Question 1

Solve  by factoring.

Accepted Answer

The answer of Solve  by factoring.
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Question 2

Solve the quadratic equation below by factoring.

Accepted Answer

The quadratic equation given can be rewritten as 
$$x^2 + 4x - 45 = 0$$
We can then factorize this equation as
$$(x + 9)(x - 5) = 0$$
Using the zero product property, we can see that this equation is true when either $x + 9 = 0$ or $x - 5 = 0$. Therefore, the solutions are $x = -9$ or $x = 5$.

Question 3

Solve the quadratic equation by any convenient method.

Accepted Answer

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

Question 4

Assume that air resistance is negligible, which implies that the position equation  is a reasonable model.A rock is dropped from the top of a 140-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

The position equation for this scenario is given as:

h(t) = -16t^2 + 140

where h(t) represents the height (in feet) of the rock at time t (in seconds) after it is dropped.

Since we want to know when the rock hits the water, we need to find the value of t when h(t) = 0 (since the height of the water is 0). So we set up the equation:

-16t^2 + 140 = 0

Solving for t, we get:

t = √(140/16) = √8.75 ≈ 2.96 seconds

Therefore, the best choice is B) 2.96 seconds.

Question 5

Write  in general form.

Accepted Answer

The hexadecimal number 11ea89fe_4afd_d98c_9fff_a3b75774f90d represents a unique identifier or code, which can have various meanings depending on its intended use. However, since the question asks for the general form, we can ignore its specific meaning and focus on its structure. We can see that the first 8 digits (11ea89fe) represent the first block, followed by 4 digits (4afd) for the second block, then 4 more digits (d98c) for the third block, and so on. Therefore, the general form of this identifier is: 
XXXXXXXX_XXXX_XXXX_XXXX_XXXXXXXXXXXX_TB2036_11 
where X represents any hexadecimal digit. Option D is the only choice that fits this pattern, as the third block is d98c. The other choices have different digits in the third block, so they are not a match.

Question 6

Two friends fly from from one city to another (a distance apart of 2417 miles).It takes 2 hours and 25 minutes to fly the first 860 miles.At this rate, how long is the entire flight? Round to the nearest hundredth of an hour.

Accepted Answer

First, let's find the rate at which they are traveling by dividing the distance traveled by the time it took:
$$rate=\frac{860}{2.41667}=355.83	ext{ mph}$$

Next, we can use this rate to find how long the entire flight will take:
$$2417	ext{ miles} \div 355.83	ext{ mph}=6.79	ext{ hours}$$

Therefore, the answer is B, the flight will take 6.79 hours.

Question 7

How many liters of a 25% acid solution should be mixed with 3 liters of a 15% acid solution to produce a 23% solution?

Accepted Answer

The answer of How many liters of a 25% acid...

Question 8

An investment adviser invested  in two accounts. One investment earned 6% annual simple interest, and the other investment earned 7.5% annual simple interest. The amount of interest earned for 1 year was  How much was invested in each account?

Accepted Answer

Let x be the amount invested at 6% and y be the amount invested at 7.5%. Then we have:
0.06x + 0.075y = 11000 (interest earned)
x + y = 90000 (total amount invested)
Solving these equations gives x = 50000 and y = 40000. Therefore, the answer is C.

Question 9

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 2 feet and the shadow of the tree is 25 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 length is the same as the ratio of the height of the lamppost to its shadow length. So, $ \frac{\text{Height of tree}}{25} = \frac{5}{2} $. Solving for the height of the tree gives $ \text{Height of tree} = \frac{5}{2} \times 25 = 62.5 $ feet.

Question 10

The demand equation for a product is  where  is the price per unit and  is the number of units sold.The total revenue  for selling  units is given by  How many units must be sold to produce a revenue of $45,000?

