Answers
Answer:
[See Below]
Step-by-step explanation:
For Point Slope Form:Point slope form is: [tex]y-y_1=m(x-x_1)[/tex]
'm' is the slope
(x1, y1) is a coordinate point.
Slope:Slope is rise over run. [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (-1,5) and (3,-3).
[tex]\frac{-3-5}{3-(-1)}=\frac{-8}{4}= -2[/tex]
The slope of the line is -2.
I will use (-1,5) as the point:
[tex]y-y_1=m(x-x_1)\rightarrow\boxed{y-5=-2(x+1)}[/tex]
For Slope Intercept:Slope intercept is: [tex]y=mx+b[/tex]
'm' - Slope
'b' - y-intercept
We can use the point slope equation to convert it into slope intercept form:
[tex]y-5=-2(x+1)\\\\y-5=-2x-2\\\\y-5+5=-2x-2+5\\\\\boxed{y=-2x+3}[/tex]
For Standard Form:Standard form is [tex]Ax+By=C[/tex]
Using out slope intercept form equation:
[tex]y=-2x+3\\\\y+2x=-2x+2x+3\\\\1y+2x=3\\\\\boxed{2x+1y=3}[/tex]
Related Questions
What is the area of the triangle below?
18
Answers
Answer:
D. 32 sq. unit s
Step-by-step explanation:
4×18/2=32
4. The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Answers
Answer:
5in³Step-by-step explanation:
The question is in complete. Here is the complete question.
"The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Base of triangle = 1in
height of triangle = 5in"
Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\
B = Base area
H = Height of the pyramid
Base area B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]
b = base of the triangle
h = height of the triangle
B = [tex]\frac{1}{2} * 5 * 1\\[/tex]
[tex]B = 2.5in^{2}[/tex]
Since H = 6inches
Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]
[tex]V = 2.5*2\\V =5in^{3}[/tex]
-12.48 -(-2.99)-5.62
Answers
Answer:
[tex]-15.11[/tex]
Step-by-step explanation:
[tex]-12.48-(-2.99)-5.62=\\-12.48+2.99-5.62=\\-9.49-5.62=\\-15.11[/tex]
Answer:
-15.11
Step-by-step explanation:
-12.48+2.99-5.62=
-9.49 - 5.62= - (9.49+5.62)=-15.11
Let the sample space be
S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Suppose the outcomes are equally likely. Compute the probability of the event E = 1, 2.
Answers
Answer:
probability of the event E = 1/5
Step-by-step explanation:
We are given;
Sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
Number of terms in sample S is;
n(S) = 10
We are given the event; E = {1, 2}
Thus, number of terms in event E is;
n(E) = 2
Now, Probability = favorable outcomes/total outcomes
Thus, the probability of the event E is;
P(E) = n(E)/n(S)
P(E) = 2/10
P(E) = 1/5
Any help would be appreciated
Answers
deandre saves rare coins. he starts his collection with 14 coins and plans to save 3 coins each month. write an equation to represent the number of coins saved, y, in terms of the number of months, x. if deandre saved for 30 months, how many coins will he have?
Answers
Answer:
equation: y = 3x + 14
number of coins after 30 months: 104 coins
Hope this helps :)
An equation is formed of two equal expressions. The number of coins that will be with Deandre after a period of 30 months is 104 coins.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
As it is given that in the initial phase Deandre saves 14 coins. While he adds 3 coins each month. Therefore, the equation that will represent the number of coins that Deandre will have after a period of x months can be written as,
y = 14 + 3x
where y is the number of coins and x is the number of months.
After a period of x=30 months, the number of coins that will be with Deandre can be written as,
[tex]y = 14 + 3x\\\\y = 14 + 3(30)\\\\y = 104[/tex]
Thus, the number of coins that will be with Deandre after a period of 30 months is 104 coins.
Learn more about Equation:
https://brainly.com/question/2263981
Evaluate f(x) = x2 + 1 for f(-1)
Answers
Answer: -1
Step-by-step explanation:
to calculate f(-1), you know that x = -1. so all you have to do is substitute:
f(-1) = (-1)2 + 1
f(-1) = -2 + 1
f(-1) = -1
Answer:
0
Step-by-step explanation:
AC =
Round your answer to the nearest hundredth.
