Part A

PLZ HELP/...... :) :?

alexdok [17]

Answer:

3 gallons of diesel weight = 22.2 pounds

The constant of variation = 7.4

The quantities vary directly

Step-by-step explanation:

Given:

5 gallons of gas weights = 37 pounds

To find

a) the weight of 3 gallons of gas.

b) if the quantities vary directly or inversely.

c) the constant of variation.

Solution:

Applying unitary method to find weight of 3 gallons of gas.

If 5 gallons weight = 37 pounds

Then, 1 gallon will weight = $\frac{37}{5}$ =7.4 pounds

Thus, 3 gallons will weight = $3\times 7.4$ = 22.2 pounds

Listing out the data we have:

1 gallon = 7.4 pounds

3 gallons = 22.2 pounds

5 gallons = 37 pounds

From the data, we find out that as the number of gallons of gas increases the weight of gas also increases. This shows that these quantities are directly proportional to each other.

The unit rate of the quantities is called the constant of variation.

Unit rate: 7.4 pounds per gallon

Thus, the constant of variation = 7.4

8 0

3 years ago

2 1 point The point, (-3, 7), is on the line y = -3x+7. True O False

sladkih [1.3K]

Step-by-step explanation:

in order to know if the the point is on the line plug in the x coordinate to check if it gives you the y coordinate as an output.
If you plug in the x coordinate and it gives you the given y coordinate then the point is on the given line
Now let us plug in the value of x=-3
$y = - 3( - 3) + 7 \\ y = - 9 + 7 \\ y = - 2$
now if you check plugging in the given x coordinate it does not give you the given y coordinate but -2
therefore the point(-3,7) is not in the line but (-3,-2) is the point in the line.

8 0

1 year ago

A rectangular room has a perimeter of 70 m and is 20m long. write and equation to represent the area

REY [17]

70m+20m+90m could be one

5 0

3 years ago

Read 2 more answers

Please help! Geometry.

FromTheMoon [43]

These are right triangles that will use either sin, cos, or tan, depending upon what you have to work with in regards to the reference angle. The first one has a reference angle of 51 with y being the side opposite it and 12 being the hypotenuse. The sin identity uses the side opposite over the hypotenuse as its formula:
$sin(51)= \frac{y}{12}$
and 12 sin(51) = y and y = 9.325
The second one has the reference angle as the unknown. You could use any of the identities here because you have all the sides of the triangle, but I will use sin again:
$sin \beta = \frac{12}{13}$
and $sin \beta =.9230769$
and $sin ^{-1}(.9230769)=67.38$
The next one has a referece angle of 13 with 24 being the side adjacent to it and the unknown being the side across from it. You will use the tangent identity here:
$tan(13)= \frac{x}{24}$
and 24 tan(13) = x so x = 5.540
The last one has a reference angle of 20 with the hypotenuse as the unknown x, and the side across from it as 10. Use the sin identity again:
$sin(20)= \frac{10}{x}$ and
$x sin(20)=10$ and
$x= \frac{10}{sin(20)}$ with x = 29.238
Everything is in regards to the reference angle; you HAVE to be able to identify the reference angle and then how the given sides are related to it.

7 0

3 years ago

1. This table shows the input and output values for an exponential function f(x).

aleksklad [387]

Answer:

Question 1) Is option C: 2. (Question 2) The correct answer is 1.09 for the K12 program. Question 3) Option A: The value of a motorcycle decreases by 12% each year. (Option C) Every year, the number of online subscribers to a service is 4 times what it was the previous year.

8 0

3 years ago