What is the constant of variation, k, of the direct variation, y = for, through (5,8)?

Answers

Answer 1

Answer:

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

Step-by-step explanation:

The constant of direction variation givens a proportion that is maintained by both x and y values for all points of a line that it passes through.

Usually represented with the variable [tex]k[/tex], it is given by:

[tex]\frac{y}{x}=k[/tex] for coordinates (x, y).

This relationship can be written as [tex]y=kx[/tex] which is also the layout for a proportional relationship.

Since coordinates are written (x, y), for point (5, 8), substitute [tex]x=5, y=8[/tex] to get the constant of variation:

[tex]8=5k,\\k=\boxed{\frac{8}{5}}[/tex]

Answer 2

Answer:

8/5

Step-by-step explanation:

Given that y varies directly with x , therefore ,

[tex]\implies y \propto x[/tex]

Let k be the constant . Therefore ,

[tex]\implies y = k x[/tex]

When the point is (5,8) ,

[tex]\implies 8 = k * 5 \\\\\implies \underline{\underline{\boxed{ k =\dfrac{8}{5}}}}[/tex]

Hence the constant of variation is 8/5.


Related Questions

If the volume of a cubical room is 2700 cm^3 . Find its length

Answers

Step-by-step explanation:

If the volume of a cubical room is 2700 cm³ .

l³=2700

l=3 (100)⅓

I dont understand what to do here, can somebody help, please? 4.2 / 6 = ____ tenths / 6 4.2 / 6 ____ tenths

Answers

Answer:

sei lá, pergunta pra tua mãe

Evaluate the function. f(x)=−x^2 Find f(−5)

Answers

Answer:

25

Step-by-step explanation:

put -5 from x so (-(-5))²=25

Solution:

For each occurence of x in f(x) substitute 4 and clculate the result

f(x)=-x^2+5 becomes

f(4)=-(4)^2+5

f(4)=-16+5

f(4)=-11

Consider this system of equations. Which shows the second equation written in slope-intercept form? y = 3 x minus 2. 10 (x + three-fifths) = 2 y y = 5 x + StartFraction 3 Over 10 EndFraction

Answers

Answer:

[tex]y = 5x + 3[/tex]

Step-by-step explanation:

Given

[tex]y = 3x - 2[/tex]

[tex]10(x + \frac{3}{5}) = 2y[/tex]

Required

The second equation in slope intercept form

We have:

[tex]10(x + \frac{3}{5}) = 2y[/tex]

Divide both sides by 2

[tex]5(x + \frac{3}{5}) = y[/tex]

Open bracket

[tex]5x + 3 = y[/tex]

Rewrite as:

[tex]y = 5x + 3[/tex]

Hence, the equation in slope intercept form is: [tex]y = 5x + 3[/tex]

Answer: I agree with the other person

Step-by-step explanation:

A post office charges 50k for a telegram of 15 words or less it charges an extra 3k for every word above 15 words find the cost of 30 words

Answers

Answer:

95k

Step-by-step explanation:

Given :

15 words or less = 50k

Every word above 15 = additional 3k

The cost of 30 words :

First 15 words = 50 k

Number of additional words = (30 - 15) = 15 words

Cost of every additional word = 3 k

Cost of 15 additional word = 15 * 3 = 45k

Total cost of 30 words :

50k + 45k = 95k

how much does 1/64 stand for

Answers

Answer:

1/64 is 0.015625 in decimals

expand: 4(w - 2)
(with the steps)​

Answers

Answer:

4w-8

Step-by-step explanation:

4(w-2)

(4*w)-(4*2)

4w-8

Answer:

4w-8

Step-by-step explanation:

4(w - 2)

Distribute

4*w - 4*2

4w-8

Select the correct answer. Rachel traveled to five different areas (A, B, C, D, and E) to study the number of buckeye butterflies and the number of monarch butterflies living there. The table shows her findings. Area Buckeye Butterflies Monarch Butterflies A 15 16 B 27 36 12 25 24 32 E 44 33 The relationship between the number of buckeye butterflies and the number of monarch butterflies is not proportional across all areas. Which two areas have buckeyes and monarchs in the same proportion? OA. areas A and B OB. areas Cand E O C. areas B and D OD. areas C and D ​

Answers

A ratio shows us the number of times a number contains another number. The two areas that have buckeyes and monarchs are in the same proportion as A and D.

