Question 1

The price of a computer fell 10% this year. If the computer now costs $621, how much did it cost last year?

Accepted Answer

The answer of The price of a computer fell 10%...

Question 2

Solve the quadratic equation below by factoring. $x ^ { 2 } + x = 72$

Accepted Answer

First, rearrange the equation to standard form: $x^2 + x - 72 = 0$. Factoring the quadratic equation, we get $(x + 9)(x - 8) = 0$, which gives the solutions $x = -9$ and $x = 8$.

Question 3

How much water must be added to 3 liters of a 47% saline solution to dilute it to a 32% saline solution? Round answer to nearest tenth of a liter.

Accepted Answer

First, let's calculate how much salt is in the original 3 liters of 47% saline solution:

3 liters x 0.47 = 1.41 liters of salt

Now, we want to dilute this solution to a 32% saline solution. Let's set up the equation:

1.41 liters of salt / (3 liters + x liters of water) = 0.32

Solving for x:

1.41 / 0.32 = 4.41

4.41 - 3 = 1.41 liters of water

So we need to add 1.41 liters of water to the original 3 liters of 47% saline solution to dilute it to a 32% saline solution. Rounded to the nearest tenth, that comes out to 1.4 liters. Therefore, the best choice is B.

Question 4

Solve $( x - 4 ) ^ { 2 } = 25$ by any convenient method.

Accepted Answer

The answer of Solve \(( x - 4 ) ^...

Question 5

To determine the height of a tree, you measure its shadow and the shadow of a five-foot lamppost. The shadow of the lamppost is 4 feet and the shadow of the tree is 45 feet. Assuming both the tree and the lamppost are standing next to each other and perpendicular to the ground, how tall is the tree? Round to the nearest tenth of a foot.

Accepted Answer

Using similar triangles, the ratio of the height of the tree to its shadow is the same as the ratio of the height of the lamppost to its shadow. So, $ \frac{height\ of\ tree}{45\ feet} = \frac{5\ feet}{4\ feet} $. Solving for the height of the tree gives $ height\ of\ tree = \frac{5\ feet}{4\ feet} \times 45\ feet = 56.25\ feet $, which rounds to 56.3 feet.

Question 6

Write $x ( x - 5 ) = - 2 x ^ { 2 } + 8$ in general form.

Accepted Answer

The answer of Write \(x ( x - 5 )...

Question 7

Solve the quadratic equation by any convenient method. $( 4 x - 5 ) ^ { 2 } - 25 = 0$

Accepted Answer

The answer of Solve the quadratic equation by any convenient...

Question 8

Two friends fly from from one city to another (a distance apart of 2930 miles). It takes 2 hours and 45 minutes to fly the first 1350 miles. At this rate, how long is the entire flight? Round to the nearest hundredth of an hour.

Accepted Answer

To find the total time of the entire flight, we can use the formula:

total time = time for first leg + time for second leg

We know that the distance for the first leg is 1350 miles, and the total distance is 2930 miles. So the distance for the second leg is:

2930 miles - 1350 miles = 1580 miles

We also know that the time for the first leg is 2 hours and 45 minutes, which is equivalent to:

2 + (45/60) = 2.75 hours

To find the speed of the plane, we can use the formula:

speed = distance / time

For the first leg:

speed = 1350 miles / 2.75 hours
speed = 490.91 mph

We can use this speed to find the time for the second leg:

time = distance / speed
time = 1580 miles / 490.91 mph
time = 3.22 hours

Now we can find the total time:

total time = time for first leg + time for second leg
total time = 2.75 hours + 3.22 hours
total time = 5.97 hours

Rounding to the nearest hundredth of an hour, we get:

total time = 5.97 hours

Therefore, the best choice is B.

Question 9

The price of a home theater system has been discounted 14%. The sale price is $269. Find the original price of the system.

Accepted Answer

The answer of The price of a home theater system...

Question 10

Solve $( x - 4 ) ^ { 2 } = 9$ by extracting square roots.

Accepted Answer

The answer of Solve \(( x - 4 ) ^...

Question 11

A rectangular pool is 40 feet wide and 65 feet long. It is surrounded on all four sides by a wooden deck of fixed width. The total area enclosed within the perimeter of the deck is 2794 square feet. What is the width of the deck?

Accepted Answer

The answer of A rectangular pool is 40 feet wide...

Question 12

The demand equation for a product is $p = 60 - 0.005 x,$ where $p$ is the price per unit and $x$ is the number of units sold. The total revenue $R$ for selling $x$ units is given by $R = x p = x ( 60 - 0.005 x ).$ How many units must be sold to produce a revenue of $180,000?

