Your classmate simplified the following rational expression and asked you if you got the same answer. Determine whether the answer below is correct. If it is not correct, simplify the expression. Show all of your work.


Rational expression: (x^(2)-1) / (x^(2)-4x-5) ÷ (2x^(2)+4x) / (6x^(2)-30x)


Your friend's answer: (2x(x-1)(x+2)) / (6x(x-5)(x-5))

Answer:

I don't know how to do please let me I will try solve the question

Answer:

bka bla bla bla sorry I newbie

Step-by-step explanation:

Hey there!

Please see attached picture for your answer!

Hope it helps!

Answer is in the attachment.

note:

make a slight change in question 1;

Notice that

• π/2 = π/3 + π/6

• π/6 = π/3 - π/6

Recall the angle sum identities for sine:

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

sin(x - y) = sin(x) cos(y) - cos(x) sin(y)

By adding these together, we get

sin(x + y) + sin(x - y) = 2 sin(x) cos(y)

==>   sin(x) cos(y) = 1/2 (sin(x + y) + sin(x - y))

Now take x = π/3 and y = π/6 :

sin(π/3) cos(π/6) = 1/2 (sin(π/2) + sin(π/6))

So the blank should be filled with cos.

Answer:

Solution given

Cos[tex]\displaystyle \theta_{1}=\frac{3}{5}[/tex]

consider Pythagorean theorem

[tex]\bold{Sin²\theta+Cos²\theta=1}[/tex]

Subtracting [tex]Cos²\theta[/tex]both side

[tex]\displaystyle Sin²\theta=1-Cos²\theta[/tex]

doing square root on both side we get

[tex]Sin\theta=\sqrt{1-Cos²\theta}[/tex]

Similarly

[tex]Sin\theta_{1}=\sqrt{1-Cos²\theta_{1}}[/tex]

Substituting value of [tex]Cos\theta_{1}[/tex]

we get

[tex]Sin\theta_{1}=\sqrt{1-(\frac{3}{5})²}[/tex]

[tex]Sin\theta_{1}=\sqrt{1-(\frac{9}{25})}[/tex]

[tex]Sin\theta_{1}=\sqrt{\frac{16}{225}}[/tex]

[tex]Sin\theta_{1}=\frac{\sqrt{2*2*2*2}}{\sqrt{5*5}}[/tex]

[tex]Sin\theta_{1}=\frac{4}{5}[/tex]

Since

In IVquadrant sin angle is negative

[tex]\bold{Sin\theta_{1}=-\frac{4}{5}}[/tex]

Answer:

[tex]\sin(\theta_1)=-\frac{4}{5}[/tex]

Step-by-step explanation:

We'll use the Pythagorean Identity [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex] to solve this problem.

Subtract [tex]\cos^2(\theta)[/tex] from both sides to isolate [tex]\sin^2(\theta)[/tex]:

[tex]\sin^2(\theta)=1-\cos^2(\theta)[/tex]

Substitute [tex]\cos(\theta)=\frac{3}{5}[/tex] as given in the problem:

[tex]\sin^2(\theta_1)=1-(\frac{3}{5}^2)[/tex]

Simplify:

[tex]\sin^2\theta_1=1-\frac{9}{25}[/tex]

Combine like terms:

[tex]\sin^2\theta_1=\frac{16}{25}[/tex]

For [tex]a^2=b[/tex], we have two solutions [tex]a=\pm \sqrt{b}[/tex]:

[tex]\sin\theta_1=\pm \sqrt{\frac{16}{25}},\\\begin{cases}\sin \theta_1=\frac{4}{5},\\\sin \theta_1=\boxed{-\frac{4}{5}}\end{cases}[/tex]

Since the sine of all angles in quadrant four return a negative output, [tex]\frac{4}{5}[/tex] is extraneous and our answer is [tex]\boxed{\sin(\theta_1)=-\frac{4}{5}}[/tex]

Answer:

4 = x

Step-by-step explanation:

f(x) =2x

Let f(x) = 8

8 =2x

Divide each side by 2

8/2 = 2x/2

4 = x

Answer:

4

Step-by-step explanation:

f(x) = 2x

When f(x) = 8, x = 8/2 = 4.

