Multiplying and dividing rational expressions

Answer:

Step-by-step explanation:

C

The area of the circular shaped pizza is A = 254.5 cm²

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the pizza be r = 9 cm

The area A of a circle with radius r is given by the formula:

A = πr²

Substituting the given radius of 9 cm, we get:

A = π(9 cm)²

A = π(81 cm²)

A ≈ 254.47 cm²

Rounding to one decimal place, we get:

A ≈ 254.5 cm²

Hence , the area of the circular pizza with a radius of 9 cm is approximately 254.5 cm²

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Answer:

-3 and -4

Step-by-step explanation:

x = 1st number

y = 2nd number

2x-4y=10

4x-4y=4

distribute first equation by -2 to eliminate x-values:

 -4x + 8y = -20

+ 4x - 4y = 4

4y = -16

y = -4

solve for 'x':

2x - 4(-4) = 10

2x + 16 = 10

2x = -6

x = -3

The solution for the given system of equations is x = -3 and y = -4.

A linear equation is defined as an equation in which the highest power of the variable is always one.

This is a system of linear equations in two variables, x and y.

The first equation is:

2x - 4y = 10

The second equation is:

4x - 4y = 4

You can solve one of the equations for one of the variables, and then substitute that expression into the other equation.

From the first equation:

2x - 4y = 10

2x = 4y + 10

x = 2y + 5

Substitute this expression of x in the second equation,

4(2y+5) - 4y = 4

8y + 20 - 4y = 4

4y = -16

y = - 4

Now, substitute this value of y in x = 2y + 5

x = 2 × -4 + 5

x = - 3

Hence, the solution for the system of equations is x = -3 and y = -4.

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Answer:

answer

I think it's 40...

[tex]20\% \: \bold{of} \: 200 \\ \\ = \frac{20}{100} \times 200 \\ \\ = \frac{20}{ \cancel{100}} \times \cancel{200} \\ \\ = 20 \times 2 \\ \\ = 40[/tex]

Answer:

Value of F(x) when x = -5 is 20

Step-by-step explanation:

Given equation;

f(x) = x² + 2x + 5

f(x) = f(-5)

Find:

Value of F(x) when x = -5

Computation:

Given function;

f(x) = x² + 2x + 5

By putting value of x in given function

f(-5) = (-5)² + 2(-5) + 5

f(-5) = (-5 x -5) + 2(-5) + 5

f(-5) = (25) - 10 + 5

f(-5) = (25) - 5

f(-5) = 20

Value of F(x) when x = -5 is 20

9514 1404 393

Answer:

  30

Step-by-step explanation:

The total price for x employees will be ...

  p(x) = {1000x for x ≤ 25; x(1000 -20(x -25)) for 25 < x ≤ 40; 700x for 40 < x}

We want p(x) = 27000.

We can check the value of x for the three different functions to see if it is in the specified domain.

  1000x = 27000   ⇒   x = 27 (not in the domain of the first segment)

__

  x(1000 -20(x -25)) = 27000

  20x(75 -x) = 27000 . . . . . collect terms, factor

  (x -37.5)^2 = -1350 +1406.25 . . . . . complete the squre

  x = 37.5 ±√56.25 = 37.5 ±7.5 = {30, 45}

  x =  30 is in the domain; x = 45 is not

__

  700x = 27000

  x ≈ 38.57 (not in the domain of the last segment)

__

So, the piecewise cost function will give a total cost of $27000 when the number of employees going for the trip is 30.

Answer:

18

Step-by-step explanation:

Take a breath :) . I've got your back.

If she caught 6 carp + 8 bass + 7 catfish, she caught 6 +8 +7 fish total = 21.

7 of 21 were catfish.

If she catches 54 fish instead of 21, (and we have to assume the ratio stays the same), how many will be catfish?

Ratios are 7:21 and x:54, but we'll write them as fractions:

7/21 = x/54

Then cross multiply:

21x = (54)(7)

21x = 378

divide both sides by 21

x = 18

If she catches 54 fish total, we predict she will catch 18 catfish.

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

If we go back to the original 7/21, we can reduce that to 1/3. Then ask what is 1/3 of 54? 18.

Answer:

y = 4/3x - 3

Step-by-step explanation:

Use this formula to find the slope first.

(y2 - y1) / (x2 - x1)

(x2, y2) --> (-3, -7)

(x1, y1) ---> (3, 1)

Now plug in:

(-7 - 1) / (-3 - 3)  =  -8 / -6  =  4/3

Now find the y intercept by plugging any points to y= 4/3x + b

I will use (3, 1).

