Benchmark 2 Multiple Choice

The given equation is already solved and the final solution is written as a decimal, which is 0.8. The equation is presented in different forms, such as 0.8, .8, x=.8, and x=0.8, but they all represent the same value, which is 0.8.

The x-intercept of an equation represents the point where the graph of the equation intersects the x-axis. To find the x-intercept, we set y equal to zero and solve for x. In this equation, y = 2x - 6, we can set y = 0 and solve for x. By substituting 0 for y, we get 0 = 2x - 6. Solving this equation, we find that x = 3. Therefore, the x-intercept is (3, 0).

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The equation y = -7 represents a horizontal line with a y-coordinate of -7. Since it is a horizontal line, it does not intersect the x-axis and therefore does not have an x-intercept.

The equation w = 0.75(L) represents the relationship between the length of the rope (L) in feet and weight (w) in ounces. This equation implies that the weight of the rope is 0.75 times the length of the rope.

Sue earns $2 for each CD and $2.50 for each DVD sold. Let's assume she sold x DVDs. The total amount she earned can be calculated as 2(305) + 2.50(x) = 950. Simplifying this equation gives us 610 + 2.50x = 950. By subtracting 610 from both sides, we get 2.50x = 340. Dividing both sides by 2.50 gives us x = 136. Therefore, Sue sold 136 DVDs.

The correct answer is (-2, 4) because when we substitute the values of x and y into the system of equations, we get the following:
y = x + 6
4 = -2 + 6
4 = 4
This shows that the values (-2, 4) satisfy both equations in the system.

The given answer suggests that the values in the list "x" are 3 and -9, and they are repeated in reverse order. This means that the list "x" contains the values 3 and -9 twice, with the first occurrence having 3 followed by -9, and the second occurrence having -9 followed by 3.

Let's assume the width of the garden is x yards. According to the given information, the length of the garden is 7 more yards than its width, which means the length is x + 7 yards. The area of a rectangle is calculated by multiplying its length and width, so we have the equation (x)(x + 7) = 60. By solving this equation, we find that x = 5. Therefore, the width of the garden is 5 yards and the length is 5 + 7 = 12 yards.

The zeros of a quadratic equation are the values of x where the equation equals zero. In this case, the quadratic equation has zeros at x = -2 and x = 1. These values can be found by setting the quadratic equation equal to zero and solving for x. The other values (-1, 2, and -1.5) are not zeros of the quadratic equation.

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In an equilateral triangle, all sides are equal in length. Therefore, if each side measures (2x + 6) inches, the perimeter of the triangle would be 3 times that length. Since the perimeter is given as 54 inches, we can set up the equation 3(2x + 6) = 54 and solve for x. Simplifying the equation gives 6x + 18 = 54. Subtracting 18 from both sides gives 6x = 36. Dividing both sides by 6 gives x = 6. Therefore, the value of x is 6.

The correct answer is B because it represents the graph of the equation 3x + 6y = 9. The equation is in standard form, where the coefficients of x and y are not equal. This means that the graph will be a straight line. By rearranging the equation to y = (-1/2)x + 3/2, we can see that the slope is -1/2 and the y-intercept is 3/2. This matches the equation of the line in graph B, confirming that it is the correct representation of the equation.

The given expression is (x + 6) (x - 2). To factorize this expression, we need to find two binomials whose product is equal to the given expression. The correct factoring is (3x - 2) (x + 2) because when we multiply these two binomials, we get (3x * x) + (3x * 2) + (-2 * x) + (-2 * 2) which simplifies to 3x^2 + 6x - 2x - 4. This is equal to the original expression (x + 6) (x - 2), confirming that (3x - 2) (x + 2) is the correct factoring.

Each person attending the party must pay $3, and the friends have contributed a total of $21. Therefore, they can pay for a maximum of $21/$3 = 7 people. Additionally, they have purchased $36 worth of snacks. So, the total amount of money available to pay for the party is $21 + $36 = $57. Since each person attending the party costs $3, the maximum number of people that can attend the party is $57/$3 = 19. Therefore, the correct answer is 19.

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The correct answer is y = (x + 4) (x - 7) because this function has x-intercepts of (-4, 0) and (7, 0). When the value of x is -4, the first factor (x + 4) becomes 0, resulting in y = 0. Similarly, when the value of x is 7, the second factor (x - 7) becomes 0, resulting in y = 0. Therefore, both x-intercepts are satisfied by this function.

The equation -3x + 6y + 5 = -7 can be simplified to -3x + 6y = -12. To find the points on the graph, we can substitute the x and y values from each given point into the equation and check if it satisfies the equation. Substituting (0, -2) gives -3(0) + 6(-2) = -12, which is true. Substituting (8, 2) gives -3(8) + 6(2) = -12, which is also true. Therefore, the points (0, -2) and (8, 2) are on the graph of the equation.

The explanation for the correct answer is not available as the question is incomplete and the options are not provided.

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The equation is x = -1, x = 1, x = 3/2, x = 2/3, x = -6. The correct solutions for the equation are x = 1 and x = 3/2. These values satisfy the equation and make it true.

The inequality given is 3(x + 2) - 7 -2. Therefore, the values -1, 4, and 0 are all part of the solution set.