If y is directly proportional to x, and y = 56 when x = 6, what is
the value of x when y = 84?
A)6
B)9
C)13
D)15


Answers

Answer 1

Answer:

B) 9

Step-by-step explanation:

According to the statement, we have the following relationship:

[tex]y \propto x[/tex]

[tex]y = k\cdot x[/tex] (Eq. 1)

Where:

[tex]k[/tex] - Proportionality constant, dimensionless.

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

Such constant is eliminated by constructing this relationship:

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

[tex]x_{2} = \left(\frac{y_{2}}{y_{1}} \right)\cdot x_{1}[/tex] (Eq. 2)

If we know that [tex]y_{1} = 56[/tex], [tex]x_{1} = 6[/tex] and [tex]y_{2} = 84[/tex], then the value of [tex]x_{2}[/tex] is:

[tex]x_{2} = \left(\frac{84}{56} \right)\cdot (6)[/tex]

[tex]x_{2} = 9[/tex]

Hence, the correct answer is B.


Related Questions

Helpppppp pleaseeeeee!!!!

Answers

Answer:

box 1, 4 and 5 are correct

Step-by-step explanation:

Box 1 is correct if you simplify the equation by multiplying both sides by 4.  When you multiply the left side by 4 you end up with 56 + 8x since 4 times [tex]\frac{1}{4}[/tex] equals 1.  The right side becomes 4 x 20 = 80.  So 56 + 8X = 80.  If you continue to solve for X, you first have to subtract 56 from both sides of the equal sign which looks like this:  56 - 56 + 8X = 80 - 56 which reduces down to 8X = 24.  Dividing both sides by 8 then reduces that equation down to X = 3.

Box 4 is also correct.  When you have an equation like [tex]\frac{1}{4}[/tex] (8x + 56), you have to multiple both numbers on the inside of the parentheses by the number on the outside of the parentheses.  So the equation is ([tex]\frac{1}{4}[/tex] X 8x) + ([tex]\frac{1}{4}[/tex] X 56) which results in 2x + 14.  The right side of the equal sign does not change so now you have

2x + 14 = 20.  To get rid of the 14 on the left, you subtract 14 from both sides.

2x + 14 - 14 = 20 - 14.  On the left, 14-14=0 so you end up with just 2x.  On the right 20-14=6.  So now you have the equation 2x = 6.  If you continue to solve for x, you divide both sides of the equal sign by 2.  This will give you x = 3.  Same as what you get by solving for x in Box 1 above.

Box 5 is also correct.  As you see above when you solve for X in both answers above, X = 3.

Find the solution to the equation
8n+5=23-2n
Round your answer to the nearest hundredth, if necessary

Answers

8n +5 -23 + 2n = O
10n = 18
n = 1.8

IN NEED OF HELP!! 15 POINTS!!

Answers

Answer:

D

Step-by-step explanation:

If you draw a line in the middle of the w they will look the same

Answer:

it would be letter D

Step-by-step explanation:

Jasper starts the month with $24 in his savings account. At the end of each week, Jasper adds
$8 to the account. Use your equation to determine how many weeks have passed when Jasper reaches $166
in his account.

Answers

55 weeks is the answer

Answer:

55 or 56 I think sorry if I'm wrong.

Step-by-step explanation:

help me, please
thank you

Answers

Answer:

6x6x6 x 7x7x7x7=7776

Step-by-step explanation:

Answer: there is a video withh the answer on yt just loo up the question

Step-by-step explanation:

PLEASE HELP!! ILL MARK BRAINLYEST!!!!!!

The solution of the equation 2 d - 6 = 5 is _____.

A. 1/2
B. 1 1/2
C. -1/2
D. 5 1/2

Answers

Answer:

the answer is b

Step-by-step explanation:

Answer:

is really is B

:))))))))))))))))))))))))))))))))))))))))

Marcela needs to find the area of a circle that
has a diameter of 30 cm.
Determine whether each expression can be used to find
centimeters
Select Yes or No for each expression.
15.70
Yes
Ο Νο
30.7
Yes
Ο Νο
152.70
Yes
Ο Νο
302.7
Yes
Ο Νο
15. 157
Yes
Ο Νο

Answers

Answer:

Step-by-step explanation:

yes no no yes

Which property is shown? 4b + 3 + 2b + 5 = 4 b + 2b + 3 + 5*

Answers

Answer:

it is communitive

Step-by-step explanation:

because the powers or variabled both equal the first and second problem

(the firt  and second term problems have to match in  answer

Your first job is to babysit a couple of times a week. You charge a flatfee of $10 for transportation back and forth to the house plus $5.50per hour. Let t be the time in hours that you babysit. Write analgebraic expression to define the amount of money you will makefor t hours of work.

