Question 1

The hypotenuse of a right triangle is 13.0, and one leg is 2.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth). ​

Accepted Answer

Let x be the length of the shorter leg. Then the longer leg is x + 2. By the Pythagorean theorem, we have:x^2 + (x + 2)^2 = 13^2x^2 + x^2 + 4x + 4 = 1692x^2 + 4x - 165 = 0(x - 10.1)(x + 16.3) = 0x = 10.1Therefore, the dimensions of the figure are 10.1, 10.1 + 2 = 12.1, and 13.0.

Question 2

The first step in the problem-solving procedure is not choosing a variable, but rather translating the main idea into symbols. Carry out the first step for the following problem.
​
If you subtract fourteen from twice a number, the result is six. What is the number?

Accepted Answer

The answer of The first step in the problem-solving procedure...

Question 3

A house and a lot are appraised at $191,700. If the value of the house is five times the value of the lot, how much is the house worth?
​
$__________

Accepted Answer

The answer of A house and a lot are appraised...

Question 4

Two joggers set out at the same time from their homes 18 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 2 mph faster than the rate of other, find the rate of each.

Accepted Answer

The answer of Two joggers set out at the same...

Question 5

The annual rate, r, compounded annually, it takes for  dollar to grow to A dollars in 4 years is given by the formula  . Find the rate necessary for a dollar to double in 4 years.
​
Give your answer to one decimal place, if required.
​
__________%

Accepted Answer

The answer of The annual rate, r, compounded annually, it...

Question 6

A professional gambler reported that at the end of the first race at the track he had doubled his money. He bet $31 on the second race and tripled the money he came with. He bet $56 on the third race and quadrupled his original bankroll. He bet $64 on the fourth race and lost it, but still had $60 left. With how much money did he start?
​
$__________

Accepted Answer

The answer of A professional gambler reported that at the...

Question 7

Two persons are to run a race, but one can run 11 meters per second, whereas the other can run 5 meters per second. If the slower runner has a 69-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?
​
Give your answer to one decimal place, if required.
​
__________ sec

Accepted Answer

The answer of Two persons are to run a race,...

Question 8

The hypotenuse of a right triangle is 13.0, and one leg is 2.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth).

Accepted Answer

The answer of The hypotenuse of a right triangle is...

Question 9

Two joggers set out at the same time from their homes 24 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 6 mph faster than the rate of other, find the rate of each. ​

Accepted Answer

Let's call the slower jogger's speed x. That means the faster jogger's speed is x + 6. We can use the formula distance = rate * time to create two equations:

First, we know that the two joggers are starting 24 miles apart and heading towards each other, so we can add their distances together to get 24 miles:

distance of jogger 1 + distance of jogger 2 = 24
xt + (x + 6)t = 24

We also know that they're going to meet somewhere in between their starting points in an hour and a half, or 1.5 hours:

t = 1.5

Now we can substitute that back into our first equation:

x(1.5) + (x + 6)(1.5) = 24

Simplifying that equation, we get:

1.5x + 1.5x + 9 = 24
3x = 15
x = 5

So the slower jogger is going 5 mph, and the faster jogger is going 5 + 6 = 11 mph. Therefore, the answer is C.

Question 10

The first step in the problem-solving procedure is not choosing a variable, but rather translating the main idea into symbols. Carry out the first step for the following problem.
​
A diagonal brace is to be placed in the wall of a room. The height of the wall is 8 ft, and the wall is 13 ft long. What is the exact length of the brace? __________ ft
​
What is the length of the brace to the nearest foot? __________ ft

Accepted Answer

The answer of The first step in the problem-solving procedure...

Question 11

The sum of three consecutive integers is 99. What are the integers?

Accepted Answer

The answer of The sum of three consecutive integers is...

Question 12

Solve the inequality. ​  ​

Accepted Answer

The answer of Solve the inequality. ​  ​
...

Question 13

Solve the inequality. ​  ​

Accepted Answer

The answer of Solve the inequality. ​  ​
...

Question 14

Two persons are to run a race, but one can run 11 meters per second, whereas the other can run 5 meters per second. If the slower runner has a 72-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time? ​

Accepted Answer

Let t be the time taken by the faster runner to catch up with the slower runner.
Distance covered by slower runner in t seconds = 5t + 72 meters
Distance covered by faster runner in t seconds = 11t meters
Since they meet, both runners cover the same distance.
5t + 72 = 11t
6t = 72
t = 12 seconds.

Question 15

Graph the solution set of the inequality. ​  ​

Accepted Answer

The answer of Graph the solution set of the inequality....

Question 16

Rewrite the word statement using symbols: The square of negative four is equal to the four squared. Classify the equation as "true ", "false ", or open, and if it is open tell whether it is a conditional, identity, or contradiction. Find the requested number(s). Rewrite the word statement using symbols: Four added to a number is equal to the sum of the number and two. ​Classify the equation as "true ", "false ", or open, and if it is open tell whether it is a conditional, identity, or contradiction.

Accepted Answer

The answer of Rewrite the word statement using symbols: The...