A
5
35
B
C
Answers
Answer:
2.87 = AC
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opp / hyp
sin 35 = AC /5
5 sin 35 = AC
2.867882182= AC
To the nearest hundredth
2.87 = AC
Which of the following statements are equivalent to the statement "Every integer has an additive inverse" NOTE: (The additive inverse of a number x is the number that, when added to x, yields zero. Example: the additive inverse of 5 is -5, since 5+-5 = 0) Integers are{ ... -3, -2,-1,0, 1, 2, 3, ...} All integers have additive inverses. A. There exists a number x such that x is the additive inverse of all integers.B. All integers have additive inverses.C. If x is an integer, then x has an additive inverse.D. Given an integer x, there exists a y such that y is the additive inverse of x.E. If x has an additive inverse, then x is an integer.
Answers
Answer:
B, C and D
Step-by-step explanation:
Given:
Statement: "Every integer has an additive inverse"
To find: statement that is equivalent to the given statement
Solution:
For any integer x, if [tex]x+y=0[/tex] then y is the additive inverse of x.
Here, 0 is the additive identity.
Statements ''All integers have additive inverses '', '' If x is an integer, then x has an additive inverse'' and ''Given an integer x, there exists a y such that y is the additive inverse of x'' are equivalent to the given statement "Every integer has an additive inverse".
Write the rectangular equation (x+5) 2 + y 2 = 25 in polar form.
Answers
Answer:
r = -10*cos(t)
Step-by-step explanation:
To write the rectangular equation in polar form we need to replace x and y by:
[tex]x=r*cos(t)\\y=r*sin(t)[/tex]
Replacing on the original equation, we get:
[tex](x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25[/tex]
Using the identity [tex]sin^2(t)+cos^2(t)=1[/tex] and solving for r, we get that the polar form of the equation is:
[tex](r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)[/tex]
The population of a city has increased by 35% since it was last measured. If the current population is 29,700 , what was the previous population?
Answers
Answer:
19305
Step-by-step explanation:
We simply take the percentage of 29700 to find how many people were added.
29700(0.35) = 10395 <== so 10395 people have been added
Subtract it from the current:
28700 - 10395 = 19305 people before.
What are the like terms in the algebraic expression? Negative a squared b + 6 a b minus 8 + 5 a squared b minus 6 a minus b Negative a squared b and negative 6 a Negative a squared b and 5 a squared b 6 a b and 5 a squared b 6 a b and negative 6 a
Answers
Answer:
The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex]
Step-by-step explanation:
The expression is:
[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]
Collect the like terms as follows:
[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]
[tex]=(-a^{2}b+5a^{2}b-a^{2}b-a^{2}b+5a^{2}b+5a^{2}b)+(6ab+6ab+6ab)-(6a-6a-6a)-b-8[/tex]
[tex]=12a^{2}b+18ab+18a-b-8[/tex]
Thus, the final expression is [tex]12a^{2}b+18ab+18a-b-8[/tex]
The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex].
Answer:
The CORRECT answer is B
Step-by-step explanation:
What is the end behavior of the graph of the polynomial function f(x) = 2x3 – 26x – 24?
Answers
Answer:
Step-by-step explanation:
Answer:
its b on edge
Step-by-step explanation:
c) Consider the time 3:40pm where the initial side is the hour hand and terminal side is the
minute hand. Draw the angle between the two hands in standard position. State the angle in
positive degrees and then restate the angle as a negative angle. (2 pts.)
Answers
Answer:
210 degrees-150 degreesStep-by-step explanation:
When the time is 3:40pm
The Initial Side (hour hand) is at 3.Terminal Side (Minute hand) is at 8.(a)The angle between the two hands in standard position is drawn and attached below.
(b)Now, each hour = 30 degrees
Therefore, the angle between 3 and 8 in an anticlockwise movement
= 7 X 30 =210 degrees
Stating the angle as a negative angle, we have:
[tex]210^\circ-360^\circ=-150^\circ\\$The angle as a negative angle is -150^\circ[/tex]
Which are true of the function f(x)=49(1/7)?select three options. A)The domain is the set of all real numbers. B) the range is the set of all real numbers. C) the domain is x >0. D)the range is y>0. E)as increases by 1, each y value is one -seventh of the previous y-value.
