If y varies directly as x, and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this
relation?
10
40
100
198

Answers

Answer 1

Answer:

10

Step-by-step explanation:

If there is a direct relation between two variables x and y then it can be represented as

y = kx ,

where y is dependent variable

x is  independent variable

k is constant of variation

_____________________________

First condition

y = 400

x = r

using y = kx then relationship will be

400 = kr

finding k here

k = 400/r

Second condition

y = r

x = 4

using y = kx then relationship will be

r = 4k

finding k

k = r/4

since  in both condition equation is same

thus, value of k will also be same

thus,

400/r = r/4

=> 400*4 = r*r

=> 1600 = r^2

[tex]\sqrt{r^{2} } = \sqrt{1600} \\r = 40[/tex]

Thus, 40 is the value of r

k = r/4 = 40/4 = 10

Thus, constant of variation is 10 which is correct choice.

To cross validate

k = 400/r = 400/40 = 10

Answer 2

Answer:

40

Step-by-step explanation:

[tex]\frac{r}{400}[/tex] = [tex]\frac{4}{r}[/tex]

cross multiply - 400*4 = 1600 and r*r = r^2

square both - √1600 = 40


Related Questions

The following graph shows a proportionality between y and x in the graph ?

Answers

Answer:

3/1 is the ans

Step-by-step explanation:

here y is in 3

and x is in 1

so proportonality will be 3/1

pls show work and explain how to do it

Answers

Step-by-step explanation:

1. We can see that the two vertical lines are parallel. Since one angle is 80º, then the other side should be 100º, since the straight line is 180º.

2. If the angle on the right is 80º, then that means the angle with y and 40º add up to 100º.

3. 100º - 40º = 60º.

Our final answer: y = 60º

I hope this helps!

Is the number a rational number? Help me out please!

Answers

Answer:

first answer

Step-by-step explanation:

Hi, this is correct because repeating decimals are rational numbers.

Rational numbers can be written by a fraction of integers.

If there is a pattern, it means that this is the division of two integers.

hope this helps

Answer:

yes

Step-by-step explanation:

Between which two integers does square root of /51 lie

Answers

Answer:

7 and 8

Step-by-step explanation:

Consider the perfect squares either side of 51

49 < 51 < 64 , thus

[tex]\sqrt{49}[/tex] < [tex]\sqrt{51}[/tex] < [tex]\sqrt{64}[/tex] , that is

7 < [tex]\sqrt{51}[/tex] < 8

Answer:

7 and 8.

Step-by-step explanation:

7^2 = 49 and 8^2 = 64.

Peter plays on the varsity basketball team. So far this season he has scored a total of 52 points. He scores an average of 13 points per game. How many more games must Peter play in order to score 117 points?​

Answers

Answer:

5 more games.

Step-by-step explanation:

117 - 52 = 65.

65 / 13 = 5.

Jackson drops a pumpkin off a balcony from
a height of 64 feet. Analyze the time in seconds it takes
for the pumpkin to smash on the ground.

Answers

Answer:

t = 1.15 seconds.

Step-by-step explanation:

The pumpkin is dropped from the height of = 64 feet.

Now we have to find the time taken to reach the pumpkin on ground. Use the below formula to find the time taken.

H = ½ gt^2

H = height

g = 9.8 (always contant )

t = time taken.

Now insert all the values in the formula.

H = ½ gt^2

64 = ½ ×9.8× t^2

(64×2) / 9.8 = t^2

t = 1.15 seconds.

Daryl is twice the difference of Amy’s age and 5. If their combined age is 50, how old is Darly

Answers

Answer:

30

Step-by-step explanation:

What is m RMS in the figure below?
RA
P
M
128°
T
A 26
B 38
C 52
D 128

Answers

Answer:

Option (B)

Step-by-step explanation:

There are two lines PS and QT intersecting each other at a point M.

It's given that m∠PMT = 128° and m∠QMR = 90°

Since ∠PMT and ∠QMS are the vertical angles so these angles will be equal in measure.

∠PMT = ∠QMS

128° = m∠QMR + m∠RMS

128° = 90° + m∠RMS

m∠RMS = 128° - 90°

m∠RMS = 38°

Therefore, Option (B) will be the answer.

Which model represents a fraction less than Three-fifths? A circle divided into 5 equal parts. 4 parts are shaded. A circle divided into 5 equal parts. 2 parts are shaded. A circle divided into 5 equal parts. 6 parts are shaded. A circle divided into 10 equal parts. 8 parts are shaded.

Answers

Answer:

The correct answer is:

A circle divided into 5 equal parts. 2 parts are shaded.

