Answer:
294
Step-by-step explanation:
The distributive property for multiplication is as follows :
a(b+c) = ab + ac
We need to evaluate 6 times 49 i.e. 6(49).
We can write 49 as (50-1)
6(50-1) = 6(50+(-1))
Here, a = 6, b = 50 and c = -1
So,
6(50+(-1)) = 6(50) + 6(-1)
= 300-6
= 294
So, answer is 294. Option (A) is somehow correct.
Answer:
c=775
Step-by-step explanation:
Answer: the Russell family used their sprinkler for 40 hours.
the Gonzalez family used their sprinkler for 20 hours.
Step-by-step explanation:
Let x represent the number of hours for which the Russell family used their sprinkler.
Let y represent the number of hours for which the Gonzalez family used their sprinkler.
The families used their sprinklers for a combined total of 60 hours. It means that
x + y = 60
The water output rate for the Russell family's sprinkler was 35L per hour. The water output rate for the Gonzalez family's sprinkler was 40L per hour. The total water output of both families was 2200L. It means that
35x + 40y = 2200- - - - - - - - - - --1
Substituting x = 60 - y into equation 1, it becomes.
35(60 - y) + 40y = 2200
2100 - 35y + 40y = 2200
- 35y + 40y = 2200 - 2100
5y = 100
y = 100/5
y = 20
x = 60 - y = 60 - 20
x = 40
<h3>
Answer: $2400</h3>
========================================================
Explanation:
x = Mason's salary in dollars for that month
x/6 = one-sixth of his salary
x/6+800 = total amount spent (the x/6 dollars and $800 combined)
In total, he spent half his salary. This means he spent x/2 dollars for the month overall.
Set the two items equal to one another. Solve for x.
x/6 + 800 = x/2
6(x/6 + 800) = 6*(x/2) ... see note at the bottom of the page
x+4800 = 3x
4800 = 3x-x
4800 = 2x
2x = 4800
x = 4800/2
x = 2400
His monthly salary is $2400
1/6 of this is (1/6)*2400 = 2400/6 = 400 dollars. Add on the $800 he also spent to get a total of 400+800 = 1200 dollars spent, which is exactly one half of the $2400. The answer is confirmed.
-------
Note: I multiplied both sides by 6 to clear out the fractions. The value 6 is the LCD in this case.
Answer:
<em>Option D: 159 3/8 cm^3 </em>
Step-by-step explanation:
1. Let us rewrite the dimensions, and the options to make this a little more clear ~ (dimensions) 5 cm, 8 1/2 cm, 3 3/4 cm ⇒ (options) 17 1/4 cm^3, 18 3/4 cm^3, 27 1/4 cm^3, and 159 3/8 cm^3
2. To find the volume of most 3-dimensional figures, you would have to multiply the Base * height, so for a rectagular prism ⇒ <em>Base * height = length * width * height</em>
3. Substitute and compute the volume through algebra:
5 cm * 8 1/2 cm * 3 3/4 cm =
5 cm * 17/2 cm * 15/4 cm =
85/2 cm^2 * 15/4 cm =
1275/8 cm^3 =
<em>159 3/8 cm^3</em>
4. This means that the<em> Volume of the Rectangular Prism = 159 3/8 cm^3 (Option D)</em>
