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olchik [2.2K]
3 years ago
7

Are the following expressions equivalent? Why or why not? 6(2x + 4) and 12x + 24

Mathematics
1 answer:
MrMuchimi3 years ago
8 0

Answer: Yes

Step-by-step explanation:

When using the distributive property, 6(2x + 4) becomes 12x + 24

6 * 2x = 12x and 6 * 4 = 24

12x + 24 = 12x + 24

Therefore, the expressions are equivalent.

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Marat540 [252]
1.) The interval of the value of x is from -5 to 1, inclusive. Remember that what is asked is the absolute value, thus the sign does not matter even if you have to subtract x from 5. Thus, the maximum value would be obtained if the x is smaller, which is 1. The minimum value is obtained when x=-5.

Absolute maximum value: x = - 5
f(-5) = ║5 - 7(-5)^2║ = ║-170║=170


Absolute minimum value: x = 1
f(1) = ║5 - 7(1)^2║ = ║-2║= 2

2.) The Mean Value Theorem (MVT) applies to functions that are continuous and differentiable on the closed and open interval of a to b, respectively. Since the function is a quadratic function, MVT can be applied. Then, this means that there is a value of c which is between a and b. This could be determined using this formula according to MVT:

f'(c)= \frac{f(b)-f(a)}{b-a}

The differentiated form would be f'(x) = -2x. Then,

-2c =  \frac{(4- 0^{2} )-(4- (-1)^{2}) }{0--1}=1

c=- \frac{1}{2}

Thus, x = -1, x = -1/2, and x=0 all lie in the function 4-x^2.
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3 years ago
Stars that are medium-sized are: A. about the size of our sun B. about four times the size of our sun C. less than half the size
aliina [53]
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8 0
3 years ago
The​ U.S.-based motorcycle manufacturer says that it expects to build 139,000 motorcycles this​ year, up from 122,000 last year.
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Solution:

we are given that

The​ U.S.-based motorcycle manufacturer says that it expects to build 139,000 motorcycles this​ year, up from 122,000 last year.

It mean the increased production is 139,000-122,000=17000

The percentage change in production can be found using the formula as below

Percenatge  \ increase=\frac{change}{Initial}*100\\
\\
\text{Substitute the values we get}\\
\\
Percenatge  \ increase=\frac{17000}{122,000}*100\\
\\
\
Percenatge  \ increase=13.93\\

Hence the percentage increase is 13.93.


3 0
3 years ago
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3 years ago
How long is 51 inches in feet?
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Answer:

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Step-by-step explanation:


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