Answer: Graph D
Open holes at 1 and 3; shading in between
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Explanation:
Let p = x-1 and q = x-3
The problem we want to solve is in the form p/q < 0
Since p/q is negative, there are two cases we have to address
- Case 1) p is positive and q is negative, or,
- Case 2) p is negative and q is positive
The signs of p and q are opposite one another. Recall this is due to the fact that dividing a positive over a negative (or vice versa) leads to a negative value.
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Let's go over Case 1
If p is positive, then
p > 0
x-1 > 0
x > 1
If q is negative, then
q < 0
x-3 < 0
x < 3
Combine x > 1 with x < 3 and we get 1 < x < 3. We'll come back to this later.
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Now case 2
If p is negative, then
p < 0
x-1 < 0
x < 1
If q is positive, then,
q > 0
x-3 > 0
x > 3
We get a contradiction.
Both "p is negative" AND "q is positive" must be true at the same time. But if p is negative, then x < 1 which contradicts x > 3 (which happens when q is positive)
Put simply: case 2 is not possible. There's no way to have p be negative at the same time q is positive. This because we're wanting x to both be smaller than 1 AND also be greater than 3 at the same time.
We must rule out case 2 and side with case 1 instead.
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The conclusion of case 1 was that 1 < x < 3
The graph of this has open holes at 1 and 3 on the number line. The shading is between the open holes to represent all values between 1 and 3, excluding the endpoints. Graph D indicates these features, so that's why graph D is the answer.
Note: the open holes indicate that x = 1 and x = 3 are not part of the solution set. Another reason x = 3 is restricted is to avoid a division by zero error.
Answer:
equation has no solutions
Step-by-step explanation:
4p - 6= 3 +4p (subtract 4p from both sides)
-6 = 3
As you can see, -6 is obviously not equal to 3, hence we can conclude that the equation has no solutions.
If Sheila started with 8 yards of fabric and used 2 1/4 yards, she will have the difference of these two values remaining. Subtract 2 1/4 from 8.
Convert the mixed fraction to an improper fraction. (Multiply its denominator by the whole number and replace the numerator with this new number.)
2 1/4 = 9/4
We now have:
8/1 - 9/4
Multiply 8/1 by 4/4 to get common denominators.
8/1 × 4/4 = 32/4
Now subtract.
32/4 - 9/4 = 23/4 = 5.75
Alternatively, we could have converted the fraction 2 1/4 to decimal form and subtracted it from 8.
2 1/4 = 2.25
8 - 2.25 = 5.75
Answer:
Sheila has 5.75 yards of fabric left.
3.4d + 3.4d = 12 + 6.5
6.8d = 18.5
<u><em>d = 2.72</em></u> (this answer is rounded. To get the full answer, divide 18.5 by 6.8)
Any number divided by 1 is still that number (it stays the same).
So you can rewrite 280 as 280/1, which is a fraction.
With 280/1, you can also get an equivalent fraction by multiplying the numerator and denominator by a number, let's say 2.
So multiplying the numerator 280 by 2 would get 560, the denominator would be 2. So another equivalent fraction would be 560/2