Will get brainiest and points

1. write an equation that relates the number of triangles in the figure (n), to the perimeter of the figure (p)

a. the equation for the perimeter is p = 5n + 7
b. the equation for the perimeter is p = 5n + 14
c. the equation for the perimeter is p = 7n + 10
d. the equation for the perimeter is p = 7n + 5

2. the table shows the relationship between the number of sports teams a person belongs to and the amount of free time the person has each week.

number of sports teams | free time (hours)
0 46
1 39
2 32
3 25

is the relationship a function that is increasing or decreasing? is the relationship a function that is linear or non-linear?

a. increasing; linear
b. increasing; non-linear
c. decreasing; linear
d. decreasing; non-linear

3. the ordered pairs ( 1, 3 ), ( 2, 9 ), ( 3, 27 ), ( 4, 81 ), and ( 5, 243 ) represent a function. what is a rule that represents this function?

a. y = x^3
b. y = 3x
c. y = 3^x
d. y = x + 2

4. the ordered pairs ( 1, 36 ), ( 2, 49 ), ( 3, 64 ), ( 4, 81 ), and ( 5, 100 ) represent a function. what is a rule that represents this function?

a. y = x^2
b. y = 36x
c. y = ( x + 5 )^2
d. y = ( x + 6 )^2

ANSWER TO QUESTION 1

Method 1: Observing a pattern.

Perimeter is the distance around the triangle.

For the first triangle, the perimeter is



Let us write the sum of the 7s and 5s in such a way that we can easily recognize a pattern.



or



For the second triangle, the perimeter is ,





For the third rectangle the perimeter is





For the nth triangle the perimeter is,





This implies,



Method 2: Using the formula

We can write the perimeter as the sequence,


where the first term is


and the constant difference is


The nth term is given by the formula,







This simplifies to,



The correct answer is B.

ANSWER TO QUESTION 2

We examine the y-coordinates of the relation to see if there is a constant difference.


Since there is a constant difference, it means the relationship is linear.

To determine whether it is decreasing or increasing, we need to find the slope using any two points.



Since the slope is negative, the relationship is a function that is decreasing.

Therefore the function is decreasing and linear.

The correct answer is C.

ANSWER TO QUESTION 3

For the ordered pair



The relation between x and y is that,



For the ordered pair,




Their relation between x and y is,



For the ordered pair



The relation is

Also,





and finally,




In each case we raise 3 to the exponent of the x-value to get the y-value.

So in general, if we have

the rule will be


The correct answer is C.

ANSWER TO QUESTION 4

For the ordered pair,



This implies that,


we can rewrite in terms of the x-value to obtain,



For the ordered pair,



This implies that,


We can rewrite this in terms of x-value to get,


Similarly






Therefore the rule is


The correct answer is C.