All categories

3 years ago

Which relation is a direct variation that contains the ordered pair (2, 7)?

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

5 0

Answer:

$y=\frac{7}{2}x$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In a direct relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

step 1

Find the value of the constant of proportionality k

we have

the ordered pair (2, 7)

$k=\frac{y}{x}$ -----> $k=\frac{7}{2}$

therefore

The relation is

$y=kx$ -----> $y=\frac{7}{2}x$

You might be interested in

one tamk of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of

Zarrin [17]

Answer:

20 gallons were used from the tank with the octane rating of 80.

Step-by-step explanation:

Given : One tank of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of 60 gallons with an octane rating of 120.

To find : How many gallons should be used from the tank with the octane rating of 80?

Solution : Let x be the volume of gas whose octane rating is 140 and

y be the volume of gas whose octane rating is 80.

Then, we form the equation as:

(1) $x\times140 + y\times80 = 60\times120$

$140x+80y = 7200$

or $7x+4y = 360$ .........[3]

(2) $x + y = 60$

Now multiply equation (2) by 4

$4x + 4y = 240$ ...........[4]

Subtract (4) from (3)

$7x+4y-4x-4y=360-240$

$3x=120$

$x=\frac{120}{3}$

$x=40$

Put x in equation [4] we get,

$4(40) + 4y = 240$

$160 + 4y = 240$

$4y = 80$

$y=\frac{80}{4}$

$y=20$

Therefore, x=40 and y=20

So, 20 gallons were used from the tank with the octane rating of 80.

7 0

3 years ago

Tanisha was asked to write an example of a linear relationship she wrote this my dog sitting service charges an initial $8.00 fe

stich3 [128]

1. 15.50
2. 23.00
3. 30.50
4. 38.00

5 0

2 years ago

What is 74 divided by 12?plz help I need this assignment done before 3:30 and it’s 2 hours until time

bogdanovich [222]

Answer:

6.16.

Step-by-step explanation:

hope this helps.

5 0

3 years ago

Read 2 more answers

Solve the compound inequality. Graph the solution<br> -2 ≤ 2x – 4 < 4

Ulleksa [173]

$-2 \ \textless \ = 2x - 4 \ \textless \ 4$

$-2+4\ \textless \ 2x\ \textless \ 4+4
 
$ $Add \ 4 \ to \ the \ whole \ equation$

$
2\ \textless \ 2x\ \textless \ 8
 
$ $Simplify \ inequality$

$1\ \textless \ x\ \textless \ \dfrac{8}{2}$ $Divide \ the \ whole \ equation \ by \ 2$

$
1\ \textless \ x\ \textless \ 4
 
$ $= (1,4)$

5 0

3 years ago

For the function f(x)=3xsquared- 2x+5 find f(1) f(-2) and f(a)

Oksanka [162]

$f(x)=3x^2-2x+5\\\\
f(1):\ \ Substitude\ 1 \ as\ x\ into\ function:\\
f(1)=3*1^2-2*1+5=3-2+5=\textbf{6}\\\\
f(-2)\ \ Substitude\ x=-2\\
f(-2)=3*(-2)^2-2*(-2)+5=3*4+4+5=12+4+5=\textbf{21}\\\\
f(a)\ \ substitude\ x=a\\
f(a)=\underline{3a^2-2a+5}$

4 0

3 years ago