Why should you find the least common denominator when adding or subtracting rational expressions?

Answer:

see graph

Step-by-step explanation:

A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.

Answer:

6 first box. 12 second box. 21 third box. 10 fourth box. 4 fifth box.

Step-by-step explanation:

Look for common denominaters, that will show you what to multiply the equation by to get rid of fractions.

Answer:

A =625 ft^2

Step-by-step explanation:

The perimeter of a square is

P = 4s where s is the side length

100 =4s

Divide each side by 4

100/4 = 4s/4

25 = s

A = s^2 for a square

A = 25^2

A =625

Answer:

The volumes of the cubes are 6³ = 216, 8³ = 512, 10³ = 1,000 and 12³ = 1,728 for a combined volume of 216 + 512 + 1,000 + 1,728 = 3456 which means that each side of the scale must have a combined volume of 3456 / 2 = 1728. This means that in order for the scale to be balanced we need to put the 12 cm cube on one side and the other 3 cubes on the other side.

Answer:

The cost to rent each chair is $2.75 and the cost to rent each table is $8.50

Step-by-step explanation:

Let the:

Cost to rent a chair = x

Cost to rent a table = y

We would form an algebraic equation.

The total cost to rent 2 chairs and 3 tables is $31

2x + 3y = 31 ...... Equation 1

The total cost to rent 6 chairs and 5 tables is $59

6x + 5y = 59 ......... Equation 2

We solve the above equation above using elimination method

Multiply Equation 1 all through by the coefficient of x = 6 in Equation 2

Multiply Equation 2 all through by the coefficient of x = 2 in Equation 1

Hence, we have:

2x + 3y = 31 ...... Equation 1 × 6

6x + 5y = 59 ......... Equation 2 × 2

12x + 18y = 186........ Equation 3

12x + 10y = 118 .…...... Equation 4

Subtracting Equation 4 from Equation 3

= 8y = 68

y = 68/8

y = 8.5

Therefore, the cost to rent a table = $8.50

Substituting 8.5 for y in Equation 1 to get the value of x

2x + 3y = 31 ...... Equation 1

2x + 3(8.5) = 31

2x = 31 - 3(8.5)

2x = 31 - 25.5

2x = 5.5

x = 5.5/2

x = 2.75

The cost to rent a chair = $2.75

Therefore, the cost to rent each chair is $2.75 and the cost to rent each table is $8.50

Answer:

x + 1 - ( 4 / x³ + 3x² + 8 )

Step-by-step explanation:

If the volume of this rectangular prism ⇒ ( x⁴ + 4x³ + 3x² + 8x + 4 ), and the base area ⇒ ( x³ + 3x² + 8 ), we can determine the height through division of each. The general volume formula is the base area [tex]*[/tex] the height, but some figures have exceptions as they are " portions " of others. In this case the formula is the base area  [tex]*[/tex] height, and hence we can solve for the height by dividing the volume by the base area.

Height = ( x⁴ + 4x³ + 3x² + 8x + 4 ) / ( x³ + 3x² + 8 ) = [tex]\frac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}[/tex] = [tex]x+\frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex] = [tex]x+1+\frac{-4}{x^3+3x^2+8}[/tex] = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex] - and this is our solution.

Answer:

[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Step-by-step explanation:

[tex]volume=base \: area \times height[/tex]

[tex]height=\frac{volume}{base \: area}[/tex]

[tex]\mathrm{Solve \: by \: long \: division.}[/tex]

[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]

[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]

[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Answer:

 A-2, B-DNE*, C-3, D-DNE, E-4, F-1

---------------------

The first attachment shows the solutions to A and C.

The second attachment shows the solutions to E and F.

There are no real number solutions to systems B and D.

_____

In general, you can solve the linear equation for y, then substitute that into the quadratic. You can subtract the x-term on the left and complete the square to find the solutions.

A.

 (3-x) +12 = x^2 +x

 15 = x^2 + 2x

 16 = x^2 +2x +1 = (x +1)^2 . . . . add the square of half the x-coefficient to complete the square; next take the square root

 ±4 -1 = x = {-5, 3) . . . . . identifies the second solution set for system A

__

B.

 (x -1) -15 = x^2 +4x

 -16 = x^2 +3x

 -13.75 = x^2 +3x +2.25 = (x +1.5)^2

roots are complex: -1.5 ±i√13.75

__

C.

 (1-2x) +5 = x^2 -3x

 6 = x^2 -x

 6.25 = x^2 -x + .25 = (x -.5)^2

 ±2.5 +.5 = x = {-2, 3} . . . . . identifies the third solution set for system C

__

remaining problems are done in a similar way.

_____

* DNE = does not exist. There is no matching solution set for the complex numbers that are the solutions to this.

---------------------

Hope this helps!

Brainliest would be great!

---------------------

With all care,

07x12!

Answer:

x = 1

Step-by-step explanation:

Set up the rational expression with the same denominator over the entire equation.

