The only factoring you need to do is already done for you:
<em>x</em>² + <em>x</em> - 12 = (<em>x</em> + 4) (<em>x</em> - 3)
What you're asked to do is decompose
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12)
into partial fractions, i.e. find <em>a</em> and <em>b</em> such that
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12) = <em>a</em> / (<em>x</em> + 4) + <em>b</em> / (<em>x</em> - 3)
Multiply both sides by <em>x</em>² + <em>x</em> - 12 :
3<em>x</em> - 4 = <em>a</em> (<em>x</em> - 3) + <em>b</em> (<em>x</em> + 4)
3<em>x</em> - 4 = (<em>a</em> + <em>b</em>) <em>x</em> + (-3<em>a</em> + 4<em>b</em>)
So we have
<em>a</em> + <em>b</em> = 3
-3<em>a</em> + 4<em>b</em> = -4
and solving this system gives
<em>a</em> = 16/7 and <em>b</em> = 5/7
so you should submit the numbers in bold:
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12) = 16 / (7 (<em>x</em> + 4)) + 5 / (7 (<em>x</em> - 3))
Answer:
x=28
Step-by-step explanation:
x+24+100+x=180
x+124+x=180
2x+124=180
2x=180-124
2x=56
divide both side by number attached to the x
therefore x=28
Okay, so keeping mind that the equation for area is A = L x W, look at the measurements you already have. 5.5 x 10^5 is the length, and 4.2 x 10^4 is the width. Switch them into full form and use a calculator to multiply the two for the area in meters.
550000 x 42000 = 23100000000, which in scientific form is 2.31 × 10^10. So that's answer one.
For the second, in kilometers, just take the full measurement you already have, 23100000000 m, transfer it into kilometers, 23100000 km, and then find its scientific notation, 2.31 × 10^7. That's answer two.
To answer the last question for which is more suitable, just consider what number you'd prefer to look at: a bigger number or a smaller one. Since the kilometer measurement number is smaller, its correct.
Summarily, the answers are 2.31 × 10^10, 2.31 × 10^7, and square kilometers, in that order.
Answer:
Step-by-step explanation:
5x+14<4 or -2(x-8)<-2
-14 -14 -2x+16<-2
5x<-10 -16 -16
÷5 ÷5 -2x<-18
x<-2 ÷-2 ÷-2
x>9 (sign changes because you divide by a negative number)
x<-2 or x>9
Answer:
$13.75
Step-by-step explanation:
the bill before the tip is x.
0.20x = 2.75
now divide both sides by .20
x= 2.75/0.20
x=13.75