What is a Ratio?

A ratio shows us the number of times a number contains another number.

The ratio of buckeyes and monarch butterflies in different areas can be written as,

Area A,

Buckeyes/Monarchs = 15/16

Area B,

Buckeyes/Monarchs = 27/36 = 3/4

Area C,

Buckeyes/Monarchs = 12/25

Area D,

Buckeyes/Monarchs = 24/32 = 3/4

Area E,

Buckeyes/Monarchs = 44/33 = 4/3

Hence, the two areas that have buckeyes and monarchs are in the same proportion as A and D.

Learn more about Ratios here:

https://brainly.com/question/1504221

#SPJ2

Answer:B and D

Step-by-step explanation:

i just took the test

modrater give answer


if 27x = 45263514282 than find the value of 200x ​

Answers

═══════ღ❦ღ══╮

[tex]\boxed{ \sf{Answer}} [/tex]

↦ First find the value of x

[tex]27x = 45263514282 \\ x = \frac{45263514282}{27} \\ x = 1676426454.89[/tex]

↦ Now, find the value of 200x

[tex]x = 1676426454.89 \\ 200x = 200 \times 1676426454.89 \\ 200x = 335285290978[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Given that,

→ 27x = 45263514282

Then we have,

To find the required value of 200x.

Before that,

find the required value of x.

→ 27x = 45263514282

→ x = 45263514282/27

→ [x = 1676426454.89]

Now we can,

Solve for the value of 200x.

→ 200x

→ 200 × (x)

→ 200 × (1676426454.89)

→ 335285290978

Hence, 200x is 335285290978.

can someone help me plz

Answers

Answer:

B

Step-by-step explanation:

lets say the cost for a pound is 2$

if the watermelon weighs 3 pounds it would cost $6.

2(3)

The weight is the variable in the parenthesis because that is what is constantly changing.

Which is the best estimate for 6.3×10 to the second power times 9.9×10 to the 3rd power written in scientific notation

Answers

Answer:

in scientific notation, the expression can be written as 6.237 x 10⁶

Step-by-step explanation:

Given;

6.3×10 to the second power times 9.9×10 to the 3rd power

Using scientific notation, it can be interpreted as;

[tex](6.3 \times 10^2) \times (9.9 \times 10^3)[/tex]

This can be simplified as;

[tex](6.3 \times 10^2) \times (9.9 \times 10^3) = (6.3\times 9.9)\times 10^{2+3}\\\\= 62.37\times 10^5 = 6.237\times 10^6[/tex]

Therefore, in scientific notation, the expression can be written as 6.237 x 10⁶

The diagram shows a right angle triangle find the size of x give your answer to 1 decimal place

Answers

Answer:

34.9°

Step-by-step explanation:

SOH

CAH

TOA

SOH ... sin(x) = 8/14

arcsin(8/14) = 34.85°

Solve the inequality. w/-2<8

Answers

Answer:

w > -16

Step-by-step explanation:

5x+1=2x-5
I need help

Answers

Answer:

x =-2

Step-by-step explanation:

5x+1=2x-5

Subtract 2x from each side

5x-2x+1=2x-2x-5

3x+1 = -5

Subtract 1 from each side

3x+1-1 = -5-1

3x=-6

Divide by 3

3x/3 = -6/3

x = -2

the question is on the image

Answers

Answer:

€3,551.05

Step-by-step explanation:

31*29=899

899*3.65=€3,551.05

the school will get an estimate of €3,551.05

4(1\:-\:2b)\:+\:7b\:-\:10
[tex]4(1\:-\:2b)\:+\:7b\:-\:10[/tex]

Answers

Answer:

-6 -b

Step-by-step explanation:

I have attached the explanation above. hopefully this will help you

Find the value of x. PLEASE HELP ASAP

Answers

Hi there!

