Algebra CA Midterm Review

To solve the equation x + 6 = 16, we need to isolate the variable x on one side of the equation. We can do this by subtracting 6 from both sides of the equation. This gives us x = 10. Therefore, the correct answer is 10.

To solve the equation -5x = 30, we need to isolate the variable x. To do this, we divide both sides of the equation by -5. This gives us x = -6. Therefore, the correct answer is -6.

The expression 5+y is evaluated by substituting the value of y, which is -12, into the expression. Therefore, 5+(-12) equals -7.

To evaluate the expression 3(x-2) + 5 for x = 5, we substitute the value of x into the expression. So, we have 3(5-2) + 5. Simplifying the expression within the parentheses, we get 3(3) + 5. Further simplifying, we have 9 + 5. Adding these two numbers together, we get 14. Therefore, the correct answer is 14.

The equation 3(x - 7) = 3x - 21 demonstrates the distributive property. This property states that when a number is multiplied by a sum or difference, it can be distributed to each term within the parentheses. In this equation, the 3 is being distributed to both x and -7, resulting in 3x - 21 on the right side of the equation.

The given expression is -30 divided by 0.6. To divide a number by a decimal, we can multiply the number by the reciprocal of the decimal. The reciprocal of 0.6 is 1/0.6, which is equal to 1.6667. Therefore, -30 divided by 0.6 is equal to -30 multiplied by 1.6667, which is approximately equal to -50.

When we substitute x = 1 into the expression 2(x - 3) + 4, we get 2(1 - 3) + 4 = 2(-2) + 4 = -4 + 4 = 0. Therefore, the correct answer is 0.

The phrase "4 times the difference of a number x and 8" can be translated into the algebraic expression 4(x-8). This expression represents multiplying the difference between x and 8 by 4.

Out of every 10 pairs of shoes that Jack sold, 6 were black. This means that 4 pairs were not black. To find the percentage of pairs that were not black, we can divide the number of pairs that were not black (4) by the total number of pairs (10) and then multiply by 100. So, (4/10) * 100 = 40%. Therefore, 40% of the pairs were not black.

To solve the equation 19 - 4x = -5, we need to isolate the variable x. We can start by subtracting 19 from both sides of the equation: -4x = -24. Then, we divide both sides by -4 to solve for x: x = 6. Therefore, the correct answer is 6.

To solve the equation (x-5)/3 = 1, we can start by multiplying both sides of the equation by 3 to eliminate the fraction. This gives us x-5 = 3. Then, we can add 5 to both sides of the equation to isolate x, resulting in x = 8. Therefore, the correct answer is 8.

To evaluate -5/12 - 4/12, we need to find a common denominator, which in this case is 12. Then, we subtract the numerators and keep the denominator the same. -5 - 4 equals -9, so the answer is -9/12. However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3. So, -9/12 simplifies to -3/4.

The inequality states that y minus 5 is less than -4. To solve for y, we can add 5 to both sides of the inequality to isolate y. This gives us y is less than 1. Therefore, the correct answer is y

The square root of 65 is a number between 8 and 9. This can be determined by finding the square roots of the numbers that are slightly smaller and slightly larger than 65. The square root of 64 is 8, and the square root of 81 is 9. Since 65 is closer to 64 than to 81, the square root of 65 must be between 8 and 9.

If 12 students represent 40% of the total number of students in the PAWS group, we can use the proportion method to find the total number of students. Let x be the total number of students. We can set up the equation 12/x = 40/100 and solve for x. Cross-multiplying gives us 12 * 100 = 40 * x. Simplifying further, we get 1200 = 40x. Dividing both sides by 40, we find that x = 30. Therefore, there were 30 students in the PAWS group.

To solve the equation 2x + 3 = x - 5, we need to isolate the variable x on one side of the equation. By subtracting x from both sides, we get x + 3 = -5. Then, by subtracting 3 from both sides, we get x = -8. Therefore, the correct answer is x = -8.

40% of a number can be found by multiplying the number by 0.40. In this case, 40% of 180 would be 180 * 0.40 = 72. Therefore, the correct answer is 72.

