1.
Round 45943 to the nearest hundreds.
Correct Answer
A. 45900
Explanation
To round 45943 to the nearest hundreds, we need to look at the digit in the tens place, which is 4. Since 4 is less than 5, we round down. Therefore, the hundreds digit and all digits to the right of it become 0. Hence, the number 45943 is rounded to 45900.
2.
Round 29.094 to the nearest hundredth.
Correct Answer
C. 29.04
Explanation
To round 29.094 to the nearest hundredth, we look at the digit in the thousandth place, which is 4. Since 4 is less than 5, we do not round up. Therefore, the hundredth place remains unchanged, and the answer is 29.04.
3.
Simplify the fraction 5/15.
Correct Answer
B. 1/3
Explanation
To simplify the fraction 5/15, we need to find the greatest common divisor (GCD) of the numerator and denominator, which is 5 in this case. By dividing both the numerator and denominator by 5, we get 1/3. Therefore, the simplified form of 5/15 is 1/3.
4.
Solve for x. x = -3 + 5
Correct Answer
D. 2
Explanation
The given equation is x = -3 + 5. By simplifying the equation, we get x = 2. Therefore, the value of x is 2.
5.
Solve for x. x = -5 x 6
Correct Answer
C. -30
Explanation
To solve for x, we need to multiply -5 by 6. The product of -5 and 6 is -30. Therefore, the value of x is -30.
6.
Simplify the expression: 8t + 4t^{2 }– 8t
Correct Answer
A. 4t^{2}
Explanation
The expression can be simplified by combining like terms. The like terms in the expression are 8t and -8t. When we combine these terms, we get 0, so they cancel each other out. Therefore, the simplified expression is 4t^2.
7.
Solve for v. 6v − v = 20
Correct Answer
C. 4
Explanation
To solve the equation 6v - v = 20, we can combine like terms by subtracting v from 6v, which gives us 5v. So the equation becomes 5v = 20. To isolate v, we divide both sides of the equation by 5, resulting in v = 4. Therefore, the correct answer is 4.
8.
Simplify the expression: –7(–1 + –9g^{2}) + 9
Correct Answer
C. 63g^{2 }+ 16
Explanation
The given expression is simplified by applying the distributive property and simplifying the terms. The negative sign outside the parentheses is distributed to each term inside, resulting in -7(-1) + 7(-9g2) + 9. Simplifying further, we get 7 + 63g2 + 9. Combining like terms, the expression simplifies to 63g2 + 16.
9.
Simplify the expression: 5(5r^{2 }+ 4r) + 2(6 – 6r)
Correct Answer
D. 25r^{2} + 8r + 12
Explanation
The given expression is simplified by distributing the numbers outside the parentheses to the terms inside the parentheses. This results in 25r^2 + 20r + 12 + 12r - 12r. Combining like terms, we get 25r^2 + 8r + 12.
10.
Simplify the expression: 6u + 2(10 – u)
Correct Answer
B. 4u + 20
Explanation
The given expression is 6u + 2(10 - u). To simplify this expression, we can distribute the 2 to both terms inside the parentheses, resulting in 6u + 20 - 2u. Combining like terms, we get 4u + 20. Therefore, the correct answer is 4u + 20.
11.
Combine any like terms in the expression. If there are no like terms, rewrite the expression.
50 + 28a^{2 }+ 11a^{2 }– 22a^{2}
Correct Answer
D. 17a^{2} + 50
Explanation
The expression can be simplified by combining the like terms. In this case, the like terms are the terms with the same variable, which is "a2". The coefficients of these terms are 28, 11, and -22. When these terms are combined, we get 17a2. The constant term in the expression is 50, which remains unchanged. Therefore, the simplified expression is 17a2 + 50.
12.
Solve for s. s / -16 + 245 = 267
Correct Answer
B. -352
Explanation
To solve for s, we need to isolate s on one side of the equation. First, we can subtract 245 from both sides to get s / -16 = 22. Then, we can multiply both sides by -16 to cancel out the -16 in the denominator and solve for s. This gives us s = -352.
13.
Find the missing length. The triangles are similar.
Correct Answer
C. 14
Explanation
The missing length can be found by using the concept of similarity between triangles. Since the triangles are similar, their corresponding sides are proportional. By comparing the given sides, we can see that the ratio of the corresponding sides is 10:12:14. Therefore, the missing length can be calculated by setting up a proportion: 10/12 = 14/x. Solving for x, we find that x = 16. Thus, the missing length is 16.
14.
Find the missing length. The triangles are similar.
Correct Answer
B. 12
Explanation
The missing length in the triangle can be found by using the concept of similarity. Since the triangles are similar, the ratio of corresponding sides will be equal. In this case, we can set up the proportion 3/12 = x/15, where x represents the missing length. Solving this proportion, we find that x = 3/12 * 15 = 3.75. However, since the given options do not include a decimal, we can round the answer to the nearest whole number, which is 4. Therefore, the missing length is 4.
15.
A car drives 50 miles east and then 40 miles due north. How far is it from where it started?
Correct Answer
B. 64 miles
Explanation
The car first drives 50 miles east and then 40 miles north. These two distances form the legs of a right triangle, with the starting point as the right angle. Using the Pythagorean theorem, we can calculate the hypotenuse of this triangle, which represents the distance from where the car started. The square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, the square of the distance is (50^2 + 40^2), which is 2500 + 1600 = 4100. Taking the square root of 4100 gives us approximately 64 miles.
16.
