Mathematics, 03.11.2020 17:00 lyricbrown9055

Select all the points that are on the line through LaTeX: (0,5)( 0 , 5 ) and LaTeX: (2,8)( 2 , 8 ). Group of answer choices LaTeX: (4,11) ( 4 , 11 ) LaTeX: (5,10) ( 5 , 10 ) LaTeX: (6,14) ( 6 , 14 ) LaTeX: (30,50) ( 30 , 50 ) LaTeX: (40,60)

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Answer from: nkh69

The points (4,11), (6,14), (30,50) lie on the line joining the points (0,5) and (2,8).

Step-by-step explanation:

The equation of the line passing through two points (x_1,y_1) and (x_2,y_2) is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

So, the equation of the line passing through two points (0,5) and ( 2, 8 ) is

$y-5=\frac{8-5}{2-0}(x-0)$

$\Rightarrow y=1.5x+5\cdots(i)$

For the point (4,11), pout x=4 in equation (i), we have

$y=1.5\times4 +5=11$ , which is given y coordinate, hence this point (4,11) lies on the line.

For the point (5,10), pout x=5 in equation (i), we have

$y=1.5\times5 +5=12.5,$ which is not the given y coordinate, hence the point (5,10) doesn't lie on the line.

For the point (6,14), pout x=6 in equation (i), we have

$y=1.5\times6 +5=14$ , which is the given y coordinate, hence the point (6,14) lies on the line.

For the point (30,50), pout x=30 in equation (i), we have

$y=1.5\times30 +5=50$ , which is the given y coordinate, hence the point (30,50) lies on the line.

For the point (40,60), pout x=40 in equation (i), we have

$y=1.5\times40 +5=65$ , which is not the given y coordinate, hence the point (40,60) doesn't lie on the line.

Hence, the points (4,11), (6,14), (30,50) lie on the line joining the points (0,5) and (2,8).

Answer from: Quest

Hello!

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

why?

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

$3x-6$

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

$3x-6=0$

$3x=6$

$x=\frac{6}{3}=2$

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

Answer from: Quest

answer: it is 8

step-by-step explanation:

you know why its 8

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Select all the points that are on the line through LaTeX: (0,5)( 0 , 5 ) and LaTeX: (2,8)( 2 , 8 )....

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