find the slope-intercept equation of the line that passes through (3,-1) and has a slope of -1

Answers

Answer 1

Answer:

y= -x+2

Step-by-step explanation:

slope formula: (y2-y1)/(x2-x1)

at the point (3,-1), it is known that x=3 and y= -1.

[y-(-1)]/(x-3)= -1 (y+1)/(x-3)= -1 (y+1)= -1(x-3) y+1= -x+3 y= -x+2

Related Questions

A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 6 tables is $54 . The total cost to rent 5 chairs and 3 tables is $36 . What is the cost to rent each chair and each table?

Answers

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The cost of each chair is $2.25.

The cost of each table is $8.25.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 2x + 4 = 5 is an equation.

We have,

Cost of each chair = x

Cost of each table = y

Now,

2x + 6y = 54 _____(1)

5x + 3y = 36 ______(2)

From (1) we get,

2x = 54 - 6y

x = (54 - 6y)/2 ______(3)

Now,

Putting (3) in (2) we get,

5(54 - 6y)/2 + 3y = 36

270/2 - 30y/2 + 3y = 36

135 - 15y + 3y = 36

99 = 12y

y = 99/12

y = 8.25 ______(4)

Now,

Putting 4 in (3) we get,

x = (54 - 6 x 8.25) / 2

x = 4.5/2

x = 2.25

Thus,

The cost of each chair is $2.25.

The cost of each table is $8.25.

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How is solving a real-world problem with a system of equations similar to solving a real-world problem with a single equation in one variable? How is the process different?​

Answers

Answer:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.

Step-by-step explanation:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.

hope it helps

:)

15 points!! Is the triangle a right triangle?

Answers

Answer: Yes.

Step-by-step explanation:

Answer:

yes, it is because the right side is the bigger side.

Step-by-step explanation:

See in a right triangle, the side that is opposite of the 90° angle is the longest side of the triangle, and is called the hypotenuse.

Simplify this equation please
48

Answers

Answer:

Please look at the attached image, thank you so much! Hope this helps! :D

Step-by-step explanation:

Answer:

6.92820323028, rounded would be 6.92. Even more rounded would be 7.

Step-by-step explanation:

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 9 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

A fence is to be built to enclose a rectangular area of 1250 square feet. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built

Answers

The dimensions of the rectangle for the most economical fence are length, L = 50 feet and width, W = 25 feet

How to find the dimensions of the rectangle for the most economical fence?

Given: Area =  1250 square feet, , cost of material along three sides = $6 per foot, cost of material for fourth sides = $18 per foot

In order to calculate the dimension of the fence

Let L and W represent the length and width of the fence respectively

Thus, the area of the fence can be represented as:

A = L × W = 1250  ---- (1)

L = 1250/W

Let the total cost to construct the fence be 'C' can be obtained if we construct the shorter side with material with a cost of $18 per foot

C = 6×(2W + L) + 18×L

C = 12W + 24L  ---- (2)

Substituting the value of L from equation 1 into equation 2 we have:

C = 12W + 24×(1250/W)

To minimize the cost we differentiate both sides with respect to W and equate the result to zero:

C = 12W + 24×(1250/W)

dC/dW = d/dW (12W + 30000/W)

0 = 12 - 30000/W²

12W² = 30000

W² = 2500

W = 50 feet

Since L = 1250/W

L = 1250/50

L = 25 feet

Therefore, the dimensions of the rectangle are length of 25 feet and width of 50 feet

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a group of four numbers has an average of 15. The first three numbers are 12,19 and 7. What is the other number

Answers

Answer:

22

Step-by-step explanation:

12 + 19 + 7 + _?_ = 15

38 + _?_ = 15

-38             -38

-----------------------

? = 23

12 + 19 + 7 + 23 = 61

                    -1

             

12 + 19 + 7 + 22 = 60

60 ÷ 4 = 15

I hope this helps!

Your car has a 15 gallon tank and can run on fuel with added
ethanol. The fuel contains either 13 percent ethanol or 69 percent
ethanol. How much of 69% percent ethanol fuel should you use so
that your tank is 40 percent ethanol?

