The fourth table is the correct answer
That would be :
4x – 10 = x2 – 5x + 10 ( y = 4x - 10 is substitute for y)
PROOF: y + 5x = x²<span> + 10
</span> (4x - 10) + 5x = x² + 10
4x - 10 = x² -5x + 10
<span>
</span>0 = x2 – 9x + 20<span> (liked terms are grouped and simplified)
PROOF: </span> 4x - 10 = x² -5x + 10
4x = x² -5x + 10 + 10
0 = x² -5x -4x + 20
0 = x² - 9x + 20
Solving:
x² - 9x + 20 = 0
x² - 5x - 4x + 20 = 0
(x - 5) (x - 4) = 0
⇒ x = 4 (as question says) OR x = 5
Answer:
m = 18
Step-by-step explanation:
Step 1: Write out equation
-1/2m = -9
Step 2: Multiply both sides by -2
m = 18
This exponential growth/decay (in this case decay because r<1) of the form:
f=ir^t, f=final value, i=initial value, r=common ratio or "rate", t=time.
Since the population decreases by 4.5% each year the common ratio is:
r=(100-4.5)/100=0.955 so we can say
P(t)=8500(0.955^t)
....
7000=8500(0.955^t)
14/17=(955/1000)^t taking the natural log of both sides
ln(14/17)=t ln(955/1000)
t=ln(14/17)/ln(955/1000)
t≈4.22 years (to nearest hundredth of a year)
Since t is the years since 2010, the population will fall to 7000 in the year (2010+4.22=2014.22, more than four years will have elapsed) 2015.
-9×+1=-×+17
-9×=-×+16 (subtract 1 from both sides)
-8×=16 ( add x to both sides)
×=-2 (divide -8 from both sides)