Since the expression on each side of the equation has the same denominator, the numerators must be equal

5x =4x+1

Move all terms containing x to the left side of the equation.

Hope this can help you

Answer:

The speed of the first train is 70 km/hr

The speed of the second train is 60 km/hr

Step-by-step explanation:

For the first train:

Travel time = 2 hours

The speed = ?

we designate the speed as V

For the second train:

The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)

speed = 10 km/hr slower than that of the first train, we can then say

the speed = V - 10

The total distance traveled by both trains in the opposite direction of one another is 215 km

we can put this problem into an equation involving the distance covered by the trains.

we know that distance = speed x time

the distance traveled by the first train will be

==> 2 hrs x V = 2V

the distance traveled by the second train will be

==> 1.25 hrs x (V - 10) = 1.25(V - 10)

Equating the above distances to the total distance between the trains, we'll have

2V + 1.25(V - 10) = 215

2V + 1.25V - 12.5 = 215

3.25V = 215 + 12.5

3.25V = 227.5

V = 227.5/3.25 = 70 km/hr     this is the speed of the first train

Recall that the speed of the second train is 10 km/hr slower, therefore

speed of the second train = 70 - 10 = 60 km/hr

The speed of the trains are 70km/hr and 60km/hr respectively.

The distance of the first train will be represented by: = 2 × D = 2D

The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).

Based on the information given in the question, the equation to solve the question will be:

2D + 1.25(D - 10) = 215

Collect like terms

2D + 1.25D - 12.5 = 215

3.25D = 215 + 12.5

3.25D = 227.5

D = 227.5/3.25

D = 70km/hour

The speed of the second train will be:

= 70 - 10 = 60km per hour.

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Answer:

C. x+4y=-8

Step-by-step explanation:

The standard form of an equation is Ax+Bx=C

y= -[tex]\frac{1}{4}[/tex]x-2

Multiply 4 by both sides

4y= -x-8

1+4y= -8

Answer:

[tex]\boxed{\sf \ \ \ [-7,0] \ \ \ }[/tex]

Step-by-step explanation:

Hello

[tex]y=x^2+7x=x(x+7) >0\\<=> x>0 \ and \ x+7 >0 \ \ or \ \ x<0 \ and \ x+7<0\\<=> x>0 \ \ or \ \ x<-7\\[/tex]

So values of x which is not in this domain is

[tex]-7\leq x\leq 0[/tex]

which is [-7,0]

hope this helps

Answer:

27°

Step-by-step explanation:

D is 72° because it alternates with B, alternate angles are equal.

2x+72°+2x= 180° because it is a straight line.

4x+72°=180°

4x=108°

x=27°

They're making me write something here so I can post the answer:

p(p + 12)

Answer: The machine depreciates during the fifth year by $4000.

Step-by-step explanation:

Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.

When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.

Then, the machine depreciates A(x) during the fifth year as

[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]

Hence, the machine depreciates during the fifth year by $4000.

Answer:

A. 9

Step-by-step explanation:

Well if you go to 190 on the y-axis and go all the way to the right you can see according to the line of best fit A. 9 should be the correct answer.

Thus,

A.9 is the correct answer.

Hope this helps :)

Answer:

A. 9

Step-by-step explanation:

A line of best fit is a line that goes through a scatter plot that will express the relationship between those points. So, if we look at 190 on the y-axis, we can approximate that on the line of best fit it would be closest to 9 on the x-axis.

Answer:

75

Step-by-step explanation:

x = 75°

yes x = 75°(OPPOSITE ANGLES ARE EQUAL)

..

Answer:

there are 620 comic books

Step-by-step explanation:

let number of comic books be x

total books=3x+x

2480=4x

2480/4=x

620=x

Answer:

Step-by-step explanation:

Let comic books be ' X '

Let Novels be ' 3x '

Now, finding the value of X

According to Question,

[tex]3x + x = 2480[/tex]

Collect like terms

[tex]4x = 2480[/tex]

Divide both sides of the equation by 4

[tex] \frac{4x}{4} = \frac{2480}{4} [/tex]

Calculate

[tex]x = 620[/tex]

Thus, There are 620 comic books in the book store.

Hope this helps...

Best regards!!

Answer:

Step-by-step explanation:

Question:

4(y - 3) = 48

1. Distribute

4y - 12 = 48

2. Simplify Like terms

4y - 12 = 48

    + 12 + 12

4y = 60

3. Solve

4y = 60

/4       /4

y = 15

4. Check:

4(y - 3) = 48

4((15) - 3) = 48

4(12) = 48

48 = 48     Correct!

Hope this helped,

Kavitha

Answer:

[tex]y=15\\[/tex]

Step 1:

To find y, we first have to multiply [tex]4(y-3)[/tex]. When we do that (4 * y, 4 * - 3), we get [tex]4y-12[/tex].

Step 2:

Our equation looks like this now:

[tex]4y-12=48[/tex]

To solve this equation, we have to add 12 on both sides so we can cancel out the -12 on the left side of the equation.