Answers

Answer: 7.5

Step-by-step explanation:

the tank is 15 gallons and you can get 13 percent ethanol or 69 percent ethanol, so you simply just get 7.5gallons of 69 percent and then 7.5 gallons of 13 percent

.69 divided by 15 is .046

.13 divided by 15 is .008

The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.

What is mixture?A mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the form of solutions, suspensions and colloids.

Given is that a car has a 15 gallon tank and can run on fuel with added

ethanol. The fuel contains either 13 percent ethanol or 69 percent

ethanol.

The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is given by -

{x} = 69% of 15 - {40% of 15}

{x} = (69/100 x 15) - (40/100 x 15)

{x} = 10.35 - 6

{x} = 4.35

Therefore, the amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.

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The length of a rectangle is 3ft longer than its width.
If the perimeter of the rectangle is,58ft find its length and width.

Answers

The length and width of the rectangle is 16 ft and 13 ft respectively.

What is the dimensions of the rectangle?

The perimeter of a rectangle = 2(length + width)

Perimeter of the rectangle = 58 ftWidth of the rectangle = w ftLength of the rectangle = (w + 3) ft

The perimeter of a rectangle = 2(length + width)

58 = 2{(w + 3) + w}

58 = 2(w + 3 + w)

58 = 2(3 + 2w)

open parenthesis

58 = 6 + 4w

subtract 6 from both sides

58 - 6 = 4w

52 = 4w

divide both sides by 4

w = 52/4

w = 13

Hence,

Width of the rectangle = w ft

= 13 ft

Length of the rectangle = (w + 3) ft

= 13 + 3

= 16 ft

Therefore, the dimensions of the rectangle is given by 16 ft and 13 ft respectively

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One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide. 7 and 2

Answers

24 units is the area of the shaded region if the "frame" is 2 units wide.

What is Area of Rectangle?

The area of Rectangle is length times of width

We know that the frame is 2 units wide, and the measure of the rectangle and the frame are:

width = 7 units

length = 12 units

Now, if we remove the frame, we will remove 2×2 units = 4 units for each measure (because for each measure we have the frame in both sides).

So the measures for the shaded rectangle are:

width = 7 units - 4 units = 3 units

length = 12 units - 4 units = 8 units.

And the area of a rectangle is given by the product between the width and length, then we have:

A = (3 units)*(8 units) = 24 square units.

Hence, 24 units is the area of the shaded region if the "frame" is 2 units wide.

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The volume of a cube with side s is s3. Edna bought a cube-shaped jewelry box that has 7-inch sides. What is the volume of the jewelry box?

Answers

The volume of the jewelry box will be;

⇒ 343 inch³

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The volume of a cube with side s = s³

And, Edna bought a cube-shaped jewelry box that has 7-inch sides.

Now,

Since,  Edna bought a cube-shaped jewelry box that has 7-inch sides.

Hence, The volume of the jewelry box = 7³

                                                           = 7 x 7 x 7

                                                           = 343 inch³

Thus, The volume of the jewelry box will be;

⇒ 343 inch³

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In your own words, tell me the difference between a geometric and an arithmetic sequence.

Answers

As several differences are there between them and is differentiated below.

What is Sequence?

A list of numbers in a specific order is called a sequence. The terms of the sequence are the various numbers that appear in it.

Let a sequence's terms be a1, a2, a3,..., an,..., etc.

The term's position is indicated by the subscripts. That implies,

Initial phrase = a1

term two = a2

term three Equals a3

….

The nth term, indicated by an, is the number that appears in the sequence at the nth place. This phrase is also known as the sequence's general phrase.

Geometric Sequence:

It is a sequence of numbers in which each new term is calculated by multiplying by a non-zero and fixed number.Multiplication or Division is done in every step.A common ratio between 2 successive terms is the common ratio.It is of the Exponential Form.

