Rational Expression & Financial Arithmetic

Answer explanation

To find the product, multiply the numerators and the denominators: \(\frac{5y^2 \cdot 9x}{3x \cdot 10y} = \frac{45y^2}{30xy} = \frac{3y}{2}\). Thus, the correct answer is \(\frac{3y}{2}\).

Answer explanation

To find the product, multiply the numerators and denominators: \(\frac{9x^5z^2 \cdot 16y^2}{8y^6 \cdot 3x^3z^2} = \frac{144x^5y^2}{24y^6x^3} = \frac{6x^2}{y^4}\). Thus, the correct answer is \(\frac{6x^2}{y^4}\).

• undefined

Answer explanation

To evaluate \( \frac{60x^3}{12x} \) at \( x = -1 \), first simplify: \( \frac{60(-1)^3}{12(-1)} = \frac{60(-1)}{-12} = \frac{60}{12} = 5 \). Thus, the answer is \( 5 \).

• undefined

Answer explanation

Substituting x = -7 into the expression gives \frac{5(-7-2)}{5(-7)-10} = \frac{5(-9)}{-35} = \frac{-45}{-35} = \frac{9}{7} = 1. Thus, the correct answer is 1.

• undefined

Answer explanation

Substituting x=2 into the expression \(\frac{x+4}{x^2+6x+8}\) gives \(\frac{2+4}{2^2+6\cdot2+8} = \frac{6}{4+12+8} = \frac{6}{24} = \frac{1}{4}\). Thus, the correct answer is \(\frac{1}{4}\).

When adding rational expressions, you must add numerators together and denominators together.

• True

• False

Answer explanation

The statement is false. When adding rational expressions, you must find a common denominator first, then add the numerators together while keeping the common denominator unchanged.

• None

Answer explanation

The rational expression is undefined when the denominator is zero. Setting \( (x-4)(x+3) = 0 \) gives \( x=4 \) and \( x=-3 \). Thus, the correct answer is \( x=4, x=-3 \).

What is debt?

• Money you have borrowed and need to pay back

• Money you make from working at a job

• Money you make from the government

• Taxes that you pay when you buy something

Answer explanation

Debt refers to money you have borrowed and need to pay back. This distinguishes it from income or taxes, which are not obligations to repay.

What is income?

• The amount you spend

• The amount you don't save

• Money taken in

Answer explanation

Income refers to the money taken in, typically from work, investments, or other sources. It is distinct from spending or savings, making 'money taken in' the correct definition.

What is interest?

• money paid by other people

• money robbed by the bank

• money paid regularly by the bank on the account

• money paid by the U.S

Answer explanation

Interest is the money paid regularly by the bank on the account, representing earnings on deposits. This distinguishes it from other options that do not accurately define interest.