Mathematics, 05.05.2020 21:13 aide12345

What is the product of (3x-9) and 6x^2-2x+5? Write your answer in standard form.

a) Show your work.

b) Is the product of (3x-9) and 6x^2-2x+5 equal to the product of (9x-3) and 6x^2-2x+5? Explain your answer.

Answers: 1

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Answer from: BreBreDoeCCx

The product of 3x-9

and

No, they are not equal

Step-by-step explanation:

a. Given

3x-9 and 6x^2-2x+5

Required

Product

The solution is as follows

First, put both expression in different brackets

(3x-9)(6x^2-2x+5)

Expand (6x^2-2x+5) bracket by (3x-9)

To do that. we first multiply (6x^2-2x+5) by 3x then by -9. This is done as follows

3x (6x^2-2x+5) - 9(6x^2-2x+5)

Now, we proceed to opening the bracket

(3x * 6x^2-3x * 2x+3x *5) - (9* 6x^2-9* 2x+9* 5)

(18x^3 -6x^2+ 15x) - (54x^2 - 18x +45)

Open both brackets

18x^3 -6x^2+ 15x -54x^2 + 18x -45

Collect like terms

18x^3 -6x^2 -54x^2 + 15x + 18x -45

18x^3 -60x^2 + 33x - 45

Hence, the product of 3x-9 and 6x^2-2x+5 is 18x^3 -60x^2 + 33x - 45

b. Given

and

and

Required

Are their products equal?

To check if they are equal or not, we find the product of both and compare the solutions

We've already solved for 3x-9 and 6x^2-2x+5 in the (a) part of this exercise, so we move to the product of 9x-3 and

The solution is as follows

First, put both expression in different brackets

(9x-3)(6x^2-2x+5)

Expand (6x^2-2x+5) bracket by (9x-3)

To do that. we first multiply (6x^2-2x+5) by 9x then by -3. This is done as follows

9x (6x^2-2x+5) - 3(6x^2-2x+5)

Now, we proceed to opening the bracket

(9x * 6x^2 - 9x * 2x + 9x *5) - (3* 6x^2 - 3 * 2x + 3* 5)

(54x^3 - 18x^2+ 45x) - (18x^2 - 6x +15)

Open both brackets

54x^3 - 18x^2+ 45x -18x^2 + 6x -15

Collect like terms

54x^3 - 18x^2 -18x^2 + 45x + 6x -15

54x^3 - 36x^2 + 51x -15

Now, we compare both answers

18x^3 -60x^2 + 33x - 45

equal to

54x^3 - 36x^2 + 51x -15

No, they're not.

Reason is that, for both expressions to be equal, we must have the same expression after expanding both of them

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

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

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

just pick what you think i need more time let me know if this

step-by-step explanation:

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