Answers
Answer:
A,D and E
Step-by-step explanation:
We are given that a function
[tex]f(x)=49(\frac{1}{7})^x[/tex]
The given function is exponential function .
The exponential function is defined for all real values of x.
Therefore, domain of f=Set of all real numbers
Substitute x=0
[tex]y=f(0)=49>0[/tex]
Range of f is greater than 0.
x=1
[tex]y(1)=\frac{49}{7}[/tex]
x=2
[tex]y=49(\frac{1}{7})^2=\frac{1}{7}y(1)[/tex]
As x increases by 1, each value of y is one-seventh of the previous y-value.
Therefore, option A,D and E are true.
Answer:
A D E
Step-by-step explanation:
Edge2020 quiz
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. 0.989 0.978 0.927 0.167 0.530
Answers
Answer:
0.989
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they find a job in their chosen field within a year after graduation, or they do not. The probability of a graduate finding a job is independent of other graduates. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation.
This means that [tex]p = 0.53[/tex]
6 randomly selected graduates
This means that [tex]n = 6[/tex]
Probability that at least one finds a job in his or her chosen field within a year of graduating:
Either none find a job, or at least one does. The sum of the probabilities of these outcomes is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.53)^{0}.(0.47)^{6} = 0.011[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.011 = 0.989[/tex]
Engineers want to design passenger seats in commercial aircraft so that they are wide enough to fit 95 percent of adult men. Assume that adult men have hip breadths that are normally distributed with a mean of 14.4 inches and a standard deviation of 1.1 inches. Find the 95th percentile of the hip breadth of adult men. Round your answer to one decimal place; add a trailing zero as needed. The 95th percentile of the hip breadth of adult men is [HipBreadth] inches.
Answers
Answer:
[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]
And if we solve for a we got
[tex]a=14.4 +1.64*1.1=16.204[/tex]
The 95th percentile of the hip breadth of adult men is 16.2 inches.
Step-by-step explanation:
Let X the random variable that represent the hips breadths of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(14.4,1.1)[/tex]
Where [tex]\mu=14.4[/tex] and [tex]\sigma=1.1[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.05[/tex] (a)
[tex]P(X<a)=0.95[/tex] (b)
We can find a quantile in the normal standard distribution who accumulates 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64
Using this value we can set up the following equation:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.95[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.95[/tex]
And we have:
[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]
And if we solve for a we got
[tex]a=14.4 +1.64*1.1=16.204[/tex]
The 95th percentile of the hip breadth of adult men is 16.2 inches.
The volume of a trianglular prism is 54 cubic units. What is the value of x?
3
5
7
9
Answers
Answer:
X is 3 units.
Step-by-step explanation:
Volume of prism is cross sectional area multiplied by length. So 1/2 ×2× x ×2 into 3x, which is equal to 6x^2. So, 6x^2=54. Therefore, x=3.
Solve the following and
make sure to write your
answer in scientific
notation.
(1.5 x 105)(5 x 103)
Answers
Answer:
7.5* 10^8
Step-by-step explanation:
(1.5 x 10^5)(5 x 10^3)
Multiply the numbers
1.5*5=7.5
Add the exponents
10 ^(5+3) = 10^8
Put back together
7.5* 10^8
This is in scientific notation
Please help me find Jebel dhanna in UAE map.
Answers
Answer:
The full name of the place is the "Danat Jebel Dhanna". The Jebel Dhanna is currently located in the Abu Dhabi. It is said that it is one of the most best beach in the UAE, they also say that it is the biggest resort, of course, with a bunch of hotels.
hope this helps ;)
best regards,
`FL°°F~` (floof)
Which is the cosine ratio of
Answers
Answer:The answer is B
Step-by-step explanation:
Answer:
Option B
Step-by-step explanation:
Cos A = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Where Adjacent = 28, Hypotenuse = 197
Cos A = [tex]\frac{28}{197}[/tex]
Deanna's Quiz Scores
Use the dot plots to answer the question
has quiz scores that are less variable and
typically higher
80 82 84 86 88 90 92 94 96 98 100
Amy's Quiz Scores
.
