What is the equation of the non-proportional relationship given by the table below?



x y
3 76
6 70
9 64
12 58
15 52
y=2x+76
y=-2x+82
y=-2x-76
y=2x-82

Answer and explanation:

Given: Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:  

Number of years 1 2 3

Option 1 (amount in dollars) 1100 1200 1300

Option 2 (amount in dollars) 1100 1210 1331  

To find:

Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2?  

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years.  

Part C: Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1?

Solution:

Part A: Linear and exponential functions can be used to describe the value of the investment after a fixed number of years using option 1 and option 2, respectively.  

Part B: (n=n+100) and (n=n+100x) are the functions for each option to describe the value of the investment f(n), in dollars, after n years.  

Part C: Yes, there will be a significant difference of 1900 in the value of Belinda's investment after 20 years if she uses option 2 over option 1.

Part A:

In the case of option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This is because, in option one, the amount increases by a fixed amount every year.

In the case of option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. This is because, in option 2, the amount increase is higher than last year.

Part B:

For option 1, the function is

For option 2, the function is

Here, x is the increase in amount every consecutive year.

Part C:

After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference between 1900.

Therefore,

Part A: Linear and exponential functions can be used to describe the value of the investment after a fixed number of years using option 1 and option 2, respectively.  

Part B: (n=n+100) and (n=n+100x) are the functions for each option to describe the value of the investment f(n), in dollars, after n years.  

Part C: Yes, there will be a significant difference of 1900 in the value of Belinda's investment after 20 years if she uses option 2 over option 1.

Hope this helps

Take 2points

Slope:-

[tex]\\ \tt\longrightarrow m=\dfrac{-1-3}{2+1}=\dfrac{-4}{3}[/tex]

Answer:

y=mx+b

The slope of a linear function can be calculated by dividing the difference between y-values by the difference in corresponding x-values of any two points on the line. The slope and initial value can be determined given a graph or any two points on the line.

For example if you want to use the points from the line (-2,4)  (7,-8) from the graph given to you you use the equation: m=(y2-y1)/(x2-x1) substitute the values: m= -8-4 / 7-(-2) = -1.3333

So the slope equals -1.3

The equation of the line is y = -1.3x + 2

I hope this helps.

Answer:

Refer to the attachment for solution

Answer:

Step-by-step explanation:

Refer to the attachment for a solution

Answer:

2

Step-by-step explanation:

Subtract -7--5=-2, there can not be a length on a rectangle of -2 so it would just be 2.

Answer:

2

Step-by-step explanation:

Step-by-step explanation:

8/24 = 21/63 = 1/3

yes it's a proportion

Answer:

1/3 and -1/3

Step-by-step explanation:

6 times 1/3 = 2
because there are absolute value brackets that means that the answer can be 1/3 or -1/3 because the absolute value brackets will make it positive regardless.

Answer:

Put parentheses around the binomial and then expand it, and then use foil

Step-by-step explanation:

Let's say I have the binomial x+y.

(x+y)^2

(x+y)(x+y)

x^2+xy+xy+y^2

x^2+y^2+2xy

Answer:

? wdym

Step-by-step explanation:

well points i guess i also need one more brainliest if you can give

Answer:

The first one answer is 4 because 8x2=16 divide by 4 will equal 4.

The second one answer is 10 because 10 x 4=40 and divided by 4 will equal 4.

The third one answer is 6/6 which will equal 1 because it is an whole number.

Answer:

1+2=180(supplemental)

3+4=180

5+6=180

7+8=180

Answer:

3,4

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

80*(1-0.2)

Since the discount is 20% off,

the sale price will be 100% - 20% = 80% of the regular price.

80% of $80

[tex] \frac{80}{100} \times 80[/tex]

[tex] \frac{8}{10} \times 80[/tex]

[tex] \frac{4}{5} \times 80[/tex]

[tex]0.8 \times 80[/tex]

= $ 64

Answer:

π represents the ratio between circumference and diameter and for any circle, its always 3.14. Circumference = pi × diameter, so using your approximation of pi it's 10×3.14 = 31.4cm.

Step-by-step explanation:

Answer:

The slope of both lines is 1/4.

Step-by-step explanation:

Line g is a vertical translation of line f so they are parallel.  Now find the slope of each line.

Line f  joins points (-2, 1) and (2, 2), so its slope is (2 - 1) / [2 - (-2)] = 1/4.

