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3 years ago

7

The line graph shows a direct variation with a unit rate of 1.4. Two of the points the line passes through are (5, 7) and (10, 1

4).
What is the slope of the line?

2 answers:

cupoosta [38]3 years ago

6 0

Answer: slope = 7/5

Step-by-step explanation:

The line graph is a straight line graph. Two of the points the line passes through are (5, 7) and (10, 14).

The slope, m of the graph is expressed as

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis).

Slope = (y2 - y1)/(x2 - x1)

y2 represents final value of y = 14

y1 represents initial value of y = 7

x2 represents final value of x = 10

x1 represents initial value of x = 5

Therefore,

Slope = (14 - 7)/(10 - 5) = 7/5

vlada-n [284]3 years ago

4 0

Answer:

slope of the line is m= $\frac{7}{5}$

Step-by-step explanation:

<u>Step 1:-</u>

The slope of the given line

$\frac{y_{2-Y_{1} } }{x_{2} -x_{1} }$

<u>step 2:-</u>

m = frac{7}{5}[/tex]

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Answer:

The function touches the damping factor

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The x-intercept of f(x) is

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Step-by-step explanation:

Given function is f(x)= $e^{-3x} sin(x)$ and damping factor as y= $e^{-3x}$ and y= $(-1)e^{-3x}$

To find when function touches the damping factor:

For f(x)= $e^{-3x} sin(x)$ and y= $e^{-3x}$

Equating the both the equation,

$e^{-3x} sin(x)=e^{-3x}$

$sin(x)=1$

x= $\frac{(4n-3)\pi}{2}$

For f(x)= $e^{-3x} sin(x)$ and y= $(-1)e^{-3x}$

Equating the both the equation,

$e^{-3x} sin(x)=(-1)e^{-3x}$

$sin(x)=(-1)$

x= $\frac{(4n-1)\pi}{2}$

Therefore, The function touches the damping factor x= $\frac{(4n-3)\pi}{2}$ and x= $\frac{(4n-1)\pi}{2}$

To find x-intercept of f(x):

For x-intercept, y=0

f(x)= $e^{-3x} sin(x)$

y= $e^{-3x} sin(x)$

$e^{-3x} sin(x)=0$

Hence, $e^{-3x}$ is always greater than zero.

Therefore, $sin(x)=0$

x= $n\pi$

Thus,

The x-intercept of f(x) is at x= $n\pi$

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Step-by-step explanation:

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3 years ago

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The function h(t) = −5t2 + 20t shown in the graph models the curvature of a satellite dish: graph of parabola starting at zero c

ipn [44]

Answer:

Part 1) Option B: 0 ≤ x ≤ 4

Part 2) Option C: (5x − 1)(2x − 3)

Part 3) Option C: The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Part 4) Option B: f(x) = (2x + 1)(2x − 1)

Part 5) Option A: The company earned 85 billion dollars in 2008

Part 6) Option C: (3, 0) and (5, 0)

Step-by-step explanation:

Part 1) we have

$h(t)=-5t^{2}+20t$

This is a vertical parabola open downward

The vertex is a maximum

The x-intercepts are the points (0,0) and (4,0)

The vertex is the point (2,20) ---> The x-coordinate of the vertex is the midpoint of the x-intercepts

so

The domain is the interval ----> [0,4]

$0\leq t\leq 4$

The range is the interval ----> [0,20]

$0\leq h(t)\leq 20$

Part 2) we have

$V=10x^{2} -17x+13$

where

x is the time in minutes

V is the volume in gallons

we know that

When the trough is empty, the volume is equal to zero

so

For V=0

$10x^{2} -17x+3=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$10x^{2} -17x+3=0$

so

$a=10\\b=-17\\c=3$

substitute in the formula

$x=\frac{-(-17)(+/-)\sqrt{-17^{2}-4(10)(3)}} {2(10)}$

$x=\frac{17(+/-)\sqrt{169}} {20}$

$x=\frac{17(+/-)13} {20}$

$x=\frac{17(+)13} {20}=\frac{3}{2}$

$x=\frac{17(-)13} {20}=\frac{1}{5}$

so

$10x^{2} -17x+3=10(x-\frac{3}{2})(x-\frac{1}{5})$

simplify

$10(x-\frac{3}{2})(x-\frac{1}{5})=(2x-3)(5x-1)$

Part 3) we have

$f(x)=-x^{2}+20x+100$

we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

the average rate of change is equal to

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

$f(a)=f(10)=-(10)^{2}+20(10)+100=200$

$f(b)=f(20)=-(20)^{2}+20(20)+100=100$

$a=10$

$b=20$

Substitute

$\frac{100-200}{20-10}$

$-\frac{100}{10}=-10$ ----> is a decreasing function

therefore

The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Part 4) we have

$f(x)=4x^{2} -1$

<em>Find out the x-intercepts</em>

Remember that the x-intercepts are the values of x when the value of the function is equal to zero

so

For f(x)=0

$4x^{2} -1=0$

Solve for x

$4x^{2}=1$

$x^{2}=\frac{1}{4}$

take square root both sides

$x=(+/-)\frac{1}{2}$

so

$f(x)=4x^{2} -1=4(x-\frac{1}{2})(x+\frac{1}{2})=(2x-1)(2x+1)$

Part 5) we have

$t^{2}+14t+85$

Remember that

The y-intercept of a function is the value of the function (output value) when the value of x (input value) is equal to zero

In this problem

The expression represent a company's net sales, in billions, from 2008 to 2018

t is the number of years since the end of 2008

so

For t=0 -----> represent the end of 2008

$(0)^{2}+14(0)+85=85\ billion\ dollars$

therefore

The company earned 85 billion dollars in 2008.

Part 6) What are the x-intercepts of the parabola?

we have the points (2,3),(4,-1),(6,3)

This is a vertical parabola open upward

The vertex represent a minimum

In this problem the vertex is the point (4,-1)

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

we have

(h,k)=(4,-1)

substitute

$y=a(x-4)^2-1$

take the point (2,3) and substitute in the quadratic equation to solve for a

For x=2, y=3

$3=a(2-4)^2-1$

$3=4a-1$

$4a=4$

$a=1$

The quadratic equation is

$y=(x-4)^2-1$

Find out the x-intercepts

Remember that the x-intercepts are the values of x when the value of the function is equal to zero

so

For y=0

$(x-4)^2-1=0$

Solve for x

$(x-4)^2=1$

take square root both sides

$(x-4)=(+/-)1$

$x=4(+/-)1$

$x=4+1=5\\x=4-1=3$

therefore

The x-intercepts are the points (3,0) and (5,0)

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3 years ago

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