1.
If a = 3 and b = —2, what is the value of the expression
Correct Answer
D. -18/91
Explanation
The value of the expression can be found by substituting the values of a and b into the expression. When a = 3 and b = -2, the expression becomes -210/31. Therefore, the correct answer is -210/31.
2.
Use this information to answer the next question.
Hours
1
1.5
2
2.5
3
Total
Charge
$58
$67
$76
$85
$94
The table above shows the total labor charges for an electrician. The electrician charges $40 for the service call, plus an hourly flat rate for the time spent on the job. Which equation best represents the relationship between the number of hours spent on the job, x, and the total charges, c?
Correct Answer
D. C = 40 + 18x
Explanation
The equation c = 40 + 18x represents the relationship between the number of hours spent on the job, x, and the total charges, c. The $40 represents the service call charge, which is a flat fee. The 18x represents the hourly rate of $18 for each hour spent on the job. Adding the two together gives the total charges.
3.
What is (x^{2} + 3x + 4) – (3x^{2} +x – 1)?
Correct Answer
B. -2x^2 + 2x + 5
Explanation
The given expression is a subtraction of two polynomials. To simplify the expression, we combine like terms. We subtract the coefficients of each term with the same degree.
For the x^2 term, we have -2x^2 - x^2 = -3x^2.
For the x term, we have 3x - x = 2x.
For the constant term, we have 4 - (-1) = 5.
Therefore, the simplified expression is -3x^2 + 2x + 5.
4.
Simplify: -5x(2x^{2} - 3x + 7)
Correct Answer
D. -10x^3+ 15x^2 - 35x
Explanation
The given expression is simplified by distributing -5x to each term inside the parentheses. This results in -10x^3 + 15x^2 - 35x.
5.
Simplify: (x – 9)(x + 8)
Correct Answer
A. X^2 â€“ x â€“ 72
Explanation
The given expression is a product of two binomials. To simplify, we can apply the distributive property. Multiplying the terms, we get x^2 - 9x + 8x - 72. Combining like terms, we have x^2 - x - 72. Therefore, the correct answer is X^2 â€“ x â€“ 72.
6.
Simplify: (x + 5)(x^{2} – 5x – 1)
Correct Answer
C. X^3 â€“ 26x â€“ 5
Explanation
The given expression is a product of two binomials. To simplify it, we can use the distributive property and multiply each term of the first binomial by each term of the second binomial. This results in the expression X^3 - 26x - 5.
7.
Translate: “The product of 9 and the quantity a decreased by 6.”
Correct Answer
B. 9(a â€“ 6)
Explanation
The correct answer is 9(a - 6). This is the correct translation of the given phrase "The product of 9 and the quantity a decreased by 6." The phrase "the product of 9 and the quantity a" can be represented as 9a, and "decreased by 6" can be represented as -6. Therefore, the expression becomes 9a - 6, which matches the given answer.
8.
Find the slope through the points (4, -2) and (-1, 6).
Correct Answer
C. -8/5
Explanation
To find the slope between two points, we use the formula (y2 - y1) / (x2 - x1). Plugging in the values from the given points, we get (6 - (-2)) / (-1 - 4), which simplifies to 8/5. Therefore, the correct answer is -8/5.
9.
Write the equation of the line given slope of 5 and y-intercept of -2.
Correct Answer
A. Y = 5x - 2
Explanation
The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 5 and the y-intercept is -2. Therefore, the equation of the line is y = 5x - 2.
10.
Write the equation of a line with slope and through the point (9, -3).
Correct Answer
B. Y = 2/3 x - 9
Explanation
The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2/3 and the line passes through the point (9, -3). To find the y-intercept, we can substitute the values of x and y from the given point into the equation and solve for b. Using the point (9, -3), we get -3 = (2/3)(9) + b. Simplifying this equation, we get -3 = 6 + b. Solving for b, we find that b = -9. Therefore, the equation of the line is y = 2/3 x - 9.
11.
Write the equation of the line through the point (-1, 5) and perpendicular to the line 4x + y = 6.
Correct Answer
C. Y = 1/4 x + 21/4
Explanation
The equation of a line perpendicular to 4x + y = 6 will have a slope that is the negative reciprocal of 1/4. The negative reciprocal of 1/4 is -4/1, which is equivalent to -4. The equation y = 1/4 x + 21/4 has a slope of 1/4, so it is not perpendicular to the given line. Therefore, the correct answer is y = -1/4 x + 19/4.
12.
Cable Bill A cable complany charges and flat monthly fee of $95 for basic channels and an additional $7 for each premium channel. Write an equation to model the cable company's monthly fees.
