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Naily [24]
3 years ago
13

The amount of gasoline remaining in the tank decreases with mileage driven. Identify the independent and dependent quantity in t

he situation.
Mathematics
1 answer:
Alinara [238K]3 years ago
5 0
I think the independent quantity would be the mileage driven and the dependent variable, the <span>amount of gasoline remaining
</span>
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Given the system of linear equations.
Karo-lina-s [1.5K]

Part A:


x + y = 9

4x + y = 6


To solve this system using substitution, begin by isolating either x or y in the first equation. I'll isolate x.


x + y = 9

x = 9 - y


Substitute this expression (9 - y) into the second equation for x and solve.


4x + y = 6

4(9 - y) + y = 6

36 - 4y + y = 6

36 - 3y = 6

-3y = -30

y = 10


To find x, substitute 10 for y into either of the original equations.


x + y = 9

x + 10 = 9

x = -1


Finally, check all work by substituting the x- and y-values into each original equation.


x + y = 9   -->   -1 + 10 = 9   -->   9 = 9   -->   True

4x + y = 6   -->   4(-1) + 10 = 6   -->   -4 + 10 = 6   -->   6 = 6   -->   True


The answer for Part A is x = -1 and y = 10; (-1, 10).


Part B:


For graphing, it's easier to get the equations into slope-intercept form. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. To get our equations into slope-intercept form, we must simply isolate y.


x + y = 9

y = 9 - x

y = -x + 9


4x + y = 6

y = 6 - 4x

y = -4x + 6


Now that we have our slope-intercept equations, we can easily graph them, since their slopes and y-intercepts are readily visible.



Let's start with the y-intercepts. They are (0, 9) and (0, 6). You can plot those points on the graph.


Now, the slopes. The slope of the first line is -1, this means it declines. To plot this, start where you plotted the y-intercept, count one unit down, and then one unit to the right, and plot that point. Continue doing that and connect the dots, and you will have plotted the first line. The slope of the second line is -4, so it also declines. For this line, count four units down, and then one to the right and plot that point. Likewise, continue this and connect the coordinates, and you will have your line. (See attachment for graph.)


The lines do indeed intersect at (-1, 10); our answer is verified by graphing.

5 0
3 years ago
Find the surface area
Nikitich [7]
The answer to the question is that the surface area is 48
3 0
3 years ago
Find the surface area of a square pyramid with a length of 5 cm and a slant height of 8cm.
Tems11 [23]
Area of the square base = 5^2 = 25 cm^2
Area of one of the triangular side = 1/2 * 5 * 8 = 20 cm^2 and there are 4 sides
So the surface area  of while pyramid = 4 * 20 + 25 = 105 cm^2

Volume of the cone = (1/3) pi r^2 h
  = (1/3) pi * 5^2 * 8
  =  209.44  ft^2
8 0
3 years ago
Will mark brainliest please help Debbie notices that the amount owed on her monthly heating bill varies inversely with the avera
Alekssandra [29.7K]

Answer:

The bill is $1837.5

Step-by-step explanation:

Given

B = Bills

T = Temperature

B\ \alpha\ \frac{1}{T} --- The variation

T = 35; when B = 210

Required

Find B when T = 40

B\ \alpha\ \frac{1}{T}

Express as an equation

B = \frac{k}{T}

Make k the subject

k = BT

<em>T = 35; when B = 210</em>

k = 35 * 210

k = 7350

When T = 40, we have:

k = BT

7350 = B * 40

Make B the subject

B = \frac{7350}{4}

B = 1837.5

7 0
3 years ago
Can someone please help me? I don't understand how to solve this.
Scilla [17]

Answer:

  (5, 15)

Step-by-step explanation:

The problem statement tells you how to solve it. You are expected to know what the midpoint formula is.

You are given that (x, y) is the unknown end point. If (Mx, My) is the midpoint, and (x1, y1) is one end point, the midpoint formula tells you ...

  Mx = (x1 +x)/2

  My = (y1 +y)/2

__

Solving these equations for x and y, you get ...

  2Mx = x1 +x

  x = 2Mx -x1

Similarly, ...

  2My = y1 +y

  y = 2My -y1

__

Filling in the given coordinates, this becomes ...

  x = 2(-2) -(-9) = -4 +9 = 5

  y = 2(7) -(-1) = 14 +1 = 15

The other endpoint is (5, 15).

_____

<em>Additional comment</em>

I like to write the midpoint formula for points A and B as ...

  M = (A +B)/2

where A and B each represent an ordered pair (or triple, in 3 dimensions). The arithmetic is done element-by-element on the ordered pairs, so this formula is equivalent to the one above.

If you solve it for B, you get ...

  B = 2M - A . . . . the other endpoint given the midpoint and one endpoint

This might be a formula you want to add to your list of useful formulas in Algebra.

3 0
2 years ago
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