Line  g  joins points (-2, -1) and (2, 0), so its slope is [0 - (-1)] / [2 - (-2)] = 1/4.

The two parallel lines have the same slope.

Answer:

(1)

since a translation of a line segment is its rigid movement, vertically or horizontally.

line 's' is parallel to line 'r' since it is a translation of line 'r'  'e' units vertically ( clearly we could see that the point P' corresponding to point P in line r is shifted 'e' units upward and point Q' in line 's' is formed by shifting corresponding point Q of line 'r' e units upward).

(2)

the slope of a line is defined as the change in y-coordinates to the change in x-coordinates of the points on that line.

slope of line r=slope of line segment PQ.

coordinates of P=(m,n) and Q=(j,k)

slope of line r=slope of PQ=
k-n ÷ j-m

(3)

the slope of line s= slope of line segment P'Q'

slope of line s=slope of P'Q'=
k+e- (n+e) ÷ j-m
=

k-n ÷ j-m

(4)

as line q is a vertical translation of line 's' 3 units down.

and P'' is the image of P'.

so coodinates of P''= (m,n+e-3)

Answer:

109 mg

Step-by-step explanation:

Answer:

1.05 Grams?

Step-by-step explanation:

Hope This Helps :)

Answer:

3 Wholes
Exact Amount: 3.5

Answer:

decimal form: 7.04 x 10^ 20

Step-by-step explanation:

answer...

Answer:

The question is not complete

Answer:

the answer is written below

Step-by-step explanation:

Let side of Inner square be S and side of Outer side be mS.

Area of Inner Square = S**2

Area of Outer Square = (mS)**2

The ratio of area of Inner Square and Outer Square is 1:m**2

i.e. Area of Outer Square will be m**2 times Area of Inner Square.

Answer:

A) The parallelogram is a rhombus

Step-by-step explanation:

A rhombus is an equally 4-sided figure with two acute angles and two obtuse angles opposite of each other.

Answer: Kate = 40/3  Her father = 50

Step-by-step explanation:

Let Kate's age in the present be K

And Kate's father's age in the present be F

3(K+5) = F+5

6(K-6) = F-6

Rearrange the first equation to get

3K+15 = F+5

3K+10 = F

Substitute that into the second question

6K-36 = 3K+10-6

3K = 40

K = 40/3

So F = 3*40/3+10 = 50

The distance closest to the distance the dog went is 31.42 ft

Since the dog moves around in one full circle, the distance the dog moves is the circumference of a circle.

The circumference of a circle C = 2πr where r = radius of circle.

Now r = length of leash = 5 foot

So, substituting r into the equation, we have

C = 2πr

C = 2π × 5 ft

C = 10π ft

C = 10 × 3.142 ft

C = 31.42 ft

So, the distance closest to the distance the dog went is 31.42 ft

Learn more about circumference of a circle here:

https://brainly.com/question/15673093

Answer:

In what? theirs no graph or picture with the question.

Step-by-step explanation:

Answer:

37/28 is the lowest form

Step-by-step explanation:

Hope this helps! :)

Answer:2.07 is the answer as of e.2020 

Step-by-Step: Mean = 270 Standard deviation = 10 x = 255 Formula for z-score, z = (x - mean)/SD z = (255 - 270) / 10 => z = -15 / 10 => z = -1.5 So by referring to z-table, -1.5 correlates to 0.0668 that implies to 0.07 So 7% of the boxes of Apples weight less than 255oz. The percentage of boxes is in the range of 255 oz and 270 oz, Now calculating the requiring percentage 50% - 7% = 43%

Solution:

Note that:

Simplifying the expression:

The simplified expression is -11x + 8.

[tex] \rm \: ( - \frac{11}{2} x + 3) - 2( \frac{11}{4} x - \frac{5}{2} )[/tex]

Distribute -2 through the parentheses

[tex] \rm \: ( - \frac{11}{2} x + 3) - \frac{11}{2} x + 5[/tex]

Remove the unnecessary parentheses

[tex] \rm \: - \frac{11}{2} x + 3 - \frac{11}{2} x + 5[/tex]

Calculate the difference

[tex] \rm \: - 11x + 3 + 5[/tex]

Calculate the sum

[tex] \boxed{ \mathfrak{ - 11x + 8}}[/tex]

Answer:

i.formula= current unit subtract previous unit

Answer:

1711568

Step-by-step explanation:

184*9302 = 1711568

Use a calculator to check your work