Answer:
-13a^2 + 170ab - 13b^2.
Step-by-step explanation:
1. 36(a+b)^2 - 49(a-b)^2
This is the difference of 2 squares: a^2 - b^2 = (a + b)(a - b).
36(a+b)^2 - 49(a-b)^2
= (6(a + b) + 7(a - b))( 6(a + b) - 7(a - b))
= (6a + 7a + 6b - 7b)( 6a - 7a + 6b + 7b)
= (13a - b)(-a + 13b)
If you require the expansion of this it is:
-13a^2 + 170ab - 13b^2.
<span>Mr. Wiley earned a commission of $9,200 on a house that sold for $184,000.
</span><span>At this rate, Mr. Wiley's commission be on a house that sells for $250,000 = ?
commission = price of house sold
$9,200 = $184,000
multiply both sides with $250,000
$9,200 x </span>$250,000 = $184,000 x $250,000
when the price is $250,000, the commission will be;
($9,200 x $250,000) / $184,000 = $250,000
$2300000/$184 = $250,000
$12,500 = $250,000
Thus, the commission is $12,500.
B. Add -12x to both sides. Then divide all terms by -2. The positive 12 on the right side will be a -6 and the -42 will be a positive 21. The inequality sign is always switched whenever the equation is divided by a negative number.
Answer:
Length = 6
Width = 3/2
Step-by-step explanation:
You can choose to go about this question in lots of different ways, but this is how i did it. I drew a diagram of the rectangle and labeled it: the height/length as x and the width as x/4 (they told us the width is a quarter of the length). They also told us that the area is 9 square units.
We know that length x width = area
So: length x width = 9
I'm gonna bring in the variables i used in the diagram, so:
x = 9
Keep solving:
= 9
Times both sides by 4:
= 36
Square root both sides for x:
<em>* remember that when you square root, its possible to have a positive or negative version of the value</em>
x = ±6
Since its impossible to have a negative length, we can say that x = 6.
X was just the variable we gave to the length of the rectangle, so now we know the length is 6. If you needed to find width as well, you can do 6/4, which simplifies to 3/2.
To double-check
- 6 x 3/2 should equal 9, since length x width = area
which it is, so we're correct!
Hope that helped : )