Oceanside Bike Rental charges 17 dollars plus 6 dollars per hour for renting a bike. Tom paid 59 dollars to rent a bike. How many hours did Tom pay to have the bike checked out?
Correct Answer
D. 7 hours
Explanation
Tom paid a total of 59 dollars to rent a bike. The rental charges include a base fee of 17 dollars plus an additional 6 dollars per hour. To find out how many hours Tom paid to have the bike checked out, we can subtract the base fee from the total amount paid (59 - 17 = 42). Then, we divide the remaining amount by the cost per hour (42 / 6 = 7). Therefore, Tom paid for 7 hours to have the bike checked out.
17.
What is the slope of this line?
Correct Answer
B. -1/2
Explanation
The slope of a line is a measure of how steep the line is. It is calculated by finding the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. In this case, the slope is -1/2, which means that for every 1 unit increase in the x-coordinate, the y-coordinate decreases by 1/2 unit.
18.
What is the equation of this line?
Correct Answer
D. Y = -4/5x +3
Explanation
The equation of the line is y = -4/5x + 3. This can be determined by comparing the given equation with the standard slope-intercept form of a linear equation, y = mx + b. In this case, the slope (m) is -4/5, which indicates that the line is downward sloping. The y-intercept (b) is 3, which means that the line intersects the y-axis at the point (0, 3).
19.
What is the equation of this line?
Correct Answer
C. Y = 1/2x - 2
Explanation
The equation of the line is y = 1/2x - 2. This can be determined by comparing the equation to the standard form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 1/2, indicating that the line has a positive slope and is increasing as x increases. The y-intercept is -2, meaning that the line intersects the y-axis at the point (0, -2). Therefore, the equation of the line is y = 1/2x - 2.
20.
Find the slope of a line that passes through the two points. (-5 , 3) and (1, 6)
Correct Answer
B. 1/2
Explanation
The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (-5, 3) and (1, 6). Plugging these values into the formula, we get (6 - 3) / (1 - (-5)) = 3 / 6 = 1/2. Therefore, the correct answer is 1/2.
21.
Write the slope-intercept form of the equation of a line that passes through the point (5 , 2) and is parallel to the line y = -3x - 4
Correct Answer
A. Y = -3x + 17
Explanation
The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. In this case, the line is parallel to y = -3x - 4, so it has the same slope of -3. The point (5, 2) lies on the line, so we can substitute these values into the equation and solve for the y-intercept. Plugging in 5 for x and 2 for y, we get 2 = -3(5) + b. Solving for b, we find that b = 17. Therefore, the equation of the line is y = -3x + 17.
22.
Write the slope-intercept form of the equation of the line that passes through the point (-2 , 4) and is perpendicular to the line y = 9x + 3
Correct Answer
C. Y = 9x + 22
Explanation
The given equation y = 9x + 3 represents a line with a slope of 9. Since the line we are looking for is perpendicular to this line, its slope will be the negative reciprocal of 9, which is -1/9.
Using the point-slope form of a linear equation, we can substitute the slope (-1/9) and the coordinates of the given point (-2, 4) into the equation y - y1 = m(x - x1).
Plugging in the values, we get y - 4 = (-1/9)(x - (-2)). Simplifying this equation gives us y - 4 = (-1/9)(x + 2).
To convert this equation into the slope-intercept form (y = mx + b), we can distribute (-1/9) and rearrange the equation to isolate y.
After simplifying, we obtain y = 9x + 22.
23.
Solve the system of equations.
y = x + 12
2x - y = 16
Correct Answer
B. (28, 40)
Explanation
The correct answer is (28, 40) because when we substitute the values of x and y into the two equations, they satisfy both equations. For the first equation, if we substitute x = 28 and y = 40, we get 40 = 28 + 12, which is true. For the second equation, if we substitute x = 28 and y = 40, we get 2(28) - 40 = 56 - 40 = 16, which is also true. Therefore, (28, 40) is the solution to the system of equations.
24.
Solve the system of equations.
x - 5y = 6
-9x -5y = -4
Correct Answer
A. (1, -1)
Explanation
The correct answer is (1, -1). This means that when we substitute x = 1 and y = -1 into both equations, both equations are satisfied. This can be verified by substituting these values into the original equations:
For the first equation, x - 5y = 6, we have 1 - 5(-1) = 1 + 5 = 6, which is true.
For the second equation, -9x - 5y = -4, we have -9(1) - 5(-1) = -9 - (-5) = -9 + 5 = -4, which is also true.
Therefore, the solution to the system of equations is (1, -1).
25.
Eliza's school is selling tickets to the annual talent show. On the first day of ticket sales, the school sold 8 senior citizen tickets and 6 student tickets for a total of $80. The school took in $101 on the second day by selling 11 senior citizen tickets and 6 student tickets. What is the price each of senior citizen ticket and one student ticket?
Correct Answer
D. $6, $7
Explanation
On the first day, the school sold 8 senior citizen tickets and 6 student tickets for a total of $80. Let's assume the price of a senior citizen ticket is x and the price of a student ticket is y. So, we can form the equation 8x + 6y = 80.
On the second day, the school sold 11 senior citizen tickets and 6 student tickets for a total of $101. Using the same variables, we can form the equation 11x + 6y = 101.
Now we have a system of equations:
8x + 6y = 80
11x + 6y = 101
By solving this system of equations, we find that x = 6 and y = 7. Therefore, the price of a senior citizen ticket is $6 and the price of a student ticket is $7.
26.
Which one do you like?
Correct Answer
A. Option 1