Hope this helped,

~cloud

Answer:

1

Step-by-step explanation:

The given equation of the function is y = -a·(x - h)² + 1

The positive constants of the equation = a, and h

The points the function crosses the x-axis = 2, and 4

Where the function crosses the x-axis, y = 0, and x = 2, and 4, therefore, when x = 2, we have;

y = 0 = -a·(2 - h)² + 1

When x = 4, we have;

0 = -a·(4 - h)² + 1

-a·(2 - h)² + 1 = -a·(4 - h)² + 1

-a·(2 - h)² = -a·(4 - h)²

(2 - h)² = (4 - h)²

±(2 - h) = +#±(4 - h)

When

(2 - h) is negative, and (4 - h) is positive, but the same magnitude, we have';

-(2 - h) = +(4 - h)

2·h = 4 + 2 = 6

h = 3

0 = -a·(4 - h)² + 1 = -a·(4 - 3)² + 1 = -a + 1

Therefore, a = 1

Answer:

Step-by-step explanation:

Answer:

Let s be the son’s current age and d be the daughter’s current age. The system of equations is:

s - 10 = 2(d - 10)

s = 3 + d

Since s is already set to an equation, we can use the substitution method for s in the other equation:

s = 3 + d

s - 10 = 2(d - 10)

3 + d - 10 = 2(d - 10)

Simplify and solve for d:

3 + d - 10 = 2(d - 10)

-7 + d = 2d - 20

-7 = d - 20

13 = d

The daughter is 13 years old. To solve for the son’s age, we will plug in the solution for d into one of the equations. The second one is simpler so we will use that:

s = 3 + d

s = 3 + 13

s = 16

The son is 16 years old. Let us use the other equation to check our solutions:

s - 10 = 2(d - 10)

16 - 10 = 2(13 - 10)

6 = 2(3)

6 = 6

It checks out. The son is 16 years old, and the daughter is 13 years old.

The present age of the daughter and son are 14 and 10 years respectively.

Let the age of the daughter be x

Let the age of the son be y

If the daughter's age is 4 years more than the son's age now, then,

x = y + 4 ............. 1

If Eight years ago, the daughters' age was thrice the son's age, then;

Daughter = x - 8

Son  = y - 8

Hence, x - 8 =3(y - 8).................. 2

Substitute equation 1 into 2 to have:

x - 8 =3(y - 8).

y + 4 - 8 = 3(y - 8)

y - 4 = 3y - 24

y - 3y = -20

-2y = -20

y = 10

Recall that x = y + 4

x = 10 + 4

x = 14

Hence the present age of the daughter and son are 14 and 10 years respectively.

LEarn more here: https://brainly.com/question/16510024

Not enough information to solve..... Please make your question more clear

Answer:

The first one.

Step-by-step explanation:

Graph lines as if the inequalities were equal signs.

X = -3 is a vertical line at x = -3, because it's less than we shade to the left. All numbers less than -3 are to the left. The line is dashed because there is no equal to. Only less than. The line is not included in the solution set.

y = -x - 1 is a line with a y-intercept of -1 and a slope of -1. All values that are less that y are below the line. Because it's less than or equal to the line is solid.

Answer:

A

Step-by-step explanation:

The vertical line  is dotted at -3 and shaded to the left

x < -3

This gives us two choices left

A and C

The other line has a y intercept at -1 and is solid and shaded to the left

It is of the form

y ≤ mx+1  

We know the slope is negative since is goes down from left to right

The only Choice is A

Answer:

(-3,-6) and (-3,2)

Step-by-step explanation:

A line with an undefined slope is vertical. In this case it must have x coordinates equal to -3

Answer:

(12xy-6x -12y)

12xy-18xy

6xy

Answer:

- xy - x + 2y

Step-by-step explanation:

5x - 13xy + 14y + 12xy - 6x - 12y ← collect like terms

= (- 13xy + 12xy) + (5x - 6x) + (14y - 12y)

= - xy - x + 2y

Step-by-step explanation:

sec²x + cosec²x = sec²x.cosec²x

1/cos²x + 1/sin²x = 1/cos²x.1/sin²x

or, (sin²x+cos²x)/sin²x.cos²x = 1/(sin²x.cos²x)

or, 1/(sin²x.cos²x) = 1/(sin²x.cos²x)

Hence,

sec²x + cosec²x = sec²x.cosec²x proved!!

