The equation that shows the profit earned for selling popcorn for x hours is y = $15m - $20
From the equation of the linear function given y = mx + b
y indicates the profit earned and x represents the time in hours.
From the question,
After 3 hours, the popcorn stand earned a profit of $25.
∴ The equation becomes $25 = 3m + b ------ (1)
and after 6 hours, the profit was $70.
∴ The equation becomes $70 = 6m + b ------- (2)
Now, we will solve the two equations simultaneously
From the first equation
$25 = 3m + b
We can write that
b = $25 - 3m ------- (3)
Substitute this into the second equation
$70 = 6m + b
We get
$70 = 6m + ($25 - 3m)
$70 = 6m + $25 - 3m
$70 - $25 = 6m - 3m
$45 = 3m
∴ m = $45 ÷ 3
m = $15
Now, substitute the value of m into equation (3)
b = $25 - 3m
b = $25 - 3($15)
b = $25 - $45
b = -$20
∴ m = $15 and b = -$20
Putting these values into the equation y = mx + b we get
y = $15m +(- $20)
∴ y = $15m - $20
Hence, the equation that shows the profit earned for selling popcorn for x hours is y = $15m - $20
Learn more here: brainly.com/question/19511111
If

is the variable of the horizontal axis, then you can solve for

to get the equation of the line in slope-intercept form in the

plane:

i.e. a line with slope

through the origin, which means it is contained in the first and third quadrants. Since the terminal side of

has a negative sine, the angle must lie in the third quadrant.
Because the slope of the line is

, you can choose any length along the line to make up the hypotenuse of a right triangle with reference angle

. Any such right triangle will have

, regardless of whether the angle is the first or third quadrant. But since

is known to lie in the third quadrant, and so

and

are both negative, you have
Answer:
The image of the point (1, -2) under a dilation of 3 is (3, -6).
Step-by-step explanation:
Correct statement is:
<em>What are the coordinates of the image of the point (1, -2) under a dilation of 3 with the origin.</em>
From Linear Algebra we get that dilation of a point with respect to another point is represented by:
(Eq. 1)
Where:
- Reference point with respect to origin, dimensionless.
- Original point with respect to origin, dimensionless.
- Dilation factor, dimensionless.
If we know that
,
and
, then the coordinates of the image of the original point is:
![\vec P' = (0,0) +3\cdot [(1,-2)-(0,0)]](https://tex.z-dn.net/?f=%5Cvec%20P%27%20%3D%20%280%2C0%29%20%2B3%5Ccdot%20%5B%281%2C-2%29-%280%2C0%29%5D)


The image of the point (1, -2) under a dilation of 3 is (3, -6).
Answer:
12,6,0
Step-by-step explanation:
18-6=12, so on so forth.
Answer:
14 ft³
Step-by-step explanation:
First, find the volume of a single cube: V = s³, where s = side length
V = s³; s = 1/5
V = (1/5)³
V = 0.008 ft³
**Note: (1/5)³ is equal to 1/125 as a fraction. I put it down in decimal form because it's easier for me to work with decimals.**
Now, to find the volume of the prism (which is <u><em>completely</em></u> filled with cubes), multiply the volume of one cube by the total number of cubes: 1750.
(1750)(0.008)
14 ft³
The volume of the prism is 14 ft³.
Hope this helps!