As per the direct variation formula, it take 11 hours : 6 minutes : 36 seconds to earn $25,000 for the restaurant.
Direct variation:
Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.
Direct variation equation: y = kx
Given,
A local fast food restaurant takes in $9000 in a 4 hours period. Write a direct variation equation for the relationship income and number of hours.
Here we need to estimate how many hours it would take the restaurant to earn $25,000.
a) Let us consider income (I) directly varies to number of hours (h) where k is the constant of variation.
I = kh ⇒ Direct variation equation
Solve for k:
9,000 = (k)(4)
k = 9,000/4
k = 2,250
b) When income (I) = 25,000, find the number of hours:
I = kh
25,000 = (2,250) (h)
h = 25,000/2,250
h = 11.11
It will take approximately 11 hours : 6 minutes : 36 seconds for the restaurant to earn $25,000.
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Answer: The second option.
Step-by-step explanation:
1. Calculate the first volume assuming that the figure is completed (with no missing part). Therefore, you must apply the formula for calculate the volume of a square prism:

Where s is the side of the base and h is the height.
2. Then:

4. The volume of the missing part is calculated with the formula of a rectangular prism:

Where l is the lenght, w is the width and h is the height. Then:

5. Therefore, you must subtract both volumes to obtained the volume of the figure:

The polynomial remainder theorem states that the remainder upon dividing a polynomial

by

is the same as the value of

, so to find

you need to find the remainder upon dividing

You have
..... | 2 ... 14 ... -58
-10 | ... -20 ... 60
--------------------------
..... | 2 ... -6 .... 2
So the quotient and remainder upon dividing is

with a remainder of 2, which means

.
Answer:
The table in the exercise can be completed with the next results:
- x y
-
2 <u>9</u>
-
4 <u>11</u>
-
6 <u>13</u>
-
8 <u>15</u>
Step-by-step explanation:
As in the exercise Janice is 7 years older than Tam, to obtain the result in the table, you must add 7 to each age in the column x, with this we can make the next formula:
Remember that x is Tam's age, and y is Janice's age, so, you must replace the x variable in each case to obtain the result to y:
When x is 2:
When x is 4:
When x is 6:
When x is 8:
At last, <u>to obtain the graph you can use the formula made: y = x + 7</u>, and you'll obtain a graph like the attached picture, <em>where each time x obtain a unit, the y variable obtain a unit too maintaining the diference of 7</em>.