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4 years ago

What is the cube root of 27a^12

2 answers:

7 0

Cube root (27a^12)
Cube root 27 = 3 because
3 * 3 * 3 = 27
Cube root a^12 = a^4 because
a^4 * a^4 * a^4 = a^12
ANSWER
3a^4

Alika [10]4 years ago

6 0

Answer:

$3 \times a^{4}$

Step-by-step explanation:

We have to find the cube root of the given expression $27a^{12}$

$\sqrt[3]{27a^{12}}$ = $\sqrt[3]{27} \times\sqrt[3]{a^{12}}$

= $\sqrt[3]{3\times3\times3} \times\sqrt[3]{a^{4} \times a^{4} \times a^{4}}$

= $3 \times a^{4}$

Therefore, $3 \times a^{4}$ is the answer.

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Instructions: Given the vertex, fill in the vertex form of the quadratic function..

miskamm [114]

Answer:

$\implies y=(x-2)^2-6$

Step-by-step explanation:

Vertex form of a quadratic equation:

$y=a(x-h)^2+k$

where:

(h, k) is the vertex
a is some constant

Given vertex: (2, -6)

⇒ h = 2 and k = -6

Substitute the values of h and k into the formula:

$\implies y=a(x-2)^2+(-6)$

$\implies y=a(x-2)^2-6$

As we have not been given a value for the constant $a$ , assume this is 1.

Therefore, the vertex form of the quadratic function with vertex (2, -6) is:

$y=(x-2)^2-6$

Learn more about vertex form here:

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2 years ago

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I could rlly use sum help - Brainliest!!!!!

atroni [7]

Answer: The answers are 4x^2(x^2+5x+3), (x–6) (x+2), (x–9), 3(x–7)(x–4), (9x–10) (9x+10), 3(y^2+2)(x^2+4), (5x+2), 2(x–4)(6x+1), 2(x + 4)(y - 4), and the factored form is (3x–4)(x–3).

Step-by-step explanation: To solve all the factoring equations, factor using the AC method or factoring the polynomials, the 3 steps are Grouping: using the sum-product pattern, common factor from the two pairs, and

rewrite the expression in factored form.

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3 years ago

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3 years ago

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Max Quimby picks Raspberries for his grandmother every Tuesday during 2 points

Greeley [361]

Answer:

Would be paid $69.75

Step-by-step explanation:

Since he is paid $0.75 per quart, and he has picked up 93 quarts, you would multiply 0.75 by 93. Which would give you $69.75.

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3 years ago

Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

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4 years ago