Answer:
-36+7x
Step-by-step explanation:
When we look at this thing for the first time, it looks like it's going to be a dog of a bear to solve, because 'q' is buried inside a squared term and a cubed term.
But this is why it's so important to learn that in math, you DON't immediately ignite your hair and go running around in circles as soon as you see the problem. The first thing you have to do <u>every</u> time is sit still, look at the problem, breathe air, and switch your brain into the 'ON' position.
Look at that big ugly fraction in the equation. Can it be simplified ? You betcha it can ! The quantity (q+r) is a factor of the numerator and denominator, so we can do some canceling.
Divide the top and the bottom of the fraction by (q+r)², and then the problem says . . .
<em>p = (q+r)/12 + 4r</em>
which is MUCH easier to unravel and solve for 'q' . Let's do this !
p = (q+r)/12 + 4r
Subtract (q+r)/12 from each side . . . p - (q+r)/12 = 4r
Subtract 'p' from each side . . . -(q+r)/12 = 4r - p
Multiply each side by -1 . . . (q+r)/12 = p - 4r
Multiply each side by 12 . . . (q+r) = 12p - 48r
Subtract 'r' from each side . . . <em>q = 12p - 49r</em>
Answer:
3. 29
4. 12
Step-by-step explanation:
I may have explained this a few more times than necessary, but agin the Pythagorean theorem. Plug in the numbers and square them. Add them, and then find the square root of that in the eNd.
Answer:
0, 2 . . . . . (any pair of consecutive even integers)
Step-by-step explanation:
You want a pair of consecutive even integers such that twice the lesser is 4 less than two times the greater.
<h3>Setup</h3>
Let x represent the lesser of the two even integers. Then the greater is (x+2) and the given relation is ...
2x = 2(x+2) -4
<h3>Solution</h3>
Simplifying gives ...
2x = 2x +4 -4
2x = 2x . . . . . . . true for any even integer x
Any pair of consecutive even integers will satisfy the relation.
one such pair is 0, 2
<em>check</em>: 2(2) -4 = 2(0)
Answer:
D. (3x - 8) (8x + 5)
Step-by-step explanation:
<em><u>To factor this trinomial, you must split the middle term into two terms, like so:</u></em>
<em><u /></em>
<em><u>Group:</u></em>
<em><u /></em>
<em><u>Take out the GCF (Greatest Common Factor):</u></em>
3x(8x + 5) -8(8x + 5)
(3x - 8) (8x + 5)