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2 years ago

6

Michelle family drove 272.48 miles. Michelle calculated that they drove 26.2 miles per gallon. of gas. how many gallon of gasoli

ne did the car use

2 answers:

Tcecarenko [31]2 years ago

8 0

It's 10.4 because you divide 272.48 by 26.2 and get 10.4

Strike441 [17]2 years ago

5 0

The answer is 10.4 gas

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Let g(x) = 2x and h(x)= x^2 -4. find (g o h)(0)

finlep [7]

The answer is -8

====================================================

Explanation:

There are two ways to get this answer

Method 1 will have us plug x = 0 into h(x) to get
h(x) = x^2 - 4
h(0) = 0^2 - 4
h(0) = 0 - 4
h(0) = -4
Then this output is plugged into g(x) to get
g(x) = 2x
g(-4) = 2*(-4)
g(-4) = -8 which is the answer
This works because (g o h)(0) is the same as g(h(0)). Note how h(0) is replaced with -4
So effectively g(h(0)) = -8 which is the same as (g o h)(0) = -8

-----------------------

The second method involves a bit algebra first
Start with the outer function g(x). Then replace every x with h(x). On the right side, we will replace h(x) with x^2-4 because h(x) = x^2-4

g(x) = 2x
g(x) = 2( x )
g(h(x)) = 2( h(x) ) ... replace every x with h(x)
g(h(x)) = 2( x^2-4 ) ... replace h(x) on the right side with x^2-4
g(h(x)) = 2x^2-8
(g o h)(x) = 2x^2-8

Now plug in x = 0
(g o h)(x) = 2x^2-8
(g o h)(0) = 2(0)^2-8
(g o h)(0) = 2(0)-8
(g o h)(0) = 0-8
(g o h)(0) = -8

Regardless of which method you use, the answer is -8

5 0

3 years ago

Which statement describes the function y = axn when a = 1 and n is odd?

kiruha [24]

Answer:

The graph is symmetric about the origin.

The graph does not pass through the origin.

Step-by-step explanation:

We're given:

the function y=axn
a = 1
n is odd

Because a = 1, then the given function can be rewritten as y = n.

The graph opens down

The function y = n will produce a horizontal line. Any function in the form of y = a single number, such as 4 or 9.3 will produce a horizontal line.

The graph is symmetric about the origin.

This is true, given the graph is a horizontal line.

The graph does not pass through the origin.

This is also true. We're given that n is an odd number. The graph will only pass through the origin if n = 0, and 0 is even.

The graph has more than one x-intercept.

This would only be true when n = 0, and this isn't possible. So, no.

4 0

2 years ago

Read 2 more answers

The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3

Alekssandra [29.7K]

Answer:

$9\pi \text{ cubic meters per hour}$

Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

If $A= 36\pi\text{ square meters}, h = 3\text{ meters}$

$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

$\implies r^2 + 3r - 18=0$

$r^2 + 6r - 3r - 18 = 0$ ( by middle term splitting )

$r(r+6)-3(r+6)=0$

$(r-3)(r+6)=0$

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

$9\pi = (12\pi + 6\pi )\frac{dr}{dt}$

$9\pi = 18\pi \frac{dr}{dt}$

$\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}$

Now,

Volume of a cylinder,

$V=\pi r^2 h$

Differentiating w. r. t. t,

$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

6 0

2 years ago

The store,s rectangular floor is 42 meters long and 39 meters wide. How many square meters of flooring do they need? Use estimat

Helga [31]

We have to find the area of the floor in order to know how many square meters of flooring they need.

The area of the floor is:
42 m* (39 m)= 1,638 m^(2)

They need 1,638 m^(2) of flooring.

Hope this helps~

8 0

2 years ago

Read 2 more answers

Show that x+y:x-y=3:2

ycow [4]

We have,

x+y:x-y=3:2

To prove that, x+ y : x - y = 3:2.

x+y=3

And,

x+y = 2

Adding (1) and (2), we get

x+y+x-y=3+2

⇒2x=5

⇒ x =

Put x = in (1), we get

+y=3

⇒ y=3-=

x+y:x-y=

=3:2

So, x+y:x-y=3:2.

8 0

2 years ago