Arithmetic Sequence:

It is a list of numbers, in which every new term alters from another preceding term by a definite quantity.Addition or Subtraction is done in every step.A common ratio between 2 successive terms.It is of the Linear Form,

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Simplify Oa Ob Oc Od 10x² -32 4 ​

Answers

Answer:

Step-by-step explanation:

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. 5x2 + 14x - 3 < 0 The solution set is O A. (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) O B. The solution set is the empty set. Which number line below shows the graph of the solution set? O A. В. + -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 7 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4. 7 8 C. + + + + + + + D. + -8 -7 -6 -5 -4 -3 -2 -1 1 3 4 7 8 -8 -7 -6 -5 -4 -3 -2 -1 1 3 4 5 7 8 E. F. + + + + -7 -6 -3 -2 -1 1 2 3 6 -8 -7 -6 -5 -4 -3 -2 -1 1 3 5 6 7 8 OG. →O H.

what are steps to solving 30,002-28,596

Answers

Answer:

1,406

Step-by-step explanation:

Will mark brainliest

Answers

The solution is Option D.

The equation of the line is y = 28x

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the total distance traveled by the car y = 476 miles

Let the total amount of gasoline x = 17 gallons

So , the equation of line is given by

y = mx + c

where m is the slope

Slope m = y /x

Substituting the value for y and x in the equation , we get

Slope m = 476 / 17

              = 28

Therefore , the equation of line is y = 28x  and the graph is given below

Hence , The equation of the line is y = 28x

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A professor had students keep track of their social interactions
for a week. The number of social interactions over the week is
shown in the following grouped frequency distribution. What is
the class width?
The class width is

Answers

The class width of the distribution is 4

What is class width?

Class width is the difference between the Upper class limit and the Lower class limit of a class interval.

Class Width = Upper Class Limit − Lower Class Limit. For example: For a class interval, 163−175, Class Width =175−163=12.

Similarly for a class interval of 75-79, the class width is 79-75= 4.

The upper class limit is 79 and the lower class limit is 75.

The class limit for all the frequency distribution is constant.

Therefore the class width of the distribution is 4

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The power P (in W) generated by a particular windmill is given by P=0.015V where V is the velocity of the wind (in
mph). Find the instantaneous rate of change of power with respect to velocity when the velocity is 5.9 mph. Round
your answer to the nearest tenth.
OA. 0.3 W/mph
OB. 3.5 W/mph
OC. 1.6 W/mph
D. 6.2 W/mph

Answers

The instantaneous rate of change of power with respect to velocity is 1.6 W/mph.

What is the rate of change function?

The pace at which one quantity changes in relation to another is known as the rate of change function.

Given, P = 0.015[tex]V^{3}[/tex]

Differentiating P with respect to V:

P′=(0.015)(3)[tex]V^{2}[/tex]

At V = 5.9 mph, then

P′=(0.015)(3)[tex]5.9^{2}[/tex] = 1.6 W/mph

Hence, the instantaneous rate of change of power is 1.6 W/mph.

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Assume gas cost $3.70 a gallon. Write an equation representing the total amount you need to spend on the car for the trip, after paying for a one time tune-up of $100.

Answers

The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Also an equation is a set of variables that are constrained through a situation or case.

Given that the 1 gallon is $3.70

x gallons = $3.70x

So, C = 3.70x

This will be the cost of x gallons

Hence "The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x".

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Jaxon goes to a restaurant and the subtotal on the bill was x dollars. A tax of 8% is applied to the bill. Jaxon decides to leave a tip of 23% on the entire bill (including the tax). Write an expression in terms of x that represents the total amount that Jaxon paid.

Answers

Answer:

Step-by-step explanation:

If the equation is going off of what is the traditional, and correct way to tip, the tip would be based off the total BEFORE tax.

Therefore, the expression for the total cost would be: x + .23x +.08x, which, simplified, would be 1.33x.

Can somebody help me with this please?

Answers

Answer: -16.66

Reason: 10*-5/3=−16.66666667 or −50/3​

A canoe rental service charges a $20 transportation fee and $30 dollars an hour to
rent a canoe. Write and graph an equation representing the cost, y, of renting a canoe
for x hours. What is the cost of renting a canoe for twelve hours?

Answers

The graph of the equation y = 30x + 20 is shown below.

It would cost $380 for 12 hours.

How to Write and Graph an Equation?

The equation of a graph can be written as y = mx + b, if we know the slope of the graph (m) and the y-intercept (b) which is the point on the y-axis that the line will intercept.