The y-intercept of a linear equation represents the point where the line intersects the y-axis. To find the y-intercept, we set x=0 in the equation x+2y=4 and solve for y. When x=0, the equation becomes 0+2y=4, which simplifies to 2y=4. Dividing both sides by 2, we get y=2. Therefore, the y-intercept is (0, 2).

The given inequality is -3x -6. So, the correct answer is x > -6.

To solve the equation (2/3)x - 4 = 4, we first need to isolate the variable x. We can start by adding 4 to both sides to get (2/3)x = 8. Next, we can multiply both sides by the reciprocal of 2/3, which is 3/2, to cancel out the coefficient of x. This gives us x = 8 * (3/2) = 12. Therefore, the correct answer is 12.

To solve the proportion (m+1)/10 = 4/5, we can cross-multiply. Cross-multiplying gives us (m+1) * 5 = 4 * 10. Simplifying further, we get 5m + 5 = 40. Subtracting 5 from both sides gives us 5m = 35. Dividing both sides by 5, we find that m = 7. Therefore, the correct answer is 7.

The given equation is 3x - y = -6. To solve for y, we need to isolate it on one side of the equation. By subtracting 3x from both sides, we get -y = -3x - 6. To solve for y, we multiply both sides by -1 to get y = 3x + 6. Therefore, the correct answer is y = 3x + 6.

The correct answer is -1

The given equation is in the form of Ax + By = C, where A = 1, B = 2, and C = 5. To find the slope, we need to rearrange the equation in the form y = mx + b, where m is the slope. By isolating y, we get 2y = -x + 5, and dividing both sides by 2, we get y = (-1/2)x + 5/2. Therefore, the slope of the line is -1/2.

The given equation is y = 2x - 3. To check if a point is a solution, we substitute the x and y values into the equation. For the point (3, 3), when we substitute x = 3 and y = 3 into the equation, we get 3 = 2(3) - 3, which simplifies to 3 = 3. Since the equation holds true, the point (3, 3) is a solution to the equation.

The slope of a line can be found using the formula: slope = (change in y)/(change in x). Given the points (-1,4) and (3,-4), the change in y is -4 - 4 = -8, and the change in x is 3 - (-1) = 4. Therefore, the slope is -8/4 = -2.

The percent of change can be calculated by finding the difference between the two weights and then dividing it by the original weight. In this case, the difference is 165 - 150 = 15 pounds. Dividing this by the original weight of 150 gives us 15/150 = 0.1. Multiplying this by 100 gives us 10%, which represents the percent of change. Therefore, the correct answer is 10% increase.

The slope of a line parallel to another line is always the same. In this case, the given line has a slope of -(1/2). Therefore, any line parallel to it will also have a slope of -(1/2).

The given expression is evaluated using the order of operations (PEMDAS/BODMAS). First, we perform the exponentiation operation: 2^2 = 4. Then, we perform the division operation: 15/5 = 3. Next, we perform the addition and subtraction operations from left to right: 20 + 3 - 4 - 4 = 15. Therefore, the correct answer is 15.

The equation y = -x+3 represents a line in slope-intercept form. The slope of the line is -1, which can be determined by finding the difference in y-coordinates (-2 - 4) and the difference in x-coordinates (1 - (-1)) of the given points (-1, 4) and (1, 2). The y-intercept of the line is 3, which can be determined by substituting the x and y coordinates of either point into the equation and solving for the y-intercept. Therefore, the equation y = -x+3 satisfies the conditions of passing through the given points.

The given expression is 40 minus the result of subtracting 3 from the cube of -2. The cube of -2 is -8, so the expression becomes 40 minus (-8+3), which simplifies to 40 minus (-5). Subtracting a negative number is the same as adding its positive counterpart, so the expression further simplifies to 40+5, which equals 45. Therefore, the correct answer is 45, not 29.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. In the given equation, y = 2x + 5, the slope is 2. Therefore, the slope of a line perpendicular to this line would be -(1/2).