Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If $y$ varies directly with $x$ and $y = 20$ when $x = 10$ , find $y$ when $x = 4$ . Write and solve a direct variation equation to find the answer. $\newline$ $y = \underline{\hspace{2em}}$

View step-by-step help

View step-by-step help

Write and solve direct variation equations

Full solution

Q. If

y

varies directly with

x

and

y = 20

when

x = 10

, find

y

when

x = 4

. Write and solve a direct variation equation to find the answer.

\newline

y = \underline{\hspace{2em}}

Select equation: Select the equation that represents direct variation. $\newline$ Since $y$ varies directly with $x$ , we can use the direct variation equation: $y = kx$ , where $k$ is the constant of proportionality.
Find $k$ : Use the given values to find the constant of proportionality ( $k$ ). $\newline$ We are given that $y = 20$ when $x = 10$ . Substitute these values into the direct variation equation to find $k$ . $\newline$ $20 = k \times 10$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $10$ to isolate k. $\newline$ $\frac{20}{10} = \frac{k \times 10}{10}$ $\newline$ $k = 2$
Write equation: Write the direct variation equation using the value of $k$ . $\newline$ Now that we know $k = 2$ , we can write the direct variation equation as $y = 2x$ .
Find $y$ : Use the direct variation equation to find $y$ when $x = 4$ . Substitute $x = 4$ into the equation $y = 2x$ to find $y$ . $y = 2 \times 4$ $y = 8$

More problems from Write and solve direct variation equations

Question

A direct variation includes the points

(4,16)

(1,n)

n

. Write and solve a direct variation equation to find the answer.

\newline

n = \_\_\_

Posted 2 months ago

Question

\newline

\newline

Similar polygons

\newline

The quadrilaterals.

\newline

JKLM

\newline

PQRS

are similar. Find the length

\newline

x

\newline

\overline{PQ}

\newline

x=\square

\newline

\newline

Posted 25 days ago

Question

Answer the questions below about the quadratic function.

\newline

f(x)=x^{2}+6 x+13

\newline

Does the function have a minimum or maximum value?

\newline

\newline

\newline

Where does the minimum or maximum value occur?

\newline

x=

\newline

\square

\newline

What is the function's minimum or maximum value?

Posted 5 hours ago

Question

Answer the questions below about the quadratic function.

\newline

f(x)=-3 x^{2}+6 x-5

\newline

Does the function have a minimum or maximum value?

\newline

\newline

\newline

What is the function's minimum or maximum value?

\newline

\square

\newline

Where does the minimum or maximum value occur?

\newline

x=

\newline

\square

Posted 5 hours ago

Question

A passenger train and a freight train start toward each other at the same time from two points

300

miles apart. If the rate of the passenger train exceeds the rate of the freight train by

15

mph and they meet after

4

hours, what is the rate of each train?

\newline

D= R \quad T

Posted 5 hours ago

Question

6

) A passenger train and a freight train start toward each other at the same time from two points

300

miles apart. If the rate of the passenger train exceeds the rate of the freight train by

15 \mathrm{mph}

and they meet after

4

hours, what is the rate of each traln?

\newline

\begin{tabular}{|c|c|c|}

\newline

D=

R \cdot

T

\newline

\newline

\newline

\newline

Posted 5 hours ago

Question

1

. In the exams given to the top

40

students, the following scores were obtained:

\newline

\begin{tabular}{llllllllll}

\newline

33

54

59

43

31

51

29

64

55

35

\newline

31

31

46

61

35

44

57

29

61

59

\newline

65

48

42

33

37

42

57

56

31

49

\newline

31

64

63

63

51

45

34

62

32

30

\newline

Posted 5 hours ago

Question

Answer the questions below about the quadratic function.

\newline

g(x)=2 x^{2}-16 x+35

\newline

Does the function have a minimum or maximum value?

\newline

\newline

\newline

What is the function's minimum or maximum value?

\newline

\square

\newline

Where does the minimum or maximum value occur?

\newline

x=

Posted 5 hours ago

Question

After the outbreak of a mysterious disease, the average wait time at a hospital increased by

70\%

. Before the outbreak, the average wait time at the hospital was

m

Posted 5 hours ago

Question

Answer the questions below about the quadratic function.

\newline

g(x)=2 x^{2}+4 x

\newline

Does the function have a minimum or maximum value?

\newline

\newline

\newline

What is the function's minimum or maximum value?

\newline

\square

\newline

Where does the minimum or maximum value occur?

\newline

x=

Posted 5 hours ago