Step-by-step explanation:
(m - 2)x + y = 2
y = -(m - 2)x + 2
8 = -(m - 2)(2) + 2
6 = -(m - 2)(2)
3 = -(m - 2)
-3 = m - 2
-1 = m
mx + 2y = k
2y = -mx + k
$ 25.00-$10.81=14.19.
14.19-0.38=13.81.
13.81-10.00=3.81.
He can buy 10 packages of the peanuts.
Answer:
x = 27/16
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
x + 5/9x = 2(3 - x)
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute 2: x + 5/9x = 6 - 2x
- Combine like terms: 14/9x = 6 - 2x
- Add 2x on both sides: 32/9x = 6
- Divide 32/9 on both sides: x = 27/16
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: 27/16 + 5/9(27/16) = 2(3 - 27/16)
- Multiply: 27/16 + 15/16 = 2(3 - 27/16)
- Subtract: 27/16 + 15/16 = 2(21/16)
- Multiply: 27/16 + 15/16 = 21/8
- Add: 21/8 = 21/8
Here we see that 21/8 does indeed equal 21/8.
∴ x = 27/16 is a solution to the equation.
<span>It looks like you're supposed to pick a combination of two answers:
an absolute-value inequality, and
a sentence describing the meaning of that inequality.
We've got two choices for each, and therefore four possible combinations of choices.
First, let's tackle the sentence description. We're told that
"it [the cost] could differ [from the average of $32] as much as $8."
That sets a maximum value for the difference; it's UP TO $8.
If the cost is less than average, it could be as little as
$32 - $8 = $24
and if the cost is more than average, it could be as much as
$32 + $8 = $40.
So the medication costs range from $24 to $40, and we want an answer that states that.
Now for the inequalities:
|x - 32| describes the SIZE of the difference. Using the absolute-value function means we don't distinguish between
x - 32
and
32 - x
as far as our interests are concerned; we eliminate the sign from the subtraction and just look at the size of the difference.
But in the case we're looking at, we've got a MAXIMUM value for the difference; it can't be more than 8. The inequality
|x - 32| ≥ 8
says the difference is 8 or MORE, so we don't want that. Instead, we want
|x - 32| ≤ 8
which says the difference is anywhere from 0 to 8.
Combining these conclusions, we see we're looking for this answer:
|x - 32| ≤ 8; The medication costs range from $24 to $40
which is the third one listed.</span>
Answer:
It increases
Step-by-step explanation:
(5/x) + 5
As x decreases, 5/x increases. So the expression increases.