Answers

Answer:

5.50t + 10

Step-by-step explanation:

Total amount of  money made will sum of

transportation fees and money charged for t hours of baby siting

Given

transportation fees of back and forth to the house = $10

also given that

fees of 1 hour babysitting = $5.50

we have to find fee for t hours baby sitting ,

fees of t hours babysitting = fees of 1 hour babysitting*t

fees of t hours babysitting = 5.50t

Total amount of  money made =  fees of t hours babysitting + transportation fees of back and forth to the house

Total amount of  money made =  5.50t + 10

Thus,

algebraic expression to define the amount of money you will make for t hours of work is 5.50t + 10

how do i factor trinomials step by step

Answers

Answer:

We are looking for two binomials that when you multiply them you get the given trinomial.

Step 1: Set up a product of two ( ) where each will hold two terms.

Step 2: Find the factors that go in the first positions.

Step 3: Find the factors that go in the last positions.

i need help now ........
..​

Answers

Answer:

Step-by-step explanation:

3 17/30

Ryan had some candy to give to his five children. He first took ten pieces for himself and then divided the rest among his children evenly. Each child received six pieces. How many pieces did he start with?

Answers

Answer:

40

Step-by-step explanation:

Answer:40

Step-by-step explanation:

10 for him

5 times 6 is 30

add 10 and 30

you get 40

Elizabeth withdrew $31 at a time from her bank account and withdrew a total of $279. Fran withdrew $46 at a time from her bank account and withdrew a total of $184. Who made the greater number of withdrawals? [ Select ] made the greater number of withdrawals, because she made [ Select ] withdrawals, while [ Select ] only made [ Select ] withdrawals.

Answers

Answer: See explanation

Step-by-step explanation:

Elizabeth withdrew $31 at a time from her bank account and withdrew a total of $279. This means Elizabeth withdrew ($279/$31) = 9 times.

Fran withdrew $46 at a time from her bank account and withdrew a total of $184. This means that Fran withdrew ($184/$46)= 4 times.

Therefore, Elizabeth made the greater number of withdrawals.

[Elizabeth] made the greater number of withdrawals, because she made [9] withdrawals, while [Fran] only made [4] withdrawals.

Match each power of a power expression with its simplified expression

Answers

1. (4^-3)^-3 = 4^9
2. (-4^9)^2 = (-4)^18
3. (4^6)^-3 = 4^-18 = 1/4^18
4. (4^0)^9 = 4^0

Answer:

answer in picture

Step-by-step explanation:

0.89 is 10 times as much as ​

Answers

Answer:

.0089

Step-by-step explanation:

what is 5 squared minus twice as much of 8

Answers

Answer:

9

Step-by-step explanation:

5^2 - 2 x 8 is the equation

first you do exponents so now the equation looks like this: 25 - 2 x 8

then (when following pemdas) you multiply to get this: 25 - 16

last, you should subtract to get your answer: 9

i hope this helps :))

A plumber charges a $50 fee plus $100 per hour to complete a plumbing job. The total amount spent on a plumbing job can be expressed by the function T(x) = 100x + 50 where x represents the number of hours spent on the plumbing job. The maximum time spent on one job per day is 8 hours. Find a reasonable domain and range for this situation.

Answers

Answer:

Between 150 and 800

T is between 150 and 800

Step-by-step explanation:

given information

charges=$50

charges per hour=$100

let the amount of time spent be x

therefore the function for the total amount is

T(x) = 100x + 50

we want to estimate the amount for 1 hour and 8 hours

for 1 hour we have

x=1

T(x) = 100x + 50

T(1) = 100(1)+ 50

T(1) = 150

for 8 hours we have

x=8

T(x) = 100x + 50

T(8) = 100(8)+ 50

T(8) = 800+50

T(8) = 850

the domain is between 150 and 800

What the distance between (-4,2) and (-4,-4)

Answers

Answer:

6

Step-by-step explanation:

u dont even need to use the distance formula for this

u can see that the x points are both the same, so just look at the distance btwn the y values.

|2| + |-4| = 6

the distance between the two is 6

What is the corresponding angle or side?