1 = 4/3(3) + b  

1 = 4 + b  (subtract 4 on both sides)

-3 = b

So the formula is

y = 4/3x - 3

Answer:

√7 / 4

Step-by-step explanation:

Trigonometrical identity are used to show the relationship between the sides and angles of a right angled triangle. Some trigonometric identities are:

sinΘ = opposite / hypotenuse, cosΘ = adjacent / hypotenuse, tanΘ = opposite / adjacent.

Given that cosΘ = 3 / 4

Therefore, cosΘ = adjacent / hypotenuse = 3 / 4

adjacent = 3, hypotenuse = 4. Let x be the opposite side, to get the opposite side, we use Pythagoras theorem:

opposite² + adjacent² = hypotenuse²

x² + 3² = 4²

x² + 9 = 16

x² = 7

x = √7

sinΘ = opposite/hypotenuse = √7 / 4

Answer:

option B

Step-by-step explanation:

The figure is combination of parallelogram and semi- circle. So,

area = area of parallelogram + area of semi-circle

[tex]Area \ of \ parallelogram = base \times height = 7 \times 6 = 42 cm^2\\\\Area \ of \ semi-circle = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times 3.5^2 = 19.2cm^2\\\\Therefore \ Area = 42 + 19.23 = 61.2cm^2[/tex]

By looking at the table, you can see that we have an x

that is paired with two different y's so this does not fit the

definition of a function which states that each x must

be paired with exactly one y.

Answer:

1:9

Step-by-step explanation:

~Refer to the attachment for the solution.

Answer: I think the answer would be 10

Step-by-step explanation:

5/8 * 16/1 = 80/8 = 10

She needs 10 sub sandwiches if there are 16 students and Mrs Bryant wants to give them 5/8 of a large sub sandwiches

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

Total number of students = 16

Each student receive = 5/8 of a large sub sandwich

Total sandwich receive = 16(5/8) = 10

Thus, she needs 10 sub sandwiches if there are 16 students and Mrs Bryant wants to give them 5/8 of a large sub sandwiches

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Answer:

22 square units

Step-by-step explanation:

Area of a triangle formula:

A = 0.5bh

Given:

b = 11

h = 4

Work:

A = 0.5bh

A = 0.5(11)(4)

A = 5.5(4)

A = 22

Answer:  2x(x+1)

Step-by-step explanation:

F(x) + G(x) =2x^2+1+2x-1

                 =2x^2+2x

                =2x(x+1)

Answer:

6x

Step-by-step explanation:

i am not quite sure why you have provided H(x), and i am assuming f(x) = 2x * 2 + 1

with that into consideration we can simplify f(x)

f(x) = 2x*2+1

= 4x+1

question -> f(x) + g(x)

= (4x+1) + (2x -1)

1 and -1 can get cancelled and 4x + 2x = 6x

thus the answer is 6x

Answer:

13 cm

Step-by-step explanation:

[tex] \sqrt{ {12}^{2} + {5}^{2} } = \sqrt{169 } = 13[/tex]

Answer:

D. by multiplying 58 by 0.17

[tex]17\% \: of \: 58 \\ = \frac{17}{100} \times 58 \\ = \frac{986}{100} \\ = 9.86[/tex]

Answer:

t=75

h=19

x=9

s=6

Your welcome (:

Answer:

10 units

Step-by-step explanation:

point A has the coordinate (1,6) and point B has the coordinates (1,2), so the difference in the y values will give height of the triangle which is 6-2 = 4

similarly the point B has the coordinates (1,2) and point C has the coordinates (6,2). Calculate the difference in x values which is 6-1 = 5 which is the base of the triangle

now use the area of a triangle formula which is 1/2 * b * h

= 1/2 * 5 * 4

= 1/2 * 20

= 10

Answer:

No solution

Step-by-step explanation:

The given lines on the graph are parallel . So they will never intersect each other. Therefore they have no solution.

Answer:

-12 w^3

Step-by-step explanation:

-9w^3  - 3 w^3

Factor out the common term

w^3( -9-3)

w^3 (-12)

Answer:

12

Step-by-step explanation:

michael Jackson

Answer

10.5

Step-by-step explanation:

to find volume is WxLxH. revurse it and divide volume by width and length to find height

Answer:

Solution given:

[tex]\frac{1}{5}(6+3+1)²[/tex]

[tex]\frac{1}{5}(10)²[/tex]

[tex]\frac{1}{5}100[/tex]

=20 is a required answer.

an isotope is an atom with a different number of____neutrons____ ,than a normal atom

Answer:

hggh

Step-by-step explanation:bmv,g,vg,cvbbgfghvc

Answer:

08 units, 3 units, V73 units

Step-by-step explanation:

Pythagoras theorem can be used to determine which  sets of side lengths are for a right triangle

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

8² + 15² = √289

8² + 3² =  √73

16² + 30² =  √1156

only the second option is correct

Answer: 4/5

Step-by-step explanation: