Using the formula , where d is the distance in miles, r is the rate, and t is the time in hours, at which rate must you travel to cover 212.5 miles in 2.5 hours? (1 point) Responses 71 mph 71 mph 106 mph 106 mph 150 mph 150 mph 85 mph
To find the rate at which you must travel to cover 212.5 miles in 2.5 hours, you need to divide the distance by the time:
rate = distance / time
rate = 212.5 miles / 2.5 hours
rate = 85 mph
Therefore, you must travel at a rate of 85 mph to cover 212.5 miles in 2.5 hours.
To find the rate at which you must travel to cover a certain distance in a given time, you can use the formula:
rate = distance / time
In this case, you want to cover 212.5 miles in 2.5 hours. Plugging those values into the formula, you get:
rate = 212.5 miles / 2.5 hours
Evaluating the expression, you get:
rate = 85 mph
Therefore, the correct answer is 85 mph.
To find the rate at which you must travel, you can use the formula:
r = d / t
where:
d = 212.5 miles (distance)
t = 2.5 hours (time)
Substituting the given values into the formula:
r = 212.5 / 2.5
Simplifying the equation:
r = 85 mph
Therefore, the rate at which you must travel to cover 212.5 miles in 2.5 hours is 85 mph.
What is the simplified form of the following expression? (1 point) Responses Image with alt text: negative 5 y z Image with alt text: negative 5 y Image with alt text: negative 5 y z squared 5y
The simplified form of the expression "-5yz^2" is "-5yz^2".
What is the simplified form of the following expression? 10yz/2z
(1 point)
Responses -5yz -5y -5yz^2 5y
To simplify the expression (10yz) / (2z), we can divide each term in the numerator by the denominator:
(10yz) / (2z) = (10y / 2) * (z / z)
Simplifying each term:
(10y / 2) = 5y
(z / z) = 1
So, the simplified form of the expression is 5y * 1, which is equal to 5y. Therefore, the correct response is 5y.
What is the simplified form of the following expression? 10yz/-2z
(1 point)
Responses -5yz -5y -5yz^2 5y
To simplify the expression (10yz) / (-2z), we can divide each term in the numerator by the denominator and simplify any common factors:
(10yz) / (-2z) = (10y / -2) * (z / z)
Simplifying each term:
(10y / -2) = -5y
(z / z) = 1
So, the simplified form of the expression is -5y * 1, which is equal to -5y. Therefore, the correct response is -5y.
The temperature at the end of the day was 64 degrees. The temperature had increased twice during the day, once by 8 degrees and another time by 4 degrees. Which expression shows what the temperature was at the start of the day? (1 point) Responses 64 – 8 – 4
64 + 8 - 4 64 - 8 + 4 78 + 5 + 7
To find the temperature at the start of the day, we need to subtract both increases from the final temperature of 64 degrees.
The correct expression is:
64 - 8 - 4
Simplifying:
64 - 8 - 4 = 52
Therefore, the temperature at the start of the day was 52 degrees. The correct response is 64 - 8 - 4.
What is the value of if x = –3, y = 4 and w = –6. (1 point) Responses 2 -2 1/2 -1/2
To find the value of the expression, we substitute the given values of x, y, and w into the expression.
The expression is not given in the question, so I cannot determine the value. Please provide the expression.
What is the value of xy/w if x = –3, y = 4 and w = –6. (1 point) Responses 2 -2 1/2 -1/2
To find the value of the expression xy/w, we substitute the given values of x, y, and w:
xy/w = (-3)(4) / (-6)
Simplifying:
xy/w = -12 / -6
This simplifies to:
xy/w = 2
Therefore, the value of xy/w when x = -3, y = 4, and w = -6 is 2.
Which of the following results in a sum or a product that is rational? Choose all that apply. (2 points) Responses 4+9 pi*5 3.45*1.2 sqrt16*sqrt14 sqrt7*sqrt2
To determine which expressions result in a rational sum or product, we need to identify those that do not involve irrational numbers or square roots of non-perfect squares.
