Answer: x = 63
Step-by-step explanation:
15/3 = 5
3 * 21 = 63
63/15 = 21/5
Answer:
3 and 9
if f(x)=x^2+13 and g(x)=12x-14
Step-by-step explanation:
So when we are looking for the intersection of two functions, we are trying to figure out when they are the same. When you think same, you should think equal (=).
So we want to find when f(x)=g(x) for x.
f(x)=g(x)
![x^2+13=12x-14](https://tex.z-dn.net/?f=x%5E2%2B13%3D12x-14)
Let's get everything to one side.
Subtracting 12x and adding 14 to both sides.
![x^2+13+14-12x=0](https://tex.z-dn.net/?f=x%5E2%2B13%2B14-12x%3D0)
I'm going to reorder the left hand side and also simplify the 13+14 part:
![x^2-12x+27=0](https://tex.z-dn.net/?f=x%5E2-12x%2B27%3D0)
Now since the coefficent of x^2 is just 1 our job is to find two numbers that multiply to be 27 and add up to be -12.
Those numbers are -3 and -9 since -3(-9)=27 and -3+(-9)=-12.
So the factored form of our equation is
![(x-3)(x-9)=0](https://tex.z-dn.net/?f=%28x-3%29%28x-9%29%3D0)
Since the product is 0, then at least one of the factors must be 0.
So we want to solve both x-3=0 and x-9=0.
x-3=0 can be solved by adding 3 on both sides. This gives us x=3.
x-9=9 can be solved by adding 9 on both sides. This gives us x=9.
The intersection of f and g happens at x=3 or x=9.
Answer:
1) X = -7
2) y = - 5
Step-by-step explanation:
1)
![- 3x - 5 = 16 \\ - 3x = 16 + 5 \\ - 3x = 21 \\ \frac{ - 3x}{ - 3} = \frac{21}{ - 3} \\ x = \frac{21}{ - 3} \\ x = - 7](https://tex.z-dn.net/?f=%20-%203x%20-%205%20%3D%2016%20%5C%5C%20%20-%203x%20%3D%2016%20%2B%205%20%5C%5C%20%20-%203x%20%3D%2021%20%5C%5C%20%20%5Cfrac%7B%20-%203x%7D%7B%20-%203%7D%20%20%3D%20%20%5Cfrac%7B21%7D%7B%20-%203%7D%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B21%7D%7B%20-%203%7D%20%20%5C%5C%20x%20%3D%20%20-%207)
2)
![- 4(y - 2) = 12 \\ - 4y - 8 = 12 \\ - 4y = 12 + 8 \\ - 4y = 20 \\ \frac{ - 4y}{ - 4} = \frac{20}{ - 4} \\ y = \frac{20}{ - 4} \\ y = - 5](https://tex.z-dn.net/?f=%20-%204%28y%20-%202%29%20%3D%2012%20%5C%5C%20%20-%204y%20-%208%20%3D%2012%20%5C%5C%20%20-%204y%20%3D%2012%20%2B%208%20%5C%5C%20%20-%204y%20%3D%2020%20%5C%5C%20%20%5Cfrac%7B%20-%204y%7D%7B%20-%204%7D%20%20%3D%20%20%5Cfrac%7B20%7D%7B%20-%204%7D%20%20%5C%5C%20%20y%20%3D%20%20%5Cfrac%7B20%7D%7B%20-%204%7D%20%20%5C%5C%20y%20%3D%20%20-%205)