4. Write the function of a linear equation that includes the
points (1,3) and (2,9).

Answers

Answer 1

Answer:

y = 6x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form ( linear function ) is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 3 ) and (x₂, y₂ ) = (2, 9 )

m = [tex]\frac{9-3}{2-1}[/tex] = [tex]\frac{6}{1}[/tex] = 6 , then

y = 6x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 3 ) , then

3 = 6 + c ⇒ c = 3 - 6 = - 3

y = 6x - 3 ← equation of linear function


Related Questions

If 343* = 494-x, what is the value of x?

5/8
8/5
2
8

Answers

Answer: [tex]\frac{8}{5}[/tex]

Step-by-step explanation:

343 is equal to 7 to the power of 3.

49 is equal to 7 to the power of 2.

You can then make the equation:

[tex](7^{3})^x = (7^2)^{4-x}[/tex]

The powers law means if something is to the power of something, it is multiplied.

So, we can remove the 7 and make the equation:

3x = 2(4-x)

3x = 8 - 2x

5x = 8

x = [tex]\frac{8}{5}[/tex]

You can verify this by plugging it in,

[tex]343^{8/5} = 11388.6066[/tex]

[tex]49^{4-(8/5)} = 11388.6066[/tex]

Dilate the figure by the scale factor. Then enter the new coordinates.
K= 2

Answers

Answer:

A(2, 8)

B(4, 4)

C(-4, 2)

Step-by-step explanation:

Multiply all the coordinates by 2

G E Which of the following segments is tangent to the circle ? 1) overline HL 2 ) overline DE 3 overline FG 4 ) overline AC

Answers

Answer:

DE

Step-by-step explanation:

........................

show that 8/15 plus 3/10 equals 5/6​

Answers

Step-by-step explanation:

find the Lcm of 15 and 10 which is 30

multiply the 2fractions by the LCM

8/15*30=16

3/10*30=9

add the products and put them all over the Lcm

(16+9)/30

=25/30 which is equivalent to 5/6 when you divide both the numerator and the denominator by 5

Picture shown PLEASE HELP

Answers

Answer:

m= –4

So, you only need to of the points to find the slope, why not choosing the first two:

[tex]m = \frac{y2 - y1}{x2 - x1} = = = > \\ m = \frac{12 - 8}{ - 3 - ( - 2)} = = = > \\ m = \frac{4}{ - 1} = - 4[/tex]

so basically, this is the slope your looking for


36 students for 3 teachers =
1.0
5
12 students for 1 teacher.

Answers

Answer:

12

Step-by-step explanation:

36 divided by 3 =12 for 1 teacher

You are walking directly away from your house.
You are 5 miles away from your house when
you start walking, so you can determine your
distance from your house by adding 5 to the
number of miles you have walked. In the
equation below, a represents the number of
miles you have walked, and y represents your
distance from home in miles.
The relationship between these two variables
can be expressed by the following equation:
y = x + 5
Identify the dependent and independent
variables.
Your distance
from home
Number of
miles you
walk
Dependent
variable
Independent
variable

Answers

Answer:

dependent: your distance from home

independent: number of miles you walk

Step-by-step explanation:

lmk if you want an explanation

The function y = f(x) is graphed below. What is the average rate of change of the
function f(x) on the interval -3 ≤ x ≤-1?

Answers

The average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.

What is the average rate of change?

The average Rate of Change of the function f(x) can be calculated as;

[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]

Interval -3 ≤ x ≤-1

a = -3, b = -1

f(a) = f(-3) = -20

f(b) = f(-1) = 0

Step 2: Find Average

[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}\\\\\\f(x) = \dfrac{f(-1) - f(-3)}{-1-(-3)}\\\\\\f(x) = \dfrac{0 - (-20)}{2}\\\\f(x) = 10[/tex]

Therefore, the average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.

Learn more about average rate;

https://brainly.com/question/20784578

#SPJ1                  

The steps for multiplying the linear expressions –2n and three-fourths n are shown. A 2-column table with 4 rows. First column is labeled Reason with entries Given, Step 1, Step 2, Step 3. Second column is labeled Step with entries (negative 2 n) (three-fourths n), negative 2 times three-fourths times n times n, (negative 2 times three-fourths) times (n times n), negative three-halves n squared. What is the mathematical reasoning for Step 1? associative property commutative property distributive property simplify

Answers

The mathematical reasoning for the first step is; Distributive Property

How to use Algebra Properties?

We want to multiply the linear expressions; -2n and ³/₄n.

