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GarryVolchara [31]

3 years ago

9

Write an equation below to express the cost (c) as a function of miles (m). The charge for a rental car is $20 plus $0.05 per mi

le.

1 answer:

vfiekz [6]3 years ago

8 0

F(m)=20+0.05m
f(m)=cost(c)
20=initial cost and will be the y-intercept
0.05=the cost per mile and will be the slope
m=the number of miles driven

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Find quotient<br> (2x-3/x) / (7/x^2)

Svetlanka [38]

Answer:

2x^3-3x/7

I hope it's helpful

8 0

3 years ago

Write the formula for a function d(x) that describes the distance between the point P and a point (x,y) on the line. You final a

vlabodo [156]

Answer:

d(x) = √[(x - 2)² + (3x - 1)²]

Step-by-step explanation:

The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given as

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

So, the distance between point (2,0) and a point (x,y)

d = √[(x - 2)² + (y - 0)²]

d = √[(x - 2)² + (y)²]

But the point (x,y) is on the line y = 3x - 1

We can substitute for y in the distance between points equation.

d(x) = √[(x - 2)² + (3x - 1)²]

QED!

6 0

3 years ago

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

$\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2$

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

A 12 in diameter will reward you with the largest slice of pizza.

3 0

3 years ago

5 – 6x = 8x + 17 and simplify <img src="https://tex.z-dn.net/?f=%5Cfrac%7B-6%7D%7B7%7D" id="TexFormula1" title="\frac{-6}{7}" al

NikAS [45]

Answer:

x = -6/7

Step-by-step explanation:

5 – 6x = 8x + 17

-5 - 5 Subtract 5 from both sides

-6x = 8x + 12

-8x - 8x Subtract 8x from both sides

-14x = 12 Divide both sides by -14

x = -12/14 Simplify

x = -6/7

7 0

3 years ago

Which graph has a slope of 1/2?

ryzh [129]

A slope of 1/2 means for every two units to the right we move up one.

We have to be careful here because the graphs don't always use the same scale for x and y.

The bottom left uses the same scale and does indeed go two units to the right for every unit up, so that one is the answer.

4 0

3 years ago

Read 2 more answers