Let's analyze each option:
1. 4 + 9π * 5
Here, 9π * 5 involves the irrational number π, so the sum is not rational.
2. 3.45 * 1.2
Both 3.45 and 1.2 are rational numbers, so their product is rational.
3. √16 * √14
Both √16 and √14 are rational numbers since 16 and 14 are perfect squares. Multiplying them results in a rational product.
4. √7 * √2
Here, √7 and √2 are irrational numbers since 7 and 2 are not perfect squares. Thus, the product is not rational.
Based on this analysis, the expressions that result in a rational sum or product are 3.45 * 1.2 and √16 * √14.
is 4 + 9 a rational sum
Yes, 4 + 9 is a rational sum. When you add 4 and 9, you get 13, which is a rational number.
is √16 * √4.a rational sum
Yes, √16 * √4 is a rational product. The square root of 16 is 4 (a rational number), and the square root of 4 is 2 (also a rational number). Therefore, when you multiply 4 and 2, you get 8, which is a rational number.
Question Molli purchased 8 apples for $2.96. While looking at her receipt, Molli divided $2.96 by 8. Why might Molli perform this calculation? (1 point) Responses in order to find the total number of apples purchased in order to find the total number of apples purchased in order to find out how much she paid per apple in order to find out how much she paid per apple in order to calculate the total amount that she owes in order to calculate the total amount that she owes in order to calculate how much money she has left
Molli might perform the calculation of dividing $2.96 by 8 in order to find out how much she paid per apple.
Note: Your teacher will grade your response to ensure that you receive proper credit for your answer. A gym membership costs $25 to join and $14 each month. Write and use an algebraic expression to find the cost of the gym membership for 6 months.
To find the cost of the gym membership for 6 months, we need to consider both the joining fee and the monthly fee.
The cost of joining the gym is $25.
The monthly fee is $14.
The total cost of the gym membership for 6 months can be calculated using the algebraic expression:
Total cost = (joining fee) + (monthly fee * number of months)
Plugging in the values:
Total cost = $25 + ($14 * 6)
Simplifying the expression:
Total cost = $25 + $84
Total cost = $109
Therefore, the cost of the gym membership for 6 months would be $109.
What is the sum? 7/3 + (-3/8)
(1 point)
Responses 65/24 47/24 -4/5 -5/4
To find the sum of 7/3 and -3/8, we need to find a common denominator.
The common denominator of 3 and 8 is 24.
Converting both fractions to have a denominator of 24:
7/3 = (7/3) * (8/8) = 56/24
-3/8 = (-3/8) * (3/3) = -9/24
Now, we can add the two fractions:
56/24 + (-9/24) = 56/24 - 9/24 = 47/24
Therefore, the sum of 7/3 and -3/8 is 47/24.
Which property is illustrated by the following statement? 2x(6) = (6)2x (1 point) Responses Associative Property of Addition Commutative Property of Multiplication Inverse Property of Multiplication Commutative Property of Addition
The property illustrated by the statement 2x(6) = (6)2x is the Commutative Property of Multiplication. This property states that changing the order of the factors in a multiplication operation does not change the result.
Order the following numbers from least to greatest. sqrt11, –0.4, (-4/3), 0.8, sqrt2 (1 point) Responses first answer = 0.8, sqrt2, (-4/3), sqrt11, –0.4 second answer = sqrt11, sqrt2, 0.8, (-4/3), –0.4 third answer = (-4/3), –0.4, 0.8, sqrt2, sqrt11, fourth answer = –0.4, 0.8, sqrt2, sqrt11, (-4/3)
To order the numbers from least to greatest, let's compare each pair of numbers:
-0.4 < (-4/3) < 0.8 < sqrt2 < sqrt11
Therefore, the correct answer is:
-0.4, (-4/3), 0.8, sqrt2, sqrt11