Answers

Answer:

Number 1 would be FK

Number 2 would be SQR

Answer:

1) FK

2) SQR

Step-by-step explanation:

In congruence statements such as these, each letter's position corresponds to the letter in the same position on the other side.

For example, in 1, MK corresponds to FK because M and F are in the same position and K is in the same position as itself (reflexive property).

In 2, FHG corresponds to SQR because each letter is in the same position in the given congruence statement.

hELP MEEEEEEEEEEEEEEEE​

Answers

Answer:

B

Step-by-step explanation:

We can use the rule [ x^y * x^z = x^y+z ] to simplify.

31^7 * 31^4

31^7+4

31^11

Best of Luck!

Can someone please help me?

Answers

B.

Explanation:

Well, I choose B. Hope I helped... trying to helppp u!!!!!

5 to the power of -3 in exponential form

Answers

1/125 or 0.008
hope this helps

Write the equation of the circle with center at (1,2) that passes through the point (3,6).

Answers

Answer:

Not sure sorry!

Step-by-step explanation:

ΔABC is reflected across the x-axis and then translated 4 units up to create ΔA′B′C′. What are the coordinates of the vertices of ΔA′B′C′ ?

A.
A′(-3, 3), B′(-1, 1), C′(-2, 3)

B.
A′(3, -3), B′(1, -1), C′(2, -3)

C.
A′(3, -5), B′(1, -7), C′(3, -5)

D.
A′(-3, 3), B′(-1, 1), C′(-2, -3)

Answers

The missing figure is attached down

Answer:

The coordinates of the vertices of Δ A'B'C' are A' (-3, 3), B' (-1, 1), C' (-2, 3) ⇒ A

Step-by-step explanation:

If the point (x, y) reflected across the x-axis , then its image is (x, -y)

If the point (x, y) translated vertically up by k units then its image is (x, y + k)

Let us solve the question using the rules above

∵ The coordinates of Δ ABC are A (-3, 1), B (-1, 3), C = (-2, 1)

∵ Δ ABC reflected across the x-axis at first

→ By using the first rule above change the signs of y coordinates

∴ The image of A = (-3, -1)

∴ The image of B = (-1, -3)

∴ The image of C = (-2, -1)

∵ Then it translated 4 units up

→ Use the second rule above, where k = 4, add each y-coordinates by 4

∴ A' = (-3, -1 + 4)

A' = (-3, 3)

∴ B' = (-1, -3 + 4)

B' = (-1, 1)

∴ C' = (-2, -1 + 4)

C' = (-2, 3)

The coordinates of the vertices of Δ A'B'C' are A' (-3, 3), B' (-1, 1), C' (-2, 3)

Answer:

Below

Step-by-step explanation:

In test, passed.

GIVING BRANLIEST TO THE RIGHT ANSWER FOR FUN :)
The equation y = 1/2x represents a proportional relationship. What is the constant of proportionary?

A. x

B. 0

C. 1/2

D. 2​

Answers

Answer:

C 1/2

Step-by-step explanation:

A transformation that changes the size or shape of a figure is
called a rigid transformation.

True
Or False

Answers

Answer:

False

Step-by-step explanation:

I think this is false

connie has a cat and a dog. For every 2 cups of dog food,the cat eats 6 ounces of cat food. Based upon the given ratio of dog food to cat food, fill in the missing data to create a table of equivalent ratios.

Answers

Answer:

21

Step-by-step explanation:

24 minus 3 is 21

What are the factors of the function represented by this graph?
y F10
48
+6
+2
H
-10
-8
-6
14
-2
2
4
6
8
10
-2
4
-6
-8

Answers

14 is ur answer like and comment

True or False: An arithmetic sequence is an exponential function with a
domain of whole numbers.

Answers

True
Please mark as brilliant

What are the coordinates of the midpoint of segment whose endpoints are A(-1,9) and B(3,8) Make sure use the decimals if necessary and write with no spaces (x,y) with you solving for x and y.

Answers

The X coordinate will be 1 and the Y will be 8.5
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