Correct Answer
A. Y = 7x + 95
Explanation
The correct answer is y = 7x + 95. This equation models the cable company's monthly fees by multiplying the number of premium channels (x) by the cost per premium channel ($7) and adding it to the flat monthly fee for basic channels ($95). This equation accurately represents the relationship between the number of premium channels and the total monthly fee.
13.
Brandi’s school was having a fundraiser for Yankee candles. Customers could buy a large candle or a small candle. On the first day, Brandi sold 4 large candles and 2 small candles for a total of $144. The second day she sold 3 large candles and 5 small candles for a total of $164. How much is one large candle and how much is one small candle?
Correct Answer
D. Large=28, Small=16
Explanation
The first equation is 4L+2s=144 and the second equation is 3L+5s=164. First you would multiply the first equation by 3 and the second by -4 so that the variable L can cancel out. Then after combining like terms you would get -14s=-224. You would then divide both sides by -14 to get s=16. Next you would multiply the first original equation by 5 and the second original equation by -2 so that the s variable cancels out. Combine like terms to get 14L=392 and divide both sides by 14 to get L=28.
14.
The school that Lisa goes to is selling tickets for their annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. On the second day the school sold 7 senior citizen tickets along with 5 student tickets for a total of $126. How much does each one senior citizen ticket and each student ticket cost?
Correct Answer
A. Senior citizen=8, Student=14
Explanation
By reading the questions you can decide that the first equation would be 4c+5s=102 and the second 7c+5s=126. Then you would multiply the first by 1 and the second by negative one so that the variable s cancels out. Then you would combine like terms and the result would be -3=-24. Divide both sides by -3 and it would make c=8. You would then take equation 1 and multiply it's parts by 7 and the second equation by -4. This would cancel out c and after combining the like terms you would be left with 15s=210. Divide both sides by 15 and s would equal 14.
15.
Solve for x: 2x+4-34 = x+10-3x
Correct Answer
C. 10
Explanation
To solve for x, we need to simplify the equation by combining like terms. Starting with the left side of the equation, we have 2x + 4 - 34, which simplifies to 2x - 30. On the right side, we have x + 10 - 3x, which simplifies to -2x + 10. Now we can set the left side equal to the right side and solve for x. 2x - 30 = -2x + 10. Adding 2x to both sides gives 4x - 30 = 10. Adding 30 to both sides gives 4x = 40. Finally, dividing both sides by 4 gives x = 10.
16.
2x + 4y = 8x + 2y = 6The slopes of these two lines are:
Correct Answer
A. Parallel
Explanation
The given equation represents two lines with the same slope. When we simplify the equation, we get 2x + 4y = 8x + 2y = 6. This can be rewritten as 2x - 8x + 4y - 2y = 6, which simplifies to -6x + 2y = 6. By rearranging this equation, we get y = 3x + 3. Since both lines have the same slope of 3, they are parallel.
17.
Which of the following lines is parallel to the line y = 4x + 1
Correct Answer
D. Y = 4x - 1
Explanation
The given line y = 4x + 1 has a slope of 4. In order for a line to be parallel to this line, it must have the same slope of 4. Among the given options, the line y = 4x - 1 has a slope of 4, making it parallel to the original line. Therefore, y = 4x - 1 is the correct answer.
18.
Which of the following lines is perpendicular to the liney = 4x + 1
Correct Answer
C. Y = -(1/4)x + 1
Explanation
The line y = -(1/4)x + 1 is perpendicular to the line y = 4x + 1 because the slopes of perpendicular lines are negative reciprocals of each other. The slope of y = 4x + 1 is 4, so the slope of the perpendicular line should be -1/4. Additionally, the y-intercept of the perpendicular line is 1, which matches the y-intercept of the given line. Therefore, y = -(1/4)x + 1 is perpendicular to y = 4x + 1.
19.
Solve the equation for y. Then identify the slope and the y-intercept.3y - 2x = 15
Correct Answer
D. M= 2/3
b= 5
Explanation
The given equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept. By solving the equation 3y - 2x = 15 for y, we can rewrite it as y = (2/3)x + 5. Therefore, the slope of the equation is 2/3 and the y-intercept is 5.
20.
Write a verbal expression for the algebraic expression (2 - y) 6.
Correct Answer
C. Two minus y times six
Explanation
The verbal expression "two minus y times six" accurately represents the algebraic expression (2 - y) 6. It indicates that the quantity y is subtracted from two, and the result is then multiplied by six.