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mars1129 [50]
3 years ago
9

​a) Find the volume of the shaded figure by subtracting the smaller volume from the larger. The formula for the volume of a rect

angular solid is V=lwh. ​b) Write the expression obtained in part ​a) in factored form.

Mathematics
1 answer:
Genrish500 [490]3 years ago
5 0

Answer:

Part A - 2a*2b Part B- 2(a*b)

Step-by-step explanation:

Part A)

V=lwh of larger prism - lwh of smaller prism

=9a*a*a-9a*b*b

=11a-9a*2b

=2a*2b

Part B)

2a*2b

=2(a*b)

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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
Christopher borrowed $22,000 for 7 years. At the end of the loan, he had paid a total of $27,390. Find the interest rate on the
oee [108]

Step-by-step explanation:

okay so we know i = prt

in this scenario

p = 22,000

r = ?

t = 7

i = 27,390

the equation for r is (i/p*t)

so now let's plug in what we know

r = 27,390/22,000 * 7

r = 1.245 / 7

<u><em>r = 8.715</em></u>

<u><em></em></u>

please rate 5 stars and vote brainliest and say thanks

5 0
3 years ago
Manny can assemble a computer by himself in 50 minutes. Lucy does the same job in 45 minutes. How long will it take to assemble
jonny [76]
Manny can assemble a computer in 50 minutes. That means, in a minute Manny does \frac{1}{50} job.

Lucy can assemble a computer in 45 minutes. That means, in a minute Lucy does \frac{1}{45} job.

If they are working together, in a minute they will do:
\dfrac{1}{50} + \dfrac{1}{45}
= \dfrac{9}{450} + \dfrac{10}{450} \text{(equalize the denominator)}
=\dfrac{19}{450}
In a minute they will do \frac{19}{450} job

To finish the job they will do it in \frac{450}{19} minutes or about 24 minutes.
5 0
4 years ago
Is the inequality always, sometimes, or never true?<br> 3x - 14 &lt; 3(x-5)
lys-0071 [83]

Answer:

3x - 14 < 3x - 15

-14 < -15

never true

Step-by-step explanation:

8 0
4 years ago
A ruler costs pence.
Katarina [22]

Answer:

2x+3(10+x)

Step-by-step explanation:

I'm not sure but I think this might be the answer

8 0
3 years ago
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