One of the tables below contains (x, y) values that were generated by a linear function.

Part I: Determine which table contains values associated with a constant slope. Find that slope value and show the work you used to come to your decision.

Part II: Using the slope you found in Part I and the values in the table, write the equation of the linear function represented by the table you selected.

Answers

Answer 1

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation for table 3 is y=(5/2)x-4.

What is the equation of a line?

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The slope for the tables,

Table 1.

m₁ = (3-1)/(5-2) = 2/3

m₂ = (43-31)/(20-17) = 12/3 = 4

Since the slope is different the relationship is not linear.

Table 2.

m₁ = (13-10)/(2-1) = 3/1

m₂ = (34-29)/(7-6) = 5/1

Since the slope is different the relationship is not linear.

Table 2.

m₁ = (6-1)/(4-2) = 5/2

m₂ = (31-26)/(14-12) = 5/2

Since the slope is the same the relationship is linear.

The equation for table 3 will,

y = (5/2)x + c

1 = (5/2)2 + c

1 = 5 + c

c = -4

Hence, the equation for table 3 is y=(5/2)x-4.

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Related Questions

log2(1/128)=x, then x =

Answers

The value of x will be -7. The expression is solved using the identity.

What is the definition of a logarithm?

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

Given expression;

[tex]\rm log_2(\frac{1}{128}) = x[/tex]

The expression is solved using the identity as;

[tex]\rm log_e1 = x\\\ e^x=1[/tex]

Apply the identity;

[tex]\rm log_2(\frac{1}{128}) = x \\\\ 2^x = \frac{1}{128}\\\\ 2^x = \frac{1}{2^7} \\\\ 2^x = 2^{-7} \\\\ x = -7[/tex]

Hence the value of x will bed -7.

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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 60 pounds each, and the small boxes weigh 25 pounds each. There are 105
boxes in all. If the truck is carrying a total of 4550 pounds in boxes, how many of each type of box is it carrying?

Answers

Answer: The truck is carrying 55 large boxes and 60 small boxes

Step-by-step explanation:

Let x represent the number of large boxes

Therefore,

The number of small boxes = 115 - x

[tex]\therefore[/tex] According to the question

60x + 25(105 -x) = 4550

60x + 2625 - 25x = 4550

35x = 4550 - 2625

35x = 1925

x = 55

Number of large boxes = x = 55

Number of small boxes = 115 - 55 = 60

Giving brainliest to whoever can accurately solve these questions first.

Question 1. Suppose $30,000 is deposited into an account paying 3.5% interest, compounded annually.

How much money is in the account after ten years if no withdrawals or additional deposits are made?

A. 41,878.94
B. 42,317.96
C. 44,350.50
D. 40,500.00

Question 2.
To collect data on the signal strengths in a neighborhood, Pamela must drive from house to house and take readings. She has a graduate student, Kevin, to assist her. Pamela figures it would take her 12 hours to complete the task working alone, and that it would take Kevin 20 hours if he completed the task by himself.

How long will it take Pamela and Kevin to complete the task together?

A. 4.6 hours
B. 5.5 hours
C. 8.2 hours
D. 7.5 hours

Answers

1. The amount of money in the account after 10 years is 42,317.96 dollars.

2. it will take Pamela and Kevin 7.5 hours to complete the task together

How to find compound interest?

Question(1)

Using compound interest formula,

[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]

where

p = principalr = raten = number of timest = time

Therefore,

p = 30,000

r = 3.5% = 0.035

t = 10

n = 1

Therefore,

[tex]A = 30000(1+\frac{0.035}{1} )^{1X10}[/tex]

A = $42,317.96

Question 2:

Pamela takes 12 hours to complete a task.

Kelvin takes 20 hours to complete same task.

The time it will take both of them can be computed as follows:

using rate principle,

let

x = time it will take both of them to do the work together.

[tex]\frac{1}{x}=\frac{1}{12} + \frac{1}{20}[/tex]

[tex]\frac{1}{x}=\frac{20+12}{240}[/tex]

[tex]\frac{1}{x}=\frac{32}{240}[/tex]

cross multiply

240 = 32x

x = 240 / 32

x = 7.5 hours

Therefore, it will take Pamela and Kevin 7.5 hours to complete the task together

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Explain a detailed solution to the advanced function 4096^x = 8

Answers

The value of x in 4096^x = 8 is 0.25

How to solve the equation?

The equation is given as:

4096^x = 8

Express 4096 as 8^4

8^(4x) = 8

Cancel the common base

4x = 1

Divide by 4

x = 0.25

Hence, the value of x in 4096^x = 8 is 0.25

Answers

Answer:

n=16

Step-by-step explanation:

What is the range of function g?

Answers

Using it's concept, the range of function g is given by:

B. [tex]\{y|y \in \mathbb{R}, y \neq -4, -3\}[/tex]

What is the range of a function?

