Algebra Trivia: MCQ Quiz! Exam

1) The solution to the equation

27 to the power of 2 x end exponent equals 9 to the power of 2 x plus 4 end exponent

is x = ____________

The solution to the equation is x = 4 because when the equation is solved, the variable x is equal to 4.

Explanation

The solution to the equation is x = 4 because when the equation is solved, the variable x is equal to 4.

Submit

2) How many increasing intervals does the following graph have?

3

2

1

0

The graph has three increasing intervals because there are three distinct sections where the values are increasing. Each time the graph transitions from a lower value to a higher value, it represents a new increasing interval.

Explanation

The graph has three increasing intervals because there are three distinct sections where the values are increasing. Each time the graph transitions from a lower value to a higher value, it represents a new increasing interval.

3) What distance does the minute hand of a clock travel in 45 minutes if its length is 12 inches?

The minute hand of a clock travels in a circular motion around the clock face. The circumference of a circle is calculated by multiplying the diameter by π (pi). In this case, the length of the minute hand is given as 12 inches, which is equal to the diameter of the circle it travels. Therefore, the distance traveled by the minute hand in 45 minutes is equal to the circumference of the circle, which is 12π inches.

Explanation

The minute hand of a clock travels in a circular motion around the clock face. The circumference of a circle is calculated by multiplying the diameter by π (pi). In this case, the length of the minute hand is given as 12 inches, which is equal to the diameter of the circle it travels. Therefore, the distance traveled by the minute hand in 45 minutes is equal to the circumference of the circle, which is 12π inches.

4) Which of the following is the standard form equation of a circle with center (2, 3) that passes through the point (4, -2)?

The standard form equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius. In this case, the center of the circle is (2, 3), so the equation starts as (x - 2)^2 + (y - 3)^2 = r^2. Since the circle passes through the point (4, -2), we can substitute these values into the equation to find the radius. By substituting (4 - 2)^2 + (-2 - 3)^2 = r^2, we get (2)^2 + (-5)^2 = r^2. Simplifying this gives us 4 + 25 = r^2, or 29 = r^2. Therefore, the standard form equation of the circle is (x - 2)^2 + (y - 3)^2 = 29.

Explanation

The standard form equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius. In this case, the center of the circle is (2, 3), so the equation starts as (x - 2)^2 + (y - 3)^2 = r^2. Since the circle passes through the point (4, -2), we can substitute these values into the equation to find the radius. By substituting (4 - 2)^2 + (-2 - 3)^2 = r^2, we get (2)^2 + (-5)^2 = r^2. Simplifying this gives us 4 + 25 = r^2, or 29 = r^2. Therefore, the standard form equation of the circle is (x - 2)^2 + (y - 3)^2 = 29.

5) What is the exact value of $c o t space open parentheses fraction numerator minus 22 straight pi over denominator 3 end fraction close parentheses$ ?

not-available-via-ai

Explanation

not-available-via-ai

6) When $Syntax error from line 1 column 55 to line 1 column 61. Unexpected '<mrow>'.$ is expanded, what is the 4th term?

not-available-via-ai

Explanation

not-available-via-ai

7) Describe the boundedness for the graph below:

Not bounded

Bounded above

Bounded below

Bounded

The graph is not bounded because it extends indefinitely in at least one direction. It does not have a specific upper or lower limit, meaning it can continue to increase or decrease without bound. Therefore, it is not bounded above or below, and overall, it is not bounded.

Explanation

The graph is not bounded because it extends indefinitely in at least one direction. It does not have a specific upper or lower limit, meaning it can continue to increase or decrease without bound. Therefore, it is not bounded above or below, and overall, it is not bounded.

8) Use trigonometric identities to simplify the expression:

tan squared x space cos space x space plus space c o t space x space sin space x

not-available-via-ai

Explanation

not-available-via-ai