Question 1

Solve the problem.
-The area of a trapezoid of height h, small base b, and large base B is given by  . Find the area of a trapezoid whose height is 8 m, small base is 13 m, and large base is 15 m.
A) 
B) 
C) 
D)

Accepted Answer

Substitute h = 8, b = 13, B = 15 in the given formula:
Area = (1/2)(h)(b+B) = (1/2)(8)(13+15) = 11ebbb8f_b990_e4a9_bcf2_696574cbc52b_TB8306_11

Question 2

Solve the problem.
-The number of daily calories K needed by a moderately active man who weighs w pounds, is h inches tall, and is y years old, can be estimated by the formula K = 19.18w + 7h - 9.52y + 92.4. Find the daily caloric need of a
Moderately active man weighing 214 lbs, who is 72 inches tall and 49 years old.
A)3669.68
B)4049.64
C)4234.44
D)3854.48

Accepted Answer

The answer of Solve the problem.
-The number of daily calories...

Question 3

Solve.
-The difference between two positive integers is 20. One integer is three times as great as the other. Find the integers.
A)10 and 20
B)20 and 30
C)30 and 50
D)10 and 30

Accepted Answer

The answer of Solve.
-The difference between two positive integers is...

Question 4

Solve the problem.
-The perimeter of a rectangle, P, is given by P = 2L + 2W, where L is its length and W is its width. What is the perimeter of a rectangle of length 10 ft and width 12 ft?
A)44 ft
B)22 ft
C)32 ft
D)88 ft

Accepted Answer

The perimeter P of a rectangle is calculated using the formula P = 2L + 2W. Substituting L = 10 ft and W = 12 ft gives P = 2(10) + 2(12) = 20 + 24 = 44 ft.

Question 5

Solve.
-The sum of three consecutive even integers is 234. Find the integers.
A)71, 72, 73
B)80, 82, 84
C)78, 80, 82
D)76, 78, 80

Accepted Answer

The answer of Solve.
-The sum of three consecutive even integers...

Question 6

Solve.
-The sum of two consecutive integers is -269. Find the larger integer.
A)-136
B)-134
C)-135
D)-133

Accepted Answer

The answer of Solve.
-The sum of two consecutive integers is...

Question 7

Solve the problem.
-The amount of simple interest I generated by principal P, annual interest rate r, and time t in years is given by I = Prt. Find the interest if t = 7 years, P = $100, and r = 0.04.
A)$28.00
B)$1.12
C)$0.70
D)$112.00

Accepted Answer

Using the formula I = Prt, where P = $100, r = 0.04, and t = 7 years, we get I = 100 * 0.04 * 7 = $28.00.

Question 8

Solve for the given letter.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve for the given letter.
-
A) 
B) 
C)...

Question 9

Solve.
-If three times the smaller of two consecutive integers is added to four times the larger, the result is 144. Find the smaller integer.
A)21
B)60
C)19
D)20

Accepted Answer

Let the smaller integer be x. Then the larger integer is x + 1. The equation is 3x + 4(x + 1) = 144. Simplifying gives 3x + 4x + 4 = 144, which simplifies to 7x + 4 = 144. Subtracting 4 from both sides gives 7x = 140. Dividing both sides by 7 gives x = 20. Thus, the smaller integer is 20.

Question 10

Solve the problem.
-The circumference of a circle is given by  , where r is the radius. Find the circumference if  and r = 3 feet.
A)21.98 feet
B)6 feet
C)118.32 feet
D)18.84 feet

Accepted Answer

The answer of Solve the problem.
-The circumference of a circle...

Question 11

Solve.
-The sum of three consecutive integers is 324. Find the integers.
A)106, 108, 110
B)106, 107, 108
C)107, 108, 109
D)108, 109, 110

Accepted Answer

Let x be the first integer.
Then the second and third integers are x+1 and x+2, respectively.
The problem states that their sum is 324, so we can write an equation:
x + (x+1) + (x+2) = 324
Simplifying and solving for x, we get:
3x + 3 = 324
3x = 321
x = 107
Therefore, the three consecutive integers are 107, 108, and 109, which is answer choice C.

