Answer:
54
Step-by-step explanation
(area of mat subtracted from area of room)-center of mat to wall
Answer:
g(g(x)=25x
Step-by-step explanation:
g(g(x) is a composition function. Think of g(x) as input. That means whatever g(x) equal that will be inside of the function g(x)
g(x) equal 5x so 5x will be the equal value going into the function g(x)
![g(x) = 5x](https://tex.z-dn.net/?f=g%28x%29%20%3D%205x)
![g(x) = 5(5x)](https://tex.z-dn.net/?f=g%28x%29%20%3D%205%285x%29)
Which equal 25x
<u>Answer:</u>
The value of m is
by using quadratic formula
<u>Solution:</u>
Given, expression is ![m+\frac{2}{3}=\frac{1}{4 m}-1](https://tex.z-dn.net/?f=m%2B%5Cfrac%7B2%7D%7B3%7D%3D%5Cfrac%7B1%7D%7B4%20m%7D-1)
Now, we have to solve the above given expression.
![\text { Now, } \mathrm{m}+\frac{2}{3}=\frac{1}{4 m}-1](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Now%2C%20%7D%20%5Cmathrm%7Bm%7D%2B%5Cfrac%7B2%7D%7B3%7D%3D%5Cfrac%7B1%7D%7B4%20m%7D-1)
By multiplying the equation with m, we get
![\begin{array}{l}{m^{2}+\frac{2}{3} m+m=\frac{1}{4}} \\\\ {m^{2}+m\left(\frac{2}{3}+1\right)=\frac{1}{4}} \\\\ {m^{2}+\frac{5}{3} m=\frac{1}{4}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7Bm%5E%7B2%7D%2B%5Cfrac%7B2%7D%7B3%7D%20m%2Bm%3D%5Cfrac%7B1%7D%7B4%7D%7D%20%5C%5C%5C%5C%20%7Bm%5E%7B2%7D%2Bm%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%2B1%5Cright%29%3D%5Cfrac%7B1%7D%7B4%7D%7D%20%5C%5C%5C%5C%20%7Bm%5E%7B2%7D%2B%5Cfrac%7B5%7D%7B3%7D%20m%3D%5Cfrac%7B1%7D%7B4%7D%7D%5Cend%7Barray%7D)
![\begin{array}{l}{12 m^{2}+20 m=3} \\ {12 m^{2}+20 m-3=0}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B12%20m%5E%7B2%7D%2B20%20m%3D3%7D%20%5C%5C%20%7B12%20m%5E%7B2%7D%2B20%20m-3%3D0%7D%5Cend%7Barray%7D)
Now, let us use quadratic formula
![\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E%7B2%7D-4%20a%20c%7D%7D%7B2%20a%7D)
Here in our problem, a = 12, b = 20, c = -3
![\begin{array}{l}{m=\frac{-20 \pm \sqrt{20^{2}-4 \times 12 \times(-3)}}{2 \times 12}} \\\\ {=\frac{-20 \pm \sqrt{400+144}}{24}} \\\\ {=\frac{-20 \pm \sqrt{544}}{24}} \\\\ {=\frac{-20 \pm 4 \sqrt{34}}{24}=\frac{-5 \pm \sqrt{34}}{6}} \\\\ {=\frac{-5+\sqrt{34}}{6} \text { or } \frac{-5-\sqrt{34}}{6}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7Bm%3D%5Cfrac%7B-20%20%5Cpm%20%5Csqrt%7B20%5E%7B2%7D-4%20%5Ctimes%2012%20%5Ctimes%28-3%29%7D%7D%7B2%20%5Ctimes%2012%7D%7D%20%5C%5C%5C%5C%20%7B%3D%5Cfrac%7B-20%20%5Cpm%20%5Csqrt%7B400%2B144%7D%7D%7B24%7D%7D%20%5C%5C%5C%5C%20%7B%3D%5Cfrac%7B-20%20%5Cpm%20%5Csqrt%7B544%7D%7D%7B24%7D%7D%20%5C%5C%5C%5C%20%7B%3D%5Cfrac%7B-20%20%5Cpm%204%20%5Csqrt%7B34%7D%7D%7B24%7D%3D%5Cfrac%7B-5%20%5Cpm%20%5Csqrt%7B34%7D%7D%7B6%7D%7D%20%5C%5C%5C%5C%20%7B%3D%5Cfrac%7B-5%2B%5Csqrt%7B34%7D%7D%7B6%7D%20%5Ctext%20%7B%20or%20%7D%20%5Cfrac%7B-5-%5Csqrt%7B34%7D%7D%7B6%7D%7D%5Cend%7Barray%7D)
Hence the value of m is
by using quadratic formula
Answer:
10°,170°,10°,170°
Step-by-step explanation:
sum of adjacent angles of parallelogram=180
one angle=10°
adjacent angles=180-10=70°
Let the unknown number be x, then
4(x - 17) = 87