Linear equations
I need help with these
Instructions: choose two linear equations in each box. Write them below. For #3-#8, find the slope and y-intercept of each equation.
Then graph each line on a coordinate plane on the next page. Label each line neatly with its corresponding equation.

Answer:

[tex]\frac{x^3 + 2x^2 -9x-18}{x^3-x^2-6x}= \frac{(x+3)}{x}[/tex]

[tex]\frac{3x^2 - 5x - 2}{x^3 - 2x^2} = \frac{3x + 1}{x^2}[/tex]

[tex]\frac{6 - 2x}{x^2 - 9} * \frac{15 + 5x}{4x}=-\frac{5}{2x}[/tex]

[tex]\frac{x^2 -6x + 9}{5x - 15} / \frac{5}{3-x} = \frac{-(x-3)^2}{25}[/tex]

[tex]\frac{x^3 - x^2 -x + 1}{x^2 - 2x+1}= x +1[/tex]

[tex]\frac{9x^2 + 3x}{6x^2} = \frac{3x + 1}{2x}[/tex]

[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} / \frac{x - 1}{x} = 3x[/tex]

Step-by-step explanation:

Required

Simplify

Solving (1):

[tex]\frac{x^3 + 2x^2 -9x-18}{x^3-x^2-6x}[/tex]

Factorize the numerator and the denominator

[tex]\frac{x^2(x + 2) -9(x+2)}{x(x^2-x-6)}[/tex]

Factor out x+2 at the numerator

[tex]\frac{(x^2 -9)(x+2)}{x(x^2-x-6)}[/tex]

Express x^2 - 9 as difference of two squares

[tex]\frac{(x^2 -3^2)(x+2)}{x(x^2-x-6)}[/tex]

[tex]\frac{(x -3)(x+3)(x+2)}{x(x^2-x-6)}[/tex]

Expand the denominator

[tex]\frac{(x -3)(x+3)(x+2)}{x(x^2-3x+2x-6)}[/tex]

Factorize

[tex]\frac{(x -3)(x+3)(x+2)}{x(x(x-3)+2(x-3))}[/tex]

[tex]\frac{(x -3)(x+3)(x+2)}{x(x+2)(x-3)}[/tex]

Cancel out same factors

[tex]\frac{(x+3)}{x}[/tex]

Hence:

[tex]\frac{x^3 + 2x^2 -9x-18}{x^3-x^2-6x}= \frac{(x+3)}{x}[/tex]

Solving (2):

[tex]\frac{3x^2 - 5x - 2}{x^3 - 2x^2}[/tex]

Expand the numerator and factorize the denominator

[tex]\frac{3x^2 - 6x + x - 2}{x^2(x- 2)}[/tex]

Factorize the numerator

[tex]\frac{3x(x - 2) + 1(x - 2)}{x^2(x- 2)}[/tex]

Factor out x - 2

[tex]\frac{(3x + 1)(x - 2)}{x^2(x- 2)}[/tex]

Cancel out x - 2

[tex]\frac{3x + 1}{x^2}[/tex]

Hence:

[tex]\frac{3x^2 - 5x - 2}{x^3 - 2x^2} = \frac{3x + 1}{x^2}[/tex]

Solving (3):

[tex]\frac{6 - 2x}{x^2 - 9} * \frac{15 + 5x}{4x}[/tex]

Express x^2 - 9 as difference of two squares

[tex]\frac{6 - 2x}{x^2 - 3^2} * \frac{15 + 5x}{4x}[/tex]

Factorize all:

[tex]\frac{2(3 - x)}{(x- 3)(x+3)} * \frac{5(3 + x)}{2(2x)}[/tex]

Cancel out x + 3 and 3 + x

[tex]\frac{2(3 - x)}{(x- 3)} * \frac{5}{2(2x)}[/tex]

[tex]\frac{3 - x}{x- 3} * \frac{5}{2x}[/tex]

Express [tex]3 - x[/tex] as [tex]-(x - 3)[/tex]

[tex]\frac{-(x-3)}{x- 3} * \frac{5}{2x}\\[/tex]

[tex]-1 * \frac{5}{2x}[/tex]

[tex]-\frac{5}{2x}[/tex]

Hence:

[tex]\frac{6 - 2x}{x^2 - 9} * \frac{15 + 5x}{4x}=-\frac{5}{2x}[/tex]

Solving (4):

[tex]\frac{x^2 -6x + 9}{5x - 15} / \frac{5}{3-x}[/tex]

