Does the equation represent a direct variation? If so, find the constant of variation. 2x - 4y = 0

Answers

Answer 1

The constant variation is 1/2

Answer 2

Direct variation is of the form y=kx

2x-4y=0 subtract 2x from both sides

-4y=-2x divide both sides by -4

y=x/2 or to be clear:

y=(1/2)x

So there is a constant of variation k=1/2 of the form y=kx, so this equation is a direct variation.

*note, it is called a direct variation because as the independent variable increases/decreases, the independent variable increases/decreases by the same factor...

Related Questions

This sequence represents the diameters of circles used to create an art project: 2.5 cm, 3.1 cm, 3.7 cm, 4.3 cm Let f(n) represent diameter in centimeters and n the term number in the sequence. Which equation represents the sequence of diameters?

Answers

ANSWER

The expression that represent the sequence of diameters is,
[tex]f(n) = 0.6n + 1.9[/tex]

EXPLANATION

The terms in the sequence are,

[tex]2.5,3.1,3.7,4.3[/tex]

The first term is
[tex]a = 2.5[/tex]

The common difference is

[tex]d = 3.1 - 2.5 = 0.6[/tex]

The formula for the nth term is given by,

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

We substitute the values in to the formula to get,

[tex]f(n) = 2.5+ (n - 1)0.6[/tex]

We expand the parenthesis to obtain,

[tex]f(n) = 2.5 + 0.6n - 0.6[/tex]

We rearrange to obtain,

[tex]f(n) = 0.6n + 2.5- 0.6[/tex]

We simplify to get,

[tex]f(n) = 0.6n + 1.9[/tex]

Answer:

[tex]f(n) = 1.9 +0.6n[/tex]

Step-by-step explanation:

The nth term of the arithmetic sequence is given by:

[tex]a_n = a_1+(n-1)d[/tex] ....[1]

where

[tex]a_1[/tex] is the first term

d is the common difference and n is the number of terms.

Here, f(n) represent diameter in centimeters and n the term number in the sequence.

Given the sequence represents the diameters of circles used to create an art project:

2.5 cm, 3.1 cm, 3.7 cm , 4.3 cm

This sequence is an arithmetic sequence with

[tex]a_1[/tex] = 2.5 and d = 0.6

Since,

3.1-2.5 = 0.6,

3.7-3.1 = 0.6

4.3-3.7 = 0.6

Substitute the given values in [1] we have;

[tex]f(n) =2.5+(n-1)(0.6)[/tex]

Using distributive property, [tex]a\cdot (b+c) = a \cdot b+ a\cdot c[/tex]we have;

[tex]f(n) = 2.5+0.6n-0.6[/tex]

Simplify:

[tex]f(n) = 1.9 +0.6n[/tex]

Therefore, the equation represents the sequence of diameters is, [tex]f(n) = 1.9 +0.6n[/tex]

The term that describes how long it takes a function to repeat its behavior is the _____

Answers

The term is called period, i.e. after every period, the function starts over again

The baker pays $0.80 per pound for sugar and $1.25 per pound for butter. Write an expression that shows how much the baker will spend if he buys 6 pounds of butter and 20 pounds of sugar.

Answers

Answer:

$0.80x + $1.25y = z

Step-by-step explanation:

the total money spent if the Baker bought 6 pounds of butter and 20 pounds of sugar would be $23.50.

The total money spent if the Baker bought 6 pounds of butter and 20 pounds of sugar would be $23.50.

What is Expression?

An expression is combination of variables, numbers and operators.

Given,

The baker pays $0.80 per pound for sugar

The baker pays $1.25 per pound for butter.

We need to write expression that shows how much the baker will spend if he buys 6 pounds of butter and 20 pounds of sugar.

Let x be the pounds for sugar

x be the pounds for butter

20x+6y=Total

As x=0.80 and y=1.25

20(0.80)+6(1.25)

16+7.5

23.5

Hence, the total money spent if the Baker bought 6 pounds of butter and 20 pounds of sugar would be $23.50.

To learn more on Expressions click:

https://brainly.com/question/14083225

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Consider the following sets. U = {ordered pairs on a coordinate plane} A = {ordered pair solutions to y = x} B = {ordered pair solutions to y = 2x} Which ordered pair satisfies A ∩ B?