Step-by-step explanation:

To determine the fraction less than three-fifths, let us convert the word problems into figures and compare the values:

[tex]Three-fifths = \frac{3}{5} = 0.6[/tex]

a) A circle divided into 5 equal parts. 4 parts are shaded (four-fifths)

[tex]Four-fifths = \frac{4}{5} = 0.8\ (more\ than\ three-fifths)[/tex]

b) A circle divided into 5 equal parts. 2 parts are shaded. (two-fifths)

[tex]Two-fifths = \frac{2}{5} = 0.4\ (less\ than\ three-fifhs)[/tex]

c) A circle divided into 5 equal parts. 6 parts are shaded = [tex]\frac{6}{5} = 1.2[/tex] (more than three-fifths)

d) A circle divided into 10 equal parts. 8 parts are shaded [tex]= \frac{8}{10} = 0.8\ (more\ than\ three-fifths)[/tex]

Therefore, the fraction less than three-fifths = A circle divided into 5 equal parts. 2 parts are shaded. (two-fifths)

A circle divided into 5 equal parts. 2 parts so the answer is B

explanation:

Hope this works<3

Please help!!! I'll mark you brainiest and give you as many Points as possible!!!!!

Answers

Answer:

Option C

Step-by-step explanation:

[tex]f(x) = 40( \frac{1}{4} )^{x} [/tex]

Answer: its a

Step-by-step explanation:

Janice published a novel. Last month the book sold 1326 copies, earning Janice a total of $1579.76. This month the book sold 1445 copies. How much should Janice expect to receive in royalties this month?

Answers

$1,721.53. That’s your answer.

HURRY!!! ILL MARK U BRAINLIEST!! After completing the fraction division StartFraction 7 Over 3 EndFraction divided by StartFraction 2 Over 9 EndFraction, Bai used the multiplication below to check his work. StartFraction 21 Over 2 EndFraction times StartFraction 2 Over 9 EndFraction = StartFraction 42 Over 18 EndFraction = StartFraction 7 Over 3 EndFraction Which is the most accurate description of Bai’s work? Bai found the correct quotient and checked his work using multiplication correctly. Bai found the correct quotient but checked his work using multiplication incorrectly. Bai found an incorrect quotient but checked his work using multiplication correctly. Bai found an incorrect quotient and checked his work using multiplication incorrectly.

Answers

Answer:

The answer is a.

Bai found the correct quotient and checked his work using multiplication correctly.

Step-by-step explanation:

I know this cuz I did the test on edge :))

Anyways plz give me the brainliest!!

Answer:

ITS A

Step-by-step explanation:

i did it on edge 2020

pls give Brainliest.

pleasee help me

2t+ 1 = 3t-1 + 3
3 4

Answers

Answer:

t = -1

Step-by-step explanation:

[tex]2t + 1 = 3t - 1 + 3[/tex]

Collect like terms and simplify

[tex]2t - 3t = - 1 + 3 - 1 \\ - t = 1[/tex]

Divide through by -1

[tex] \frac{ - t}{ - 1} = \frac{ 1}{ - 1} \\ t = - 1[/tex]

Answer:

t = - 2

Step-by-step explanation:

[tex]\frac{2t + 1}{3} = \frac{(3t-1) + 3}{4}[/tex]

First we need to cross multiply to get rid of the division to make it easier to solve.

Multiply 2t+1 by 4 and (3t-1) + 3 by 3

4 ( 2t + 1 ) = 3 ( ( 3t - 1 ) + 3 ) On the right we need to combine terms.

4 ( 2t + 1 ) = 3 ( 3t - 1 + 3 )

4 ( 2t + 1 ) = 3 ( 3t + 2 )   Multiply

4 * 2t + 4 * 1 = 3 * 3t + 3 * 2     Remember order of operations. Multiplication comes before addition and subtraction.

4 * 2t + 4 * 1 = 3 * 3t + 3 * 2

8t + 4 = 9t + 6      Subtract 8t from each side

8t - 8t + 4 = 9t - 8t + 6

4 = t + 6       Subtract 6 from each side

4 - 6 = t + 6 - 6

4 - 6 = t

- 2 = t

90 + 12 = 6(15 + 12)


Answers

The answer for your question is 102

-2, -1, -1, 0, -1, 1, -2, … Find the next 3 numbers in the sequence above. Describe the pattern.

Answers

Answer:  -2, -1, -1, 0, -1, 1, -2, -1, -1, 0

Step-by-step explanation:

When you are looking at the problem

" -2, -1, -1, 0, -1, 1, -2, … Find the next 3 numbers in the sequence above. Describe the pattern."

you want to observe the pattern, now For example

1, 2, -1, -4 .. and so on

so there is a pattern here if looked at hard enough it goes 1 - 2 = -1 - -3 = -4

when you find the pattern it gets really easy.

Hope this helped!

Which list of integers is in order from greatest to least? -11, -18, -33, 9, 24 -33, 24, -18, -11, 9 24, 9, -33, -24, -11 24, 9, -11, -24, -33

Answers

Question

Which list of integers is in order from greatest to least?

a) -11, -18, -33, 9, 24

b) -33, 24, -18, -11, 9

c) 24, 9, -33, -24, -11

d) 24, 9, -11, -24, -33

Answer:

d) 24, 9, -11, -24, -33

Step-by-step explanation:

The question asked us which list of integers is in order from greatest to least. This means, we should arrange the integers in descending order from the highest to the least or lowest number.