The range of a function is the set that contains all possible output values for the function. In a graph, it is the values of y.

In this graph, y assumes all values except y = -3 and y = -4, hence the range is given by:

B. [tex]\{y|y \in \mathbb{R}, y \neq -4, -3\}[/tex]

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City planners are planning to build a new community park. They agree that the park will be rectangular in shape, but the proposed
dimensions changed. At the most recent meeting, it was determined that the length would remain at 21.6 meters but that the width
would increase by 4.7 meters. So, the park would now cover an area of 714.96 square meters.
Which equation can be used to determine the original width of the park?

Answers

Answer:

Step-by-step explanation:

The area of the rectangular park will be the product of its length and width. This relation is used to write an equation to find the original width of the park.

Width

Let w represent the original width of the park in meters. The new width is 4.7 meters more, so is represented by (w +4.7).

Other dimensions

The length of the park is given as 21.6 meters. The area is given as 714.96 square meters.

Area formula

The various dimensions of the park are related by the area formula:

A = LW

714.96 = 21.6(w +4.7)

Answer: The answer is C i took the k12 5.21 unit test

Step-by-step explanation:

Pls help! Geometry
Find the area

Answers

It’s been a while but I got 364.14

i believe the correct answer should be 364.14 maybe

If cos a = 0.871 and cos ß= 0.338 with both angles' terminal rays in Quadrant-I, find the values of
tan(a + 3) =
Your answers should be accurate to 4 decimal places.

Answers

Answer:

tan(α+β) ≈ -5.8688

Step-by-step explanation:

You can use the formula for the tangent of the sum of angles, or you can use a calculator to find the angles. The latter is much simpler.

Calculator solution

tan(α+β) = tan(arccos(0.871) +arccos(0.338))

tan(α+β) ≈ -5.8688

Note that the two angles total slightly more than 90°, so the tangent of their sum is a large negative number.

Trig identity solution

The use of trig identities also requires a calculator, and many more steps.

The tangent of the angle can be found from the cosine using ...

tan(x) = √((1/cos(x))² -1)

tan(α) = √((1/0.871)² -1) ≈ √(1.1481056² -1) ≈ 0.56404479

tan(β) = √((1/0.338)² -1) = √(2.9585799² -1) ≈ 2.7844559

And the tangent of the sum of angles is ...

tan(α +β) = (tan(α) +tan(β))/(1 -tan(α)tan(β))

tan(α+β) = ((0.56404479 +2.7844559)/(1 -(0.56404479)(2.7844559))

tan(α+β) = 3.3485007/(1 -1.5705579)

tan(α+β) ≈ -5.8688

Additional comment

The approximate angles are ...

α ≈ 29.4249°

β ≈ 70.2448°

Then α+β ≈ 99.6699°

please help! :(
Kathy distributes jelly beans among her friends. Alia gets 4^2 fewer jelly beans than Kelly, who gets 3^3 jelly beans. How many jelly beans does Alia get?

a. 4^2 - 3^3
b. 3^3 + 4^2
c. 4 - 3^3
d. 3^3 - 4^2
e. 3^2 - 4^3

Answers

Answer:

Step-by-step explanation:

k gets 3^3

a gets 4^2

subtract 3^3-4^2=d.

Is the relation depicted in the chart below a function?

Answers

The true statement is (a) it is a function

How to determine the relation?

For a relation to be a function, the following must be true:

Each x value must be paired with exactly one y value

From the table of values, all x values have exactly one y value

This means that the relation is a function

Hence, the true statement is (a) it is a function

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The correct option regarding whether the relation is a function is:

It is a function.

When does a relation represents a function?

A relation represents a function if each input X is mapped to only one output Y.

In this problem, this statement is true(input 3 is mapped to output 10 twice, same output so ok), hence it is a function.

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if the following data were linearized using logarithms, what would be the equation of the regression line? Round the slope and y-intercept of the regression line to three decimal places. x2,3,4,5,6 y73,77,85,101,133

A. log(y) =-1.706x + 0.064
B. log(y) =-0.064x + 1.706
C. log(y) = 1.706x + 0.064
D. log(y) = 0.064x + 1.706

Answers

The regression equation is (d) log(y) = 0.064x + 1.706

How to determine the regression equation?

The table of values is given as:

x 2 3 4 5 6

y 73 77 85 101 133

Calculate the logarithm of the y values.

So, we have:

x 2 3 4 5 6

log(y) 1.86 1.89 1.93 2 2.12

Next, we enter the above values in a regression calculator.

