PLEASE HELP THIS IS WORTH 50 POINTS!!!

The correct equations in the question are:

(a) [tex]\dfrac{x}{x^2+x-2}[/tex]   (b) [tex]\dfrac{6-x}{x^2-3x-54}[/tex]

Answer:

Step-by-step explanation:

From above:

a) [tex]\dfrac{x}{x^2+x-2}[/tex]  

We are to find the roots of the quadratic equation at the denominator.

i.e.

x²+x-2 =  x² + 2x - x - 2

= x(x+2) - 1(x+2)

= (x -1 ) (x + 2)

Thus;

[tex]\mathbf{\dfrac{x}{x^2+x-2} = \dfrac{A}{x-1} + \dfrac{B}{x+2}}[/tex]

b) [tex]\dfrac{6-x}{x^2-3x-54}[/tex]

The quadratic equation roots can be calculated by finding two numbers that if we multiply then, we will get -54 and if we add or subtract them, we will get -3

x²-3x -54 =  x² - 9x +6x - 54

=  x(x-9) + 6(x-9)

= (x + 6) (x - 9)

[tex]\mathbf{\dfrac{6-x}{x^2-3x-54} = \dfrac{A}{x+6} + \dfrac{B}{x-9}}[/tex]

9514 1404 393

Answer:

  0 ft

Step-by-step explanation:

The line hangs down 15 feet from the top of each pole, so the distance between them must be zero if the total line length is 30 feet.

Answer:

There is descending of 8260 feet in altitude for all 4 balloons.

Answer: y+1 = 5(x-1)

Step-by-step explanation:

Answer:

The second one I believe

Answer:

83.100559

Step-by-step explanation:

0.179x=14.857

x=14.857/0.179

x=83.100559

Answer:

40% as a decimal is 0.4

40% as a fraction is 2/5

Step-by-step explanation:

Let's go over each of these step by step.

First, let's see 40% as a fraction.

Since 40% is out of 100%, we can rewrite that as 40/100.

If you want to simplify it, let's do the following.

40/100

Divide both sides by 20, and you'll end up with:

2/5.

Now, let's do 40% as a decimal.

This is pretty simple.

40% is 40/100 as said before, and to find it as a decimal,

let's divide 40 and 100.

40 divided by 20 = 0.4

Therefore, we can conclude the following:

40% as a fraction is 40/100, or 2/5.

40% as a decimal is 0.4

Hope this helped! :)

Given:

Length of the rectangle = [tex]x^3y^4[/tex] inches

Width of the rectangle = [tex]xy^7[/tex] inches

To find:

The ratio of the length of the rectangle to width of the rectangle.

Solution:

We have,

Length = [tex]x^3y^4[/tex] inches

Width = [tex]xy^7[/tex] inches

So, the ratio of the length of the rectangle to width of the rectangle is

[tex]Ratio=\dfrac{Length}{width}[/tex]

[tex]Ratio=\dfrac{x^3y^4}{xy^7}[/tex]

[tex]Ratio=\dfrac{x\times x^2\times y^4}{x\times y^4\times y^3}[/tex]

Cancel out the common factors.

[tex]Ratio=\dfrac{x^2}{y^3}[/tex]

[tex]Ratio=x^2:y^3[/tex]

Therefore, the required ratio is [tex]x^2:y^3[/tex].

how I'm supposed to answer this

Answer:

we need the total pieces

Step-by-step explanation:

how many pieces of the ancient ceramic bowl are there

4 pieces out of what?

we need the total pieces

Answer:

slope = 7/4

Step-by-step explanation:

slope is found by figuring the change in y-values over the change in x-values.  Look for points on the line that go through an intersection of the graph lines exactly.  I found the points (3, 4) and (-1, -3)

difference of y/difference of x = 4-(-3) / 3-(-1)   =  7/4

Answer:

0.26

is the answer

Answer:

The first graph would be y=5x+2

The second graph would be y=3x+3

The third graph would be y=2x+3

Step-by-step explanation:

First Graph: The x-intercept would be (-0.4, 0). The y-intercept would be (0, 2). The line in the graph goes through both of the points.