24< 9< -11< -24 < -33

Hence, from the greatest to the least =

24, 9, -11, -24, -33

Option d), is correct.

What is the justification for the step taken from line 2 to line 3?

Answers

Answer:

They subtracted 2x from both sides.

Step-by-step explanation:

They removed 2x from each side because in order to find x it will have to be removed on one side. Since 2x - 2x = 0 it is 2x is out of the equation for the right side and on the left side -2x -(-4x) = -6x which means that there is one x variable left in the equation thus making it solvable.

Two angles from a liner pair. The measure of one angle is 4 times the measure of the other angle. Find the measure of each angle

Answers

Answer:

x = 36 degrees, the smaller angle.

4(36) = 144 degrees, The larger angle.

36 + 144 = 180 degrees.

Cleomenius.

Answer:

x = 36 degrees, the smaller angle.4(36) = 144 degrees, The larger angle.36 + 144 = 180 degrees.

Step-by-step explanation:

(1)adjacent- two non-overlapping angles that share a common vertex and a common side

(2)the non-common sides are opposite rays.

(3)adds up to 180

Find and describe the error in the followig work -3(2x+3)=21 -6x+9=21 -6x=12 x=-2

Answers

Answer:

-3(2x+3)=21 does not become -6x+9=21 because wrong foiling.

Step-by-step explanation:

When you distribute -3 with 2x+3 you multiply both values by -3.

-3*2x = -6x

-3*3 = -9 <- This is where the error is. It's -9, not +9.

Describe the steps to copy angle CAB∠ C A B.

Answers

Answer:

Step-by-step explanation:

Construction: To copy angle CAB.

i. On angle CAB, with center A and any radius; draw an arc to intersect CA at E and AB at F.

ii. Place a divider at EF to copy the angle.

iii. Draw a separate straight line MN of approximate length to AB.

iv. Mark point P on MN. Place the divider with radius EF at P to mark Q.

v. Draw a line LM from M through Q.

vi. Therefore, angle CAB would be equal to angle LMN.

What would happen if I double the 4 and the 6 in 4-6

Answers

The answer is -4. The answer just is multiplied by 2.

Solve for x. Round if needed. Image is below.

Answers

Answer:

x = 16

Step-by-step explanation:

3x + 1 = 49 ( vertical angles )

Subtract 1 from both sides )

3x = 48 ( divide both sides by 3 )

x = 16

Shanelle invested $10,000, and at the end of one year, she received $805 in interest. She invested part of the money in an account earning 10% simple interest and the remaining money in an account earning 7%simple interest. How much did she invest in each account?

Answers

Step-by-step explanation:

Let the first part be x. Then,

the second part will be (10000-x).

So, According to question,

(10% of x) + { 7% of (10000-x)} = 805

(10/100*x) +{7/100*(10000-x)} = 805

(x/10) + (70000-7x/100) = 805

Then,

We will take the lcm of 10 and 100 which is 100 and then add both the fractions.

Solution:

10x + 70000-7x/ 100 = 805

3x + 70000/100 = 805

3x + 70000 = 805*100

3x + 70000 = 80500

3x = 80500-70000

3x = 10500

x = 10500/3

x = 3500

So the first part is 3500.Then,

the second part will be (10000-3500)

= 6500

HOPE IT WILL HELP YÔÛ.♥️♥️

15+21 distributive property

Answers

The answer is 36

Explanation

what would be the answer to g+3=17

Answers

Answer:

g = 14

Step-by-step explanation:

g + 3 = 17

minus 3 from both sides

g = 14

Definición de forma estándar y ejemplo????

Answers

Answer:

Las reglas para escribir un número en forma estándar es que primero escribes un número entre 1 y 10, luego escribes × 10 (a la potencia de un número). En una calculadora, generalmente ingresa un número en forma estándar de la siguiente manera: Escriba el primer número (el que está entre 1 y 10). Presione EXP

Step-by-step explanation:

The parking lot at a grocery store has 90 cars in it. 90% of the cars are blue. How many cars are blue?
a 10 cars
b 81 cars
c 810 cars
d 100 cars

Answers

Answer:

81 blue cars

Step-by-step explanation:

Total Cars = 90

How much % are blue = 90

=> 90 x 90/100 = How many cars are blue

=> 8100/100 = the number of cars that were blue

=> 81 = cars that were blue.

There 81 blue cars in the parking lot.

[GIVING BRAINIEST] What is 18/6

Answers

Answer:

3

Step-by-step explanation:

18/6 = 3

5j+15=12j-13 please solve

Answers

Answer:

j=4

Step-by-step explanation:

5j+15=12j-13

Answer: j = 4

Step-by-step explanation:

5j + 15 = 12j - 13

5j = 12j - 28                  Subtract 15 from both sides        

-7j = -28                        Subtract 12j from both sides

j = 4                               Divide -7 from both sides

Convert the decimal to a fraction. 0.185

Answers

Answer:

37/200

Step-by-step explanation:

.185= 185/1000

reduce to- 37/200

Hope this helps.

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