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Which explains whether or not the function represents a direct variation?

s2008m [1.1K]

Answer:

The function represents a direct variation

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 $y/x=k$ or $y=kx$

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

Let

$A(0,0)$ ------> the line passes through the origin

$B(2,10)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=10/2=5$

$C(4,20)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=20/4=5$

$D(6,30)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=30/6=5$

$E(8,40)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=40/8=5$

The value of k is equal in all the points of the table and the line passes through the origin

therefore

The function represents a direct variation

the equation of the direct variation is equal to

$f(x)=5x$

4 0

3 years ago

Read 2 more answers

If line KM bisects angle JKL, angle JKL = 92 degrees, and angle MKL = (5x+1) degrees, find the value of

kherson [118]

The value of the variable x is found to be x = 9.

<h3>What is termed as angle bisector?</h3>

In geometry, an angle bisector is a line that divides an angle into two equal angles.
A bisector is something that divides a shape or thing into two equal portions.
An angle bisector is a ray that divides an angle into two equal components of the same measurement.

A bisected angle divides the two sides in equals.

JKM = LKM

As, both are equal.

Then, each of these angles are 1/2 the angle JKL.

1/2 JKL = MKL

1/2 ×( 92) = 5x + 1

Further simplifying;

46 = 5x+1

Subtract 1 from each side

46-1 = 5x

45 = 5x

Divide each side by 5

45/5 = 5x/5

x = 9

Thus, the value of the unknown variable is found to be x = 9 units.

To know more about the angle bisector, here

brainly.com/question/14399747

#SPJ9

6 0

11 months ago

PLS HELP ASAP If -2 is added to each of the x and y intercepts of the line 3x + 2y = 6, find the new equation of the line

ella [17]

Answer:

3x + 2y = -4

Step-by-step explanation:

x intercept of the line occurs at y = 0

Given the equation 3x+2y = 6

3x+2(0) = 6

3x = 6

x = 2

The x intercept is at (2, 0)

Adding -2 to each axis will give (2-2, 0-2) = (0, -2)

y intercept of the line occurs at x = 0

Given the equation 3x+2y = 6

3(0)+2y = 6

2y = 6

y =3

The x intercept is at (0, 3)

Adding -2 to each axis will give (0-2, 3-2) = (-2, 1)

The new coordinates are (0, -2 and (-2, 1)

Using the point slope form of the equation y - y0 = m(x-x0)

slope m = y2-y1/x2-x1

m = 1-(-2)/-2-0

m = 1+2/-2

m = -3/2

Using m = -3/2 and (0, -2)

y - (-2) = -3/2(x-0)

y+2 = -3/2 x

2(y+2) = -3x

2y+4 = -3x

-3x-2y = 4

3x + 2y = -4

Hence the required equation is 3x + 2y = -4

7 0

2 years ago

Shankar has decided to train to be a Carbucks Barrista. Being young and inexperienced, for every order he makes a mistake in mak

astra-53 [7]

Answer:

Step-by-step explanation:

Since each trial is independent of the other

no of mistakes he does is binomial with p = 1/3

a) the probability that he makes no mistakes on his first 10 orders but the 11th order is a mistake

= $(\frac{2}{3}) ^{10} *\frac{1}{3}\\=\frac{2^{10} }{3^{11} }$

b) Prob that shanker quits = P(Shankar does I one mistake and Fran does not do the first one)+Prob (Shanker does mistake in the II one while Fran does both right)

= $\frac{1*5}{3*6} +\frac{2}{3} \frac{1}{3}(\frac{5}{6})^2 =\frac{5}{18} +\frac{50}{216} \\=\frac{55}{108}$

6 0

3 years ago

Pleaseee answer correctly !!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!

dimaraw [331]

Answer:

OS is congruent to SQ

Step-by-step explanation:

4 0

3 years ago