Answer:
![x=-3\:or\:x=\frac{3}{2}](https://tex.z-dn.net/?f=x%3D-3%5C%3Aor%5C%3Ax%3D%5Cfrac%7B3%7D%7B2%7D)
Step-by-step explanation:
The given parabola has equation
![2x^2+5x-9=2x](https://tex.z-dn.net/?f=2x%5E2%2B5x-9%3D2x)
We rewrite in standard form to obtain:
![2x^2+5x-2x-9=0](https://tex.z-dn.net/?f=2x%5E2%2B5x-2x-9%3D0)
![2x^2+3x-9=0](https://tex.z-dn.net/?f=2x%5E2%2B3x-9%3D0)
Split the middle terms to get:
![2x^2+6x-3x-9=0](https://tex.z-dn.net/?f=2x%5E2%2B6x-3x-9%3D0)
Factor by grouping:
![2x(x+3)-3(x+3)=0](https://tex.z-dn.net/?f=2x%28x%2B3%29-3%28x%2B3%29%3D0)
![(x+3)(2x-3)=0](https://tex.z-dn.net/?f=%28x%2B3%29%282x-3%29%3D0)
![x=-3\:or\:x=\frac{3}{2}](https://tex.z-dn.net/?f=x%3D-3%5C%3Aor%5C%3Ax%3D%5Cfrac%7B3%7D%7B2%7D)
X=4 x=-4 Due to the difference in squares theorem
NO. The mirror will not fit in a space that is 15 inches by 16 inches
<em><u>Solution:</u></em>
Given that area of mirror is 225 square inches
![width = 13\frac{3}{4} \text{ inches }](https://tex.z-dn.net/?f=width%20%3D%2013%5Cfrac%7B3%7D%7B4%7D%20%5Ctext%7B%20inches%20%7D)
Converting the above mixed fraction we get,
![width = 13\frac{3}{4} = \frac{13 \times 4 + 3}{4} = \frac{55}{4} \text{ inches }](https://tex.z-dn.net/?f=width%20%3D%2013%5Cfrac%7B3%7D%7B4%7D%20%3D%20%5Cfrac%7B13%20%5Ctimes%204%20%2B%203%7D%7B4%7D%20%3D%20%5Cfrac%7B55%7D%7B4%7D%20%5Ctext%7B%20inches%20%7D)
Let us find the length of mirror
The area of mirror is given as:
area of mirror = length x width
Substituting the given values,
![225 = length \times \frac{55}{4}\\\\length = 225 \times \frac{4}{55}\\\\length = 225 \times 0.0727\\\\length = 16.36](https://tex.z-dn.net/?f=225%20%3D%20length%20%5Ctimes%20%5Cfrac%7B55%7D%7B4%7D%5C%5C%5C%5Clength%20%3D%20225%20%5Ctimes%20%5Cfrac%7B4%7D%7B55%7D%5C%5C%5C%5Clength%20%3D%20225%20%5Ctimes%200.0727%5C%5C%5C%5Clength%20%3D%2016.36)
Thus length of mirror is 16.36 inches
<em><u>Will the mirror fit in a space that is 15 inches by 16 inches?</u></em>
NO. The mirror will not fit in a space that is 15 inches by 16 inches
Because length of mirror is 16.36 inches whereas the given space is 15 inches long
16.36 > 15 so the length of mirror will not fit inside the space
Also width of mirror is
inches which is less than the given space whose width is 16 inches
13.75 < 16 so the width of mirror will not fit inside the space
Answer:
x^2 - y^2) - (x^2 -3x +2)
Step-by-step explanation: