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3 years ago

X^2 - 8 = -4 solve by completing the square

Mathematics

1 answer:

NikAS [45]3 years ago

7 0

x = ±2

Step-by-step explanation:

x² - 8 = -4

x² = -4 + 8

x² = 4

x = ± √4

x = ± 2

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What is the volume of the cube shown?

SOVA2 [1]

The answer is the last one.

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3 years ago

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How do you solve for a and b showing your work

Mariulka [41]

Answer:

a) 4

b) $\frac{1}{2} \sqrt{y^5}$

Step-by-step explanation:

PART A

Simplify the expression by solving out the square roots.

$\frac{\sqrt{16} \sqrt{p} }{\sqrt{p}}$ = $\frac{4 \sqrt{p} }{\sqrt{p}}$

You can cancel out the $\sqrt{p}$ on the top and bottom.

So, a should be 4.

PART B

Solve out the square root. The square root is pretty much the 1/2 power, so you can divide the exponents by half.

$\frac{\sqrt{y^{10}} }{\sqrt{4y^{5}} }$ = $\frac{y^{5}}{2y^{\frac{5}{2}} }$

You can subtract exponents to divide them. So the y variable becomes $y^{5 - 5/2}$ , or $y^{5/2}$ .

Then, the overall expression is $\frac{1}{2} y^{\frac{5}{2} }$ , or you can turn that into $\frac{1}{2} \sqrt{y^5}$ .

5 0

4 years ago

Given that f(x) = x2 + 5x + 6 and g(x) = x + 2, find (fºg)(x) and

PolarNik [594]

Answer:

$(f\circ g)(x)=x^2+9x+20$

Step-by-step explanation:

We have the two functions:

$f(x)=x^2+5x+6\text{ and } g(x)=x+2$

And we want to find:

$(f\circ g)(x)$

This is equivalent to:

$(f\circ g)(x)=f(g(x))$

Therefore, we will have:

$f(x+2)$

By substitution:

$f(x+2)=(x+2)^2+5(x+2)+6$

Simplify. Square and distribute:

$f(x+2)=(x^2+4x+4)+(5x+10)+6$

Rearrange:

$f(x+2)=(x^2)+(4x+5x)+(4+10+6)$

Combine like terms:

$f(x+2)=(f\circ g)(x)=x^2+9x+20$

7 0

3 years ago

Need help on this. thank you

Leno4ka [110]

Answer:

x²

Step-by-step explanation:

Let "d" represent the divisor (what goes in the blank). Then you have ...

... (x²y)/d = y

Multiplying by d gives ...

... x²y = yd

And dividing by y gives the desired value:

... x² = d

The divisor is x².

5 0

3 years ago

Find the sum of the first 50 terms below. an=3n+2

andrey2020 [161]

Step-by-step explanation:

1st term = a(1) = 3(1) + 2 = 5

50th term = a(50) = 3(50) + 2 = 152

Sum of first 50 terms = (5 + 152) * (50/2) = 3925.

3 0

3 years ago