Answer:
x=2
Step-by-step explanation:
use distributive property: x^2+2x-1=4
remove the -1 by adding 1 on both sides: x^2+2x=5
use the guadratic fromula: ax²+bx+c=0
plug in the equation x^2+2x-5=0
a,b and c are the coefficients to plug into the formula
a=1, b=2, c=-1
Finally, you will find that x=2
The distance in kilometers in scientific notation 
<h3>Scale factors</h3>
Scale factors are values or constants multiplied with a variable
If Alvin and Simon raced a distance of 
kilometers and they need to race 7 times that distance in a kilometer, the distance traveled will be:
- Distance travelled =
- Distance travelled =
Hence the distance in kilometers in scientific notation
Learn more on distance here: brainly.com/question/23848540
Answers:
- <u>24000 dollars</u> invested at 4%
- <u>18000 dollars</u> was invested at 7%
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Work Shown:
x = amount invested at 4%
If she invests x dollars at 4%, then the rest (42000-x) must be invested at the other rate of 7%
She earns 0.04x dollars from that first account and 0.07(42000-x) dollars from the second account
This means we have
0.04x+0.07(42000-x)
0.04x+0.07*42000-0.07x
0.04x+2940-0.07x
-0.03x+2940
This represents the total amount of money earned after 1 year.
We're told the amount earned in interest is $2220, so we can say,
-0.03x+2940 = 2220
-0.03x = 2220-2940
-0.03x = -720
x = -720/(-0.03)
x = 24000 dollars is the amount invested at 4%
42000-x = 42000-24000 = 18000 dollars was invested at 7%
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As a check, we can see that
18000+24000 = 42000
and also
0.04x = 0.04*24000 = 960 earned from the first account
0.07*18000 = 1260 earned from the second account
1260+960 = 2220 is the total interest earned from both accounts combined
This confirms our answers.
Let u = x.lnx, , w= x and t = lnx; w' =1 ; t' = 1/x
f(x) = e^(x.lnx) ; f(u) = e^(u); f'(u) = u'.e^(u)
let' find the derivative u' of u
u = w.t
u'= w't + t'w; u' = lnx + x/x = lnx+1
u' = x+1 and f'(u) = ln(x+1).e^(xlnx)
finally the derivative of f(x) =ln(x+1).e^(x.lnx) + 2x
There are two triangles: a small one to the left and a big one, which includes the small one. They both have a common angle (the leftmost angle) and since (we can assume) the two columns meet the floor at right angles, they both have two equal angles. This means they are similar (AAA).
Let the distance of the base of the stairs to the tallest column be d.
Because matching sides of similar triangles are in the same ratio,
4 / 6 = d / (6 + 12)
4 / 6 = d / 18
(4 * 18) / 6 = d
d = 12
The answer is C
