PLEASE HELP, 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

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.

kudzordzifrancis kudzordzifrancis · Answer 2 · 2018-11-29T08:10:56+01:00

ANSWER TO QUESTION 1

Method 1: Observing a pattern.

Perimeter is the distance around the triangle.

For the first triangle, the perimeter is

[tex]P = 7 + 7 + 5[/tex]

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

[tex]P = 14+ 5[/tex]

or

[tex]P = 14+ 5 \times 1[/tex]

For the second triangle, the perimeter is ,

[tex]P =7 + 7 + 5 + 5[/tex]

[tex]P = 14+ 5 \times 2[/tex]

For the third rectangle the perimeter is

[tex]P = 7 + 7 + 5 + 5 + 5[/tex]

[tex]P = 14+ 5 \times 3[/tex]

For the nth triangle the perimeter is,

[tex]P = 7 + 7+ 5 + 5 + 5 + ...n \: times[/tex]

[tex]P = 14+ 5 \times n[/tex]

This implies,

[tex]P = 14+ 5n[/tex]

Method 2: Using the formula

We can write the perimeter as the sequence,

[tex]19,24,29,... [/tex]
where the first term is
[tex]a = 19[/tex]

and the constant difference is
[tex]d = 24 - 19 = 29 - 24 = 5[/tex]

The nth term is given by the formula,

[tex]P(n) = a + (n - 1)d[/tex]

[tex]P(n) = 19 + 5(n - 1)[/tex]

[tex]P(n) = 19 + 5n - 5[/tex]

This simplifies to,

[tex]P(n) = 5n + 14[/tex]

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.

[tex]46 - 39 = 39 - 32 = 32 - 25 = 7[/tex]
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.

[tex]Slope = \frac{46 - 39}{0 - 1} = - \frac{7}{1} = - 7[/tex]

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
[tex]( 1, 3 )[/tex]
[tex]x = 1 \: and \: y = 3[/tex]

The relation between x and y is that,

[tex]y = {3}^{1} = 3[/tex]

For the ordered pair,

[tex]( 2, 9 ),[/tex]
[tex]x = 2 \: and \: y = 9[/tex]

Their relation between x and y is,

[tex]y = {3}^{2} = 9[/tex]

For the ordered pair
[tex] ( 3, 27 )[/tex]
[tex]x = 3 \: \: and \: \: y = 27[/tex]

The relation is
[tex]y = {3}^{3} = 27[/tex]
Also,

[tex]( 4, 81 )[/tex]

[tex]y = {3}^{4} = 81[/tex]

and finally,

[tex]( 5, 243 )[/tex]

[tex]y = {3}^{5} = 243[/tex]
In each case we raise 3 to the exponent of the x-value to get the y-value.

So in general, if we have
[tex](x,y)[/tex]
the rule will be
[tex]y = {3}^{x} [/tex]

The correct answer is C.

ANSWER TO QUESTION 4

For the ordered pair,

[tex]( 1, 36 ),[/tex]
[tex]x = 1 \: \: and \: y = 36[/tex]
This implies that,

[tex]y = {6}^{2} [/tex]
we can rewrite in terms of the x-value to obtain,

[tex]y = (1 + 5) ^{2} [/tex]

For the ordered pair,

[tex] ( 2, 49 ),[/tex]
[tex]x = 2 \: \: and \: \: y = 49[/tex]
This implies that,
[tex]y = {7}^{2} [/tex]

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

[tex]y = {(2 + 5)}^{2} [/tex]
Similarly

[tex]y = 64 \Rightarrow \: y = {(3 + 5)}^{2} [/tex]

[tex]y = 81 \Rightarrow \: y = {(4 + 5)}^{2} [/tex]
[tex]y = 100 \Rightarrow \: y = {(5 + 5)}^{2} [/tex]

Therefore the rule is
[tex]y = {(x+ 5)}^{2} [/tex]

The correct answer is C.