Answer:
b
Step-by-step explanation:
Answer:
(3, -3)
Step-by-step explanation:
If a point is dilated about the origin rule to be followed,
(x, y) → (kx, ky)
where k is a scale factor by which the point is being dilated.
If a point R having coordinates (1, -1) is dilated by scale factor of 3, coordinates of the image will be [3×1, 3(-1)]
Therefore, coordinates of the image R' will be (3, -3)
Answer:
labor fee: $15.15, quart of oil: $1.25
Step-by-step explanation:
You solve this by setting up two equations, one for each car.
First we have to define what variables we need and what they mean.
To be solvable, you need as many equations as you have variables.
Let's call the labor fee x and the cost of oil per quart y.
This means we'll be needing two equations to have any chance of solving this. Since we have one equation per car, this looks promising!
Car 1: x + 5y = 21.4
Car 2: x + 7y = 23.9
To solve these, you combine them into one equation by eliminating one variable:
Rewriting the first: x = 21.4 - 5y
So, we can substitute 21.4 - 5y for x in the second. Then we have an equation with only y:
21.4 - 5y + 7y = 23.9
2y = 23.9-21.4 = 2.5
y = 1.25
Plugging this value back into the rewritten first gives us the labour fee:
x = 21.4 - 5*1.25 = 15.15
9514 1404 393
Answer:
x = -6 (correct answer)
mistakes were made in Step 2 and Step 5.
Step-by-step explanation:
The mistake is made in Step 2, application of the distributive property. This is often a source of error. Here, the error is in signs.
Step 1: 12 = -2(x -4) -8
Step 2: 12 = -2x +8 -8 . . . . . . the correct step 2
Step 3: 12 = -2x . . . . . . . . . . . like terms combined
Step 4: -6 = x . . . . . . . . . . . . . divide by -2
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<em>Check</em>
12 = -2(-6 -4) -8 = -2(-10) -8 = 20 -8 = 12 . . . . answer checks OK
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<em>Comment on other mistake</em>
In the original Step 5, -2 was divided on the right and added on the left. This is a violation of the properties of equality, so guarantees a wrong answer. The same operation must be performed on both sides of the equation.
An additional mistake was made in that the answer was not checked.
