Answer:
x = 22.5 cm
Step-by-step explanation:
In similar triangles, corresponding sides are in same ratio
![\frac{FG}{AB}=\frac{FH}{AC} = \frac{GH}{BC}\\\\\\ \frac{GH}{BC}=\frac{FG}{AB}\\\\\frac{x}{15}=\frac{13.5}{9}\\](https://tex.z-dn.net/?f=%5Cfrac%7BFG%7D%7BAB%7D%3D%5Cfrac%7BFH%7D%7BAC%7D%20%3D%20%5Cfrac%7BGH%7D%7BBC%7D%5C%5C%5C%5C%5C%5C%20%5Cfrac%7BGH%7D%7BBC%7D%3D%5Cfrac%7BFG%7D%7BAB%7D%5C%5C%5C%5C%5Cfrac%7Bx%7D%7B15%7D%3D%5Cfrac%7B13.5%7D%7B9%7D%5C%5C)
![x = \frac{13.5}{9}*15\\\\x = 1.5*15\\\\x = 22.5](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B13.5%7D%7B9%7D%2A15%5C%5C%5C%5Cx%20%3D%201.5%2A15%5C%5C%5C%5Cx%20%3D%2022.5)
<h2>
Answer:</h2><h2>
Misty needs 27.13 ounces of 72% acid and 57.87% of 25% acid solution.</h2>
Step-by-step explanation:
85 ounces of 40% acid solution = 85 (0.4) = 34
Also, x + y = 85 ... (1)
0.72x + 0.25y = 34
72x + 25y = 3400 ...(2)
multiply eq (1) by 25, we get 25x + 25y = 2125 ... (3)
subtracting eq(2) and (3), we get 47x = 1275
x = 27.13 substitute in eq(1), we get
y = 57.87
Misty needs 27.13 ounces of 72% acid and 57.87% of 25% acid solution.
Answer:
a=2, b=0
Step-by-step explanation:
Given:
f(x) = x^3 + x^2 - ax +b is divisible by (x^2 -x)
Need to find:
Values of a and b.
Solution:
Factor
(x^2-x) = (x)(x-1)
if x^3 + x^2 - ax +b is divisible by (x)(x-1), then
both x and (x-1) are roots to f(x), therefore
x=0 or x=1 are roots to f(x).
Using the factor theorem,
f(x=0) = 0 => 0+0-0+b = 0 => b=0
f(x=1)=0 => 1+1-a+b=0 => 1+1-a+0 = 0 => a=2
That is a=2, b=0
Now factor f(x) with a=2, b=0
f(x) = x^3 + x^2 - ax +b
= x^3 + x^2 - 2x
= x (x^2 + x - 2)
= x (x+2) (x-1)
Thus both x and (x-1) are factors... checks.
<h3>x is 2 and y is -2</h3>
<em><u>Solution:</u></em>
Given that,
3x-2 equal x-y equals 4
Which means,
3x - 2 = x - y = 4
Therefore,
x - y = 4
Also,
3x - 2 = 4
Simplify above expression
3x - 2 = 4
3x = 4 + 2
3x = 6
Divide both sides by 3
x = 2
Substitute x = 2 in x - y = 4
2 - y = 4
y = 2 - 4
y = -2
Thus x is 2 and y is -2
Answer:
ln[xy/sqrt(z+4)]
Step-by-step explanation:
lnx+ln(y^4)-ln((z+4)^1/2)
The logarithms property states that logxy can be written as log(x)+log(y)
ln(xy)-ln(z+4)^1/2
The logarithms property also states that logx/y can be written as log(x)-log(y)
ln(xy)/ln(z+4)^1/2
ln(xy/(z+4))^1/2
ln[xy/sqrt(z+4)]
Hence by using the logarithms properties In x + 4 In y - 1/2 In (z + 4) can be written as ln[xy/sqrt(z+4)]