High School Math Exam Quiz

Explanation
The given expression is a polynomial of degree 3. To factor it, we can look for common factors among the terms. In this case, the common factor is x. Factoring out x from each term gives us x(x^2 + 2x + 2). Therefore, the factored form of x^3 + 2x^2 + 2x is x(x^2 + 2x + 2).

Explanation
The slope of a line is determined by the coefficient of x in its equation when it is in the form y = mx + b. To find the slope of a line parallel to 3x - 2y = 9, we need to rearrange the equation to isolate y. By subtracting 3x from both sides and dividing by -2, we get y = -1.5x + 4.5. The coefficient of x is -1.5, which is the slope of the line. Therefore, any line parallel to 3x - 2y = 9 will also have a slope of -1.5.

Explanation
The mean of a set of numbers is calculated by adding up all the numbers in the set and then dividing the sum by the total number of values. In this case, the sum of 3, 5, 1, 2, 9, and 4 is 24. Dividing 24 by 6 (the total number of values) gives us a mean of 4. Therefore, the correct answer is 4.

Explanation
The midpoint of a line connecting two points can be found by taking the average of the x-coordinates and the average of the y-coordinates of the two points. In this case, the x-coordinates are 0 and 6, so the average is (0+6)/2 = 3. The y-coordinates are 0 and 8, so the average is (0+8)/2 = 4. Therefore, the midpoint is (3, 4).

Explanation
The given function f(x) = 3x - 1 represents a linear equation where the input value x is multiplied by 3 and then subtracted by 1. To find f(a), we substitute the value of a into the equation. Therefore, f(a) = 3a - 1.

Explanation
The given equation is a quadratic equation in the form of (3x + 4)(2x + 3) = 0. In order for the equation to be true, either (3x + 4) must equal 0 or (2x + 3) must equal 0.

Setting (3x + 4) = 0, we can solve for x:
3x + 4 = 0
3x = -4
x = -4/3

Setting (2x + 3) = 0, we can solve for x:
2x + 3 = 0
2x = -3
x = -3/2

Therefore, the values of x that make the equation true are -4/3 and -3/2.

Explanation
When x = -2, substituting it into the equation y = (x - 1)^2 gives us y = (-2 - 1)^2, which simplifies to y = (-3)^2. Squaring a negative number gives a positive result, so (-3)^2 is equal to 9. Therefore, when x = -2, y is equal to 9.

Explanation
To find the value of x that makes the equation "5x - 3 = 22" true, we need to isolate the variable x. By adding 3 to both sides of the equation, we get 5x = 25. Then, dividing both sides by 5, we find that x = 5.

Explanation
When x = -1, the equation y = 2^x can be rewritten as y = 2^(-1). Any number raised to the power of -1 is equal to its reciprocal, so 2^(-1) is equal to 1/2. Therefore, y is equal to 2-Jan.

Explanation
The midpoint formula states that the coordinates of the midpoint of a line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (12 + x)/2 = 7, which gives x = 2. Similarly, the y-coordinate of the midpoint is (5 + y)/2 = 2, which gives y = -1. Therefore, the coordinates of point Q are (2, -1).

Explanation
When x = -2 and y = 2, we can substitute these values into the expression 3x^3 - y^5. This gives us 3(-2)^3 - (2)^5. Simplifying further, we have 3(-8) - 32. Evaluating this expression, we get -24 - 32 = -56. Therefore, the correct answer is -56.

Explanation
To find f(g(x)), we substitute g(x) into f(x). Since g(x) = 2x + 1, we can replace x in f(x) with 2x + 1. Therefore, f(g(x)) = 3(2x + 1) - 2 = 6x + 3 - 2 = 6x + 1.

Explanation
The equation y = (x - 1)^2 represents a parabola with its vertex at (1, 0). When x = 0, substituting it into the equation gives y = (0 - 1)^2 = 1. Therefore, the value of y when x = 0 is 1.

Explanation
If $2500 is invested at an 8% simple interest rate for 25 years, the account will accumulate interest over time. Simple interest is calculated by multiplying the principal amount ($2500) by the interest rate (8%) and the number of years (25). The formula for simple interest is I = P * R * T, where I is the interest, P is the principal amount, R is the interest rate, and T is the time in years. Therefore, the interest earned would be $5000. Adding the interest to the principal, the total amount in the account after 25 years would be $7500.

Explanation
To find the value of 222 - (x + y), we need to substitute the given values of x and y. Since x = -5 and y = -7, we can substitute these values into the equation. Therefore, 222 - (-5 + -7) simplifies to 222 - (-12), which is equal to 222 + 12. This gives us a final result of 234.