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.
Ok. So first, we calculate the slope!
m=(y2-y1)÷(x2-x1)= (5-2)÷(3-1)=3/2.
Now that we have the slope, we can start to write an equation for the line by plugging in the given points. b is the y-intercept.
y=mx+b.
2=(3/2)1+b
b=2-(3/2)=2-1.5=.5 or 1/2
so the y-int is (0,.5 or 1/2) .
Next, we have to find the x-int.
to do that, we just plug in 0 for the y.
0=1.5x+.5
x=-.5/1.5= (1/3)
so the x-intercept is
(1/3 or .33,0).
Answer:
If Jack adopted half of the spaniel puppies, and there are 4 spaniel puppies, that means that he adopted 2 puppies.
If Carmen adopted half of the beagle puppies, and there are 6 beagle puppies, then Carmen adopted 3 puppies. This means that Carmen adopted more puppies than Jack.
Step-by-step explanation:
1/2 of 4 = 2
1/2 of 6 = 3
Answer:
no, it is not a proportional relationship.
Step-by-step explanation:
if you divide 315 by 175 you get 1.8
if you multiply 315 by 1.8, you don’t get 420. therefore this is not a proportionally relationship.
hope this helps!
59/100 would be your answer. Hope this helps!