From the calculator, we have the following summary:

Sum of X = 20Sum of Y = 9.8Mean X = 4Mean Y = 1.96Sum of squares (SSX) = 10Sum of products (SP) = 0.63

The regression equation is then represented as:

log(y) = bx + a

Where:

b = SP/SSX = 0.64/10 = 0.064

a = MY - bMX = 1.96 - (0.064*4) = 1.706

So, we have:

log(y) = 0.064x + 1.706

Hence, the regression equation is (d) log(y) = 0.064x + 1.706

Answers

Answer:

p=M/V. by rearranging this formula you get

V=M/p

V=560kg/7kg/m³

=80m³ b/c kg canceled kg

p=M/V

=352kg/220m³

=1.6kg/m³

Pls Help (question is in pic)

1. If the function holds true, in what year would the cost of mailing a first class letter reach 60 cents.

2. In 2007, the cost of mailing a first-class letter was 41 cents. Has the inflation rate stayed constant since 1991?

Answers

Based on the function given, the year when the cost of mailing a first class letter would reach 60 cents is 2007.

If the cost of mailing a first-class letter is 41 cents, then the inflation rate has not stayed constant.

What year does the cost reach 60 cents?

0.60 = 0.29 (1.046)^t

0.60 / 0.29 = (1.046)^t

log (2.07) = t x log (1.046)

t = 16 years

Added to 1991:

= 1991 + 16

= 2007

The cost of mailing a first-class ticket was 41 cents however which means that inflation was not constant.

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how many 4 digit numbers can I make only using the numbers 5533?

Answers

0 because if nothing can go in to 5533 that wouldn’t be above 10,000

If a bond is trading at a premium, what is the relationship between the bond's coupon rate, current yield and yield to maturity?

Answers

A bond purchased at a premium, it will have a yield to maturity and current yield that is lower than its coupon rate.

What is a Premium bond?

This is usually above its face value which may be as a result of the interest rate being higher than the current market interest rates.

When a bond is traded at a premium, the yield to maturity and current yield will be lower than its coupon rate.

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In a plane, line b is parallel to line f, line f is parallel to line g, and line h is perpendicular to line b.

Answers

The statement that cannot be true is that g cannot be parallel to h (g ║h)

How to know parallel lines in a plane?

On the plane ,

line b is parallel to line f.

Therefore,

b ║ f

line f is parallel to line g,

Therefore,

f ║ g

line h is perpendicular to line b.

h ⊥ b

Therefore,

Since line h is perpendicular b, line b is perpendicular to h.

b can be parallel to g on the plane.

g cannot be parallel to h because h is perpendicular to b.

h can be perpendicular to f because b is parallel to f.

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What is the value of "y" that satisfies the expression below?

1 y + 12 = 6 ( 1 y + 1 )

Round your answer to 2 decimal points (i.e. #.##)

Answers

Answer:

1.20

Step-by-step explanation:

1y + 12 = 6 (1y + 1)

1y + 12= 6y + 6

12 - 6 = 6y - 1y

6 = 5y

y = 6/5

y = 1.2

I don't what you meant by rounding to 2 decimal points so my answer is

1.20

0
Fantastic Catering completed the following selected
transactions during May 2016:
• May 1: Prepaid rent.for three months, $2,700
• May 5: Received and paid electricity bill, $240
• May 9: Received cash for meals served to
customers, $2,700
•
May 14: Paid cash for kitchen equipment, $2,400
May 23: Served a banquet on account, $2,900
May 31: Made the adjusting entry for rent (from
May 1).
•
• May 31: Accrued salary expense, $1,800
• May 31: Recorded depreciation for May on
kitchen equipment, $730
To see what to study next, go to your Study Plan.

Answers

Based on the type of transaction that Fantastic Catering completed, the types of accounting basis they are in will be:

Cash Basis Accrual Basis

May 1 (2,700) 0

May 5 (240) (240)

May 9 2,700 2,700

May 14 (2,400) 0

May 23 0 2,900

May 31 0 (1,800)

May 31 0 ( 900 )

May 31 0 ( 730)

When are the cash and accrued basis used?

The cash basis is used for when cash transactions have happened. There has to be cash changing hands for this to be recorded like the prepaid rent and the payment for kitchen equipment.

The accrual basis is used for all payments and revenue including both cash transactions and those that are recorded on account such as the banquet on May 23 and accrued salaries.

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select the value of y in terms of x.
please help

Answers

Answer: A

Step-by-step explanation:

By the exterior angle theorem,

[tex]x+y=138\\\\\implies y=138-x[/tex]

Given: FB ║ CG ∠BFE and ∠C are supplementary. Prove CA ║ FE

Answers

Answer:

Step-by-step explanation:

1) [tex]FB \parallel CG[/tex], [tex]\angle BFE[/tex] and [tex]\angle C[/tex] are supplementary (given)

2) [tex]\angle ABF \cong \angle C[/tex] (corresponding angles theorem)

3) [tex]\angle BFE[/tex] and [tex]\angle ABF[/tex] are supplementary (supplements of congruent angles are congruent)

4) [tex]CA \parallel FE[/tex] (converse of the same-side interior angles theorem)

3 red balls, 4 white balls, and 1 green ball are in a bag. Balls are drawn without replacement. Find the probability that the red balls can be drawn before the green ball is drawn.

