Question 1

Solve for the indicated variable.
-Solve for r.

Accepted Answer

The answer of Solve for the indicated variable.
-Solve for r....

Question 2

Solve the problem.
-A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s = 16t2 + 32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 187 feet?

Accepted Answer

To find the time it takes for the ball to fall 187 feet, set s = 187 and solve the equation 16t^2 + 32t = 187. Rearranging gives 16t^2 + 32t - 187 = 0. Using the quadratic formula, t = (-32 ± √(32^2 - 4*16*(-187)))/(2*16). Solving this gives t ≈ 2.6 seconds.

Question 3

Solve the problem.
-A lot is in the shape of a right triangle. The shorter leg measures 150 m. The hypotenuse is 50 m longer than the length of the longer leg. How long is the longer leg?

Accepted Answer

The longer leg can be found using the Pythagorean theorem. Let x be the length of the longer leg, then the hypotenuse is x + 50. The equation is $150^2 + x^2 = (x + 50)^2$. Solving for x gives x = 200 m.

Question 4

Solve the problem.
-An open box is to be made from a rectangular piece of tin by cutting two inch squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular
Piece of tin.

Accepted Answer

The answer of Solve the problem.
-An open box is to...

Question 5

Solve the problem.
-The following table shows the height of a football at various times during a punt.  Use a graphing calculator to find a quadratic regression curve that expresses the height in terms of the time. Use the regression equation to find the approximate number of seconds that it will take for the ball to reach the
Hands of the punt returner, who is 6' tall.

Accepted Answer

The answer of Solve the problem.
-The following table shows the...

Question 6

Solve the problem.
-A barge travels along a river between Metro City and Smithport, which are 50 miles apart. The speed of the current is 2.4 mph. If the barge can make the downstream trip in 5.9 hours less than it can travel the upstream
Trip, then what is the barge's speed in still water? Round your answer to one decimal place.

Accepted Answer

The correct answer is A.The barge's speed in still water is 6.8 mph. This is because the barge's speed downstream is 2.4 mph faster than its speed in still water, and its speed upstream is 2.4 mph slower than its speed in still water. Therefore, the difference between the barge's speed downstream and upstream is 4.8 mph. Since the barge can make the downstream trip in 5.9 hours less than it can travel the upstream trip, the barge's speed in still water must be 4.8 mph / 2 = 2.4 mph. Therefore, the barge's speed in still water is 2.4 mph + 4.4 mph = 6.8 mph.

Question 7

Solve for the indicated variable.
-Solve for v.

Accepted Answer

The answer of Solve for the indicated variable.
-Solve for v....

Question 8

Solve for the indicated variable.
-Solve for y.

Accepted Answer

The answer of Solve for the indicated variable.
-Solve for y....

Question 9

Solve the problem.
-A rectangular garden has dimensions of 25 feet by 17 feet. A gravel path of consistent width is to be built around the garden. How wide can the path be if there is enough gravel for 400 square feet?

Accepted Answer

The area of the garden is 25 ft * 17 ft = 425 square feet. The total area, including the path, minus the garden area equals the area available for the path, which is 400 square feet. Let the width of the path be x feet. The dimensions of the garden plus the path will be (25 + 2x) by (17 + 2x). The equation for the area including the path is (25 + 2x)(17 + 2x) = 425 + 400. Simplifying gives 4x^2 + 84x - 400 = 0. Solving for x gives x = 4 feet as the width of the path that uses exactly 400 square feet of gravel.

Question 10

Solve the problem.
-A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 ft. Find the length of the ladder if the length is 5 ft more than its distance from the wall.

Accepted Answer

Using the Pythagorean theorem, let the distance from the wall be x. Then, the ladder's length is x + 5. We have x^2 + 15^2 = (x + 5)^2. Solving this gives x = 20, so the ladder's length is 25 ft.

Question 11

Solve the problem.
-The position of an object moving in a straight line is given by  where s is in feet 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 18 feet?

Accepted Answer

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

Question 12

Solve for the indicated variable.
-Solve for a. A =

Accepted Answer

The answer of Solve for the indicated variable.
-Solve for a....

Question 13

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 20
Meters?

Accepted Answer

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

Question 14

Solve for the indicated variable.
-Solve for x.

Accepted Answer

The answer of Solve for the indicated variable.
-Solve for x....

Question 15

Solve the problem.
-A square has an area of 49 square inches. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45 square inches. Find the dimensions of the rectangle.

