Mathematics, 31.10.2020 08:10 cld3331

Thomas graphed the line that represents the equation y=34x. Which ordered pairs represent points on the line?

Select all that apply.

(8,1/6)
(−2/3,1/2)
(4,3)
(2,3/2)
(−8,−6)

Answers: 1

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Answer from: ashanti93

The ordered pairs represent points on the line are

(4, 3) ⇒ C

(2, $\frac{3}{2}$ ) ⇒ D

(-8, -6) ⇒ E

Step-by-step explanation:

To find the ordered pairs represent points on the line, substitute x by the x-coordinate of each point, if the value of y equals the y-coordinate of the point, then the point is on the line.

∵ The equation is y = $\frac{3}{4}$ x

∵ The ordered pair is (8, $\frac{1}{6}$ )

→ Substitute x by 8

∴ y = $\frac{3}{4}$ (8)

∴ y = 6

∵ The value of y does not equal the y-coordinate of the ordered pair

∴ The ordered pair (8, $\frac{1}{6}$ ) does not represent a point on the line

∵ The ordered pair is ( $\frac{-2}{3}$ , $\frac{1}{2}$ )

→ Substitute x by $\frac{-2}{3}$

∴ y = $\frac{3}{4}$ ( $\frac{-2}{3}$ )

∴ y = $\frac{-1}{2}$

∵ The value of y does not equal the y-coordinate of the ordered pair

∴ The ordered pair ( $\frac{-2}{3}$ , $\frac{1}{2}$ ) does not represent a point on the line

∵ The ordered pair is (4, 3 )

→ Substitute x by 4

∴ y = $\frac{3}{4}$ (4)

∴ y = 3

∵ The value of y equal the y-coordinate of the ordered pair

∴ The ordered pair (4, 3) represents a point on the line

∵ The ordered pair is (2, $\frac{3}{2}$ )

→ Substitute x by 2

∴ y = $\frac{3}{4}$ (2)

∴ y = $\frac{3}{2}$

∵ The value of y equal the y-coordinate of the ordered pair

∴ The ordered pair (2, $\frac{3}{2}$ ) represents a point on the line

∵ The ordered pair is (-8, -6 )

→ Substitute x by -8

∴ y = $\frac{3}{4}$ (-8)

∴ y = -6

∵ The value of y equal the y-coordinate of the ordered pair

∴ The ordered pair (-8, -6) represents a point on the line

Answer from: Quest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.

Answer from: Quest

X=3 and y=4 is the answer

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