1.
Solve 2/3 + 11/18
Explanation
The given question asks to solve the addition of 2/3 and 11/18. To add fractions, we need to find a common denominator, which in this case is 18. We then convert both fractions to have a denominator of 18. 2/3 becomes 12/18 and 11/18 remains the same. Adding these fractions gives us 23/18. The mixed number form of 23/18 is 1 5/18. The decimal form of 23/18 is 1.27777778.
2.
Find the Slope of a line with the points (-4,6) and (1,10)
Correct Answer
C. 4/5
Explanation
To find the slope of a line, we use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (-4,6) and (1,10). Plugging these values into the formula, we get (10 - 6) / (1 - (-4)), which simplifies to 4/5. Therefore, the correct answer is 4/5.
3.
What is the length of c? a = 9 ft, b = 5ft, and c = ?
Correct Answer
A. √106 ft
Explanation
The length of c can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, a = 9 ft and b = 5 ft. Thus, c^2 = 9^2 + 5^2 = 81 + 25 = 106. Taking the square root of 106 gives us the length of c, which is approximately √106 ft.
4.
Solve the equation 3(6 + 5y) = 2(-5 + 4y)
Correct Answer
B. Y = -4
Explanation
To solve the equation, we first distribute the numbers inside the parentheses. This gives us 18 + 15y = -10 + 8y. Next, we combine like terms by subtracting 8y from both sides, which gives us 10y = -28. Finally, we divide both sides by 10 to solve for y, which gives us y = -2.8. However, since the options provided are whole numbers, we round -2.8 to the nearest whole number, which is -3. Therefore, the correct answer is y = -4.
5.
Solve the equation (2/3)x - 1/6 = (1/2)x + 5/6
Correct Answer
D. 6
Explanation
The correct answer is 6. This is because when solving the equation (2/3)x - 1/6 = (1/2)x + 5/6, we can simplify it by multiplying every term by 6 to eliminate the fractions. This results in 4x - 1 = 3x + 5. By rearranging the equation, we get x = 6.
6.
What is the perimeter of the figure?
Correct Answer
A. 19 ft
7.
What are the coordinates of the points on the top triangle? (put a comma between your answers, placing them in order of A, B, C)[e.g. (5,6), (10, 123), (57, 88)]
Correct Answer
(-2,4), (2,3), (-1,1)
(-2, 4), (2, 3), (-1, 1)
(-2,4),(2,3),(-1,1)
(-2, 4),(2, 3),(-1, 1)
8.
What would be the correct expression to represent the are of the circle? π is pi
Correct Answer
A. 49 π
Explanation
The correct expression to represent the area of a circle is given by multiplying the square of the radius by pi. In this case, the radius is 7, so the expression becomes 7^2 * π, which simplifies to 49π.
9.
A dripping faucet wastes 3 cups of water every 24 hours. How much water is wasted in a week?
Correct Answer
C. 21 cups
Explanation
If a dripping faucet wastes 3 cups of water every 24 hours, then in a week (which consists of 7 days), it will waste 3 cups x 7 days = 21 cups of water.
10.
A rectangular swimming pool is surrounded by a concrete sidewalk that is 3 ft wide. The dimension of the rectangle created by the sidewall are 21 ft by 31 ft.Find the length and then width of the pool. Then find the area of the pool. (use commas between multiple answers)
Correct Answer
25, 15, 375
25 ft, 15 ft, 375 ft sq
25,15,375
25 ft,15 ft, 375 ft
25ft,15ft,375ft^2
Explanation
The length of the pool is 25 ft and the width is 15 ft. The area of the pool is 375 sq ft.