[tex]4y-12(+12)=48(+12)[/tex]

[tex]4y=60[/tex]

Now, we can divide 4 on both sides to get y  by itself.

[tex]4y/4\\60/4[/tex]

[tex]y=15[/tex]

Answer:

The probability is 0.04746

Step-by-step explanation:

Firstly, we calculate the z-score here

Mathematically;

z-score = x-mean/SD/√n

Where from the question;

x = 85, mean = 90 , SD = 15 and n = 25

Plugging these values into the equation, we have;

Z = (85-90)/15/√25 = -5/15/5 = -1.67

So the probability we want to calculate is ;

P(z > -1.67)

We use the standard normal distribution table for this;

P(z > -1.67) = 0.04746

Hello!

Answer:

Table B.

Step-by-step explanation:

An inverse of a function means that the x and y values are swapped in comparison to the original function. For example:

We can use points on the table:

[tex]f(x)[/tex] = (7, 21)

The inverse of this function would 7 as its y value, and 21 as its x value:

[tex]f^{-1} (x)[/tex] = (21, 7)

The only table shown that correctly shows this relationship is table B.

Answer:

I think it is

Step-by-step explanation:

Answer:

5n√2m^ - 3mn

Step-by-step explanation:

Answer:

DEA

Step-by-step explanation:

Answer:

b. 0.585

Step-by-step explanation:

According to Bayes' theorem:

[tex]P(A|B)=\frac{P(B|A)*P(A)}{P(B)}[/tex]

Let A = Person is infected, and B = Person tested positive. Then:

P(B|A) = 93.9%

P(A) = 5.8%

P(B) = P(infected and positive) + P(not infected and positive)

[tex]P(B) = 0.058*0.939+(1-0.058)*0.041\\P(B)=0.09308[/tex]

Therefore, the probability that a person has the disease given that the test result is positive, P(A|B), is:

[tex]P(A|B)=\frac{0.939*0.058}{0.09308}\\P(A|B)=0.585[/tex]

The probability is 0.585.

Answer:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

Step-by-step explanation:

For this case we have the following function:

[tex] y= x^4 -36x^2[/tex]

We can find the first derivate and we got:

[tex] y' = 4x^3 -72x[/tex]

In order to find the concavity we can find the second derivate and we got:

[tex] y'' = 12x^2 -72[/tex]

We can set up this derivate equal to 0 and we got:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

Answer:

120

Step-by-step explanation:

Let's say you put them on the shelf one by one, from left to right.

You can pick 1 of the 5 for the first position.

5

Now you have 4 books left. You pick one out of those 4 for the second position.

5 * 4

There are 3 choices left for the 3rd position.

5 * 4 * 3

2 left for the 4th position.

5 * 4 * 3 * 2

Finally, there is one book left for the 5th position.

5 * 4 * 3 * 2 * 1

Now we multiply:

5 * 4 * 3 * 2 * 1 = 120

Step-by-step explanation:

The center of a circle is the point in the circle which is equidistant to all the edges of thr circle. The point a is the center, while point b is an arbitrary point in the circle. Find attachment for the diagram.

Answer:

i think that this question is wrong

Step-by-step explanation:

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is C, Incenter.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

In a triangle, the point at which all the angle bisectors of the triangle meet is known as the Incenter.

Since In ΔRST, all the angles are bisected by the angle bisector, and the point at which all the angle bisectors meet is represented by U. Thus, it can be concluded that the point U represents the incenter of the triangle.

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Answer:

(a)11

(b)12

Step-by-step explanation:

The first term, a = 1

The last term, l=121

Sum of the series, [tex]S_n=671[/tex]

Given an arithmetic series where the first and last term is known, its sum is calculated using the formula:

[tex]S_n=\dfrac{n}{2}(a+l)[/tex]

Substituting the given values, we have:

[tex]671=\dfrac{n}{2}(1+121)\\671=\dfrac{n}{2} \times 122\\671=61n\\$Divide both sides by 61\\n=11[/tex]

(a)There are 11 terms in the arithmetic progression.

(b)We know that the 11th term is 121

The nth term of an arithmetic progression is derived using the formula:

[tex]a_n=a+(n-1)d[/tex]

[tex]a_{11}=121\\a=1\\n=11[/tex]

Therefore:

121=1+(11-1)d

121-1=10d

120=10d

d=12

The common  difference between them​ is 12.

Answer:

The Taylor series is   [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

Step-by-step explanation:

From the question we are told that

      The function is  [tex]f(x) = sin (x)[/tex]

This is centered at  

       [tex]a = 2 \pi[/tex]

Now the next step is to represent the function sin (x) in it Maclaurin series form which is  

          [tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]

=>       [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

   Now since the function is centered at  [tex]a = 2 \pi[/tex]

We have that

           [tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]

This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]

           [tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]

Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]

This because  [tex]2 \pi[/tex] is a constant

   Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is

             [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

Answer: Reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05.

Step-by-step explanation: Trust me