The first step will be to express them with the multiplication sign to get and factorize;

-2n × ³/₄n

Now, since n is common to both terms, we will factorize it out to get;

n(-2 × ³/₄)

Now, that operation above is termed as a distributive property because we know that the algebra distributive property is;

a(b + c) = ab + ac

Or a(b × c) = ab × ac

Read more about Algebra Properties at; https://brainly.com/question/11131460

#SPJ1

Answer:

communitave property i think

Step-by-step explanation:

Will a stand that can hold up to 40 pounds support a21-kilograms television? Explain. Use 2.2 lb=1kg.

Answers

Answer: No

Step-by-step explanation:

Weight limit = 40 Lb

Weight given = 21 kg

Conversion factor

2.2 Lb = 1 kg

2.2 x 21 = 46.2

46.2 Lb = 21 kg

46.2 > 40, the stand cannot support the TV

TV > stand

i would appreciate your help

Answers

__________________________________________________________

[tex]\text{\textbf{Hello!} In this question, we are trying to figure out the \underline{equation} of the line}\\\text{with the given information.}[/tex]
__________________________________________________________

[tex]\textbf{Explanation:}\\\quad{}\\\text{In the question, we were given our \emph{slope} (gradient) and a \emph{point}. This will help}\\\text{us solve our problem.}\quad{}\\\\\text{Slope: 2 }\\\\\text{Point: (1, 4)}\\\quad{}\\\text{In order to find the equation, we will be using the \underline{point-slope formula:}}\\\quad{}\\y - y1 = m(x - x1)\\\quad{}\\\text{With this equation, we would plug in our given values to its}\\\text{correct variable and solve.}[/tex]
__________________________________________________________


[tex]\textbf{Solve:}\\\\\text{Use the point-slope formula to solve.}\\\\y - y1 = m(x - x1)\quad{}\\\\\text{Plug in 2 to m, 1 to x1, 4 to y1 and then solve.}\\\\y - 4 = 2(x - 1)\\\\\text{Use the \underline{distributive property} to distribute the 2.}\\\\y - 4 = 2x - 2\\\\\text{Add 4 to both sides to cancel the 4 on the left and move the remainder}\\\text{to the right side of the equal sign.}\\\\y = 2x + 2\\\\\text{Since we can't simplify any further, our answer is: \fbox{y = 2x + 2}}[/tex]
__________________________________________________________

[tex]\textbf{Answer:}\\\\\text{Therefore, the equation of the line (our final answer) would be \fbox{y = 2x + 2}}[/tex]
__________________________________________________________

What’s the answer? How do I find the opposite

Answers

Answer:

I think the answer is 4

Step-by-step explanation:

13 7in 7in 7in volume and surface area pyramid

Answers

The Volume and Surface Area of Prism is 294 in² and 114.33 in³.

What is pyramid?

A large structure built especially in ancient Egypt that usually has a square base and four triangular sides meeting at a point and that contains tombs.

Surface rea of rectangular prism,

= 2( lb +bh +lh)

= 2 ( 7*7 + 7*7+ 7*7)

= 2 ( 49+49+49)

= 2*3*49

= 294 in²

Now, Volume,

= bhl/3

= 7*7*7/3

= 114.33 in³

Learn more about volume and surface area here:

https://brainly.com/question/23302816

#SPJ1

Given that y varies directly as x², find the percentage increase in y when x doubles.

Answers

Answer:400%

Step-by-step explanation: by the commutativity of multiplication we find (2x)^2=4(x^2)=4(y)

Which expression is equivalent to
i need help asap

Answers

i’m not sure if this is correct but i think it’s c

can u give the direct answer of 1 and 2

Answers

[tex] {a}^{3} . \\ \\ {a}^{5}. \\ \\ {a}^{9} . \\ \\ {a}^{m + n}. \\ \\ {x}^{1} = x.\\ \\ {x}^{3}. \\ \\ {x}^{3}. \\ \\ {x}^{m - n} . \\ \\ {y}^{6} . \\ \\ {y}^{12} . \\ \\ {y}^{18} . \\ \\ {y}^{ab}. \\ \\ 1. \\ \\ 1. \\ \\ {px}^{1} = px.[/tex]

••••••••••••••••••••••••••••••••••••••

[tex]343 .\\ \\ 16 .\\ \\ 3125 .\\ \\ \frac{ - 8}{27} .[/tex]

Helppp! Which linear inequality is represented by the graph

Answers

the answer is c because the line is solid so it is less than or equal to since it is also shaded below. secondly, the slope is 2/3 because it moves up two and over three, and the y-intercept is 0.2 or 1/5

PLS HELP I DONT KNOWWW!!

