The altitude of an airplane is decreasing at a rate of 43 feet per second. What is the change in altitude of the airplane over a period of 31 seconds?(2 points)
To find the change in altitude over a period of time, we need to multiply the rate at which the altitude is decreasing by the time period.
The rate at which the altitude is decreasing is 43 feet per second, and the time period is 31 seconds.
Therefore, the change in altitude over a period of 31 seconds is 43 feet/second × 31 seconds = 1333 feet.
So, the change in altitude of the airplane over a period of 31 seconds is 1333 feet.
Use properties of rational numbers to multiply the following.
-8 × (-32)
(2 points)
Responses
To multiply two negative numbers, we multiply the absolute values of the numbers and then assign a negative sign to the product.
So, -8 × -32 = 8 × 32 = 256.
Therefore, the product of -8 and -32 is 256.
2 4/5 x - 4/5
To multiply mixed numbers, we first convert them to improper fractions.
2 4/5 can be written as (2 × 5 + 4)/5 = 14/5.
So, the expression 2 4/5 × -4/5 can be written as 14/5 × -4/5.
To multiply fractions, we multiply the numerators together and the denominators together.
(14/5) × (-4/5) = (14 × -4) / (5 × 5) = -56/25.
Therefore, the product of 2 4/5 and -4/5 is -56/25.
- 7/8 x - 2/5
To multiply fractions, we multiply the numerators together and the denominators together.
For -7/8 x -2/5, we have (-7 x -2) / (8 x 5) = 14/40.
To simplify this fraction, we can reduce it by dividing the numerator and the denominator by their greatest common factor, which is 2.
14/40 = (14 ÷ 2) / (40 ÷ 2) = 7/20.
Therefore, the product of -7/8 and -2/5 is 7/20.
Which expression represents another method of computing the product given below?
(2 points)
Since the given product is -7/8 x -2/5, another method of computing it is by taking the product of the absolute values and then applying the appropriate sign for the product.
So, the expression that represents this method is:
|-7/8| x |-2/5|
This expression will give the same result as the original expression when we take the product of their absolute values and then apply the appropriate sign.
Which expression represents another method of computing the product given below?
6.15 x -3.11
Since the given product is 6.15 x -3.11, another method of computing it is by factoring out any common factors and multiplying the remaining values.
So, the expression that represents this method is:
(3.11 x -2) x (6.15 ÷ 2)
This expression will give the same result as the original expression when we factor out the common factor of 3.11 and multiply the remaining values.
A number is multiplied by 70. The result is zero.
Which of these was multiplied by 70?(2 points)
If the result of multiplying a number by 70 is zero, then the number that was multiplied by 70 must be zero.
Therefore, the number that was multiplied by 70 is zero.
A number is multiplied by 70. The result is zero.
Which of these was multiplied by 70?(2 points)
Responses
a number less than zero
a number less than zero
zero
zero
a number greater than one
a number greater than one
a number between zero and one
The correct option is "zero". The number that was multiplied by 70 to give a result of zero is zero itself.
Use properties of rational numbers to multiply the following.
81 × (-28.54)
(2 points)
a x b
To multiply a whole number by a decimal, we can ignore the decimal point for now and perform the multiplication as we normally would with whole numbers. Then, we will determine the placement of the decimal point in the product.
81 x 28.54 = 2,314.74
However, to properly account for the decimal point, we count the total number of decimal places in the original numbers being multiplied. In this case, 81 is a whole number and -28.54 has two decimal places.
Therefore, the product of 81 and -28.54 is -2,314.74.