Answer:
<em>In 5 years the product of their ages will be 208</em>
Step-by-step explanation:
The age of two children is 11 and 8 years.
Let's call x the number of years ahead.
We need to find when the product of their future ages is 208. The 11 years old child will be 11+x years old and the other child will be 8+x years, thus:
(11+x)(8+x)=208
Operating:
![88+11x+8x+x^2=208](https://tex.z-dn.net/?f=88%2B11x%2B8x%2Bx%5E2%3D208)
Simplifying:
![x^2+19x-120=0](https://tex.z-dn.net/?f=x%5E2%2B19x-120%3D0)
Factoring:
(x-5)(x+24)=0
Solving:
x=5, x=-24
The negative solution is not valid, thus x=5
In 5 years the product of their ages will be 208
Answer:
30x10 12
Step-by-step explanation:
Answer:
-2x-5y+8z+4.5=0
Step-by-step explanation:
Let (x,y,z) be the coordinates of the point lying on the needed plane. This point is equidistant from the points (-3, 5, -4) and (-5, 0, 4), so
![d_1=\sqrt{(x-(-3))^2+(y-5)^2+(z-(-4))^2}=\sqrt{(x+3)^2+(y-5)^2+(z+4)^2}\\ \\d_2=\sqrt{(x-(-5))^2+(y-0)^2+(z-4)^2}=\sqrt{(x+5)^2+y^2+(z-4)^2}\\ \\d_1=d_2\Rightarrow \sqrt{(x+3)^2+(y-5)^2+(z+4)^2}=\sqrt{(x+5)^2+y^2+(z-4)^2}\\ \\(x+3)^2+(y-5)^2+(z+4)^2=(x+5)^2+y^2+(z-4)^2\\ \\x^2+6x+9+y^2-10y+25+z^2+8z+16=x^2+10x+25+y^2+z^2-8z+16\\ \\-4x-10y+16z+9=0\\ \\-2x-5y+8z+4.5=0](https://tex.z-dn.net/?f=d_1%3D%5Csqrt%7B%28x-%28-3%29%29%5E2%2B%28y-5%29%5E2%2B%28z-%28-4%29%29%5E2%7D%3D%5Csqrt%7B%28x%2B3%29%5E2%2B%28y-5%29%5E2%2B%28z%2B4%29%5E2%7D%5C%5C%20%5C%5Cd_2%3D%5Csqrt%7B%28x-%28-5%29%29%5E2%2B%28y-0%29%5E2%2B%28z-4%29%5E2%7D%3D%5Csqrt%7B%28x%2B5%29%5E2%2By%5E2%2B%28z-4%29%5E2%7D%5C%5C%20%5C%5Cd_1%3Dd_2%5CRightarrow%20%5Csqrt%7B%28x%2B3%29%5E2%2B%28y-5%29%5E2%2B%28z%2B4%29%5E2%7D%3D%5Csqrt%7B%28x%2B5%29%5E2%2By%5E2%2B%28z-4%29%5E2%7D%5C%5C%20%5C%5C%28x%2B3%29%5E2%2B%28y-5%29%5E2%2B%28z%2B4%29%5E2%3D%28x%2B5%29%5E2%2By%5E2%2B%28z-4%29%5E2%5C%5C%20%5C%5Cx%5E2%2B6x%2B9%2By%5E2-10y%2B25%2Bz%5E2%2B8z%2B16%3Dx%5E2%2B10x%2B25%2By%5E2%2Bz%5E2-8z%2B16%5C%5C%20%5C%5C-4x-10y%2B16z%2B9%3D0%5C%5C%20%5C%5C-2x-5y%2B8z%2B4.5%3D0)
GCFvof 18 and 32 is 2.
Happy studying ^-^
21n+14 you have to find the value of n