Answers

Answer:

3rd option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, - 1) ← 2 points on the line

m = [tex]\frac{-1-(-2)}{4-0}[/tex] = [tex]\frac{-1+2}{4}[/tex] = [tex]\frac{1}{4}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = [tex]\frac{1}{4}[/tex] x - 2 ← equation of line

This can be solved using the gradient-intercept formula:

y = mx + c

where,
m is the gradient, and
c is the y-intercept (where the line crosses the y-axis)

Gradient can be calculated using the following formula, or rise/run:

m = (y2 - y1)/(x2 - x1)
= (-1 - - 2)/(4 - 0)
= 1/4

Therefore, using the gradient-intercept form:
y = mx + c
y = (1/4)x + (-2) (-2 is the point where the line crosses the y-axis)

Therefore, y = (1/4)x - 2 or Option C is the answer

I need help with dis math problem (img included)

Answers

Answer:

4500 sec

Step-by-step explanation:

1hr 15min= 75 min

75 x 60=4500

Calculate the unpaid balance, finance charge, and new balance using the unpaid balance method. Note: Interest rate is given as a monthly rate
Previous balance:$179.32
Payments/credits:$85.00
Unpaid balance:$
Monthly rate:1.25%
Finance charge:$
New purchases=$117.42
New balance=$

Answers

The Unpaid balance is $94.32, Finance charge is $1.179 and new balance is $148.079.

Finance charge

Unpaid balance:

Unpaid balance=Previous balance-Payments/credits

Unpaid balance=$179.32-$85.00

Unpaid balance= $94.32


Finance charge:

Finance charge =Finance charge×Monthly rate

Finance charge=$94.32×1.25%

Finance charge=$1.179

New balance:

New balance =Previous balance-(New purchases-Payments/credits)+Finance charges

New balance=$179.32-($117.42-$85.00)+$1.179

New balance=$179.32-$32.42+$1.179

New balance=$148.079

Therefore the Unpaid balance is $94.32, Finance charge is $1.179 and new balance is $148.079.

Learn more about finance charge here:https://brainly.com/question/3436429

#SPJ1

Answer:

94.32

1.18

212.92

in order

Step-by-step explanation:

What is the range of f(x) = 3x + 9?

Answers

Answer:

The range is all real numbers.

Step-by-step explanation:

The function shown is a line (and not a horizontal line).

The range is all the y's on the graph or all the y's that can be generated by the equation of the function.

f(x) = 3x + 9

You could put ANY, literally any, number in place of the f(x) and be able to calculate an x for it. Looking at the graph of this line, you could go up and down the y-axis to infinity in either direction, and the graph of the line would be there.

The range is All Real Numbers.

Angela is an electrical engineer who is testing the voltage of a circuit given a certain current and resistance. she uses the following formula to calculate voltage:

the circuit she tests has a current of 3 + j 4 amps and a resistance of 4 - j 6 ohms.

what is the voltage of the circuit?

Answers

The Voltage of the given Circuit is gotten as; V = 36 - 2j Volts

How to multiply Vectors?

We are given;

Current; I = 3 + 4j amps

Resistance; R = 4 - 6j ohms

From ohms law, we know that;

V = IR

Thus;

V = (3 + 4j) * (4 - 6j)

V = 12 + 16j - 18j - 24j²

Now, in vector notation; j² = -1. Thus;

V = 12 - 2j + 24

V = 36 - 2j Volts

Read more about Vector Multiplication at; https://brainly.com/question/3184914

#SPJ1

Find the value of x. Round the length to the nearest tenth.

Answers

Answer:

5.1 yd

Step-by-step explanation:

tan(25°) = x/11

x = 11tan(25°)=5.1 yd

Please Help! What is the value of x?

Answers

Answer:

4.1968

Explanation:

Given that:

angle: 25°

opposite: x

adjacent: 9

So, use the tan rule:

opposite/adjacent = tan(x)

x/9 = tan(25)

x = 9tan(25)

x = 4.1968

tanØ=Perpendicular/Basetan25=x/9x=9tan25x=4.1968

Option A

helpppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

70

Step-by-step explanation:

Valeria doesnt want any lollipops left over, but identical, so that means you have to add. You can divide the two colors otherwise you get a decimal, which you cant break a lollipop into, or an indefinite letter, a lollipop cant fit in that as well. The only sensible thing is to add them.

How many dogs were in the sample?

Answers

each number under the leaves section would be a dog


answer: 11

Answer:

11

Step-by-step explanation:


Is (x + 7) a factor of f(x) = x³ - 3x² + 2x - 8?

Answers

Answer:

x=-7

0=(-7)³-3(-7)²+2(-7)-8

=-343-147-14-8

0≠-512

x+7 isn't a factor

PLEASE HELP ASAP

If "x" varies directly with "y," and
x = -19 when y = 14, what is
"x" when y = 2?
Enter the number that belongs in the green box.
Reduce to simplest form.
X = -
Notice that the negative sign has already been entered.

