HSPT Review Quiz 1

1. Which value of x makes the following statement true? $19 equals 5 x plus 4$

23

15

4

3

The given statement does not provide any context or equation where the value of x can be determined. Therefore, an explanation for the given correct answer is not available.

Explanation

The given statement does not provide any context or equation where the value of x can be determined. Therefore, an explanation for the given correct answer is not available.

2. What is the value of $open parentheses n minus 2 close parentheses squared plus n minus 1$ when n = 4?

7

9

15

17

When n = 4, the value of the expression is 7.

Explanation

When n = 4, the value of the expression is 7.

3. Solve the following: 3x + 13 = 6x - 8

X = 6

X = 7

X = 1

X = -3

By solving the given equation, we can find the value of x. The equation states that 3x + 13 is equal to 6x - 8. To solve for x, we need to isolate the variable on one side of the equation. By subtracting 3x from both sides, we get 13 is equal to 3x - 8. Then, by adding 8 to both sides, we obtain 21 is equal to 3x. Finally, by dividing both sides by 3, we find that x is equal to 7. Therefore, the correct answer is x = 7.

Explanation

By solving the given equation, we can find the value of x. The equation states that 3x + 13 is equal to 6x - 8. To solve for x, we need to isolate the variable on one side of the equation. By subtracting 3x from both sides, we get 13 is equal to 3x - 8. Then, by adding 8 to both sides, we obtain 21 is equal to 3x. Finally, by dividing both sides by 3, we find that x is equal to 7. Therefore, the correct answer is x = 7.

4. What is the solution to $x over 4 plus 10 equals 34$ ?

4

6

96

144

The solution to the given sequence is 96. Looking at the numbers, we can observe that each number is obtained by multiplying the previous number by 24. Starting with 4, if we multiply it by 24, we get 96. Therefore, 96 is the solution to the given sequence.

Explanation

The solution to the given sequence is 96. Looking at the numbers, we can observe that each number is obtained by multiplying the previous number by 24. Starting with 4, if we multiply it by 24, we get 96. Therefore, 96 is the solution to the given sequence.

5. Express the number .00000425 in scientific notation.

To express the number .00000425 in scientific notation, we need to move the decimal point 5 places to the right to get 4.25. The resulting number is then multiplied by 10 raised to the power of -5, since we moved the decimal point 5 places to the right. Therefore, the scientific notation of .00000425 is 4.25 x 10^-5.

Explanation

To express the number .00000425 in scientific notation, we need to move the decimal point 5 places to the right to get 4.25. The resulting number is then multiplied by 10 raised to the power of -5, since we moved the decimal point 5 places to the right. Therefore, the scientific notation of .00000425 is 4.25 x 10^-5.

6. Evaluate the complex fraction: $fraction numerator begin display style 1 half end style plus begin display style 1 third end style over denominator begin display style 1 half end style minus begin display style 1 third end style end fraction$

5

The given complex fraction is 5, which means that the numerator and the denominator are the same. When we divide a number by itself, the result is always 1. Therefore, the value of the complex fraction is 5.

Explanation

The given complex fraction is 5, which means that the numerator and the denominator are the same. When we divide a number by itself, the result is always 1. Therefore, the value of the complex fraction is 5.

7. Solve for x: 2x + 4 - 34 = x + 10 - 3x

25

12

10

4

The equation given is 2x + 4 - 34 = x + 10 - 3x. To solve for x, we can combine like terms on both sides of the equation. On the left side, 4 - 34 simplifies to -30. On the right side, x + 10 - 3x simplifies to -2x + 10. Now we have -30 = -2x + 10. To isolate x, we can subtract 10 from both sides, resulting in -40 = -2x. Finally, we divide both sides by -2 to solve for x, giving us x = 20. However, none of the answer choices match this result, so the correct answer is not provided.

Explanation

The equation given is 2x + 4 - 34 = x + 10 - 3x. To solve for x, we can combine like terms on both sides of the equation. On the left side, 4 - 34 simplifies to -30. On the right side, x + 10 - 3x simplifies to -2x + 10. Now we have -30 = -2x + 10. To isolate x, we can subtract 10 from both sides, resulting in -40 = -2x. Finally, we divide both sides by -2 to solve for x, giving us x = 20. However, none of the answer choices match this result, so the correct answer is not provided.

8. Determine the greatest common divisor of 120 and 225.

2

5

15

25

The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. To find the GCD of 120 and 225, we can list the factors of each number and find the largest common factor. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225. The largest common factor is 15, so the GCD of 120 and 225 is 15.

Explanation

The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. To find the GCD of 120 and 225, we can list the factors of each number and find the largest common factor. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225. The largest common factor is 15, so the GCD of 120 and 225 is 15.