Accepted Answer

The answer of The demand equation for a product is...

Question 13

How many liters of a 27% acid solution should be mixed with 5 liters of a 19% acid solution to produce a 26% solution?

Accepted Answer

The answer of How many liters of a 27% acid...

Question 14

An investment adviser invested $\$ 120,000$ in two accounts. One investment earned 8% annual simple interest, and the other investment earned 10.5% annual simple interest. The amount of interest earned for 1 year was $\$ 10,850.$ How much was invested in each account?

Accepted Answer

Let x be the amount invested at 8%, then (120,000 - x) is invested at 10.5%. The equation is 0.08x + 0.105(120,000 - x) = 10,850. Solving gives x = 70,000 and 120,000 - x = 50,000.

Question 15

Solve $9 + 16 x ^ { 2 } + 24 x = 0$ by factoring.

Accepted Answer

The equation can be rewritten as $16x^2 + 24x + 9 = 0$, which factors to $(4x + 3)^2 = 0$, leading to $x = -\frac{3}{4}$.

Question 16

Solve the quadratic equation below by extracting square roots. Round to two decimal places. $3 x ^ { 2 } - 2 \left( x ^ { 2 } - 3 \right) = 15$

Accepted Answer

The answer of Solve the quadratic equation below by extracting...

Question 17

Solve: $20 x ^ { 2 } + 37 x + 15 = 0$

Accepted Answer

The answer of Solve: \(20 x ^ { 2 }...

Question 18

Assume that air resistance is negligible, which implies that the position equation $s = - 16 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ is a reasonable model. A rock is dropped from the top of a 180-foot cliff that overlooks the ocean. How long will it take for the rock to hit the water? Round to the nearest hundredth of a second.

Accepted Answer

Since the rock is dropped (not thrown), its initial velocity $v_0 = 0$. The position equation simplifies to $s = -16t^2 + s_0$, where $s_0 = 180$ feet (the height of the cliff). Setting $s = 0$ (when the rock hits the water), we get $0 = -16t^2 + 180$. Solving for $t$, we find $t \approx 3.35$ seconds.

Question 19

Use the discriminant to determine the number of real solutions of the quadratic equation below. $4 x ^ { 2 } + 9 x + 3 = 0$

Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $D = b^2 - 4ac$. For the given equation, $a = 4$, $b = 9$, and $c = 3$, so $D = 9^2 - 4(4)(3) = 81 - 48 = 33$. Since $D > 0$, the equation has two real solutions.

Question 20

Variable costs depend on the number of units produced. Fixed costs are the same regardless of how many units are produced. A company has fixed monthly costs of $11,000 and variable monthly costs of $7.00 per unit. The company has $75,000 available each month to cover costs. Find the greatest number of units the company can produce each month.

Accepted Answer

The greatest number of units the company can produce each month is 9142 units. This is because the company has $75,000 available each month to cover costs, and the fixed monthly costs are $11,000. This leaves $64,000 to cover variable costs. The variable monthly costs are $7.00 per unit, so the company can produce 9142 units each month (64,000 / 7 = 9142.857142857143).

Quiz 2: Equations and Inequalities

The price of a computer fell 10% this year. If the computer now costs $621, how much did it cost last year?

Solve the quadratic equation below by factoring. $x ^ { 2 } + x = 72$

How much water must be added to 3 liters of a 47% saline solution to dilute it to a 32% saline solution? Round answer to nearest tenth of a liter.

Solve $( x - 4 ) ^ { 2 } = 25$ by any convenient method.

Write $x ( x - 5 ) = - 2 x ^ { 2 } + 8$ in general form.

Solve the quadratic equation by any convenient method. $( 4 x - 5 ) ^ { 2 } - 25 = 0$

Two friends fly from from one city to another (a distance apart of 2930 miles) . It takes 2 hours and 45 minutes to fly the first 1350 miles. At this rate, how long is the entire flight? Round to the nearest hundredth of an hour.

The price of a home theater system has been discounted 14%. The sale price is $269. Find the original price of the system.

Solve $( x - 4 ) ^ { 2 } = 9$ by extracting square roots.

A rectangular pool is 40 feet wide and 65 feet long. It is surrounded on all four sides by a wooden deck of fixed width. The total area enclosed within the perimeter of the deck is 2794 square feet. What is the width of the deck?

The demand equation for a product is $p = 60 - 0.005 x,$ where $p$ is the price per unit and $x$ is the number of units sold. The total revenue $R$ for selling $x$ units is given by $R = x p = x ( 60 - 0.005 x ) .$ How many units must be sold to produce a revenue of $180,000?

