High School Math (Algebra) Pre-test Quiz

To evaluate the expression 10 - 2(3), we first simplify the multiplication within the parentheses: 2(3) equals 6. Then, we substitute this value back into the expression: 10 - 6 equals 4. Therefore, the correct answer is 4.

The given expression is 6 - 32. When we subtract 32 from 6, we get -26. However, the answer choices provided do not include -26. Therefore, none of the answer choices match the result of the expression. Thus, the correct answer is not available.

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To solve the equation 3x - 3 = 9, we need to isolate the variable x. Adding 3 to both sides of the equation, we get 3x = 12. Then, dividing both sides by 3, we find x = 4. Therefore, the correct answer is x = 4.

To simplify the expression (2x^3)^2, we need to apply the exponent to both the coefficient and the variable. When we raise a power to another power, we multiply the exponents. In this case, we have (2x^3)^2, so the exponent 2 is applied to both 2 and x^3. Therefore, we have 2^2 * (x^3)^2 = 4x^6.

The given expression is sqrt(200). We can simplify this by finding the largest perfect square that divides 200. Since 100 is the largest perfect square that divides 200, we can rewrite sqrt(200) as sqrt(100*2). Taking the square root of 100 gives us 10, so the expression simplifies to 10*sqrt(2). Therefore, the correct answer is 10*sqrt(2).

The y-intercept of an equation represents the point where the line intersects the y-axis. To find the y-intercept, we need to set x=0 and solve for y. In this equation, if we substitute x=0, we get y+2(0)=6, which simplifies to y=6. Therefore, the y-intercept of the equation is 6.

The slope of an equation represents the rate at which the y-values change with respect to the x-values. In the given equation, y = -2x + 3, the coefficient of x is -2. This means that for every unit increase in x, the y-value decreases by 2 units. Therefore, the slope of the equation is -2.

To solve the equation 2k + 3 + 5k = 10, you should perform the first step by simplifying and combining like terms:

2k + 5k = 7k

Now, the equation becomes:

7k + 3 = 10

This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a  

In this case, a = 1, b = -1, and c = -2. Substituting these values into the quadratic formula, we get:

x = (1 ± √((-1)^2 - 4 * 1 * -2)) / (2 * 1) x = (1 ± √(1 + 8)) / 2 x = (1 ± √9) / 2 x = (1 ± 3) / 2  

This gives us two possible solutions:

x = (1 + 3) / 2 = 4 / 2 = 2 x = (1 - 3) / 2 = -2 / 2 = -1

Therefore, the solutions to the equation x^2 - x - 2 = 0 are x = 2 and x = -1.Sources and related content