Answers

The value of x when y = 2 is -19/7

How to solve for x?

A direct variation from x to y is represented as:

x = ky

Where k represents the variation constant.

x = -19 when y = 14.

So, we have:

-19 = 14k

Make k the subject

k = -19/14

Substitute k = -19/14 in x = ky

x = -19y/14

When y = 2, we have:

x = -19 * 2/14

Evaluate

x = -19/7

Hence, the value of x when y = 2 is -19/7

Read more about direct variation at:

https://brainly.com/question/6499629

#SPJ1

state one example of 2 numbers where the LCM of the 2 numbers is the product of those numbers. explain your answers​

Answers

Answer:

See below

Step-by-step explanation:

3 and 5     have a LCM of 15    which is  3 * 5

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that triangle RST is congruent to triangle RSQ given that RS ⊥ ST, RS ⊥ SQ, and ∠STR ≅ ∠SQR.

Answers

1) [tex]\overline{RS} \perp \overline{ST}, \overline{RS} \perp \overline{SQ}, \angle STR \cong \angle SQR[/tex] (given)

2) [tex]\overline{RS} \cong \overline{RS}[/tex] (reflexive property)

3) [tex]\angle RST[/tex] and [tex]\angle RSQ[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\triangle RST \cong \triangle RSQ[/tex] (AAS)

Other Questions
are sunglasses allowed at school on really hot UV rays and days 30.10 cmO7 cm10 cm4 cmHow many triangles are needed to draw the net of this object? The p wave on an electrocardiogram (ecg) represents the depolarization of cells in the: Which approach allows us to understand how the decisions of the different eras have longlasting implications or impact on present-day? which sugar is called milk sugar when was the dictionary invented Question 9 of 34When you graph displacement versus time (a displacement-time graph), whatvariable is on the y-axis?O A. SpeedOB. DisplacementC. TimeO D. VelocitySUBMIT Select the correct texts in the passage.Which phrase best states the author's opinion on assisting children's development?adapted excerpt from "Some Rights of Children as Persons" in School Educationby Charlotte MasonA very interesting and instructive educational experiment on these lines has lately been tried in Hackney, where Mr. Sargent got together someeighty boys and girls under the conditions of an ordinary elementary school.The results seem to have been purely delightful; the childrendeveloped an amazing capacity for drawing, perhaps because so soon as they were familiar with the outlines of the flower and foliage of a givenplant, for example, they were encouraged to form designs with these elements. The really beautiful floral designs produced by these girls andboys, after quite : short art training, would surprise parents whose children have been taught drawing for years with no evident result. Thesechildren developed themselves a great deal on their school magazine also, for which they wrote tales and poems, and essays, not prescribedwork, but self-chosen. The children's thought was stimulated, and they felt they had it in them to say much about a doll's ball, Peter, the schoolcat, or whatever other subject struck their fancy. They felt their feet* as the nurses say of children when they begin to walk; and ournon-success in education is a good deal due to the fact that we carry children through their school work and do not let them feel their feet. Garry called in a food order to feed his sales team. when he arrived to pick up, it was not what he ordered. the store associate quickly made it right, and offered a substantial discount to make up for the mistake. there was no need to check with the supervisor, and garry was satisfied with the result. what aspect of good customer service was in place (c) .... (d) ...... (e) ..... e LA ZERAK LJU LEARNING garon est malade ? a ... gommes veux-tu ? ... page ? Which statement best explains how nationalism helped cause World War I?It fueled rivalries between European nations.It united Europe against the Ottoman Empire.It led to revolution against Russian imperialism. Suzy invests $2,600 in an account that earns 2.3% annual interest, compounded continuously. What is the value of the account after 10 years? Round to the nearest dollar Ari is a generous employer who truly values his workers. He is constantly praising the work his employees do and finds many ways to show his appreciation. Needless to say, Ari's employees like him a lot. However, they don't trust him. Ari does not like making decisions and, therefore, often fails to take care of important problems. Moreover, Ari does not like conflict and will often let his employees get away with inappropriate behavior on the job. Ari would most likely be considered a ____________. Please helpppp I really need please pls solvequestion attached as image Determine if management made the correct decision to not process the table cleaner further by doing the following.(1) Calculate the companys total weekly gross profit assuming the table cleaner is not processed further.Total weekly gross profit$enter total weekly gross profit in dollars (2) Calculate the companys total weekly gross profit assuming the table cleaner is processed further.Total weekly gross profit The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)=14 x b+5/2 how to solved theses question (4.27)-10.42+2.93-6 explain which is an effect of manifest destiny? A date for creation or revisionis mandatory for all web pages?