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4 years ago

Which of the following choices lists the correct values of a,h, and k for the function f(x)=5x^2?

Mathematics

1 answer:

Whitepunk [10]4 years ago

5 0

Answer:

Step-by-step explanation:

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Rationalize the denominator of $\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, whe

musickatia [10]

Rationalizing the denominator involves exploiting the well-known difference of squares formula,

$a^2-b^2=(a-b)(a+b)$

We have

$(\sqrt{16}-\sqrt2)(\sqrt{16}+\sqrt2)=(\sqrt{16})^2-(\sqrt2)^2=16-2=14$

so that

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{32}(\sqrt{16}+\sqrt2)}{14}$

Rewrite 16 and 32 as powers of 2, then simplify:

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{2^5}(\sqrt{2^4}+\sqrt2)}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{2^2\sqrt2(2^2+\sqrt2)}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{4\sqrt2(4+\sqrt2)}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+4(\sqrt2)^2}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+8}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{8\sqrt2+4}7$

So we have A = 8, B = 2, C = 4, and D = 7, and thus A + B + C + D = 21.

3 0

3 years ago

A circle has an area of 200.96 units2 and a circumference of 50.24 units. If the radius is 8 units, what can be said about the r

AleksandrR [38]

Answer:

C. The ratio of the area to the circumference is equal to half the radius.

Step-by-step explanation:

The area of a circle can be written as;

Area A = πr^2

The circumference of a circle is;

Circumference C = 2πr

Using the formula, w can derive the relationship between the two variables.

A = kC

k = A/C

Substituting the two formulas;

k = (πr^2)/(2πr) = r/2

So,

A = (r/2)C

A/C = r/2

The ratio of the area to the circumference is equal to half the radius.

Given;

Area = 200.96

Circumference = 50.24

Radius = 8

To confirm;

k = r/2 = 8/2 = 4

Also,

A/C = 200.96/50.24

A/C = 4

6 0

3 years ago

Help asap ill give brainliest

Natali [406]

Answer:

147

Step-by-step explanation:

5 0

3 years ago

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Violin strings are parallel. Viewed from above, a violin bow in two different positions forms two transversals to the violin str

V125BC [204]

Answer:

x = 10; y = 20

Step-by-step explanation:

8x + y = 100 (alternate exterior angles are congruent)

4x + y = 60 (corresponding angles are congruent)

Subtract the second equation from the first equation.

4x = 40

x = 10

Substitute x = 10 in first equation and solve for y.

8(10) + y = 100

y = 20

3 0

3 years ago

An Olympian swam the 200-meter freestyle at a speed of 1.8 meters per second. An Olympic runner ran the 200-meter dash in 21.3 s

BlackZzzverrR [31]

Speed = Distance/Time

Runner Speed = 200/21.3 = 9.4 m/s

Swimmer Speed = 1.8 m/s

9.4 - 1.8 = 7.6 m/s

C

5 0

4 years ago

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