Answer:

Step-by-step explanation:

Answer:

6x+8+4x+2=180

so!! 10x+10=180

10x=170

x=17

Answer:

[tex]x=17[/tex]

Step-by-step explanation:

The two angles labelled [tex]6x+8[/tex] and [tex]4x+2[/tex] are co-interior angles. When two parallel lines are cut by a traversal, co-interior angles are supplementary, meaning they add up to 180 degrees. Therefore, if line L is parallel to line M, [tex]6x+8[/tex] and [tex]4x+2[/tex] must be supplementary:

[tex]6x+8+4x+2=180[/tex]

Combine like terms:

[tex]10x+10=180[/tex]

Subtract 10 from both sides:

[tex]10x=170[/tex]

Divide both sides by 10:

[tex]x=\frac{170}{10}=\boxed{17}[/tex]

Answer:

Tanya will get approximately $0.07 per square foot.

This can be solved by creating a ratio between the amount she is paid and the amount of square feet she cleans.

(1500)/(107)=(1)/(x) = 0.0713

Answer:

0.0713

Step-by-step explanation:

Tanya will get approximately $0.07 per square foot.

This can be solved by creating a ratio between the amount she is paid and the amount of square feet she cleans.

(1500)/(107)=(1)/(x) = 0.0713

Answer:

√74

Step-by-step explanation:

Answer:

I think it's a

Step-by-step explanation:

hsjshbwibs hshhsvsu hshsbsbus

Answer:

Step-by-step explanation:

Being able to do this requires that you understand what is being asked and that you understand domain. This is a piecewise function, made up of 4 different parts, and each part has a domain different from every other part. Now look at the solutions. We are given coordinates, x and y. So this is how this problem is done.

In a. the coordinate is (-1, 1), right? x = -1 here, so the equation that we "pick" (I'll explain that in a sec) has to have a domain where -1 will fall. The first part of this piecewise has a domain of less than or equal to -11. Is -1 less than or equal to -11? No, it is not. -1 is greater than -11, so the equation we "pick" to use will not be this one. Look at the next piece of the function and note its domain. This domain is that x is greater than -11 and less than 5. Does -1 fit in that domain? Is -1 included in that spread of numbers? Yes it is, so that is the equation we will use. By use I mean that we will plug in -1 for x and see if y = 1 (that number comes from the coordinate (-1, 1) where y = 1). The equation is y = x + 2 and plugging in -1 for x:

y = -1 + 2 so

y = 1 and this point is on the piecewise. Let's do one more example so you can see how it looks when it DOESN'T work out, ok?

Look at b. The coordinate is (-2, -10). x = -2, so the same domain, same equation: x + 2. We plug in -2 for x to find y:

y = -2 + 2 so

y = 0.  0 does not equal -10, so this point is not on that graph.

The key here is picking the equation whose domain includes your x value and evaluating the equation at that value of x to find y.

AB is the same as A multiplied by B. In order to get this value, we need to figure out the value of A and B.

We have two equations here:

a + 5b = 2b + 13

a = 3b - 5

The second equation already has A isolated. So, we can take that equation and plug in the value for A. Doing so will allow us to solve for B.

(3b - 5) + 5b = 2b + 13

8b - 5 = 2b + 13

6b - 5 = 13

6b = 18

b = 3

Now that we know B, we can use our equation that isolated A.

a = 3(3) - 5

a = 9 - 5

a = 4

Therefore, a = 4 and b = 3, and ab = 12.

Hope this helps!

Answer:

3rd Part

(14÷2) + 3

Step-by-step explanation:

The 3rd part is the answer and on solving the equation, 10 comes as the answer.

Answer:

(14 ÷ 2) + 3

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Equation of line is y=2x-2

Answer:

x= 1

Step-by-step explanation:

Work is shown in the picture

Answer:

                  Answer:bf                  

Step-by-step explanation:

Answer:

3.6

Step-by-step explanation:

Hi there!

We are given this expression:

.6√36 (.6*√36)

And we want to find the value of it

.6 can be re-written as 0.6

In that case,

0.6*√36

First, simplify what's under the radical: √36, which is equal to 6 (6*6=36)

The expression then becomes:

0.6*6

Multiply those numbers together

0.6*6=3.6

Hope this helps!

Answer:

x = 17

Step-by-step explanation:

(x-3)2 = 7

Divide both sides by two

(x-3)2 = 7

2 2

x-3= 31/2

x= 31/2-3

x= 1/2 or 0.5