Second Graph: x = -1.

y=3

The line in the graph goes through both.

Third Graph:  x = -1.5

y = 3

The line also goes through both.

Answer:

6

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

-(-2) is equal to +2, so the equation is 3+2 which is 5

Answer:

[tex]m=\frac{4}{5}[/tex]

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Point (1, -3)

Point (-4, -7)

Step 2: Find slope m

Answer:

0.5, 50%

Step-by-step explanation:

Answer:

I hope this helps!

Answer:

The equation is y =6x-84.

Step-by-step explanation:

We need to find the equation of the line that is perpendicular to the given line and passes through the given point.

y = − 1/6x − 5; (14, 0)

Slope of required line

The equation of given line [tex]y = - \frac{1}{6} x - 5[/tex] is in slope-intercept form.

Comparing it with general formula of slope-intercept form [tex]y=mx+b[/tex] where m is slope and b is y-intercept. The slope of line m is: -1/6

So, the slope of required line that is perpendicular to given line is 6 because the equation of line that we need to find is perpendicular to the given line, so their slopes will be: [tex]m_1=-\frac{1}{m_2}[/tex]

So, slope = 6

Finding y-intercept of required line

Using slope =6 and point (14,0) we can find y-intercept of required line by slope-intercept formula

[tex]y=mx+b\\0=6(14)+b\\0=84+b\\b=-84[/tex]

Equation of required line:

The equation of required line having slope (m)= 6 and y-intercept (b)= -84 is:

[tex]y=mx+b\\y=6x-84[/tex]

The equation is y =6x-84.

Answer:

1. true 2. true 3.true 4. false 5. false

Step-by-step explanation: 4/4-3/4 is 1/5. You multiply the top first (4-3=1) and the bottom isn't supposed to change. so the answer is 1/4

Answer:

See below

Step-by-step explanation:

[tex]( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) = 1 - 2 { \cos}^{2} \theta \\ \\ LHS = ( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) \\ \\ = \sin^{2} \theta - \cos^{2} \theta \\ \\ =1 - \cos^{2} \theta - \cos^{2} \theta \\( \because \sin^{2} \theta =1 - \cos^{2} \theta) \\ \\ = 1 - 2 { \cos}^{2} \theta \\ = RHS[/tex]

Thus proved

Answer:

1.5

Step-by-step explanation:

Answer:

1.5 i think

Step-by-step explanation:

1/4:2/8 so it would be 1/4 and 1/8 or 1.5

Answer:

because ΔMLN ≅ ΔYZX

=> MN = YX = 4

Step-by-step explanation:

Answer:

I think its four

Step-by-step explanation:

Answer:

26.

Step-by-step explanation:

Given, BD is a median. As it divides the AC equally, that's why it will AD=CD. Given, AD= 6x+10 and CD= 2x+12

Now, AD=  CD

or, 6x+10=2x+12

or, 6x-2x= 12-10

or, 4x= 2

or, x= 1/2

So the value of x is 1/2. As BD divided AC equally, both AD and CD will be equal and AD+CD= AC.

So, 6x+10+2x+12= AC

or, 8x+22= AC

or, 8 X (1/2) + 22= AC

or, 4+22 = AC

or, AC= 26.=

Answer:

(6,0)

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Rise/run

10/30

I hope this is right and that it helps.

Answer:

30 girls, 20 boys

Step-by-step explanation:

in the tape diagram, we see a ration of 3:2 girls:boys

To solve, make it an equation`

3x+2x=50

5x=50

x=10

Then you multiply by 3 and 2 to get 30 and 20

Answer:

20:30

Step-by-step explanation:

50 divided into five is ten. There are exactly five boxes that make up ten kids for each box. There boxes are 30 kids in three boxes while two boxes are 20 kids and if you put all of that together it makes a total of 50 kids.

Answer:

x=−9. Explanation: x=12 is a line parallel to the y-axis passing through all points in the plane with an x-coordinate of 12. therefore a line ...

x=−9 Explanation: x=12 is a line parallel to the y-axis passing through all points in the plane with an x-coordinate of 12 therefore a line parallel ... More

Answer:

Is it 11.6%?

Step-by-step explanation:

I divided 290/250