Accepted Answer

The side of the square is 7 inches (since 7^2 = 49). If x is added to the length and removed from the width, the new dimensions are (7 + x) and (7 - x). The area of the rectangle is 45, so (7 + x)(7 - x) = 45. Solving gives x = 2, so the dimensions are 5 in. by 9 in.

Question 16

Solve the problem.
-The area of a square is 81 square centimeters. If the same amount is added to one dimension and removed from the other, the resulting rectangle has an area 9 square centimeters less than the area of the square. How much is
Added and subtracted?

Accepted Answer

The side of the square is √81 = 9 cm. Let x be the amount added and subtracted. The new dimensions are (9+x) and (9-x), and their product is 81 - 9 = 72. So, (9+x)(9-x) = 72. Simplifying gives x = 3.

Question 17

Solve for the indicated variable.
-Solve for t.

Accepted Answer

The answer of Solve for the indicated variable.
-Solve for t....

Question 18

Solve the problem.
-A rug is to fit in a room so that a border of consistent width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 40 square feet, how wide will the border be?

Accepted Answer

The area of the room is 12 ft * 15 ft = 180 square feet. The area of the rug is 40 square feet, so the area of the border is 180 - 40 = 140 square feet. Let x be the width of the border. The dimensions of the rug will then be (12 - 2x) by (15 - 2x), and the area of the rug is (12 - 2x)(15 - 2x) = 40. Solving for x gives x = 3.5 ft.

Question 19

Solve the problem.
-The demand equation for a certain product is P = 65 - 0.002x, where x is the number of units sold per week and P is the price in dollars at which one is sold. The weekly revenue R is given by R = xP. What number of units
Sold produces a weekly revenue of $80,000?

Accepted Answer

To find the number of units sold that produces a weekly revenue of $80,000, we substitute the demand equation into the revenue equation: R = xP = x(65 - 0.002x). Setting R = $80,000 and solving the quadratic equation 80,000 = 65x - 0.002x^2 gives us the solutions x = 1281 or x = 31,219.

Question 20

Solve the problem.
-If an amount of money, called the principal, P, is deposited into an account that earns interest at a rate r, compounded annually, then in two years that investment will grow to an amount A, given by the formula
A = P(1 + r)2. If a principal amount of $4000 grows to $5198.40 in two years, what is the interest rate?

Accepted Answer

The interest rate is 14%.The formula for the amount of money in an account after two years is A = P(1 + r)2. We know that the principal amount is $4000 and the amount after two years is $5198.40. So we can plug these values into the formula and solve for r:5198.40 = 4000(1 + r)25198.40 = 4000(1 + r)(1 + r)5198.40 = 4000(1 + 2r + r2)5198.40 = 4000 + 8000r + 4000r24000r2 + 8000r - 1198.40 = 0(200r - 14)(20r + 85.28) = 0r = 14 or r = -0.4264Since the interest rate cannot be negative, the only valid solution is r = 14%.

Quiz 1: Equations, Inequalities, and Modeling

Solve for the indicated variable. -Solve for r.

Solve the problem. -A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s = 16t2 + 32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 187 feet?

Solve the problem. -A lot is in the shape of a right triangle. The shorter leg measures 150 m. The hypotenuse is 50 m longer than the length of the longer leg. How long is the longer leg?

Solve the problem. -An open box is to be made from a rectangular piece of tin by cutting two inch squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular Piece of tin.

Solve for the indicated variable. -Solve for v.

Solve for the indicated variable. -Solve for y.

Solve the problem. -A rectangular garden has dimensions of 25 feet by 17 feet. A gravel path of consistent width is to be built around the garden. How wide can the path be if there is enough gravel for 400 square feet?

Solve the problem. -A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 ft. Find the length of the ladder if the length is 5 ft more than its distance from the wall.

Solve the problem. -The position of an object moving in a straight line is given by where s is in feet 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 18 feet?

Solve for the indicated variable. -Solve for a. A =

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 20 Meters?

Solve for the indicated variable. -Solve for x.

Solve the problem. -A square has an area of 49 square inches. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45 square inches. Find the dimensions of the rectangle.

Solve the problem. -The area of a square is 81 square centimeters. If the same amount is added to one dimension and removed from the other, the resulting rectangle has an area 9 square centimeters less than the area of the square. How much is Added and subtracted?

Solve for the indicated variable. -Solve for t.

Solve the problem. -A rug is to fit in a room so that a border of consistent width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 40 square feet, how wide will the border be?

Solve the problem. -The demand equation for a certain product is P = 65 - 0.002x, where x is the number of units sold per week and P is the price in dollars at which one is sold. The weekly revenue R is given by R = xP. What number of units Sold produces a weekly revenue of $80,000?