Therefore:

Slope/unit rate (m) =  $30 per hour

Rental service charges is the y-intercept (b) = $20

To write the equation, substitute m = 30 and b = 20 into y = mx + b:

y = 30x + 20

See the attachment below for the graph of the equation.

Substitute x = 12 into the equation y = 30x + 20 to find the cost of renting canoe for 12 hours:

y = 30(12) + 20

y = $380

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two packages of cookies cost $9.50. How much do seven packages cost?Try using a proportion to solve or finding unit rate?

Answers

Answer:

$33.25

1 package is $4.75

Step-by-step explanation:

9.5 divided by 2 is 4.75, that is how much one package costs.

4.75 times 7 is 33.25, that's seven packages worth.

If the variance of the data values in a sample is 289, what is the standard
deviation of the data values?
O A. 17
OB. 19
OC. 18
O D. 16

Answers

Answer:

17

Step-by-step explanation: ..

Given the function f (x)= x2 −5x + 6 , evaluate

Answers

Actually 20 is the answer

A student is using colored beads to make a model of magnesium hydroxide, Mg(OH)2. Magnesium atoms are
represented by orange beads, oxygen atoms by green beads, and hydrogen atoms by blue beads.

Model bead color key.
Magnesium orange beads O (orange)
Oxygen green beads O (green)
Hydrogen blue beads O (blue)

What combination of beads should the student use for the model?

Answers

The combination of beads that the student will use to make a model of  magnesium hydroxide, Mg(OH)₂ is

Magnesium orange beads - 1Oxygen green beads  - 2Hydrogen blue beads - 2

What is model of molecule?

Molecule models depict the positions of the various atoms, roughly to scale, and typically with color coding, as well as how they are joined together.

These models are helpful tools for visualizing the structures and shapes of groupings of atoms, which is vital for understanding the behavior of molecules

Over the course of the development of contemporary atomic theory, models have been employed to represent atom configurations.

The model of magnesium hydroxide, Mg(OH)₂ will require the atoms in the ratio:

Magnesium : Oxygen : Hydrogen = 1 : 2 : 2

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No
0.7

What’s the percentage

Answers

Answer: 70%

Step-by-step explanation:

0.7
----- x 100% = 70%

 1

Answer:

70%

Step-by-step explanation:

When turning a decimal into a percent always bring the decimal point two places to the right.

0.7.0.

070%

70%

In ARST, r = 71 cm, /T=48° and /R=37°. Find the length of t, to the nearest 10th of
a centimeter.

Answers

In the given triangle, the length of side t is 87.7 cm

Calculating the length of a side in a triangle

From the question, we are to determine the length of t.

From the given information,

r = 71 cm

∠T = 48°

∠R = 37°

From the law of sines, we can write that

t / sin T = r / sin R

t / sin 48° = 71/sin 37°

t = (71 × sin 48°)/sin 37°

t = 87.6736

t ≈ 87.7 cm

Hence, the length of t is 87.7 cm

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I’m certain year, there were 86 female officials in congress, which comprised of the House of Representatives and the senate. If there were 58 more female me members of the House of Representatives than female senators, find the number of females in each house of congress

Answers

Answer:

58 members of the House of Representatives, and 28 members of the senate.

Step-by-step explanation:

We can find the answer to this by simply subtracting:

86 - 58 = 28

So, there are 58 members of the House of Representatives, and 28 members of the senate.

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Julie likes to make bead necklaces. She has 296 beads altogether, but has 32 more round beads than square beads. How much of each bead does she have?

Answers

I don’t know if this is right but I think it is 264

Explain why the slope(m) of this line is
2/6

Answers

The slope is 2/6 because the rise is 2 while the run is 6

rise             2

-------    =    -------

run              6

what is the slope of a line that is parallel to the line connecting point O (-5,1) and point P (2,3)?

Answers

Answer:

2/7

Step-by-step explanation:

2 parallel lines have the same slope

we just need to find the slope of the line with the point’s connecting O and P

We use y2-y1/x2-x1 to find slope

3-1/2-(-5)

2/7

2/7 is the slope

Hopes this helps please mark brainliest

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