Answers

Answer:

(0,0)

Step-by-step explanation:

We have,

U = { (x,y) : x,y belong to real numbers }

A = { (x,y) : (x,y) is a solution of y=x }

B = { (x,y) : (x,y) is a solution of y=2x }

We need to find the ordered pair (x,y) that belong to A[tex]\bigcap[/tex]B.

Let, (x,y) belong to A[tex]\bigcap[/tex]B

i.e. (x,y) belong to A and (x,y) belong to B

i.e. y = x and y = 2x

i.e. x = 2x

i.e. x = 0

Now, substitute x= 0 in any of the equation say y = x, we get y = 0.

Hence, the ordered pair satisfying A[tex]\bigcap[/tex]B is (0,0).

For a set U, The ordered pair satisfies A ∩ B is mathematically given as

x = 0, y = 0 (0,0)

Which ordered pair satisfies A ∩ B?

Question Parameter(s):

U = {ordered pairs on a coordinate plane}

A = {ordered pair solutions to y = x}

B = {ordered pair solutions to y = 2x}

if (x,y) belongs to AnB

y = x and y = 2x

x = 0

In conclusion, subsituting we have

y = x and y = 2x

y = 0

Answers

You can turn them into decimals:

3/10 = 0.3 and 4/8 = 0.5

0.3 is less than 0.5, so you will use the symbol <

< that's the answer because 4/8 is a bigger number than 3/10

Tim answered all the questions on his math test but got 10 answers wrong. He received 4 points for every correct answer, and there was no penalty for wrong answers. His score was 76 points.Write an equation to determine the total number of questions (q)(q)left parenthesis, q, right parenthesis on Tim's math test. And Find the total number of questions on his math test.

Answers

76/4=19 So with 19 questions correct and 10 incorrect, 29 questions were on the test. p.s. If I misunderstood and this isn't answering all your questions just comment or pm.

The equation is

4(q-10)=76

The amount of questions is

29 questions

True or False? The point-slope form of a line is y + y1 = m(x + x1), where m is the slope and (x1, y1) is a point on the line. It's false right?

Answers

False.

Point-slope form is: y-y1=m(x-x1)

They used sums instead of differences...

Answer:

False

The correct point slope form passing through points (x1,y1) is [tex](y-y1)=m (x-x1)[/tex] .

Step-by-step explanation:

The formula for the point slope form passing through the point (a,b) is given by.

[tex](y-b)=m (x-a)[/tex]

Where m is the slope .

As given in the question.

m is the slope and (x1, y1) is a point on the line.

Thus the point slope form becomes

[tex](y-y1)=m (x-x1)[/tex]

Therefore the correct point slope form passing through points (x1,y1) is [tex](y-y1)=m (x-x1)[/tex] .

I draw a card 50 times from a standard 52 deck and gets a heart 8 times what's the probability that I draw a heart on the next draw

Answers

To solve this problem, let us first define what probability is. By standard definition, probability is the ratio of how many times a selected event occurred over the total number of events which occurred. Hence:

Probability = number of times a selected event occurred / total number of events

In this case, our selected event is the drawing of a heart which occurred 8 times. While our total event is the total number of drawing of cards which occurred 50 times. Hence, the probability is:

Probability = 8 / 50

Probability = 4 / 25 = 0.16 = 16%

Therefore there is a 4/25 or 0.16 or 16% chance that the next draw will be a heart.

Seth is trying to find the unit price for a package of blank discs on sale at 10 for 5.49, his answer was $1.82 per disc is he correct?

Answers

Seth is incorrect, because on sale, 1 disc would cost about $0.55.
I figured this out by dividing 5.49 by 10, and got $0.549 which rounds to $0.55.

If this is incorrect, I am sorry, but I am 99.9% sure that I am correct.

A rectangular tabletop has a length of 4 3/4 feet and an area of 11 7/8 square feet. What is the width of the table top?

Answers

Well to find this first you will divide the area by the length.
If you can use a calculator just put 11.875/4.75 which gives you as your width 2.5.
If you can't then change them into irregular fractions so...
11 7/8 --> 95/8
4 3/4 --> 19/4
Then divide them
95/8 / 19/4
95/8 * 4/19
380/152= 2.5 or 2 1/2

some kids like to ride their bikes to and from school let d be the distance in miles from a kid home to school write 2 expression to represent how far a kid travel by bike in 4 weeks

Answers

Expression 1; If your friend bikes 1.5 miles home from school each day for 4 weeks, they bike a total of - miles in that time period. The math I did was multiply 5 by 4 to get 20 school days in 4 weeks, and multiplied 1.5 by 20 to get 30 miles biked in 4 weeks.
Expression 2; If you bike 3.25 miles home from school each day, using the same math shown in the previous expression, substituting 1.5 for 3.25. Using that math, you would bike 65 miles in 4 weeks.

Sarcastic conclusion; You and your friend both get quite the leg day just to get home from school!

The whole is 8. One part is 8. What is the other part? Tell how you know.

Answers

I assume that the question here refers to addition, because that's what "part of" suggests- it's the closest mathematical operation that makes sense.

In an addition 8+x=8

x, the "other part" has to be 0 - this i means that the first part of 8 is 8 and the other is an "empty part"

What is the equation of the line that is parallel to y = -2x + 4 and goes through the point (1,7)

Answers

Answer: y = -2x+9

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

Work Shown:

The slope of the line y = -2x+4 is m = -2
Any line parallel to this line will also have a slope of m = -2
Parallel lines have equal slopes

Plug this slope, along with the given point (x1,y1) = (1,7) into the point slope formula. Then isolate y

y - y1 = m(x - x1)
y - 7 = -2(x - 1)
y - 7 = -2x + 2
y - 7 + 7 = -2x + 2 + 7
y = -2x + 9

one of the comers of a cube is sliced off the resulting cross section will have a minimum of ? Sides ?

Answers

a corner of a cube connects 3 sides to each other,

then add the side of the cut

so it would have 4 sides

A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building.
In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot

Answers

The first step in solving a problem is illustrating it just as what the picture shows. The ladder represents the hypotenuse, or the longest side of the right triangle. It measures 14 feet. The base measures 6 feet. The height of the top of the ladder from the base of the wall is denoted as x. Since this is a right triangle, the special equations for Pythagorean theorems would apply. The equation is

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the other shorter legs. Substituting the values,

14^2 = 6^2 + x^2
x^2 = 14^2 - 6^2
x^2 = 160
x = 4√10 = 12.65 feet

The height of the building from the top of the ladder is 12.6 ft

The situation forms a right angle triangle.

Right angle triangle:

A right angle triangle is a triangle that has one of its sides as 90 degrees.

Therefore,

The length of the ladder is the hypotenuse side.

The bottom of the ladder distance from the base of the building is the adjacent side of the triangle. Therefore,

The height of the building from the top of the ladder is the opposite sides. Therefore, using Pythagoras theorem.

c² = a² + b²

14² - 6² = b²

b² = 196 - 36

b² = 160

b = √160

b = 12.6491106407

b = 12.6 ft

learn more on right triangle here: https://brainly.com/question/12553755

How do you do solve this question?

Answers

In 14 minutes, Dan has already traveled 840 miles

14 • 60 = 840

Since Jake bikes 210 per minute, you would need to divide the total number of miles that Dan has traveled in 14 minutes (840 miles) by the amount of miles Jake can travel in one minute (210).

840 ÷ 210 = 4 minutes

Answer: 4 minutes

Greg has decreased his running time by minute each of the last six weeks. Write an expression to represent the total change in his time over the last six weeks. Then, find the total change.

Answers

Total change in relation to when Greg first started decreasing his run time : -6 minutes (at the end of 6 weeks)

Expression : -x (x is the number of weeks)

what is 7a + 10 = 2a

Answers

7a-2a=-10
5a=-10
a=-10/2
a=-5

Here's the answer to you question

A flooring company ships 13x13 inch tile in boxes of 11 tiles each, on pallets containing 40 boxes (Check Work Required. Please Help)

A) How many square feet does each box contain?
B) How many square feet will a pallet of tile cover?

Answers

Each tile cover an area of 13 in*13 in= 1.08 ft *1.08 ft= 1.17 square feet.

A) Each box contains 11 tiles, each of which covers 1.17 square feet.

So the area each box covers is 11*1.17 square feet=12.87 square feet

B) A pallet contains 40 boxes, each of which covers 12.87 square feet,

so one pallet covers 40*12.87 square feet=514.8 square feet.

Answer:

A) 12.87 square feet

B) 514.8 square feet.

On her math quiz, Sandra lost 8 points for incorrect answers, but she gained 5 points for a bonus question. What is the sum of the points Sandra lost and gained?

Answers

[tex]8[/tex] lost

[tex]5[/tex] gained

[tex](-8)+5=-(8-5) = -3[/tex]

Answer:
-3 points

PLEASE HELP!! 20 POINTS <33

Answers

[tex](x-x_a)^2+(y-y_a)^2}=r^2 \\ x_a=3, \ \ y_a=5, \ \ r=2 \\ \\ \\ (x-3)^2+(y-5)^2}=2^2 \\ \boxed{(x-3)^2+(y-5)^2=4}[/tex]

The first equation is the answer

What are the steps for constructing a circumscribed circle for using only a compass and a straightedge?

Answers

Find the incenter of the triangle.
Draw a perpendicular from the incenter to one of the sides. Mark the point of intersection with the side.
Set the distance between compass points to the distance between the point of intersection and the incenter. This is the radius of the circle

Construct the perpendicular bisector of one side of triangle
Construct the perpendicular bisector of another side
Where they cross is the center of the Circumscribed circle
Place compass on the center point, adjust its length to reach any corner of the triangle, and draw your Circumscribed circle!

on july 4 180 people hiked on the trail. of these 1/3 camped overnight. how many of the hikers dis not camp overnight

Answers

1 - 1/3= 2/3

180(2/3)= 120

120 hikers did not camp overnight.

Hopefully, this helps!

(Picture) please help asap!

Answers

0 to 1 is broken down into 9 equal spaces

the dot is on the 5th line

so it would be 5/9

What is p−m ⋅ pn equal to?

Answers

(p - m)*pn

= p²n - pnm

The answer is
p−m ÷ n

Find the greatest number
0.9,0.91,9/10

Answers

0.9=0.9/1=9/10=90/100

0.91=0.91/1=9.1/10=91/100

9/10=90/100

90/100<91/100

the greatest is 91/100 or 0.91

Please help!
The number line below represents which combined inequality?
number line with a closed circle on negative 2, shading to the left and a closed circle on 4, shading to the right
x greater than or equal to −2 or x less than or equal to 4
x greater than or equal to −2 and x less than or equal to 4
x less than or equal to −2 or x greater than or equal to 4
x less than or equal to −2 and x greater than or equal to 4

Answers

I'm doing interval notations right now in pre-calculus, this how this notation should be written, (-∞,-2] or [4,∞), but this, (x ≤ -2] or [4 ≤ x), means the same thing. closed circle gets a bracket and an open circle gets a parenthesis, infinity always gets a parentheses because it is not a number. hope this helps

Answer:

Step-by-step explanation:

I just did it on edge 2021 :)

what rate is equivalent to 72/9

Answers

8/1 is equivalent to 72/9

The highest score that is a record for a particular video game is 19,749 points. The lowest score on record for the same video game is 176 points. Which of the following inequalities best shows the range of scores recorded on the game?

Answers

According to my algebra knowledge, the answer is D.

They key is the less than or equal to sign.

Have a blessed day :)

Let x represent the score that the individual can get
The highest score that is a record for a particular video game is 19,749 points, and it means that the individual could get 19749 points or lower than that, so the inequality will be like this:
[tex]x \leq 19749[/tex]
Next, the lowest score on record for the same video game is 176 points, and it also means that the individual could get 176 points or lower, so the inequality will be:
[tex]x \geq 176[/tex].
Finally, we have the two inequality we want and let's combine them, to get:
[tex]176 \leq x \leq 19749[/tex]. As a result, D is your final answer. Hope it help!

A local hamburger shop sold a combined total of 646 hamburgers and cheeseburgers on Saturday. There were 54 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?

Answers

646-54 = 592

592/2 = 296

296+54 = 350

350+296 = 646

there were 350 hamburgers and 296 cheeseburgers sold

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