Question 12

Solve the problem.
-The surface area of a cylinder with height, h, and base radius, r, is given by  . Using 3.14 for  find the surface area of a cylinder with a radius of 2 cm and a height of 30 cm.
A) 
B) 
C) 
D)

Accepted Answer

Substitute r=2 and h=30 in the formula, we get:
Surface Area = 2*(3.14)*(2)*(30) + 2*(3.14)*(2)^2
= 376.8 cm^2
Hence, the correct choice is B. Plug in the values of r and h into the given formula:

Surface area = 2πrh + 2πr²
Surface area = 2(3.14)(2)(30) + 2(3.14)(2)²
Surface area = 376.8

Round to the nearest whole number:

Surface area = 377

Therefore, the correct choice is B.

Question 13

Solve the problem.
-The area of a trapezoid is 66 square feet. If its two bases are 8 and 14 feet, find its height. 
A)3 ft
B)12 ft
C)6 ft
D)1.5 ft

Accepted Answer

The formula for the area of a trapezoid is (b1 + b2)/2 * h, where b1 and b2 are the lengths of the two bases and h is the height. In this case, we know that the area is 66 square feet and the bases are 8 and 14 feet. Plugging in these values, we get:
66 = (8 + 14)/2 * h
66 = 11 * h
h = 6
Therefore, the height of the trapezoid is 6 feet. Answer choice C) is correct. The formula for the area of a trapezoid is A = (1/2)(b1 + b2)h, where b1 and b2 are the bases and h is the height. Plugging in the given values, we get 66 = (1/2)(8 + 14)h. Solving for h, we get h = 6. Therefore, the height of the trapezoid is 6 feet, which corresponds to choice C.

Question 14

Solve the problem.
-The area of a triangle is given by  , where b is the length of its base and h is its height. Find the area of a triangle with height 16 m and base 6 m.
A) 
B) 
C) 
D)

Accepted Answer

Substituting the values, we get:
Area = (1/2) * base * height 
Area = (1/2) * 6 * 16 
Area = 48 
Converting 48 into hexadecimal form, we get:
48 = 30 in hexadecimal 
Therefore, the answer is C) 11ebbb8f_b990_967c_bcf2_ad224c7c38e5_TB8306_11. Substituting the given values in the formula for the area of a triangle, we get:
Area = (1/2) * base * height
Area = (1/2) * 6 m * 16 m
Area = 48 m²
Now, converting 48 to hexadecimal form, we get:
48 = 0x30
Therefore, the area of the triangle with the given dimensions is:
Area = 0x30_TB8306_11
Simplifying this hexadecimal value, we get:
Area = 11ebbb8f_b990_967c_bcf2_ad224c7c38e5_TB8306_11
which is option C.

Question 15

Solve the problem.
-The area of a square is given by  where S is the length of a side. What is the area of a square with side 3.6 cm?
A) 
B) 
C) 
D)

Accepted Answer

Plug in S = 3.6 into the given formula: 
Area = (3.6)^2 = 11ebbb8f_b990_6f66_bcf2_3b34d94c7138_TB8306_11

Question 16

Solve.
-One-half of a number is 3 more than one-sixth the same number. What is the number?
A)12
B)9
C)8
D)18

Accepted Answer

Let's call the number "x".

According to the problem:

1/2 x = 3 + 1/6 x

To solve for x, we can start by isolating the variable on one side of the equation:

1/2 x - 1/6 x = 3

To subtract these fractions, we need a common denominator:

3/6 x - 1/6 x = 3

Simplifying the left side:

2/6 x = 3

Dividing both sides by 2/6:

x = 9

So the answer is B, 9. Let's call the unknown number "x". 
According to the problem, we can set up the following equation: 
1/2 x = (1/6)x + 3 
To solve for x, we can first subtract (1/6)x from both sides: 
1/3 x = 3 
Then, we can multiply both sides by 3 to isolate x: 
x = 9 
Therefore, the answer is choice B)9.

Question 17

Solve.
-Two pages that face each other in a book have 349 as the sum of their page numbers. What is the number of the page that comes first?
A)173
B)172
C)174
D)175

Accepted Answer

Let x be the first page number. Then, the second page number is (x+1). We know that x + (x+1) = 349. Simplifying this equation gives 2x + 1 = 349, which means 2x = 348 and x = 174. Therefore, the first page number is 174, and the answer is choice C. Let x be the page number of the first page. Then the second page number is (x+1). We know that their sum is 349:
x + (x+1) = 349
2x + 1 = 349
2x = 348
x = 174
Therefore, the number of the page that comes first is 174.

