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3 years ago

Solve for x. A) 46 B) 38 C) 45 D) 40

Mathematics

1 answer:

yarga [219]3 years ago

8 0

Answer:

C) 45

Step-by-step explanation:

By Basic Proportionality Theorem:

$\frac{x}{18} = \frac{20}{8} \\ \\x = \frac{18 \times 20}{8} \\ \\ x = \frac{360}{8} \\ \\ x = 45$

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3 years ago

If x² + x² + x² = 6, what is x?

max2010maxim [7]

Answer:

Square root of 2

Step-by-step explanation:

3x²=6

Divide each side by 3: 3x² ÷ 3=6÷3

X²=2

Then square root each side

So answer is square root of 2

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3 years ago

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3 years ago

Two girls aged 12 years and 15 years divide $72 in the ratio of their ages. How much does each girl receive?

nikdorinn [45]

Answer:

12 years = 16 USD

15 years = 20 USD

Step-by-step explanation:

15 years =72:4= 18 we round to 20 for 15 years

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3 years ago

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How do you rationalize the numerator in this problem?

maw [93]

To solve this problem, you have to know these two special factorizations:

$x^3-y^3=(x-y)(x^2+xy+y^2)\\ x^3+y^3=(x+y)(x^2-xy+y^2)$

Knowing these tells us that if we want to rationalize the numerator. we want to use the top equation to our advantage. Let:

$\sqrt[3]{x+h}=x\\ \sqrt[3]{x}=y$

That tells us that we have:

$\frac{x-y}{h}$

So, since we have one part of the special factorization, we need to multiply the top and the bottom by the other part, so:

$\frac{x-y}{h}*\frac{x^2+xy+y^2}{x^2+xy+y^2}=\frac{x^3-y^3}{h*(x^2+xy+y^2)}$

So, we have:

$\frac{x+h-h}{h(\sqrt[3]{(x+h)^2}+\sqrt[3]{(x+h)(x)}+\sqrt[3]{x^2})}=\\ \frac{x}{\sqrt[3]{(x+h)^2}+\sqrt[3]{(x+h)(x)}+\sqrt[3]{x^2}}$

That is our rational expression with a rationalized numerator.

Also, you could just mutiply by:

$\frac{1}{\sqrt[3]{x_h}-\sqrt[3]{x}} \text{ to get}\\ \frac{1}{h\sqrt[3]{x+h}-h\sqrt[3]{h}}$

Either way, our expression is rationalized.

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3 years ago