Answers

The probability that the red balls can be drawn before the green ball is drawn is 3/8.

What is Probability?

The probability is the measure of the likelihood of an event to happen.

Given:

red balls= 3

white balls = 4

green balls = 1

So, Probability of red balls

=3/8

Probability of green balls

=1/7

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The function g(x) is graphed on the coordinate grid. What is the domain of g(x)? x≥5 x>5 x≥0 x>0

Answers

The domain of the function g(x) is x >= 5

How to determine the domain?

The complete question is added as an attachment

From the graph, we have the smallest value of x to be 5.

And the value of x increases to the right

This means that:

x >= 5

Hence, the domain of the function g(x) is x >= 5

Answers

Answer:

55 Wide and 75 Long works.

Step-by-step explanation:

Since the Perimeter of the original is likely 80 + 80 +50 + 50 = 260 since it it a rectangular lot, 55 + 75 + 55 + 75 = 260 as well, meaning no change in perimeter. Now when we look at the area 80 x 50 = 4000, but

55 x 75 = 4125, leading to a larger plot

f (x) = 7 |x-5| + 9 does the absolute graph shrink or stretch

Answers

Answer:

it shrink

if the number outside the absolute value is greater than 1 it shrinks

if the numerous is smaller than 1 it stretches

remember the saying about the parent function if you run less than 1 mile you are wider than the parent

if you run more than a mile here the number is 7 so it's skinner yhan the

Step-by-step explanation:

Jack pays 1.74$ for 6 packs of gum. How much does he pay for one

Answers

The answer is $10.44

Answer:

$0.29 and if you want to round it up then it is going to be $0.30

Step-by-step explanation:

You are asking what 1 pack of gum costs. We already know that 6 packs of gum costs $1.74 and we need to find the unit rate which is basically what one pack of gum costs so in order to do that we need to [tex]\frac{1.74}{6}[/tex] which is 0.29 and that is the cost of 1 pack of gum. Hope that helps and also can you please mark me as brainlist. Thank you

A cone-shaped paper water cup has a height of 12 cm and a radius of 6 cm. If the cup is filled with water to one-sixth its height, what portion of the volume of the cup is filled with water?

Answers

Answer:

1/216

Step-by-step explanation:

The ratio of volumes of similar shapes is the cube of the scale factor. The filled portion of the cone is similar to the entire cone.

Linear scale factor

If the filled height is 1/6 of the total height, the scale factor for linear dimensions is 1/6.

Volume scale factor

The scale factor for the volume is the cube of the scale factor for linear dimensions. it is ...

(1/6)³ = 1/216

The volume of the filled portion of the cup is 1/216 of the volume of the cup.

The total interest on a discounted loan is $80. If James received $880 into his bank account on drawdown, and the loan lasts for 6 months, what is the (simple) interest rate? Give your answer as a percentage to the nearest tenth of a percent.

Answers

With the use of formula, the interest rate is 18.2%

How can Simple Interest be Calculated ?

The Interest is the product of the principal, time and the rate in percentage. That is, I = PTR / 100

Where

P is the Principal = $880T is the time = 6 months = 0.5 yearR is the rate = ?I is the interest = $80

Substitute all the parameters into the formula

80 = (880 x 0.5R)/100

cross multiply

8000 = 440R

R = 8000/440

R = 18.2%

Therefore, the (simple) interest rate is 18.2%

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Select the properties of a square? please answer, I'm desperate

Answers

Answer:

all are the properties of square

Step-by-step explanation:

all are correct

Boating: A paddleboat moves at a rate of 12 mph in still water. If the rover’s current moves at a rate of 3 mph, how long will it take the boat to travel 36 miles downstream and 36 miles upsteam? (Two answers)

Answers

The time taken by the boat to travel 32 miles downstream is 2.1 hours and for upstream 3.56 hours.

What is speed?

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

Given that:-

A paddleboat moves at a rate of 12 mph in still water. If the rover’s current moves at a rate of 3 mph.how long will it take the boat to travel 36 miles downstream and 36 miles upstream?

The time taken by the boat upstream will be calculated as:-

( B + W ) Td = D

( 12 + 3 ) Td = 32

( 15 ) Td = 32

Td = 32 / 15 = 2.1 hours

The time taken by the boat downstream will be calculated as:-

( B - W ) Tu = D

( 12 - 3 ) Tu = 32

9 Tu = 32

Tu = 32 / 9 = 3.56 hours.

Therefore the time taken by the boat to travel 32 miles downstream is 2.1 hours and for upstream 3.56 hours.

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