Expand x^2 - 6x + 9 and factorize 5x - 15

[tex]\frac{x^2 -3x -3x+ 9}{5(x - 3)} / \frac{5}{3-x}[/tex]

Factorize

[tex]\frac{x(x -3) -3(x-3)}{5(x - 3)} / \frac{5}{3-x}[/tex]

[tex]\frac{(x -3)(x-3)}{5(x - 3)} / \frac{5}{3-x}[/tex]

Cancel out x - 3

[tex]\frac{(x -3)}{5} / \frac{5}{3-x}[/tex]

Change / to *

[tex]\frac{(x -3)}{5} * \frac{3-x}{5}[/tex]

Express [tex]3 - x[/tex] as [tex]-(x - 3)[/tex]

[tex]\frac{(x -3)}{5} * \frac{-(x-3)}{5}[/tex]

[tex]\frac{-(x-3)(x -3)}{5*5}[/tex]

[tex]\frac{-(x-3)^2}{25}[/tex]

Hence:

[tex]\frac{x^2 -6x + 9}{5x - 15} / \frac{5}{3-x} = \frac{-(x-3)^2}{25}[/tex]

Solving (5):

[tex]\frac{x^3 - x^2 -x + 1}{x^2 - 2x+1}[/tex]

Factorize the numerator and expand the denominator

[tex]\frac{x^2(x - 1) -1(x - 1)}{x^2 - x-x+1}[/tex]

Factor out x - 1 at the numerator and factorize the denominator

[tex]\frac{(x^2 - 1)(x - 1)}{x(x -1)- 1(x-1)}[/tex]

Express x^2 - 1 as difference of two squares and factor out x - 1 at the denominator

[tex]\frac{(x +1)(x-1)(x - 1)}{(x -1)(x-1)}[/tex]

[tex]x +1[/tex]

Hence:

[tex]\frac{x^3 - x^2 -x + 1}{x^2 - 2x+1}= x +1[/tex]

Solving (6):

[tex]\frac{9x^2 + 3x}{6x^2}[/tex]

Factorize:

[tex]\frac{3x(3x + 1)}{3x(2x)}[/tex]

Divide by 3x

[tex]\frac{3x + 1}{2x}[/tex]

Hence:

[tex]\frac{9x^2 + 3x}{6x^2} = \frac{3x + 1}{2x}[/tex]

Solving (7):

[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} / \frac{x - 1}{x}[/tex]

Change / to *

[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} * \frac{x}{x-1}[/tex]

Expand

[tex]\frac{x^2-2x-x+2}{4x} * \frac{12x^2}{x^2 - 2x} * \frac{x}{x-1}[/tex]

Factorize

[tex]\frac{x(x-2)-1(x-2)}{4x} * \frac{12x^2}{x(x - 2)} * \frac{x}{x-1}[/tex]

[tex]\frac{(x-1)(x-2)}{4x} * \frac{12x^2}{x(x - 2)} * \frac{x}{x-1}[/tex]

Cancel out x - 2 and x - 1

[tex]\frac{1}{4x} * \frac{12x^2}{x} * \frac{x}{1}[/tex]

Cancel out x

[tex]\frac{1}{4x} * \frac{12x^2}{1} * \frac{1}{1}[/tex]

[tex]\frac{12x^2}{4x}[/tex]

[tex]3x[/tex]

Hence:

[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} / \frac{x - 1}{x} = 3x[/tex]

Answer:

68.5

Step-by-step explanation:

each pack 7.5 kg

price for each pack $3

he bought 3

7.5 x 3=22.5

22.5 x3=66.5

Answer:

V = pi x radius x 2 x height OR pi x diameter x height

Hope that helps!

Answer:

the formula for the volume of a cylinder is V=πr²h

Answer:0.028

Step-by-step explanation: 0.07 x 0.4= 0.028

Answer:

false

Step-by-step explanation:

Answer:

x = 0.3333333333

Step-by-step explanation:

Simplifying

42x = 14

Solving

42x = 14

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '42'.

x = 0.3333333333

Simplifying

x = 0.3333333333

Answer:

120 deg

Step-by-step explanation:

There is an angle symbol in the equilateral triangle and another symbol in half of the vertex angle. Those two angles are congruent.

