Answer:
Y = 2
X = 3
Step-by-step explanation:
Substitution:
6(4y-5) - y = 16
24y-30-y=16
23y=46
Y = 2
So then:
6x-2 = 16
6x = 18
X = 3
Answer:x=-3
Step-by-step explanation:
2x-1=-7
Add 1 to each side
2x=-6
Divide each side by 2
x=-3
Answer:
Area of the shaded region = (6x + 3)
Step-by-step explanation:
Area of the shaded region = Area of the large rectangle - Area of the small rectangle
Area of the large rectangle = Length × Width
= (x + 2)(x + 2)
= (x + 2)²
= x² + 4x + 4
Area of the small rectangle = (x - 1)(x - 1)
= (x - 1)²
= x² - 2x + 1
Area of the shaded region = (x² + 4x + 4) - (x² - 2x + 1)
= 6x + 3
Area of the shaded region = (6x + 3)
Answer:
f(x) = 12*(2)^x
Step-by-step explanation:
A generic exponential equation is written as:
f(x) = A*(r)^x
And we also know that this equation passes through:
(-1, 6)
(0, 12)
(1, 24)
(2, 48)
For the second point, (0, 12) we know that when f(0) = 12
Then:
f(0) = 12 = A*(r)^0
And for every real number different than zero, a^0 = 1
Then:
f(0) = A*1 = A = 12
Then the equation is:
f(x) = 12*(r)^x
Now we can use one of the other points, like (1, 24)
Then f(1) = 24
We can solve:
f(1) = 24 = 12*(r)^1 = 12*r
24/12 = r
2 = r
Then the equation is f(x) = 12*(2)^x
Now we need to check if this function also passes through the points (-1, 6) and (2, 24):
f(-1) = 12*(2)^-1 = 12/2 = 6
f(2) = 12*(2)^2 = 12*4 = 48
Nice.
So we can see that the function is f(x) = 12*(2)^x