Find the LCD of the rational expressions in the list

Answer:  The answer is 30 inches.

Answer:

36

Step-by-step explantion:
1 x 1 = 1 so each cube is 1 square inch

2 x 6= 12

12 x 3 = 36

Answer:

Step-by-step explanation:

Given:

To Find:

Solution:

Let's assume :

We know that,

[tex]\: \: \dashrightarrow\sf \: \: \: Length \times Width = Area_{(Rectangle)} \\ \\ [/tex]

On Substituting the required values, we get:

[tex] \\ \: \: \dashrightarrow\sf \: \: \:(2x+ 4)(x) = 126 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2 {x}^{2} + 4x = 126 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2 {x}^{2} + 4x - 126 =0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2( {x}^{2} + 2x - 63) = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: {x}^{2} + 2x - 63 = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: {x}^{2} - 7x + 9x - 63 = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:x(x - 7) + 9(x - 7) \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:(x - 7)(x + 9) = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: \purple {x = 7 \: or \: - 9} \\ \\ [/tex]

Length of the side of the rectangle can't be negative. So, x = 7

Hence,

Answer:

       length = 18 m

       width  = 7 m

Step-by-step explanation:

       Let the width of the rectangle = w m

                                            Length = ( 2w + 4) m

Area of rectangle = 126 square meters

length * width     = 126

 (2w + 4) * w        = 126

     2w² + 4w       = 126

     2w² + 4w - 126 = 0

Divide the entire equation by 2

        w² + 2w - 63  = 0

        Sum  = 2

    Product = -63

   Factors  =  9 , (-7)        { 9 +(-7) = 2  & 9*(-7) = -63}

w² +  9w - 7w - 63 = 0       {rewrite the middle term using the factors}

w( w + 9) - 7(w + 9) =0

        (w +9)(w - 7)  = 0

{Ignore w +9 = 0, as measurement will not come in negative}

w - 7 = 0

       w = 7

length = 2w + 4

           = 2*7 + 4

           = 14 + 4

            = 18

Answer:

y-intercept, when x = 0, y = -6

x-intercept, when y = 0, x = 6

Step-by-step explanation:

y-intercept, when x = 0, y = -6

x-intercept, when y = 0, x = 6

Hope this helps, so sorry if I am wrong!

Answer:

A ≈ 1313.19

Step-by-step explanation:

By using the formula [tex]A = 2 \pi r h + 2 \pi r^{2}[/tex] we can just fill in the information with what we know, which is Diameter = 22, Radius = Diameter/2 = 11. The height is 8. So in doing so we get [tex]A = 2\pi (11)(8)+2\pi (11)^{2}[/tex], which
equals ≈ [tex]1313.18573[/tex].

Answer:

(3x + 5)(9x^2 - 15x + 25)

Step-by-step explanation:

27x^3 + 125

= (3x)^3 + 5^3

= (3x + 5) ((3x)^2 - (3x)(5) + 5^2)

= (3x + 5)(9x^2 - 15x + 25)

FYI: a³ + b³ = (a + b)(a² – ab + b²)

Answer:

(3x + 5)(9x² - 15x + 25)

Step-by-step explanation:

This is given in the form : a³ + b³

Identity :

Solving :

Answer:

The total is 130 apples.

Step-by-step explanation:

If the ratio of green to red apples is 2:3 and there is a total of 78 red apples, we can divide 78/3 which is 26. Since this is 1/3 of 78 we can multiply that by 2 to get 52 which is 2/3 of 78 which is the total amount of green apples. We dont stop here however. The question askes for the total amount of apples so we att 52 and 78 to get 130 which is the total amount of apples.