How many liters of a 27% acid solution should be mixed with 5 liters of a 19% acid solution to produce a 26% solution?

An investment adviser invested $\$ 120,000$ in two accounts. One investment earned 8% annual simple interest, and the other investment earned 10.5% annual simple interest. The amount of interest earned for 1 year was $\$ 10,850.$ How much was invested in each account?

Solve $9 + 16 x ^ { 2 } + 24 x = 0$ by factoring.

Solve the quadratic equation below by extracting square roots. Round to two decimal places. $3 x ^ { 2 } - 2 \left( x ^ { 2 } - 3 \right) = 15$

Solve: $20 x ^ { 2 } + 37 x + 15 = 0$

Use the discriminant to determine the number of real solutions of the quadratic equation below. $4 x ^ { 2 } + 9 x + 3 = 0$

Quiz 2: Equations and Inequalities

The price of a computer fell 10% this year. If the computer now costs $621, how much did it cost last year?

Solve the quadratic equation below by factoring. x2+x=72x ^ { 2 } + x = 72x2+x=72

How much water must be added to 3 liters of a 47% saline solution to dilute it to a 32% saline solution? Round answer to nearest tenth of a liter.

Solve (x−4) 2=25( x - 4 ) ^ { 2 } = 25(x−4) 2=25 by any convenient method.

Write x(x−5) =−2x2+8x ( x - 5 ) = - 2 x ^ { 2 } + 8x(x−5) =−2x2+8 in general form.

Solve the quadratic equation by any convenient method. (4x−5) 2−25=0( 4 x - 5 ) ^ { 2 } - 25 = 0(4x−5) 2−25=0

Two friends fly from from one city to another (a distance apart of 2930 miles) . It takes 2 hours and 45 minutes to fly the first 1350 miles. At this rate, how long is the entire flight? Round to the nearest hundredth of an hour.

The price of a home theater system has been discounted 14%. The sale price is $269. Find the original price of the system.

Solve (x−4) 2=9( x - 4 ) ^ { 2 } = 9(x−4) 2=9 by extracting square roots.

A rectangular pool is 40 feet wide and 65 feet long. It is surrounded on all four sides by a wooden deck of fixed width. The total area enclosed within the perimeter of the deck is 2794 square feet. What is the width of the deck?

How many liters of a 27% acid solution should be mixed with 5 liters of a 19% acid solution to produce a 26% solution?

An investment adviser invested $120,000\$ 120,000$120,000 in two accounts. One investment earned 8% annual simple interest, and the other investment earned 10.5% annual simple interest. The amount of interest earned for 1 year was $10,850.\$ 10,850.$10,850. How much was invested in each account?

Solve 9+16x2+24x=09 + 16 x ^ { 2 } + 24 x = 09+16x2+24x=0 by factoring.

Solve the quadratic equation below by extracting square roots. Round to two decimal places. 3x2−2(x2−3) =153 x ^ { 2 } - 2 \left( x ^ { 2 } - 3 \right) = 153x2−2(x2−3) =15

Solve: 20x2+37x+15=020 x ^ { 2 } + 37 x + 15 = 020x2+37x+15=0

Use the discriminant to determine the number of real solutions of the quadratic equation below. 4x2+9x+3=04 x ^ { 2 } + 9 x + 3 = 04x2+9x+3=0

Solve the quadratic equation below by factoring. $x ^ { 2 } + x = 72$

Solve $( x - 4 ) ^ { 2 } = 25$ by any convenient method.

Write $x ( x - 5 ) = - 2 x ^ { 2 } + 8$ in general form.

Solve the quadratic equation by any convenient method. $( 4 x - 5 ) ^ { 2 } - 25 = 0$

Solve $( x - 4 ) ^ { 2 } = 9$ by extracting square roots.

An investment adviser invested $\$ 120,000$ in two accounts. One investment earned 8% annual simple interest, and the other investment earned 10.5% annual simple interest. The amount of interest earned for 1 year was $\$ 10,850.$ How much was invested in each account?

Solve $9 + 16 x ^ { 2 } + 24 x = 0$ by factoring.

Solve the quadratic equation below by extracting square roots. Round to two decimal places. $3 x ^ { 2 } - 2 \left( x ^ { 2 } - 3 \right) = 15$

Solve: $20 x ^ { 2 } + 37 x + 15 = 0$

Use the discriminant to determine the number of real solutions of the quadratic equation below. $4 x ^ { 2 } + 9 x + 3 = 0$