Answer:
3 inches
Step-by-step explanation:
If we're gonna have some sort of increase each year, it's gonna pop up in our model attached to a variable, because it represents some kind of <em>change</em>, and <em>variables can change</em>. Looking at our equation, the 28.6 represents our starting point: the boy is 28.6 inches tall when he's 2 years old. The 3a term, then, represents the boy's increasing height each year. When he's 3 years old, a = 1, and so h = 3 + 28.6 = 31.6 inches. When he's 4, a = 2, and h = 3 + 31.6 = 34.6. The increase is always <em>3 inches</em>.
X + y is the number of students who were surveyed.
x is the number who own a bike.
y is the number who don't.
the ratio of the ones who own a bike and the ones who were surveyed is x / (x + y)
that ratio is 7/8.
you get x / (x + y) = 7/8
multiply both sides of this equation by (x + y) to get x = (x + y) * 7/8
simplify to get x = 7/8 * x + 7/8 * y
subtract 7/8 * x from both sides of this equation to get:
1/8 * x = 7/8 * y
solve for x to get x = 7 * y
this means that the number of students who own a bike is 7 times the number of students who don't.
divide both sides of that equation by y to get x/y = 7/1.
that means that the ratio of students who own a bike to the number of students who don't is equal to 7/1.
the problem states that the difference between the number who own a bike and the number who don't is 72.
this means that x - y = 72
from the equation of x = 7 * y, replace x with 7 * y in the equation of x - y = 72 to get:
7 * y - y = 72
simplify to get 6 * y = 72
divide both sides of that equation by 6 to get y = 72/6 = 12
this means that the number of students who do not own a bike is 12.
since x = 7 * y, then x = 7 * 12 = 84.
this means that the number of students who own a bike is 84.
since the number of students is x + y, this means that the number of students who were surveyed is 84 + 12 = 96.
let's see if this is right.
96 students were surveyed.
84 own a bike and 12 don't.
the difference between the ones who own a bike and the ones who don't is 84 - 12 = 72.
the ratio of the ones who own a bike and the number surveyed is 84/96 = 7/8.
solution is 96 students were surveyed.
Notice that 8 can be written in exponential form of 
When you see 
, recognize that 
3 × 
= 8
Hence, the answer is 
. Which means 256.
Here is some indices rules/formulas you might find helpful as well:
3.
4^3 is equal to 64. Therefor log4(64) must be equal to 3.
Y/2=1-x
y=2-2x
y(-2)=2-2(-2)=2+4=6, (-2,6)
So (-2, 6) is an ordered pair from x+y/2=1
