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2 years ago

Which expression is equivalent to 7a³ (8a² + a)²-4a³? Simplify.

1 answer:

8 0

$7a³ (8a² + a)²-4a³ \\ \\ 7 {a}^{3}(8 { {a}^{2} + a)(8 {a}^{2} + a )} - 4 {a}^{3} \\ \\ 7 {a}^{3} ( {8a}^{2} (8 {a}^{2} + a ) + a(8 {a}^{2} + a ) - 4 {a}^{3} \\ \\ 7 {a}^{3} (64 {a}^{4} + 8{a}^{3} + 8 {a}^{3} + {a}^{2} ) - 4 {a}^{3} \\ \\ 7 {a}^{3} (64 {a}^{4} + 16 {a}^{3} + {a}^{2} ) - 4 {a}^{3} \\ \\ 448 {a}^{7} + 112 {a}^{6} + 7 {a}^{5} - 4 {a}^{3} \\ \\ {a}^{3} (448 {a}^{4} + 112 {a}^{3} + 7 {a}^{2} - 4).$

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What expression Is equivalent to 27/125 (3/5)3 (3/4)2 (3/5) 3 5

victus00 [196]

$\frac{27}{125 } = \frac{ 3^{3} }{ 5^{3} } = (\frac{3}{5} )^3$

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4 years ago

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The population of a town is 18,000.

Eddi Din [679]

If the town decreases at a rate of 8% per year, it would take 6 years.

100% - 8% = 92%

We would multiply each population per year by 0.92 as the town is decreasing in population by 8% per year

1st year: 18,000 • .92 = 16,560

2nd year: 16,560 • .92 = 15,235.2

3rd year: 15,235.2 • .92 = 14,016.384

4th year: 14,016.384 • .92 = 12,894.72

5th year: 12,894.72 • .92 = 11,863.1424

6th year: 11,863.1424 • .92 = 10,914.091

10,914 is less than 11,000 meaning it would take 6 years for the population to be fewer than 11,000 if the town is decreasing in population at a rate of 8% per year

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3 years ago

How many degrees is the angle below?

umka2103 [35]

Answer:

30 degrees

Step-by-step explanation:

the line (not at the 0) is what you measure from. Because the angle is visibly acute, we know that it must be less than 90 degrees, therefore the angle cannot be 150 degrees but 30 degrees (from the lower line)

7 0

4 years ago

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Calculate the average rate of change of f(x) = 1 x - x2 - 2 for 3 ≤ x ≤ 6. A) -163 18 B) -18 163 C) 163 18 D) 18 163

larisa86 [58]

To solve this we are going to use the average rate of change formula: $A(x)= \frac{f(b)-f(a)}{b-a}$
where
$A(x)$ is the average rate of change of the function
$f(a)$ is the position function evaluated at $a$
$f(b)$ is the position function evaluated at $b$
$a$ is the first point in the interval
$b$ is the second point in the interval

We can infer for our problem that the first point is 3 and the second point is 6, so $a=3$ and $b=6$ . Lets replace those values in our formula:
$A(x)= \frac{f(b)-f(a)}{b-a}$
$A(x)= \frac{f(6)-f(3)}{6-3}$
$A(x)= \frac{6-6^2-2-(3-3^2-2)}{3}$
$A(x)= \frac{-32-(-8)}{3}$
$A(x)= \frac{-32+8}{3}$
$A(x)= \frac{-24}{3}$
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We can conclude that the average rate of change of the function f(x) = 1 x - x2 - 2 for 3 ≤ x ≤ 6 is -8

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3 years ago

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Zepler [3.9K]

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Step-by-step explanation:

3.325 divided by 9.5 = 0.35

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