.
.
..
80 82 84 86 88 90 92 94 96 98 100
Answers
Answer:
1.90.93
2.90.27
Step-by-step explanation:
Answer:
one above correct
Step-by-step explanation:
1st - 90.93
2nd-90.27
The management of a chain of frozen yogurt stores believes that t days after the end of an advertising campaign, the rate at which the volume V (in dollars) of sales is changing is approximated by V ' ( t ) = − 26400 e − 0.49 t . On the day the advertising campaign ends ( t = 0 ), the sales volume is $ 170 , 000 . Find both V ' ( 6 ) and its integral V ( 6 ) . Round your answers to the nearest cent.
Answers
Answer:
Step-by-step explanation:
Given the rate at which the volume V (in dollars) of sales is changing is approximated by the equation
V ' ( t ) = − 26400 e^− 0.49 t .
t = time (in days)
.v'(6) can be derived by simply substituting t = 6 into the modelled equation as shown:
V'(6) = − 26400 e− 0.49 (6)
V'(6) = -26400e-2.94
V'(6) = -26400×-0.2217
V'(6) = $5852.88
V'(6) = $5,853 to nearest dollars
V'(6) = 585300cents to nearest cent
To get v(6), we need to get v(t) first by integrating the given function as shown:
V(t) = ∫−26400 e− 0.49 t dt
V(t) = -26,400e-0.49t/-0.49
V(t) = 53,877.55e-0.49t + C.
When t = 0, V(t) = $170,000
170,000 = 53,877.55e-0 +C
170000 = 53,877.55(2.7183)+C
170,000 = 146,454.37+C
C = 170,000-146,454.37
C = 23545.64
V(6) = 53,877.55e-0.49(6)+ 23545.64
V(6) = -11,945.63+23545.64
V(6) = $11,600 (to the nearest dollars)
Since $1 = 100cents
$11,600 = 1,160,000cents
⅝ of a school's population are girls. There are 129 boys. If each classroom can hold 25 students. How many classroom does the school have ?
Answers
Answer:
AT least 14 classrooms to hold the total number of students
Step-by-step explanation:
Since we don't know the numer of girls in the school, let's call it "x".
What we know is that the number of girls plus the number of boys gives the total number of students. This is:
x + 129 = Total number of students
Now, since 5/8 of the total number of students are girls, and understanding that 5/8 = 0.625 in decimal form, then we write the equation that states:
"5/8 of the school's population are girls" as:
0.625 (x + 129) = x
then we solve for "x":
0.625 x + 0.625 * 129 = x
0.625 * 129 = x - 0.625 x
80.625 = x (1 - 0.625)
80.625 = 0.375 x
x = 80.625/0.375
x = 215
So now we know that the total number of students is: 215 + 129 = 344
and if each classroom can hold 25 students, the number of classroom needed for 344 students is:
344/25 = 13.76
so at least 14 classrooms to hold all those students
What is the solution of √1-3x = x+3 ?
Answers
Answer:
{-1, -8}
Step-by-step explanation:
Please enclose "1 - 3x" inside parentheses so the reader will know that you want the square root of all of "1 - 3x".
Squaring both sides of the given equation, we get:
1 - 3x = x^2 + 6x + 9, or x^2 + 6x + 8 + 3x, or
x^2 + 9x + 8 = 0. Factoring, we get: (x + 8)(x + 1) = 0, so that the solutions are {-1, -8}.
Answer:
I hope the given equation is :
{-1, -8}
First step to solve this equation to remove square root from the left side. So, take square on each sides of the equation. Therefore,
1 - 3x = (x + 3)²
1 - 3x = (x + 3)*(x + 3) Since a² = a * a
1 - 3x = x² + 3x + 3x + 3² By multiplication.
1 - 3x = x² + 6x + 9 Combine the like terms.
x² + 6x + 9 - 1 + 3x = 0 Subtract 1 and add 3x from each sides of equation
x² + 9x + 8 = 0 Combine the like terms.
Next step is to factor the trinomial to solve the above equation for x.
