Question 1

Find the length of the unknown side.

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Question 2

Factor the binomial completely.

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Question 3

Find the perimeter.

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Question 4

Once an antibiotic is introduced to bacteria, the number of bacteria decreases exponentially. For example, beginning with 1 million bacteria, the amount present  t  days from the time penicillin is introduced is given by the function

Rounding to the nearest thousand, determine how many bacteria are present after 6 days.

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Question 5

Multiply the conjugates.

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Question 6

A car travels west 8 miles and then north 15 miles. How far is the car from its starting point?

Accepted Answer

The distance from the starting point can be found using the Pythagorean theorem, where the total distance is the hypotenuse of a right triangle with sides of 8 miles and 15 miles. Thus, the distance is √(8^2 + 15^2) = √(64 + 225) = √289 = 17 miles.

Question 7

Clear parentheses and combine like terms.

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Question 8

Graph the function

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Question 9

Factor completely.

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Question 10

Find the simple interest and the total amount including interest.

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Question 11

Simplify the expression. Write the answer in exponent form.

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Question 12

Apply the appropriate property to simplify the expression.

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Question 13

Solve the equation by using the quadratic formula.

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Question 14

b  is inversely proportional to  c . If  b  is 2 when  c  is 10 , find  b  when  c=5 .

Accepted Answer

When two quantities are inversely proportional, it means that when one quantity increases, the other decreases at a rate such that their product is constant. Given $b \propto \frac{1}{c}$, when $b = 2$, $c = 10$, so their product is $2 \times 10 = 20$. To find $b$ when $c = 5$, we set up the equation $b \times 5 = 20$, solving for $b$ gives $b = 4$.

Question 15

Multiply the polynomials.

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Question 16

Subtract the polynomials.

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Question 17

Factor the binomial completely.

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Question 18

Use the commutative and associative properties of real numbers and the properties of exponents to simplify the expression.

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Question 19

Simplify the expression. Write the answer in exponent form.

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Question 20

Use the distance formula to find the distance between the two points.

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Quiz 4: Living in a Nonlinear World

Find the length of the unknown side.

Factor the binomial completely.

Find the perimeter.

Multiply the conjugates.

A car travels west 8 miles and then north 15 miles. How far is the car from its starting point?

Clear parentheses and combine like terms.

Graph the function

Factor completely.

Find the simple interest and the total amount including interest.

Simplify the expression. Write the answer in exponent form.

Apply the appropriate property to simplify the expression.

Solve the equation by using the quadratic formula.

b is inversely proportional to c . If b is 2 when c is 10 , find b when c=5 .

Multiply the polynomials.

Subtract the polynomials.

Factor the binomial completely.

Use the commutative and associative properties of real numbers and the properties of exponents to simplify the expression.

Simplify the expression. Write the answer in exponent form.

Use the distance formula to find the distance between the two points.