You are planning a field trip for the school to go from Indianapolis to Orlando, Florida. A round trip is 2000 miles. The school bus will average 8 miles per gallon.
How many gallons will the school bus need to make this round trip? If the cost is $3.50 per gallon of gas then what is the total fuel cost?
Write out and then solve. Show all of your steps.
To find the number of gallons needed for the round trip, we divide the total distance by the average mileage per gallon.
Gallons = Distance / Average mileage per gallon
Gallons = 2000 / 8
Gallons = 250
Therefore, the school bus will need 250 gallons of gas for the round trip.
To find the total fuel cost, we multiply the number of gallons by the cost per gallon.
Total fuel cost = Gallons * Cost per gallon
Total fuel cost = 250 * $3.50
Total fuel cost = $875
The total fuel cost for the round trip is $875.
Create a table that has 5 points that meets both of the following conditions:
the y-intercept is 5
the slope is 3
Explain how you know that the y-intercept is 5.
Explain how you know that the slope is 3.
Math
To create a table with 5 points that meet the given conditions, we can use the formula for a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Given that the y-intercept is 5, we can write our linear equation as y = 3x + 5.
To find the points, we can choose different values for x and calculate the corresponding y-values using the equation.
Let's choose x-values of -2, -1, 0, 1, and 2:
For x = -2:
y = 3(-2) + 5
y = -6 + 5
y = -1
Therefore, the point is (-2, -1).
For x = -1:
y = 3(-1) + 5
y = -3 + 5
y = 2
Therefore, the point is (-1, 2).
For x = 0:
y = 3(0) + 5
y = 0 + 5
y = 5
Therefore, the point is (0, 5).
For x = 1:
y = 3(1) + 5
y = 3 + 5
y = 8
Therefore, the point is (1, 8).
For x = 2:
y = 3(2) + 5
y = 6 + 5
y = 11
Therefore, the point is (2, 11).
Hence, the table of 5 points that meet the given conditions is:
| x | y |
| -2 | -1 |
| -1 | 2 |
| 0 | 5 |
| 1 | 8 |
| 2 | 11 |
Fill in the blanks so that the following system of linear equations has infinite solutions.
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=
0
�
+
4
y=0x+4
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=
y=
�
+
x+
To make the system of linear equations have infinite solutions, we need to make sure the equations are equivalent.
The first equation is already in the form y = 0x + 4, which means it is already equivalent to y = 4.
To make the second equation equivalent, we need to choose the numbers that will make it the same as the first equation. Since the first equation is y = 4, we can choose any number for x and set y equal to 4.
For example, we can choose x = 0. This would make the second equation y = 0 + 0 + 4, which simplifies to y = 4.
Therefore, the second equation is already equivalent to y = 4.
The system of linear equations with infinite solutions is:
y = 4
y = 4
Write an equation from slope-intercept form (
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=
�
�
+
�
y=mx+b ) from the table below.
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x
�
y
0
0
5
5
7
7
−
2
−2
14
14
−
9
−9
21
21
−
16
−16
�
=
y =
�
+
x +
To write an equation from slope-intercept form (y = mx + b) using the given table, we need to find the values of the slope (m) and the y-intercept (b).
From the table, we can observe that the slope remains constant at 2 since the change in y for every change in x is always 2.
Next, we need to determine the y-intercept (b). To do this, we can select any of the points from the table. Let's choose the point (0, 5).
Plugging in the values of the slope (m = 2) and the chosen point (x = 0, y = 5) into the slope-intercept form (y = mx + b), we can solve for b:
5 = 2(0) + b
5 = 0 + b
b = 5
Now that we have determined the values of m and b, we can write the equation from slope-intercept form:
y = 2x + 5
Solve the following inequality.
−
5
7
�
≤
5
7
−5
y ≤5
�
y
The given inequality is:
-5/7 ≤ y ≤ 5/7
This means that y is greater than or equal to -5/7 and less than or equal to 5/7.
So, the solution to the inequality is:
y ∈ [-5/7, 5/7]
This represents all the values of y that satisfy the given inequality.
Find the slope between the points
(
8
,
−
1
)
(8, −1) and
(
−
2
,
8
)
(−2, 8) .
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=
m=