78/3 = 26

26*2 = 52

52+78 = 130

Answer:

Option #4: [tex]4\left(x+8\right)-10\ge 42[/tex]

Step-by-step explanation:

[tex]4\left(x+8\right)-10\ge 42[/tex]

x ≥ 5

Answer:

4th option

Step-by-step explanation:

the inequality shows x ≥ 5

solving the inequalities

- 7(3x - 7) + 21 ≥ 50

- 21x + 49 + 21 ≥ 50

- 21x + 70 ≥ 50 ( subtract 70 from both sides )

- 21x ≥ - 20

divide both sides by - 21 reversing the symbol as a result of dividing by a negative quantity , then

x ≤ [tex]\frac{20}{21}[/tex] ← not the required solution

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

- 4(- x + 8) - 10 ≤ 8

4x - 32 - 10 ≤ 8

4x - 42 ≤ 8 ( add 42 to both sides )

4x ≤ 50 ( divide both sides by 4 )

x ≤ 12.5 ← not the required solution

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

- 7(3x - 7) + 21x ≥ - 50

- 21x + 49 + 21x ≥ - 50 ( subtract 49 from both sides )

0 ≥ - 99 ← not the required solution

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

4(x + 8) - 10 ≥ 42

4x + 32 - 10 ≥ 42

4x + 22 ≥ 42 ( subtract 22 from both sides )

4x ≥ 20 ( divide both sides by 4 )

x ≥ 5 ← Required solution

Answer:

5

Step-by-step explanation:

5,10,15,20,25,30,35,40,45,50

6,12,18,24,30,36,42,48,54

[tex]6 sin² x + 4 cos²x = Stanx[/tex]

[tex]Correct option is B)

Given, 4cos2x+6sin2x=5

[/tex]

[tex]⇒4cos2x+4sin2x+2sin2x=5

⇒2sin2x=1⇒sin2x=21=(21)2

⇒x=nπ±4π

[/tex]

[tex]~~~~~~6 \sin^2 x + 4 \cos^2 x = 5 \tan x \\\\\implies 3 \cdot 2\sin^2 x + 2 \cdot 2 \cos^2 x = 5 \tan x\\ \\\implies 3(1- \cos 2x ) + 2( 1 + \cos 2x) = 5 \tan x\\\\\implies 3 - 3 \cos 2x +2 +2 \cos 2x = 5 \tan x\\\\\implies 5- \cos 2x = 5 \tan x\\ \\\implies 5 - \left(\dfrac{1- \tan^2 x}{ 1+ \tan^2 x} \right)=5 \tan x\\\\\implies \dfrac{5+5 \tan^2x -1 + \tan^2 x}{1+ \tan^2 x} = 5 \tan x\\\\\implies 4 + 6\tan^2 x = 5( \tan x)(1+ \tan^2 x)\\\\\implies 4 +6\tan^2 x = 5 \tan x + 5 \tan^3 x[/tex]

[tex]\implies 5\tan^3 x -6 \tan^2 x+5 \tan x-4=0\\\\\implies 5 \tan^3 x - 5 \tan^2 x - \tan^2x + \tan x+ 4\tan x -4=0 \\\\\implies 5\tan^2 x(\tan x-1) -\tan x(\tan x-1) +4(\tan x-1)=0\\\\\implies ( \tan x - 1)( 5 \tan^2 x- \tan x +4) =0\\\\\implies \tan x =1\\\\\implies x = n \pi+ \dfrac{\pi}4[/tex]

Answer:

First choice.

Step-by-step explanation:

The third side cannot be 26 or greater ( as 11 + 15 = 26).

Answer:

it is A i think

Step-by-step explanation:

From the figure, the value of tan j is 13/9

The tangent of an angle is calculated using:

tan(j) = opposite/adjacent

From the figure, we have:

opposite = 13

adjacent = 9

So, we have:

tan(j) = 13/9

Hence, the value of tan j is 13/9

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Answer:

35

Step-by-step explanation:

it takes 5 weeks to make 100 since 20 x 5 = 100

100 x 7 = 700

5 x 7 = 35

Answer:

It will take 35 weeks.

The marginal cost is the change in the total cost that arises when the quantity produced is incremented, the cost of producing additional quantity.

a). First construct total variable cost for each level Q -- simply multiply Q by AVC. So

Q TVC

1 1

2 4

3 9

4 16

5 25

6 36

Now calculate marginal cost as the change in TVC for each level Q.