Question 17

The annual rate, r, compounded annually, it takes for 1 dollar to grow to D dollars in 3 years is given by the formula  . Find the rate necessary for a dollar to double in 3 years. ​

Accepted Answer

The answer of The annual rate, r, compounded annually, it...

Question 18

If you add two to twice a number, the result is twelve. What is the number?

Accepted Answer

The answer of If you add two to twice a...

Question 19

Rewrite the word statement using symbols. ​
The square of negative five is equal to the opposite of five squared.
​

Accepted Answer

The answer of Rewrite the word statement using symbols. ​
The...

Question 20

Graph the solution set of the inequality. ​  ​

Accepted Answer

The answer of Graph the solution set of the inequality....

Quiz 6: The Nature of Algebra

The hypotenuse of a right triangle is 13.0, and one leg is 2.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth) .

The first step in the problem-solving procedure is not choosing a variable, but rather translating the main idea into symbols. Carry out the first step for the following problem. If you subtract fourteen from twice a number, the result is six. What is the number?

A house and a lot are appraised at $191,700. If the value of the house is five times the value of the lot, how much is the house worth? $__________

Two joggers set out at the same time from their homes 18 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 2 mph faster than the rate of other, find the rate of each.

The annual rate, r, compounded annually, it takes for dollar to grow to A dollars in 4 years is given by the formula . Find the rate necessary for a dollar to double in 4 years. Give your answer to one decimal place, if required. __________%

The hypotenuse of a right triangle is 13.0, and one leg is 2.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth).

Two joggers set out at the same time from their homes 24 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 6 mph faster than the rate of other, find the rate of each.

The sum of three consecutive integers is 99. What are the integers?

Solve the inequality.

Solve the inequality.

Two persons are to run a race, but one can run 11 meters per second, whereas the other can run 5 meters per second. If the slower runner has a 72-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?

Graph the solution set of the inequality.

The annual rate, r, compounded annually, it takes for 1 dollar to grow to D dollars in 3 years is given by the formula . Find the rate necessary for a dollar to double in 3 years.

If you add two to twice a number, the result is twelve. What is the number?

Rewrite the word statement using symbols. The square of negative five is equal to the opposite of five squared.

Graph the solution set of the inequality.

Quiz 6: The Nature of Algebra

The hypotenuse of a right triangle is 13.0, and one leg is 2.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth) . ​

The first step in the problem-solving procedure is not choosing a variable, but rather translating the main idea into symbols. Carry out the first step for the following problem. ​ If you subtract fourteen from twice a number, the result is six. What is the number?

A house and a lot are appraised at $191,700. If the value of the house is five times the value of the lot, how much is the house worth? ​ $__________

Two joggers set out at the same time from their homes 18 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 2 mph faster than the rate of other, find the rate of each.

The annual rate, r, compounded annually, it takes for dollar to grow to A dollars in 4 years is given by the formula . Find the rate necessary for a dollar to double in 4 years. ​ Give your answer to one decimal place, if required. ​ __________%

The hypotenuse of a right triangle is 13.0, and one leg is 2.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth).

Two joggers set out at the same time from their homes 24 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 6 mph faster than the rate of other, find the rate of each. ​

The sum of three consecutive integers is 99. What are the integers?

Solve the inequality. ​ ​

Solve the inequality. ​ ​

Two persons are to run a race, but one can run 11 meters per second, whereas the other can run 5 meters per second. If the slower runner has a 72-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time? ​

Graph the solution set of the inequality. ​ ​

The annual rate, r, compounded annually, it takes for 1 dollar to grow to D dollars in 3 years is given by the formula . Find the rate necessary for a dollar to double in 3 years. ​

If you add two to twice a number, the result is twelve. What is the number?

Rewrite the word statement using symbols. ​ The square of negative five is equal to the opposite of five squared. ​

Graph the solution set of the inequality. ​ ​

The hypotenuse of a right triangle is 13.0, and one leg is 2.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth) .

The first step in the problem-solving procedure is not choosing a variable, but rather translating the main idea into symbols. Carry out the first step for the following problem. If you subtract fourteen from twice a number, the result is six. What is the number?

A house and a lot are appraised at $191,700. If the value of the house is five times the value of the lot, how much is the house worth? $__________

The annual rate, r, compounded annually, it takes for dollar to grow to A dollars in 4 years is given by the formula . Find the rate necessary for a dollar to double in 4 years. Give your answer to one decimal place, if required. __________%

Two joggers set out at the same time from their homes 24 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 6 mph faster than the rate of other, find the rate of each.

Solve the inequality.

Solve the inequality.

Two persons are to run a race, but one can run 11 meters per second, whereas the other can run 5 meters per second. If the slower runner has a 72-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?

Graph the solution set of the inequality.

The annual rate, r, compounded annually, it takes for 1 dollar to grow to D dollars in 3 years is given by the formula . Find the rate necessary for a dollar to double in 3 years.

Rewrite the word statement using symbols. The square of negative five is equal to the opposite of five squared.

Graph the solution set of the inequality.