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3 years ago

15

Divide using long division.

" alt="(x^{2} -5)" align="absmiddle" class="latex-formula"> ÷ $(x-5)$

1 answer:

Morgarella [4.7K]3 years ago

4 0

Answer:

The quotient = x + 5 and the remainder = 20

Step-by-step explanation:

$\frac{x^{2}+0-5 }{x-5}=x+\frac{5x-5}{x-5}$

$\frac{5x-5}{x-5}=5+\frac{20}{x-5}$

The quotient = x + 5 and the remainder = 20

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Determine whether each equation is True or False. In case you find a "False" equation, explain why is False.

elixir [45]

Answer:

(1) TRUE.

(2) FALSE.

(3) FALSE.

(4) TRUE.

(5) FALSE.

Step-by-step explanation:

(1) $\sqrt{32} = 2^{\frac{5}{2} }$

$2^{\frac{5}{2} } = (\sqrt{2} )^5 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 4\sqrt{2}\\\\\sqrt{32} = \sqrt{16 \ \times \ 2}\ = \ \sqrt{16} \ \times \ \sqrt{2} \ = \ 4\sqrt{2}$

Thus, the equation is TRUE.

(2) $16^{\frac{3}{8} } = 8^2$

$16^{\frac{3}{8} } =(2^4)^{\frac{3}{8} } = 2^\frac{3}{2} }= (\sqrt{2} )^3 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 2\sqrt{2} \\\\8^2 = 64$

Thus, the equation is FALSE.

(3) $4^{\frac{1}{2} } = \sqrt[4]{64}$

$4^{\frac{1}{2} }= \sqrt{4} = 2\\\\\sqrt[4]{64} = (64)^{\frac{1}{4} } = (2^6)^{\frac{1}{4} }= 2^{\frac{6}{4} } = 2^{\frac{3}{2} }=(\sqrt{2} )^3 = (\sqrt{2} \times \sqrt{2} \times \sqrt{2} ) = 2\sqrt{2}$

Thus, the equation is FALSE.

(4) $2^8 = (\sqrt[3]{16} )^6$

$2^8 = 256\\\\ (\sqrt[3]{16} )^6 = (16)^{\frac{6}{3} } = (2^4)^{\frac{6}{3} } = (2)^{\frac{24}{3} } = 2^8 = 256$

Thus, the equation is TRUE.

(5) $(\sqrt{64} )^{\frac{1}{3} } = 8^{\frac{1}{6} }\\\\$

$8^{\frac{1}{6} } = (2^3)^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} } = \sqrt{2} \\\\(\sqrt{64} )^{\frac{1}{3} } = (2^6)^{\frac{1}{3} } = 2^{\frac{6}{3} } = 2^2 = 4$

Thus, the equation is FALSE.

4 0

3 years ago

The graph of y=f(x)y=f(x) is shown below. Find all values of xx for which f(x)>0f(x)>0

Rzqust [24]

Answer:

(-∞, -7) ∪ (-3, ∞)

Step-by-step explanation:

The line y=0 is the x-axis. The graph is above the x-axis for x < -7 and for x > -3. The solution set is ...

(-∞, -7) ∪ (-3, ∞)

4 0

2 years ago

Ill Mark Brainliest if you answer correctly. The figure below shows a shaded circular region inside a larger circle:

pogonyaev

First we have to find the areas of both circle using the formula

$Area = \pi r^2$

For larger circle,

$Area= \pi(5)^2 = 25 \pi$

For smaller circle,

$Area = \pi (4)^2 = 16 \pi$

Required probability

$= \frac{25 \pi -16 \pi}{25 \pi} *100 = \frac{9}{25}*100 = 36%$

Correct option is the second option .

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3 years ago

Nora invested $1,500 in a bond at a simple interest rate of 3%. How much will the bond be worth in total after 10 years?

attashe74 [19]

<h2>The bond will be worth in total after 10 years is =$1,950</h2>

Step-by-step explanation:

Given,

Nora invested $1,500 in at a bond simple interest rate of 3%

here P= $1500 R= 3% and t = 10year

Simple interest(I) = $\frac{P\times R \times t }{100}$

=$ $\frac{1500\times 3 \times 10}{100}$

=$ 450

<h3>The bond will be worth in total after 10 years is = $1,500+ $450</h3><h3> =$1,950</h3>

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3 years ago

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atroni [7]

Answer:

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Step-by-step explanation:

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2 years ago