[tex]\large\boxed{A. \text{ } 7}[/tex]

The following trapezoidal theorem states that:

Middle segment = average of top and bottom side

Thus:

M = 1/2(b1 + b2)

21 - x = 1/2(17 + 11)

Solve:

21 - x = 1/2(28)

21 - x = 14

Subtract 21 from both sides:

-x = 14 - 21

-x = -7

Multiply both sides by -1:

x = 7

what is the average cost of 7 articles if 3 of them cost 30k each and the rest cost 12.5k each ​

Answers

[tex] {\bold{\red{\huge{\mathbb{QUESTION}}}}} [/tex]

what is the average cost of 7 articles if 3 of them cost 30k each and the rest cost 12.5k each

[tex]\bold{ \red{\star{\blue{GIVEN }}}}[/tex]

TOTAL NUMBER OF ARTICLE= 7

ARTICLES FOR 30K = 3

ARTICLES FOR 12.5K = 7-3= 4

[tex]\bold{\blue{\star{\red{TO \: \: FIND}}}}[/tex]

Average cost of 7 articles

[tex] \bold{ \green{ \star{ \orange{FORMULA \: USED}}}}[/tex]

[tex] \red{AVERAGE = \frac{TOTAL \: COST}{ NUMBER \: OF\: ARTICLES }}[/tex]

[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]

[tex]Average \: cost \: of \: 7 \: articles - > \\ \frac{(3 \times 30k) + (12 .5k \times 4)}{7} \\ \frac{90k + 50k}{7} \\ \frac{140k}{7} \\ \blue {Average \: cost \: of \: 7 \: articles - >} \\ 20k[/tex]

I need help with my math!!!!!!!

Answers

Answer:

B is the answer because the graph is translated 2 down. the translation cannot be included within the radical sign, so it can't be C

Complete the transformations below. Then enter the final coordinates of the figure.

A" (,)
B" (,)
C" (,)
HELP! PLZ.

Answers

Answer:

Step-by-step explanation:

If a point (x, y) is translated by 4 units horizontally right and 1 unit upwards, coordinates of the image point will be,

(x, y) → (x + 4. y + 1)

Therefore, vertices of the image triangle ABC will be,

A(2, 2) → A'(2+4, 2+1)

           → A'(6, 3)

B(5, -1) → B'(5+4, -1+1)

           → B'(9, 0)

C(1, -2) → C'(1+4, -2+1)

           → C'(5, -1)

Then reflected across y-axis.

Rule for the reflection across y-axis will be,

(x, y) → (-x, y)

A'(6, 3) → A"(-6, 3)

B'(9, 0) → B"(-9, 0)

C'(5, -1) → C"(-5, -1)

Answer:

A"(-6, 3)

B"(-9, 0)

C"(-5, -1)

Step-by-step explanation:

Jim is designing a seesaw for a children’s park. The seesaw should make an angle of 45 degrees with the ground, and the maximum height to which it should rise is 1 meter, as shown below: What is the maximum length of the seesaw? Choices: A) 1 meter B) 1.4 meters C) 2 meters D) 0.5 meters

Answers

Answer:

B) 1.4

Step-by-step explanation:

The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.

sin(B)=opp/hyp

The maximum length of the seesaw is 1.4 meters

Trigonometric ratio

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let h represent the length of the seesaw, hence using trigonometric ratio:

sin(45) = 1 / h

h = 1.4 meters

The maximum length of the seesaw is 1.4 meters

Find out more on Trigonometric ratio at: https://brainly.com/question/1201366

The death rate per 100,000 for lung cancer is 7 among non-smokers and 71 among smokers. The death rate per 100,000 for coronary thrombosis is 422 among non-smokers and 599 among smokers. The prevalence of smoking in the population is 55%. What is the relative risk of dying of coronary thrombosis for smokers versus nonsmokers

Answers

Answer:

1.4194

Step-by-step explanation:

death rate per 100000 for cancer

for non smokers, death rate = 7

for smokers death rate = 71

death rate per 100000 coronary thrombosis

for non smokers = 422

for smokers = 599

relative risk of dying from cancer

= number of smokers / number of non smokers

= 71/7

= 10.14

relative risk of dying from coronary thrombosis

= number of smokers/number of non smokers

= 599/422

= 1.419

the relative risk of dying of coronary thrombosis is 1.4194

= 10.14

the letter v has an unknown value. If you multiply v by 16, the product is 4.what is the value of v?