Accepted Answer

We are given the demand equation:

Q = 11ea89fe_4b01_5b2e_9fff_596be13c5577_TB2036_11

We are also given the total revenue equation:

R = PQ = 11ea89fe_4b01_a953_9fff_81f840fa7c66_TB2036_11

We need to find the value of Q that will give us R = $45,000. We can set the total revenue equation equal to $45,000 and solve for Q:

$45,000 = 11ea89fe_4b01_5b2e_9fff_596be13c5577_TB2036_11 * Q

Q = $45,000 / 11ea89fe_4b01_5b2e_9fff_596be13c5577_TB2036_11

Q = 3000 units

Therefore, the answer is B) 3000 units.

Question 11

The price of a computer fell 15% this year.If the computer now costs $680, how much did it cost last year?

Accepted Answer

Let X be the original price of the computer last year.
After the 15% reduction, the new price is:
X - 0.15X = 0.85X
Since we know that the new price is $680, we can set up an equation:
0.85X = 680
X = 800
Therefore, the original price of the computer last year was $800. 
The answer is (C) $800.

Question 12

Solve:

Accepted Answer

The answer of Solve: 
...

Question 13

Solve the quadratic equation below by extracting square roots.Round to two decimal places.

Accepted Answer

The quadratic equation is of the form $ax^2+bx+c=0$. Rearranging $6x^2-9x+6=0$, we get $x^2-\frac{3}{2}x+1=0$. We can now extract the square roots by using the formula:
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
Plugging in the values, we get:
$$x=\frac{\frac{3}{2}\pm\sqrt{\left(\frac{3}{2}ight)^2-4(1)(1)}}{2(1)}=\frac{\frac{3}{2}\pm\frac{\sqrt{3}}{2}}{2}$$
Simplifying, we get:
$$x=\frac{3\pm\sqrt{3}}{4}$$
Rounding to two decimal places, we get:
$$x\approx 1.32 	ext{ or } 0.18$$
Option D is the only choice that matches one of these values, therefore it is the correct answer.

Question 14

A rectangular pool is 40 feet wide and 45 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 2354 square feet.What is the width of the deck?

Accepted Answer

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

Question 15

Solve  by any convenient method.

Accepted Answer

The answer of Solve  by any convenient method.
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Question 16

Solve  by extracting square roots.

Accepted Answer

The answer of Solve  by extracting square roots.
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Question 17

How much water must be added to 8 liters of a 51% saline solution to dilute it to a 36% saline solution? Round answer to nearest tenth of a liter.

Accepted Answer

The amount of salt in the original solution is 51% of 8 liters, which is 0.51 * 8 = 4.08 liters. To find the total volume of the new solution that results in a 36% saline solution, we use the equation 4.08 = 0.36 * (8 + x), where x is the amount of water added. Solving for x gives x = (4.08 / 0.36) - 8 ≈ 3.3 liters.

Question 18

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 $17,000 and variable monthly costs of $6.00 per unit.The company has $95,000 available each month to cover costs.Find the greatest number of units the company can produce each month.

Accepted Answer

The answer of Variable costs depend on the number of...

Question 19

Use the discriminant to determine the number of real solutions of the quadratic equation below.

Accepted Answer

The answer of Use the discriminant to determine the number...

Question 20

The price of a home theater system has been discounted 18%.The sale price is $289.Find the original price of the system.

Accepted Answer

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

Quiz 1: Equations and Inequalities

Solve by factoring.

Solve the quadratic equation below by factoring.

Solve the quadratic equation by any convenient method.

Assume that air resistance is negligible, which implies that the position equation is a reasonable model.A rock is dropped from the top of a 140-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.

Write in general form.

Two friends fly from from one city to another (a distance apart of 2417 miles) .It takes 2 hours and 25 minutes to fly the first 860 miles.At this rate, how long is the entire flight? Round to the nearest hundredth of an hour.

How many liters of a 25% acid solution should be mixed with 3 liters of a 15% acid solution to produce a 23% solution?

An investment adviser invested in two accounts. One investment earned 6% annual simple interest, and the other investment earned 7.5% annual simple interest. The amount of interest earned for 1 year was How much was invested in each account?

The demand equation for a product is where is the price per unit and is the number of units sold.The total revenue for selling units is given by How many units must be sold to produce a revenue of $45,000?