In the last race , the first car in the pit used 1 3/4 tanks of gas, the second car used 2 1/8 and the third car used 1 1/2 tank
1 answer:
Answer: tanks of gas
Step-by-step explanation:
Let the x be the number of tanks of gas, then
The amount of gas used by first car=
The amount of gas used by second car=
The amount of gas used by third car=
Thus, the total change in the amount of gas for all three cars=
Since, the amount of gas tanks of gas is used for all three cars.
Therefore, the total amount would be negative .
hence, the answer is tanks of gas.
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A) Answer: A. 22.5 cm, 30 cm, and 37.5 cm
Setting the unity measurement as x, the three sides will be 3·x, 4·x, and 5·x. The sum of the three sides will be (3 + 4 + 5)·x = 12·x; this corresponds to the perimeter, therefore:
12·x = 90 cm
We can solve for x:
x = 90 / 12 = 7.5 cm
Hence, the sides will be:
7.5 · 3 = 22.5 cm
7.5 · 4 = 30 cm
7.5 · 5 = 37.5 cm
This situation is represented in option A (which is also the only option whose sides add up to 90).
B) Answer: C. never true
We have:
6 + 8x - 9 = 11x + 14 - 3x
Bring all the terms with x on the left, by subtracting from both sides 11x and -3x, and all the numbers on the right by subtrcting from both sides 6 and -9:
6 + 8x - 9 - 11x - (-3x) - 6 - (-9) = 11x + 14 - 3x - 11x - (-3x) - 6 - (-9)
Cancel out the opposite terms from each side:
8x - 11x + 3x = 14 - 6 + 9
Combine likely terms:
0x = 17
Now you should ask yourself: what number multiplied by zero gives 17 as a result? The answer is none because a number multiplied by zero always equals zero.
Hence, the statement is never true.
C) Answer:
We have:
5r + 4 ≤ 5
Subtract 4 from both sides:
5r + 4 - 4 ≤ 5 - 4
Combine likely terms:
5r ≤ 1
Divide both sides by 5:
To graph the set of solutions, you need to set:
y₁ = 5x + 4 and
y₂ = +5
Plot these two lines:
y₂ is a horizontal line at a height of 5;
y₁ is a line passing through (0, 4) and (1, 9)
The set of solutions will be the part of the graph in which y₁ lies underneath y₂ (see picture attached), that happens for .
First, we are going to rewrite it as a parabola equation.
Rewrite.
Divide by 8.
Factor out coefficient.
Then, we are going to convert x into square form.
Convert the whole expression into square form.
Simplify.
Subtract 6 from both sides.
Divide by coefficient.
Rewrite in standard form.
The radius of the circle will be -2. Also, no matter what the sign says, the radius has to always be positive.
Have a nice day! :)
Rewrite.
Divide by 8.
Factor out coefficient.
Then, we are going to convert x into square form.
Convert the whole expression into square form.
Simplify.
Subtract 6 from both sides.
Divide by coefficient.
Rewrite in standard form.
The radius of the circle will be -2. Also, no matter what the sign says, the radius has to always be positive.
Have a nice day! :)