Algebra 2 Competency Test

Submit

2. 5x ^1/2+7=22

1/3

3

9

1/9

The equation given is 5x * 1/2 + 7 = 22. To solve this equation, we first simplify the left side by multiplying 5x with 1/2, which gives us 5x/2. Then, we add 7 to this result. So, the equation becomes 5x/2 + 7 = 22. To isolate the variable x, we subtract 7 from both sides, resulting in 5x/2 = 15. To solve for x, we multiply both sides by 2/5, canceling out the 2 and 5 on the left side and leaving us with x = 30/5, which simplifies to x = 6. However, none of the answer choices match this result, so the correct answer is not available.

Explanation

The equation given is 5x * 1/2 + 7 = 22. To solve this equation, we first simplify the left side by multiplying 5x with 1/2, which gives us 5x/2. Then, we add 7 to this result. So, the equation becomes 5x/2 + 7 = 22. To isolate the variable x, we subtract 7 from both sides, resulting in 5x/2 = 15. To solve for x, we multiply both sides by 2/5, canceling out the 2 and 5 on the left side and leaving us with x = 30/5, which simplifies to x = 6. However, none of the answer choices match this result, so the correct answer is not available.

3. 5x ^1/2+7=22

1/3

3

9

1/9

The equation given is 5x (1/2) + 7 = 22. To solve for x, we first simplify the equation by multiplying 5 and (1/2), which equals 2.5. Then we subtract 7 from both sides, resulting in 2.5x = 15. Finally, we divide both sides by 2.5, giving us x = 6. Therefore, the correct answer is 6.

Explanation

The equation given is 5x (1/2) + 7 = 22. To solve for x, we first simplify the equation by multiplying 5 and (1/2), which equals 2.5. Then we subtract 7 from both sides, resulting in 2.5x = 15. Finally, we divide both sides by 2.5, giving us x = 6. Therefore, the correct answer is 6.

4. Which statement is TRUE about the rational function $fraction numerator x over denominator x plus 2 end fraction$ ?

There is a vertical asymptote at x=2

There is point discontinuity at x=2

The domain is all real numbers from (-2) to 2.

There is a vertical asymtote at x=(-2)

The function is continuous.

The statement "There is a vertical asymptote at x=(-2)" is true because a vertical asymptote occurs when the denominator of a rational function equals zero. In this case, the denominator of the rational function has a factor of (x+2), which means that x=(-2) is the value that makes the denominator zero. Therefore, there is a vertical asymptote at x=(-2).

Explanation

The statement "There is a vertical asymptote at x=(-2)" is true because a vertical asymptote occurs when the denominator of a rational function equals zero. In this case, the denominator of the rational function has a factor of (x+2), which means that x=(-2) is the value that makes the denominator zero. Therefore, there is a vertical asymptote at x=(-2).

5. X^-2=9

3

1/3

-1/3

-3

not-available-via-ai

Explanation

not-available-via-ai

6. X^-2=9

3

1/3

-1/3

-3

The given equation is x-2=9. To solve for x, we need to isolate it on one side of the equation. Adding 2 to both sides gives us x=11. Therefore, the correct answer is 11. However, none of the options provided match 11. Therefore, the correct answer is not available.

Explanation

The given equation is x-2=9. To solve for x, we need to isolate it on one side of the equation. Adding 2 to both sides gives us x=11. Therefore, the correct answer is 11. However, none of the options provided match 11. Therefore, the correct answer is not available.

Submit

8. Solve $x squared minus 12 x equals 28$

14

(-2)

14 and (-2)

None of the above

The given question asks for the solution to the expression 14 / (-2). The correct answer is 14 and (-2) because dividing 14 by -2 gives a quotient of -7. Therefore, the solution to the expression is -7.

Explanation

The given question asks for the solution to the expression 14 / (-2). The correct answer is 14 and (-2) because dividing 14 by -2 gives a quotient of -7. Therefore, the solution to the expression is -7.

9. The imaginary number $i to the power of 54$ is equivalent to

(-1)

1

None of these

The imaginary number is equivalent to (-1) because it is the square root of -1. In mathematics, the imaginary unit is denoted by the symbol "i", and it is defined as the square root of -1. Therefore, (-1) is the correct answer as it represents the imaginary number.

Explanation

The imaginary number is equivalent to (-1) because it is the square root of -1. In mathematics, the imaginary unit is denoted by the symbol "i", and it is defined as the square root of -1. Therefore, (-1) is the correct answer as it represents the imaginary number.

10. Under which conditions is negative?

None of the above

not-available-via-ai

Explanation

not-available-via-ai

11. The expanded form of is

not-available-via-ai

Explanation

not-available-via-ai