Could someone please check my math questions? any help will be greatly appreciated!
Questions~
16. A car’s speed before a sudden stop can be estimated by the formula
S = √(30gk) , where
S = speed of the car in mph,
g = drag factor, and
k = length of skid mark in feet.
The drag factor during a recent crash was 0.8. What was the approximate speed of the car if it created skid marks 93 feet long?
a. 34 mph
b. 47 mph
c. 68 mph
d. 85 mph
Answer~ d
17. The length of a rectangle is (3x – 7) inches and its width is (x + 5) inches. Find an expression for the perimeter of the rectangle.
a. 4x - 35
b. 4x - 2
c. 8x - 4
d. 8x - 35
Answer~c
18. Which of the following sets does not contain only rational numbers?
a. -5, p/2, 0.5, -0.12
b. -0.4, -0.3333.. , 6.8, 6.888…
c. 11/7, 5/4, 8/5, 32/19
d. ½, ¼, 1/8, 1/16
Answer~ b
19. What is the value of (-3)^
x when x = 3.
a. -27
b. -9
c. 9
d. 27
Answer~a
20. Which rational number lies between √10 and √12 ?
a. 45/14
b. 47/13
c. 47/19
d. 52/17
Answer~a
21. A shelter has enough food to feed an average of 80 hungry people a day for 14 days. If an average of 32 people are at the shelter each day, how long will the food last?
a. 5.6 days
b. 35 days
c. 183 days
d. 200 days
Answer~b
22. Which of the following numbers is a solution of the inequality 9 – x > 2? (NOTE: the > sign has a line under it)
a. 7
b. 8
c. 9
d. 10
Answer~ a
23. What is the value of the expression [(5)(9) / x] + 6x when x = -3?
a. -33
b. -9
c. 3
d. 33
Answer~b
24.What is the solution of 30| x | = 10?
a. -3 and 3
b. 3
c. 1/3
d. -1/3 and 1/3
answer~ d
25. Which step can you use to solve the equation 3x = -12?
a. Divide each side by -12.
b. Divide each side by 3.
c. Multiply each side by -12.
d. Multiply each side by 3.
Answer ~ I think it's a or c
Let's go through each question step-by-step:
16. To find the speed of the car, we need to substitute the given values into the formula S = √(30gk).
Given values: g = 0.8 and k = 93.
Substituting these values, we get S = √(30 * 0.8 * 93).
Calculating this expression, we find S ≈ 84.85 mph.
None of the given answer choices match the calculated speed. Therefore, it seems like none of the options provided are correct.
17. The perimeter of a rectangle is given by the formula P = 2(Length + Width).
Given values: Length = (3x - 7) and Width = (x + 5).
Substituting these values, we get P = 2((3x - 7) + (x + 5)).
Simplifying the expression inside the parenthesis, we get P = 2(4x - 2).
Further simplifying, P = 8x - 4.
The correct answer is c. 8x - 4.
18. To determine which set does not contain only rational numbers, we need to assess the numbers in each set.
a. All numbers in the set are rational.
b. The number -0.3333... is a repeating decimal and therefore rational. All numbers in this set are rational.
c. All numbers in the set are rational.
d. All numbers in the set are rational.
Therefore, option b. -0.4, -0.3333..., 6.8, 6.888... does not contain only rational numbers.
19. To find the value of (-3)^x when x = 3, we substitute the value of x into the expression.
(-3)^3 = -3 * -3 * -3 = -27.
The correct answer is a. -27.
20. To determine which rational number lies between √10 and √12, we can approximate the square roots.
√10 ≈ 3.16
√12 ≈ 3.46
The rational number 45/14 ≈ 3.214, which lies between √10 and √12.
The correct answer is a. 45/14.
21. To find how long the food will last, we need to divide the total amount of food by the number of people eating per day.
Total food = 80 people x 14 days = 1120 meals
Number of people per day = 32
Food will last = 1120 meals / 32 people = 35 days.
The correct answer is b. 35 days.
22. To solve the inequality 9 - x > 2, we need to isolate x.
First, subtract 9 from both sides: 9 - x - 9 > 2 - 9
Simplifying, -x > -7
Remember that when dividing or multiplying by a negative number, the inequality sign has to be flipped:
x < 7
Among the given options, only a. 7 satisfies the inequality 9 - x > 2.
23. To find the value of [(5)(9) / x] + 6x when x = -3, substitute the value of x into the expression.
[(5)(9) / (-3)] + 6(-3) = -45 / 3 - 18 = -15 - 18 = -33.
The correct answer is a. -33.
24. To solve the equation 30| x | = 10, we need to remove the absolute value.
Divide both sides by 30: | x | = 10/30 = 1/3
Now we have two possible cases: x = 1/3 or x = -1/3
The correct answer is d. -1/3 and 1/3.
25. To solve the equation 3x = -12, we need to isolate x.
Divide both sides by 3: 3x / 3 = -12 / 3
Simplifying, x = -4
The correct step to solve this equation is b. Divide each side by 3.
Sure, let's go through each question one by one and find the correct answers.
16. The formula given is S = √(30gk). We are given g = 0.8 and k = 93. Plugging in these values, we get S = √(30 * 0.8 * 93). Evaluating this expression gives us S = √(2232). Approximating the square root gives us S ≈ 47.3 mph. So the correct answer is b. 47 mph.
17. The perimeter of a rectangle can be found by adding up all the sides. In this case, the length is (3x - 7) and the width is (x + 5). So the perimeter expression becomes 2(3x - 7) + 2(x + 5). Simplifying gives us 6x - 14 + 2x + 10. Combining like terms gives us 8x - 4. So the correct answer is c. 8x - 4.
18. To determine which set contains only rational numbers, we need to check if each number can be expressed as a fraction. Looking at the sets:
a. All the numbers can be expressed as fractions.
b. -0.4 and 6.8 can be expressed as fractions, but -0.3333... and 6.888... cannot.
c. All the numbers can be expressed as fractions.
d. All the numbers can be expressed as fractions.
So the set that does not contain only rational numbers is set b. Answer is b.
19. Evaluating (-3)^x when x = 3 gives us (-3)^3 = -27. So the correct answer is a. -27.
20. To find a rational number between √10 and √12, we need to find a fraction whose square root is between those two numbers. Looking at the options, 45/14 is the closest to being a decimal between √10 and √12. So the correct answer is a. 45/14.
21. The shelter has enough food to feed 80 people for 14 days, so the total amount of food is 80 * 14 = 1120 servings. If an average of 32 people are at the shelter each day, then the food will last for 1120 / 32 = 35 days. So the correct answer is b. 35 days.
22. We need to find a number that satisfies the inequality 9 - x > 2. Solving this inequality, we subtract 9 from both sides to get -x > 2 - 9 -> -x > -7. Multiplying both sides by -1, the inequality flips and we get x < 7. So the number that is a solution is a. 7.
23. Substituting x = -3 into the expression [(5)(9) / x] + 6x gives us [(5)(9) / -3] + 6(-3) = -45/-3 + (-18) = 15 - 18 = -3. So the correct answer is b. -9.
24. To find the solution of 30| x | = 10, we divide both sides by 30, which gives | x | = 10/30 = 1/3. Since absolute value refers to the distance from zero, the equation | x | = 1/3 has two possible solutions: x = 1/3 and x = -1/3. So the correct answer is d. -1/3 and 1/3.
25. To solve the equation 3x = -12, we want to isolate x. We can do this by dividing both sides by 3, giving us (3x)/3 = -12/3 -> x = -4. So the correct answer is b. Divide each side by 3.
I have provided the explanations for each question alongside the answers. Let me know if you have any further questions!