Answer:
g(g(x)) = 4x + 9
Step-by-step explanation:
To obtain g(g(x)) substitute x = g(x) into g(x) , that is
g(g(x))
= g(2x + 3)
= 2(2x + 3) + 3 ← distribute parenthesis
= 4x + 6 + 3 ← collect like terms
= 4x + 9
Well first you would just have to look at the equation for the volume of a pyramid. This is:
V = (length * width * height) / 3
and so we can just say all pyramids have a volume of V.
So now we want the base to be 3 times bigger which means we would have to multiple the length and width by 3 and the new volume equation would be
V = (3*length * 3 * width * height) / 3
we can factor the two 3's from the parenthesis and get
V = 9(l * w * h) /3
if we are looking at a ratio of how much the volume increases we can say
aV = b(l * w * h) /3
since:
V = (l * w * h) / 3
then:
aV = bV, divide both sides by V and:
a = b
using this we can see that the volume increases by a factor of 9 for 3 times bigger
now for 6 times
V = (6 * l * 6 * w * h) / 3, pull 6 * 6 out
V = 36(l * w * h) /3
and this one increases by factor of 36
if we see a pattern it always increases by the square of the factor of the growoth of the base
so for 9 times bigger it would be 9^2 = 81
and for 27 times bigger it would be 27^2 = 729
Answer:
Option A is the correct answer.
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
From the graph,
y2 = 6
y1 = 2
x2 = 3
x1 = 1
Slope,m = (6 - 2)/(3 - 1) = 4/2 = 2
To determine the intercept, we would substitute x = 3, y = 6 and
m= 2 into y = mx + c. It becomes
6 = 2 × 3 + c = 6 + c
c = 6 - 6 = 0
The equation becomes
y = 2x
Answer:
No it does not form a triangle.
Step-by-step explanation:
If the lengths satisfy the Pythagorean Theorem (a2+b2=c2) then it is a right triangle.