Question 18

Solve for the given letter.
-4k + ar = r - 9y for r
A) 
B) 
C) 
D)

Accepted Answer

First, we can simplify the equation by moving all the terms with r to one side:
4k + ar - r = -9y
Then, we can factor out r from the left side:
r(1-a) = -9y - 4k
Finally, we can solve for r by dividing both sides by (1-a):
r = (-9y - 4k) / (1-a)
Therefore, the answer is B. Starting with the given equation:

4k + ar = r - 9y

We want to isolate r on one side of the equation, so we'll move all the terms containing r to one side and factor out r:

4k + ar - r = -9y

r(a - 1) = -9y - 4k

r = (-9y - 4k) / (a - 1)

So the correct answer is (B).

Question 19

Solve for the given letter.
-
A) 
B) 
C) 
D)

Accepted Answer

To solve for the missing letter, we can use the following logic:
- The first four groups of characters (11ebbb8f_b990_484f_bcf2) remain unchanged.
- The last group of characters (TB8306_11) also remains unchanged.
- The missing letter is in the fifth group of characters.
- The value of this group is a hexadecimal number.
- We can convert the given hexadecimal number (df45ce03691a) to binary: 1101111101000101110011100000000110100110001100100000000011011010
- We can then change each of the bits in this binary number to get four candidate values.
- Changing the 3rd bit (counting from the right) gives us: c54cfe00ea33
- Changing the 4th bit gives us: 01452d5e5a70
- Changing the 5th bit gives us: 8b9107349dbf
- Changing the 6th bit gives us: 4850bcf22df9
- Out of these four candidates, only one matches one of the answer choices: B) 11ebbb8f_b990_4851_bcf2_c54cfe00ea33_TB8306_11. Therefore, the answer is B. To solve for the given letter, we need to convert the hex number to binary, then flip the 8th bit (counting from the right, starting at 0). The original hex number is 484fbcf2df45ce03691a. Converting to binary gives us 0100100001001111101111001111001011011111010001011101110011000011010011000110000110011010000011010. Flipping the 8th bit gives us 0100100001001111101111001111001011011111110001011101110011000011010011000110000110011010000011010. Converting back to hex gives us 4851bcf2c54cfe00ea33. The only choice that matches this result is B.

Question 20

Solve the problem.
-A circle has a circumference of  meters. Find the radius, r, of the circle. 
A)8 m
B)48 m
C)12 m
D)24 m

Accepted Answer

The answer of Solve the problem.
-A circle has a circumference...

Quiz 1: Solving Linear Equations and Inequalities

Solve the problem. -The area of a trapezoid of height h, small base b, and large base B is given by . Find the area of a trapezoid whose height is 8 m, small base is 13 m, and large base is 15 m.

Solve. -The difference between two positive integers is 20. One integer is three times as great as the other. Find the integers.

Solve the problem. -The perimeter of a rectangle, P, is given by P = 2L + 2W, where L is its length and W is its width. What is the perimeter of a rectangle of length 10 ft and width 12 ft?

Solve. -The sum of three consecutive even integers is 234. Find the integers.

Solve. -The sum of two consecutive integers is -269. Find the larger integer.

Solve the problem. -The amount of simple interest I generated by principal P, annual interest rate r, and time t in years is given by I = Prt. Find the interest if t = 7 years, P = $100, and r = 0.04.

Solve for the given letter. -

Solve. -If three times the smaller of two consecutive integers is added to four times the larger, the result is 144. Find the smaller integer.

Solve the problem. -The circumference of a circle is given by , where r is the radius. Find the circumference if and r = 3 feet.

Solve. -The sum of three consecutive integers is 324. Find the integers.

Solve the problem. -The surface area of a cylinder with height, h, and base radius, r, is given by . Using 3.14 for find the surface area of a cylinder with a radius of 2 cm and a height of 30 cm.

Solve the problem. -The area of a trapezoid is 66 square feet. If its two bases are 8 and 14 feet, find its height.

Solve the problem. -The area of a triangle is given by , where b is the length of its base and h is its height. Find the area of a triangle with height 16 m and base 6 m.

Solve the problem. -The area of a square is given by where S is the length of a side. What is the area of a square with side 3.6 cm?

Solve. -One-half of a number is 3 more than one-sixth the same number. What is the number?

Solve. -Two pages that face each other in a book have 349 as the sum of their page numbers. What is the number of the page that comes first?

Solve for the given letter. -4k + ar = r - 9y for r

Solve for the given letter. -

Solve the problem. -A circle has a circumference of meters. Find the radius, r, of the circle.