For that break downn the constant 8 into two multiples so that the addition of the multiples will result the coefficient of x = 9.
So, 8 = 1 * 8
Addition of 1 and 8 will give 9. So, next step is to replace 9x with 1x + 8x. So,
x² + 1x + 8x + 8 = 0
(x² + 1x) + (8x + 8) = 0 Group the terms.
x ( x + 1) + 8 (x + 1 ) = 0 Take out the common factor from each group.
(x +1 ) ( x + 8 ) = 0 Take out the common factor (x + 1).
So, x + 1 = 0 and x + 8 = 0 Set up each factor equal to 0.
Hence, x = -1 and - 8.
Next step is to plug in -1 and -8 in the original equation to cross check the solutions.
For x = -1,
Simplify each sides separately.
2 = 2
2 = 2 is correct. So, x = -1 satisfy the equation.
Hence, x = -1 is the real solution of the given equation.
Similarly let's plug in x = -8 now. So,
Simplify each sides separately.
5 = 2
5 = 2 is not true. So, x = -8 is the extraneous solution.
Therefore, the only solution is x = -1.
Hence, the correct choice is C.
Hope this helps you!
Step-by-step explanation:
mark brainlies plssssssssss
Let f be the function that determines the area of a circle (in square cm) that has a radius of r cm. That is, f ( r ) represents the area of a circle (in square cm) that has a radius of r cm.Use function notation to complete the following tasks
a. Represent the area (in square cm) of a circle whose radius is 4 cm.
b. Represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm.
Answers
Answer:
(a)f(4) square cm.
(b)f(10.91)-f(10.9) Square centimeter.
Step-by-step explanation:
f(r)=the area of a circle (in square cm) that has a radius of r cm.
(a)Area (in square cm) of a circle whose radius is 4 cm.
Since r=4cm
Area of the circle = f(4) square cm.
(b) When the radius of the increases from 10.9 to 10.91 cm.
Area of the circle with a radius of 10.91 = f(10.91) square cm.Area of the circle with a radius of 10.9 = f(10.9) square cm.Change in the Area = f(10.91)-f(10.9) Square centimeter.
AC =
Round your answer to the nearest hundredth.
с
6
B
40°
А
Answers
Answer:
5.03
Step-by-step explanation:
Answer:
5.03 = AC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 40 = AC /6
6 tan 40 = AC
5.034597787 = AC
To the nearest hundredth
5.03 = AC
Find the equation of the line.
Use exact numbers.
y=
Answers
Answer:
y = 2x+4
Step-by-step explanation:
First we need to find the slope using two points
(-2,0) and (0,4)
m = (y2-y1)/(x2-x1)
m = (4-0)/(0--2)
= 4/+2
= 2
we have the y intercept which is 4
Using the slope intercept form of the line
y = mx+b where m is the slope and b is the y intercept
y = 2x+4
Jiangsu divided 751.6 by 10 by the power of 2 and got a quotient of 0.7516. yesseinafhinks that the quotient should be7.516. Who is correct?
Answers
Answer:
yesseinafhinks
Step-by-step explanation:
Dividing by 10² is also the same thing as multiplying by 10^-2. In that case, we simply move the decimal places only 2 places back. That would give us 7.516, not 0.7516 (which is 3 times, not 2).
I would really appreciate it if you could help me please
Answers
Answer:
Yes, triangle GYK is similar to triangle BAK.
Step-by-step explanation:
The sides of each triangle are proportional to each other.
Take the longest side of each triangle. You are comparing line AK with line KY.
The proportion is 15/25.
Now, take the shortest side of each triangle. You are comparing line KB with GK.
The proportion is 6/10.
To determine if the triangles are proportional, we can see if the two proportions are equal to each other:
15/20=6/10
3/5=6/10
Correct! 3/5 equals to 6/10. Therefore, the two triangles are similar because their sides are proportional.
Hope this helps :)
Answer:
O Yes!
Step-by-step explanation:
We would check whether the proportionality of their sides is equal
Taking proportionality
= [tex]\frac{6}{10} = \frac{15}{25}[/tex]
Cross Multiplying
6 × 25 = 15 × 10
150 = 150
So, ΔABK is similar to ΔGKY