Q MC

1 1

2 3

3 5

4 7

5 9

6 11

b) with price = 10, firm will produce 5 but not 6 units.

c) calculate total profits at Q=5. Total revenue is $50, total costs is $25+$16 = $41. Since there are profits to be made, more firms will enter, shifting the supply curve out, Price will fall, quantity goes up. Each firm will supply the same or less as price falls.

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Answer:

1/2

Step-by-step explanation:

First square area = 4cm^2, thus the side length is 2cm

Second square area = 16cm^2, thus the side length is 4cm

This gives a ratio of 2/4, simplifying yields 1/2

Answer:

Step-by-step explanation:

#hope it helps!

Answered by ReyvREYV111

Answer:

The string contains 6 ones and 8 zeros, thus 14 bits in total.

Step-by-step explanation:

Hope this helps.

Answer: 6 pieces

Step-by-step explanation:

      He is cutting the board into pieces each measuring [tex]\frac{1}{8}[/tex] of a foot. The original board is [tex]\frac{3}{4}[/tex] of a foot long. This means he is dividing, so we will solve the problem by doing the following.

     [tex]\displaystyle \frac{3}{4}/\frac{1}{8}[/tex]

     [tex]\displaystyle\frac{3}{4}*\frac{8}{1}[/tex]

     [tex]\displaystyle\frac{3*8}{4*1}[/tex]

     [tex]\displaystyle\frac{24}{4}[/tex]

     [tex]\displaystyle6[/tex]

     He can cut the board into 6 pieces, each measuring [tex]\frac{1}{8}[/tex] of a foot.

Answer:

See below

Step-by-step explanation:

The turtle’s distance from his starting point is increasing between 0 and 6

seconds (which means it is getting larger in that time interval)

The turtle’s distance from his starting point is constant between 6 and 8 seconds (which means it is not moving in that time interval!)

The turtle’s distance from his starting point is decreasing between 8 and 12

seconds (which means it is getting smaller in that time interval)

Answer:

0-6, 6-8, 8-12

Step-by-step explanation:

For this, we'll have to use the numbers along the x-axis to measure. The line begins moving in a positive direction (up) from 0 to 6, which at that point, it remains stationary until 8 seconds. It then moves in a negative direction (down) all the way to 12.

If I can explain or elaborate in any way, please let me know.

Hope this helps!

Hi Student!

The first step that we need to take when approaching this problem is to extract the important information that was given in the problem statement.  Reading through it, we can see that we are given a circumference of a pipe being 9.24 centimeters.  After that, they are asking for us to determine what the diameter of the pipe is and tell us to use 3.14 instead of π.

Now that we have completed the information gathering, we can move onto the part of plugging in our values and solving for the unknown.

Plug in the values

Divide both sides by 3.14

Therefore, after solving for our unknown being the diameter we were able to determine that it is around 2.942675 centimeters using the Circumference formula.

Answer:

f(3)=11

Step-by-step explanation:

f(x) = 2x + 5

to find f(3) we simply plug in 3 where ever x is

So f(3) = 2(3) + 5

==> multiply 2 and 3

f(3) = 6 + 5

==> add 6 and 6

f(3) = 11

Answer:

None

Step-by-step explanation:

By using the equation a^2 +b^2=c^2 we can see if it will work.

Substitute a for 6 and b for 2 to get 6^2+2^2=40

when you [tex]\sqrt{40}[/tex] you don't get 7 therefore you cant make any triangles

Answer:

The new points to the triangle will be:
[tex]A(1,4)\\ B(1,1)\\ C(-1,1)[/tex]

Step-by-step explanation:

Because the reflection point is at [tex]x=2[/tex], all x values will subtract their distances from [tex]x=2[/tex] to get their new values. The y values remain the same.

The starting values are:

[tex]A(3,4)\\ B(3,1)\\ C(5 ,1)[/tex]

Point [tex]A[/tex] is 1 unit away from [tex]x=2[/tex], so we'll subtract 1 from 2 to get the new x value: [tex]2 - 1 = 1[/tex], so [tex]A(1,4)[/tex].

