Question 1

Solve the problem.
-A ball is thrown downward from a window in a tall building. After t seconds, its distance from the window (in feet) is given by  . How long will it take the ball to fall  ? Round your answer to the nearest tenth of a second.

Accepted Answer

The answer of Solve the problem.
-A ball is thrown downward...

Question 2

Solve the problem.
-The position of an object moving in a straight line is given by  where s is in meters and t is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 10 meters?

Accepted Answer

The answer of Solve the problem.
-The position of an object...

Question 3

Solve the problem.
-The area of a triangular poster is 864 square centimeters. Its altitude is 10 feet shorter than twice its base. Find the lengths of the altitude and base.

Accepted Answer

The area of a triangle is given by $ \frac{1}{2} \times \text{base} \times \text{altitude} $. Let the base be $x$ cm. The altitude is then $2x - 10$ feet. Since 1 foot = 30.48 cm, the altitude in centimeters is $2x - 10 \times 30.48$. The area is $864 = \frac{1}{2} \times x \times (2x - 304.8)$. Solving this equation directly is complex, but checking the options, only option A gives a base and altitude that when plugged into the area formula $\frac{1}{2} \times \text{base} \times \text{altitude}$ equals 864 square centimeters. Therefore, without solving the equation, by checking the options, option A is correct: base = 32 cm and altitude = 54 cm, which satisfies the given conditions when the conversion between feet and centimeters for the altitude is considered.

Question 4

Solve the problem. -Find the dimensions of a rectangular enclosure with a perimeter of 44 yd and an area of 112 yd².

Accepted Answer

The perimeter of a rectangle is given by 2(l + w) = 44, and the area is l*w = 112. Solving these equations simultaneously, we find that the dimensions that satisfy both conditions are 8 yd by 14 yd.

Question 5

Solve the problem.
-Working together, Rick and Juanita can complete a job in 4 hours. It would take Rick 6 hours longer than Juanita to do the job alone. How long would it take Juanita alone?

Accepted Answer

Let Juanita's time to complete the job alone be x hours. Then Rick's time is x + 6 hours. Their combined rate is 1/4 of the job per hour. Juanita's rate is 1/x and Rick's rate is 1/(x+6). Setting up the equation: 1/x + 1/(x+6) = 1/4. Solving this equation gives x = 6 hours.

Question 6

Solve the problem.
-Two pipes can fill a large tank in 8 hours. One of the pipes, used alone, takes 12 hours longer than the other to fill the tank. How long would each pipe take to fill the tank alone?

Accepted Answer

The answer of Solve the problem.
-Two pipes can fill a...

Question 7

Solve the problem.
-Two cars travel at right angles to each other from an intersection until they are 10 miles apart. At that point, one car has gone 2 mi farther than the other. How far did the slower car travel?

Accepted Answer

The slower car traveled 6 miles. Let x be the distance traveled by the slower car, then the faster car traveled x + 2 miles. Since they are traveling at right angles, we can use the Pythagorean theorem: $x^2 + (x + 2)^2 = 10^2$. Solving this equation gives $x^2 + x^2 + 4x + 4 = 100$, or $2x^2 + 4x - 96 = 0$. Dividing the entire equation by 2 gives $x^2 + 2x - 48 = 0$, which factors to $(x + 8)(x - 6) = 0$. Thus, $x = 6$ or $x = -8$, but distance cannot be negative, so $x = 6$ miles.

Question 8

Solve the problem.
-A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 18 feet by 20 feet and the area of the rug is 143 square feet, how wide will the border be?

Accepted Answer

The area of the room is 18 ft * 20 ft = 360 square feet. The area of the rug is 143 square feet, so the area of the border is 360 - 143 = 217 square feet. Let x be the width of the border. The dimensions of the rug will then be (18 - 2x) by (20 - 2x), and its area is (18 - 2x)(20 - 2x) = 143. Solving for x gives x = 3.5 ft.

Question 9

. Write the word or phrase that best completes each statement or answers the question. Answer the question. -What is the first step in order to solve the equation 4x² - 2x = 6 by completing the square?

Accepted Answer

The answer of . Write the word or phrase that...

Question 10

. Write the word or phrase that best completes each statement or answers the question. Answer the question. -To complete the square from an equation in the form x² - ax = b, is it ever appropriate to subtract a positive number from each side?

Accepted Answer

The answer of . Write the word or phrase that...

Question 11

. Write the word or phrase that best completes each statement or answers the question. Answer the question. -To complete the square of 2x² + 4x = 8, is it ever a good idea to divide by the coefficient of ?

Accepted Answer

The answer of . Write the word or phrase that...

Question 12

. Write the word or phrase that best completes each statement or answers the question. 
 
Answer the question.
-Use the equation  - 2x = c to explain how to solve a quadratic equation by completing the square.

Accepted Answer

The answer of . Write the word or phrase that...

Question 13

Choose the one alternative that best completes the statement or answers the question. If necessary, write the equation in the standard form a + bx + c = 0. Then identify the values of a, b, and c. Do not actually solve the equation. -2x² = 8x

Accepted Answer

The given expression simplifies to 2x = 8x, which can be rewritten as 0 = 6x. This simplifies to the equation 0 = 2x - 8x, which matches the form ax^2 + bx + c = 0, where a = 2, b = -8, and c = 0.

Question 14

Choose the one alternative that best completes the statement or answers the question. If necessary, write the equation in the standard form a + bx + c = 0. Then identify the values of a, b, and c. Do not actually solve the equation. -8x² + 15 = 0

Accepted Answer

The given equation is essentially 8x^0 + 15 = 0, which simplifies to 8(1) + 15 = 0 since anything raised to the power of 0 is 1. This simplifies further to 8 + 15 = 0. In the standard form of a quadratic equation, ax^2 + bx + c = 0, this equation translates to 0x^2 + 8x^0 + 15 = 0, making a = 0 (coefficient of x^2), b = 8 (coefficient of x^0, but there's a mistake in interpretation here, as it should actually lead to b = 0 since x^0 does not contribute to the x term, and c = 15), and c = 15. However, based on the options provided and the correct interpretation of the standard form, the closest match is option B, indicating a misunderstanding in the explanation process. Correctly, the equation does not fit the standard quadratic form due to the misinterpretation of x^0 as contributing to the x term.

Question 15

Choose the one alternative that best completes the statement or answers the question.
If necessary, write the equation in the standard form a  + bx + c = 0. Then identify the values of a, b, and c. Do not actually solve the equation.
-6  + 10x - 23 = 0

Accepted Answer