MATH SOLVE

2 months ago

Q:
# PLEASE HELP, WILL GET BRAINIEST AND POINTS1. 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 + 14C. The equation for the perimeter is P = 7n + 10D. The equation for the perimeter is P = 7n + 52. 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 25Is the relationship a function that is increasing or decreasing? Is the relationship a function that is linear or non-linear?A. Increasing; LinearB. Increasing; Non-LinearC. Decreasing; LinearD. Decreasing; Non-Linear3. 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^3B. y = 3xC. y = 3^xD. y = x + 24. 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^2B. y = 36xC. y = ( x + 5 )^2D. y = ( x + 6 )^2

Accepted Solution

A:

1. B. The equation for the perimeter is P = 5n + 14
2. C. Decreasing; Linear
3. C. y = 3^x
4. C. y = (x+5)^2
1. Look at the 3 figures. You'll notice that in all three figures, there is always 2 sides of length 7 exposed and 1 side of length 5 exposed for each individual triangle. So the formula is 7*2 + 5n which simplifies to 14 + 5m. Looking at the available options, only option "B" is equivalent.
2. Looking at the table, as the number of teams a person belongs to, the number of free hours gets smaller, so the function is decreasing. To check if the function is linear, check if the change in the value of the function has a constant ratio with the change in the input. So let's see
Input changes from 0 to 1 for a change of 1. Output changes from 46 to 39, for a change of -7. -7/1 = -7
Input changes from 1 to 2 for a change of 1. Output changes from 39 to 32, for a change of -7, -7/1 = -7
Input changes from 2 to 3 for a change of 1. Output changes from 32 to 25, for a change of -7, -7/1 = -7
So the change in the output is always -7 for each change of 1 in the input. Therefore the function is linear.
Therefore the answer is "C. Decreasing; Linear"
3. Let's check each option and see what fits.
A. y=x^3
* We have the pair (1,3). 1^3 = 1. And 1 is not equal to 3, so this option doesn't fit and is therefore wrong.
B. y = 3x
* We have the pair (1,3) 3*1 = 3. 3 and 3 fit. So far, so good. Let's check the next pair.
(2,9). 3*2 = 6. And 6 is not equal to 9. So this option too is wrong.
C. y = 3^x
Checking (1,3). 3^1 = 3. Good
Checking (2,9). 3^2 = 9. Good
Checking (3,27). 3^3 = 27. Good
Checking (4,81). 3^4 = 81. Good
Checking (5,243). 3^5 = 243. Good
This matches all the points given. So this is the correct answer. But let's check option D just to make sure.
D. y = x+2
Checking (1,3). 1+3 = 3. Good
Checking (2,9). 2+3 = 5. Not a match. So this isn't a good choice.
4. Same method as #3 above. Just check each option against the order pairs we have and see if all of them fit.
A. y = x^2
Checking (1,36). 1^2 = 1. Not a match. Bad option.
B. y = 36x
Checking (1,36). 36 * 1 = 36. Good.
Checking (2,49). 36 * 2 = 72. Not a match. Bad option.
C. y = (x+5)^2
Checking (1,36). (1+5)^2 = 6^2 = 36. Good.
Checking (2,49). (2+5)^2 = 7^2 = 49. Good.
Checking (3,64). (3+5)^2 = 8^2 = 64. Good.
Checking (4,81). (4+5)^2 = 9^2 = 81. Good.
Checking (5,100). (5+5)^2 = 10^2 = 100. Good.
They all match, so this is the correct option.
D. y = (x+6)^2
Checking (1,36). (1+6)^2 = 7^2 = 49. Not a match. Bad option.