side lengths of a triangle cannot be negative, x = -2√34 is an extraneous solution which means that x = 2√34.
Read more on Brainly.com - https://brainly.com/question/17033938#readmore
Step-by-step explanation:
What is the solution to the equation below? log 20xrise 3-2logx=4
Answer:
[tex]x = 500[/tex]
Step-by-step explanation:
Given
[tex]log20x^3 - 2logx = 4[/tex]
Required
Solve for x
[tex]log20x^3 - 2logx = 4[/tex]
Using law of logarithm which says;
[tex]nlogx = logx^n[/tex]
The expression becomes
[tex]log20x^3 - logx^2 = 4[/tex]
Also, using laws of logarithm which says:
[tex]loga - logb = log\frac{a}{b}[/tex]
The expression becomes
[tex]log(\frac{20x^3}{x^2}) = 4[/tex]
[tex]log(20x) = 4[/tex]
Also, using laws of logarithm which says
[tex]If\ loga = b\\then\ a = 10^b[/tex]
The expression becomes
[tex]20x = 10^4[/tex]
[tex]20x = 10000[/tex]
Divide through by 20
[tex]\frac{20x}{20} = \frac{10000}{20}[/tex]
[tex]x = \frac{10000}{20}[/tex]
[tex]x = 500[/tex]
Answer:
500
Step-by-step explanation:
Find the missing side lengths. Leave your answers as radicals in simplest form.
ANSWER QUICK
Answer:
C
Step-by-step explanation:
It is an iscoceles triangle because there are 180 degrees in a triangle and the right angle plus the 45 degree equals 135 and 180 minus 135 is 45.
Since it is an iscoceles triangle that means that n = 3 and the pythagorean theorom says that a^2 + b^2 = c^2 which means that m = 3^2 plus 3^2 with a root.
3^2 is 9 so you get 18
the root of 18 is infinite, however can be simplified to 3 root to 2 because 3 times 3 equals 9 times 2 equals a root of 18
Hope this helps!
Attachment Below, please help, I'm not timed
Answer:
Step-by-step explanation:
x + 2x + 4x = 49
7x = 49
x = 7
2(7)= 14 hours he worked on Wednesday
Please could I have some help :)
Answer:
a) x = 128 degrees
b) Angle APD is the arc angle, which is equal to the central angle x subtended by the arc. Therefore angle APD = 128 degrees (and not 116 degrees)
Step-by-step explanation:
Given:
attached diagram
ABC is a straight line
Solution:
a) Find x
ABC is a straight line
angle ABD = supplement of CBD = 180-CBD = 180-116 = 64 degrees.
x is the central angle of the arc APD
so angle ABD is the inscribed angle which equals half of the arc angle =>
angle ABD = x/2 = 64 degrees
Solve for x
x/2 = 64
x = 2*64
x = 128 degrees
b.
Angle APD is the arc angle, which is equal to the central angle x subtended by the arc. Therefore angle APD = 128 degrees (and not 116 degrees)
PLSSS HELP State the maximum number of turns the graph of each function could make 1. f(x)=x^5-3x+1 2.f(x)=-x^7-7x^5-4x^3
Answer:
max for 5th-degree: 4 turns. This function: 2 turns.max for 7th-degree: 6 turns. This function: 0 turns.Step-by-step explanation:
In general, the graph of an n-th degree function can make n-1 turns. However, in specific cases, the number of turns is limited by the number of real zero-crossings of the derivative.
__
1. This 5th-degree function can have at most 4 turns. However, the derivative, f'(x) = 5x^4 -3, has only two (2) real zeros. Hence the graph of this function can only have 2 turns.
__
2. This 7th-degree function can have at most 6 turns. However, the derivative, f'(x) = -7x^6 -35x^4-12x^2, has an even-multiplicity root at x=0 only. The derivative never crosses 0. Hence the graph makes no turns.