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3 years ago

11

Many gas stations give a discount for paying with cash instead of a credit card. William’s local gas station gives a discount of

$0.05 per gallon. He fills his car with 20 gallons of gas. How much will William save by paying cash instead of credit card?

1 answer:

sattari [20]3 years ago

5 0

0.05 x 20 = 1
William will be saving $1

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Pls help me i just need help

Ray Of Light [21]

Step-by-step explanation:

the total cost is, of course, first the cost to buy the copier, and then the running costs per copy made.

it is really that easy.

the equations just put this into mathematical form :

A

y = 0.02×x + 800

B

y = 0.06×x + 600

please notice, we put $600 or $800 in as constant term, because these costs are the starting costs that we have, even if we never make a single copy (x = 0).

and then the total cost goes up with every copy we make.

I cannot draw here.

so, to find the number of copies where both copier systems would cost the same, means we have to say both equating deliver the same result :

0.02×x + 800 = 0.06×x + 600

200 = 0.04×x

x = 200 / 0.04 = 5000

when making 5000 copies both costs are the same.

4 0

3 years ago

If the maximum value of y=-3x² + mx + 10 is 37, find the values of m.

uysha [10]

Step-by-step explanation:

y = -3x² + mx + 10

dy/dx = -6x + m.

When dy/dx = 0, -6x + m = 0. => x = m/6.

We have y = -3(m/6)² + m(m/6) + 10 = 37.

=> -m²/12 + m²/6 = 27

=> -m² + 2m² = 324

=> m² = 324

=> m = 18 or m = -18.

5 0

3 years ago

Read 2 more answers

Which of the following expressions are equivalent to -45+12

meriva

Answer:

-45 + 12 is equal to -33

and <u>Choice A </u> is also equal to -33.

Step-by-step explanation:

7 0

2 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

Could anyone solve this equation

Ainat [17]

I)
8 - 3x = 23
-3x = 15
x = -5

ii)
5x - 16 = 34
5x = 50
x = 10

iii)
2 - 5x = -3
-5x = -5
x = 1

6 0

3 years ago