All categories

3 years ago

Why does.the equation y=3x+5 NOT represent a proportional relationship

Mathematics

1 answer:

sergiy2304 [10]3 years ago

5 0

Answer:

The equation not represent a proportional relationship because the line don't passes through the origin

Step-by-step explanation:

we know that

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

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

In this problem we have

$y=3x+5$

This is the equation of the line in slope intercept form

where

the slope is m=5

the y-intercept is b=5

Remember that in a proportional relationship the value of b must be equal to zero (because the line passes through the origin)

therefore

The equation not represent a proportional relationship because the line don't passes through the origin

You might be interested in

!!!! I need help with numbers 1 and 9 please !!!!!

Nataly_w [17]

(1)

given $\frac{j}{6}$ = $\frac{9}{10}$ ( cross- multiply )

10j = 54 ( divide both sides by 10 )

j = $\frac{54}{10}$ = $\frac{27}{5}$ ← in simplest form

(9)

let h be the hours worked daily , then

3h = 20 $\frac{2}{3}$ = $\frac{62}{3}$ ( divide both sides by 3 )

h = $\frac{62}{3}$ ÷ 3

= $\frac{62}{3}$ × $\frac{1}{3}$ = $\frac{62}{9}$ = 6 $\frac{8}{9}$

She worked 6 $\frac{8}{9}$ hours each day

5 0

3 years ago

How to solve this one

ivolga24 [154]

The x,y = -6, -5. Hope this helped, and have a great day! :D

6 0

3 years ago

Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y1 = x2 + 2x + 3 y2 = 2x + 12F

Svet_ta [14]

Answer:

$A = \int\limits^3__-3}{9}-{x^{2}} \, dx = 36$

Step-by-step explanation:

The equations are:

$y = x^{2} + 2x + 3$

$y = 2x + 12$

The two graphs intersect when:

$x^{2} + 2x + 3 = 2x + 12$

$x^{2} = 0$

$x_{1} = 3\\x_{2} = -3$

To find the area under the curve for the first equation:

$A_{1} = \int\limits^3__-3}{x^{2} + 2x + 3} \, dx$

To find the area under the curve for the second equation:

$A_{2} = \int\limits^3__-3}{2x + 12} \, dx$

To find the total area:

$A = A_{2} -A_{1} = \int\limits^3__-3}{2x + 12} \, dx -\int\limits^3__-3}{x^{2} + 2x + 3} \, dx$

Simplifying the equation:

$A = \int\limits^3__-3}{2x + 12}-({x^{2} + 2x + 3}) \, dx = \int\limits^3__-3}{9}-{x^{2}} \, dx$

Note: The reason the area is equal to the area two minus area one is that the line, area 2, is above the region of interest (see image).

3 0

3 years ago

polygon ABCD is defined by the points A(-4,2), B(-2,4), C(1,3), and D(2,2). match the coordinates of the points you f the transf

Tomtit [17]

Answer:

D' ..................> (-2,2)

C'' .................> (3,-1)

A''' ................> (4,-2)

B'' .................> (4,2)

Step-by-step explanation:

Before we begin, we should remember the rotation rules:

1- Rotation 90° clockwise:

Coordinates (x,y) become (y,-x)

2- Rotation 90° counter clockwise:

Coordinates (x,y) become (-y,x)

3- Rotation 180° clockwise:

Coordinates (x,y) become (-x,-y)

4- Rotation 270° counter clockwise:

Coordinates (x,y) become (y,-x) ...........> same as rotation 90° clockwise

Now, let's consider the given problem:

1- Coordinates of D' if polygon ABCD rotates 90° counter clockwise to create A'B'C'D'

Original coordinates of point D are (2,2)

Rotation 90° counter clockwise means that the new coordinates will be (-y,x) which is (-2,2)

2- Coordinates of C'' if polygon ABCD rotates 90° clockwise to create A''B''C''D''

Original coordinates of point C are (1,3)

Rotation 90° clockwise means that the new coordinates will be (y,x) which is (3,-1)

3- Coordinates of A''' if polygon ABCD rotates 180° clockwise to create A'''B'''C'''D'''

Original coordinates of point A are (-4,2)

Rotation 180° clockwise means that the new coordinates will be (-x,-y) which is (4,-2)

4- Coordinates of B'' if polygon ABCD rotates 270° counter clockwise to create A''B''C''D''

Original coordinates of point B are (-2,4)

Rotation 270° counter clockwise means that the new coordinates will be (y,-x) which is (4,2)

Hope this helps :)

5 0

3 years ago

Name the solid and find its volume. Use 3.14 as the approximate value of pi.

sineoko [7]

It is given in the question that the solid is a cone with height of 16 units and radius of 7 units .

The formula of volume of cone is

$V = \frac{1}{3} \pi r^2 h$

To find the volume, we substitute the given values of r and h and use 3.14 for pi. That is

$V = \frac{1}{3} *3.14*7^2 *16 = 820.6 \ units \ cube$

And that's the required volume of the cone .

7 0

3 years ago