Answers

Answer:

v = 0.25

Step-by-step explanation:

v = ?

v x 16 = 4 (given)

v = 4/16

v = 0.25

Checking:

[ 0.25 x 16 = 4]

Answer:

1/4 or 0.25 (as a decimal)

Step-by-step explanation:

We know that v has an unknown value.

When it is multiplied by 16, we would get the product.

Turn it into an equation:

16x = 4

Find x:

4 ÷ 16 = 0.25 or 1/4

Now we’ve find x:

16 x 1/4 = 4

Which is a true equation

So x equals 0.25 or 1/4 (as a fraction)

I’d recommend choose fraction bu whatever is up to you!

2(5x-3)=24
find what x is?

Answers

Answer:

x = 3

Step-by-step explanation:

2(5x - 3) = 24

Divide both sides by 2.

5x - 3 = 12

Add 3 to both sides.

5x = 15

Divide both sides by 5.

x = 3

what is the slope of the line shown below? (enter your answer as a decimal if necessary.)

Answers

Answer: The slope is 2 -Please mark brainliest

1. Find the X and Y values of each point

X1: 1

X2: -1

Y1: 3

Y2: -1

2. Subtract X1 from X2 and Y1 from Y2

Y: -1-3=-4

X: -1-1=-2

3. Divide the X value by the Y value

-4/-2=2

The slope of the line shown on the coordinate plane is 2.

Answer:

2

Step-by-step explanation:

(X1,Y1)=(1,3)

(X2,y2)=(-1,-1)

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

= -1-3/-1-1

= -4/-2

= 2

Graph the image of T(

10,

7) after a rotation 270° counterclockwise around the origin.

Answers

Answer:

[tex]T' = (-7,10)[/tex]

Step-by-step explanation:

Given

[tex]T = (10,7)[/tex]

[tex]r = 270^o[/tex] counterclockwise

Required

Graph of T'

The rule to this is:

[tex](x,y) \to (-y,x)[/tex]

So, we have:

[tex]T(10,7) \to T' (-7,10)[/tex]

Hence:

[tex]T' = (-7,10)[/tex]

See attachment for graph

identify the unit rate shown in the graph
Choices:
A. 1/3 mile per hour
B. 3 hours per mile
C. 3 miles per hour
D. 4 miles per hour

Answers

The answer is C or 3 miles per hour

how is it 3?:

there is a point at 6 and another at 3 all we do is 6 - 3 = 3

Find the distance between A (2,0,-1) and B (3,1,4) and find the mid-point of line segment AB."

Answers

Step-by-step explanation:

To Find :-

Distance between the two points .

Solution :-

Using Distance Formula ,

> d = √{ ( 2-3)² + (0-1)² + (-1-4)² }

> d = √{ (-1)² + (-1)² + (-5)² }

> d = √{ 1 + 1 + 25 }

> d = √26 .

Using midpoint formula ,

> m = ( 2+3/2 , 0+1/2 , -1+4/3 )

> m = ( 5/2 , 1/2 , -3/3 )

> m = ( 2.5 , 0.5 , -1 )

Solve |x - 5| = 7 ......

Answers

Answer:

12,-2

Step-by-step explanation:

can someone help me with this?​

Answers

Answer:

-64 is the 26th number

it's an arithmetic sequence because the difference between the number is constant : -3

they are all -3 in difference

Step-by-step explanation:

an = a1 + (n-1)d

an = the nᵗʰ term in the sequence

a1=the first term in the sequence

d=the common difference between terms

-64 = 11 + (n - 1)-3

-64=11 -3n+3

-78 = -3n

n = 26

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