 

Point [tex]B[/tex] is also 1 unit away from [tex]x=2[/tex], so we'll subtract 1 from 2 to get the new x value: [tex]2 - 1 = 1[/tex], so [tex]B(1,1)[/tex].

Point [tex]C[/tex] is 3 units away from [tex]x=2[/tex], so we'll subtract 3 from 2 to get the new x value: [tex]2 - 3 = -1[/tex], so [tex]C(-1,1)[/tex].

Amiya + Ravi = 72

x + 2x = 72

3x = 72

x = 72/3

x = 24

therefore Amiya has 24 stamps

Huiling has 8 more than Amiya = 24 + 8 = 32stamps

hope it helps...!!!

If the function is y = 4.5x. Then the rate of change of the function expressed as a unit rate will be 4.5.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A bike rental company charges a fee per hour.

The charge, in dollars, is the same each hour.

The ordered pairs (3, 13.50) and (5, 22.50) represent the corresponding hours, x, and cost, y.

Then the linear equation is given as

[tex]\begin{aligned} \rm y - 22.5 &= \rm \dfrac{22.5 - 13.5}{5 - 3} (x- 5)\\\\\rm y - 22.5 &= \rm 4.5x - 22.5\\\\\rm y &= \rm 4.5x \end[/tex]

Then the rate of change of the function expressed as a unit rate will be

[tex]\rm \dfrac{dy}{dx} = \dfrac{d}{dx} (4.5x )\\\\\dfrac{dy}{dx} = 4.5[/tex]

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Answer:

Step-by-step explanation:

Question 1:

x² = -8x - 7

x² + 8x = -7

(x + 4)² = 9

So the answer is (x + 4)² = 9

Question 2:

(x + 4)² = 9

So x = -4 ± 3

a. The number of square cm of paper that would be used to make 4 caps is 3154.56 cm².

b. For the cake to have the required dimensions, they should order 1 kg of cake.

a.

The number of square cm of paper that would be used to make 4 caps is 3154.56 cm².

To find the number of square cm paper would be used to make 4 caps, we need to find the area of a cone.

The area of a cone, A = πr² + πr[√(h² + r²)] where

Now given that the base circumference of the cone is C = 44 cm. So,

C = 2πr where r = radius of base

So, r = C/2π = 44 cm/2π = 22 cm/3.142 = 7 cm

The height of the cone, h = 24 cm

So, A = πr² + πr[√(h² + r²)]

A = π(7 cm)² + π(7 cm)[√((24 cm)² + (7 cm)²)]

A = π(7 cm)² + π(7 cm)(7)[√((4 cm)² + (1 cm)²)]

A = 49π cm² + 49π cm[√(16 cm² + 1 cm²)]

A = 49π cm² + 49π cm[√(17 cm²)]

A = 49π [1 cm² + 4.123 cm²)]

A = 49π [5.123 cm²)]

A = 251.032π

A = 788.64 cm²

Since the area of one cap is A = 788.64 cm²,

the area of 4 caps is A' = 4A

= 4 × 788.64 cm²

= 3154.56 cm²

So, the number of square cm of paper that would be used to make 4 caps is 3154.56 cm².

b.

For the cake to have the required dimensions, they should order 1 kg of cake.

To find the amount of cake to be ordered, we need to find the volume of a cake since it is the volume of a cylinder.

The volume of a cylinder is V = πd²h/4 where

Substituting the values of the variables into the equation, we have

V = πd²h/4

V = π(24 cm)²(14 cm)/4

V = π(576 cm)²(14 cm)/4

V = 8064π cm³/4

V = 2016π cm³

V = 6333.45 cm³

So the volume of the cake is 6333.45 cm³

Since 650 cm³ equals 100 g, 6333.45 cm³ = 6333.45 cm³ × 100 g/650 cm =  974.4 g = 0.974 kg ≅ 1 kg.

So, for the cake to have the required dimensions, they should order 1 kg of cake.

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