The measure of the vertex angle is 2 * 60 deg = 120 deg

Answer: 120 deg

Answer:

1. A=πr2=π·4.62≈66.4761

A≈66.48

2. A=πr2=π·22≈12.56637

A≈12.57

please mark as brainiest

Answer:

1. 66.48

2. 12.57

Step-by-step explanation:

Formula is A = ㅠr^2

The radius is that half line :))

Answer:

[tex]c. \\ x(x+3)[/tex]

Step-by-step explanation:

Answer:

C)

Step-by-step explanation:

Answer: The ratio of eggs, eggs, to two cups of flour. Let me write two cups of flour. Cups of flour. In either case is, is four eggs for every three cups of flour 5/2

Step-by-step explanation: Im not sure through

Answer:

1 i know its one hope it help

Step-by-step explanation:

List all prime factors for each number.

Prime Factorization of 2 shows:

2 is prime  =>  21

Prime Factorization of 7 shows:

7 is prime  =>  71

Prime Factorization of 8 is:

2 x 2 x 2  =>  23

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 2, 7

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 7 = 56

In exponential form:

LCM = 2^3 x 7^1 = 56

LCM = 56

Therefore,

LCM(2, 7, 8) = 56

Answer:

its C. 8 :) please give me brainlist

Answer: The answer is 9a^2 - 3a + 1/4

Step-by-step explanation:

Hope this helpfull.

But Im so sorry if this not helpfully

Step-by-step explanation:

b 8 is the answer

simplify to2^4^(3/4) then 2^3 then that simplies to 8

Answer:

y=3x-7

Step-by-step explanation:

i plotted the point, and used the slope to get the equation

Answer:

$900

Step-by-step explanation:

Given that:

Principal, p = 5000

Interest, r = 6%

Period, t = 3 years

Using the relation :

Simple interest = Principal * Rate * Time

Simple interest = $5000 * 0.06 * 3

Simple interest = $900

Hence, amount of interest earned = $900

Answer:

1)whole numbers

2)integers

3)rational numbers

Answer:

The constant is 2.50

I believe the equation would look like 2.5x=17.5

and x would equal 7

Answer:

-5+5

= 0

Step-by-step explanation:

Answer:

-5+5

= 0

Step-by-step explanation:

Answer:

it's 80% of 125

the value of x = 125

Step-by-step explanation:

Answer:

Is it Khan Academy? You do 5.8 - 2.7 = 3.1

Step-by-step explanation:

Hope that helps!

Answer:

First option is the correct answer.

[tex] (m + n - 1) \sqrt{p} [/tex]

Step-by-step explanation:

[tex]m\sqrt{p} + n\sqrt{p} - \sqrt{p} \\ \\ = (m + n - 1) \sqrt{p} [/tex]

Answer:

1 and 7/10 pounds?

Step-by-step explanation:

because if its 4/10 more you add 3/10 and 4/10 im pretty sure

Answer:

PLEASE MARK BRAInliest

Step-by-step explanation:

tweety weighed 17/10 pounds last year.

Answer:

Step-by-step explanation:

Answer:

b my

Step-by-step explanation:

valentines

bbg

In the kitchen triangle,  the largest angle will be at counter

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that kitchens have a working triangle between the sink (S), the counter (C), and the oven (O).

The distance between the sink in the oven is 8 feet.

The distance between the sink and the counter is 6 feet,

The distance between the oven and the counter at 7 feet.

we need to find in the kitchen triangle, where is the largest angle

SO=8

SC=6

OC=7

Hence, in the kitchen triangle,  the largest angle will be at counter

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ2

Answer:

The number to use are 10, 7, 20 and 3.

Step-by-step explanation:

Given

[tex]17 * 23[/tex]

Required

Which numbers would be used using the area model or partial products

The number to use are 10, 7, 20 and 3.

This is shown below:

[tex]\begin{array}{ccc}{ } & {10} & {7} & {20} & { } & { } \ \\ {3} & { } & { } \ \end{array}[/tex]

When the numbers are multiplied, we get:

[tex]\begin{array}{cccc}{ } & {10} & {7} & {} & {20} & {200} &{140} &{=340}\ \\ {3} & {30 } & {21 } &{=51} \ \end{array}[/tex]

[tex]Total = 340 + 51[/tex]

[tex]Total = 391[/tex]

Answer:

y = 6

Step-by-step explanation:

I'm going to assume you want to solve for y.

Step 1: Move all constants to 1 side, isolating y and its coefficient:

14 = 3y - 4

14 + 4 = 3y - 4 + 4

18 = 3y

Step 2: Divide both sides by 3 to solve for y:

3y = 18

3y / 3 = 18 / 3

y = 6

Final answer: y = 6