Answers INMT3 Integrated Math 3 Sem 1 26-27Modeling with Quadratic Equations

Modeling with Quadratic Equations — Unit test Answers

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Which expression is equivalent to ?

StartFraction m minus 4 Over (m + 4) (m + 2) EndFraction

StartFraction (m + 4) (m + 2) Over m minus 4 EndFraction

StartFraction (m minus 4) (m + 2) Over m + 4 EndFraction

StartFraction m + 4 Over (m minus 4) (m + 2) EndFraction

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Which expression is equivalent to the expression below?

StartFraction 1 Over (m + 4) (m + 3) EndFraction

StartFraction 1 Over (m minus 4) (m minus 3) EndFraction

StartFraction m minus 4 Over m minus 3 EndFraction

StartFraction m + 3 Over m + 4 EndFraction

Identify the graph of the rational function with an x-intercept at (–4, 0) and (4, 0), a vertical asymptote at x = 2, and an oblique asymptote at y = x + 2.

Option

Which statement is true about the discontinuities of the function f(x)?

There are asymptotes at and .

There are holes at and .

There are asymptotes at and .

There are holes at and .

What is the difference?

StartFraction 2 (x + 6) Over (x + 4) (x minus 4) EndFraction

StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction

StartFraction x minus 3 Over (x + 5) (x minus 4) EndFraction

StartFraction negative 2 (x minus 6) Over (x + 4) (x minus 4) EndFraction

How many extraneous solutions does the equation below have?

Ted can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. When they work together, the situation can be modeled by the equation, where t is the number of hours it would take to clear the field together.How long will it take Ted and Jacob to clear the field together?

12 minutes

50 minutes

1 hour 12 minutes

2 hours 30 minutes

Max can mow a lawn in 45 minutes. Jan takes twice as long to mow the same lawn. If they work together, the situation can be modeled by the following equation, where t is the number of minutes it would take to mow the lawn together.How long will it take Maxine and Jan to mow the lawn together?

30.0 minutes

45.0 minutes

67.5 minutes

135.0 minutes

The equation shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. What happens to the density as the volume approaches 0?

The density approaches infinity.

The density approaches 0.

The density approaches 1.

The density approaches 13.

Marshall bought 32 ounces of mixed nuts, which are estimated to be 30% peanuts. Which expression can be used to find the percentage of peanut concentration of the final mix if he adds x ounces of peanuts?

mc012-1.jpg

mc012-2.jpg

mc012-3.jpg

mc012-4.jpg

Which graph represents the function ?

On a coordinate plane, a hyperbola is shown. A curve opens up and to the right in quadrant 1, and another curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0.

On a coordinate plane, a hyperbola is shown. A curve opens up and to the right in quadrant 1, and another curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0.25.

On a coordinate plane, a hyperbola is shown. A curve opens up and to the left in quadrant 2, and another curve opens down and to the right in quadrant 4. A vertical asymptote is at x = 0.

On a coordinate plane, a hyperbola is shown. A curve opens up and to the left in quadrant 2, and another curve opens down and to the right in quadrant 4. A vertical asymptote is at x = 0.25.

The increase in a person’s body temperature T(t), above 98.6ºF, can be modeled by the function , where t represents time elapsed. What is the meaning of the horizontal asymptote for this function?

The horizontal asymptote of y = 0 means that the person’s temperature will approach 98.6ºF as time elapses.

The horizontal asymptote of y = 0 means that the person’s temperature will approach 0ºF as time elapses.

The horizontal asymptote of y = 4 means that the person’s temperature will approach 102.6ºF as time elapses.

The horizontal asymptote of y = 4 means that the person’s temperature will approach 4ºF as time elapses.

Which graph represents a function that has the domain (–∞, –4) ⋃ (–4, 3) ⋃ (3, ∞), has a y-intercept at (0, 3), and is increasing on the interval (0, 4)?

Option

Which statement describes the vertical asymptotes of the graph of ?

The graph has no vertical asymptote.

The graph has a vertical asymptote at x = 8 only.

The graph has a vertical asymptote at x = –8 only.

The graph has vertical asymptotes at both x = 8 and x = –8.

What is the solution to the equation ?

y = –4 and y = 4

y = 0

all real numbers

no solution

The cost of catering a dinner is $11.95 per person plus $25 for delivery and setup. Which statement is true about the graph of the function that represents the average cost per person?

The horizontal asymptote y = 0 represents that the cost per person approaches $0 as the number of people increases.

The horizontal asymptote y = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.

The vertical asymptote x = 0 represents that the cost per person approaches $0 as the number of people increases.

The vertical asymptote x = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.

How can Ari simplify the following expression?

Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerator by the reciprocal of the denominator.

Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerators and multiply the denominators.

Divide the numerator and the denominator by a – 3. Then divide the numerator by the denominator.

Divide the numerator and the denominator by a – 3. Then simplify the numerator and simplify the denominator.

The inverse variation equation shows the relationship for a cruise ship’s travel between the rate of travel, x, and the time to travel, y for a distance of 600 miles. What is the rate of travel in miles per hour (mph) if the trip takes 24 hours?