In a circle with an 8-inch radius, a central angle has a measure of 60°. How long is the segment joining the endpoints of the arc cut off by the angle?

8
8√2
8√3

Answer:

The total revenue generated by the firm is:

[tex]P(x) = 75x^3-5x^{\frac{5}{2}}[/tex]

Step-by-step explanation:

The average cost per TV is:

[tex]r(x) =\frac{P(x)}{x}[/tex]

Where x is the number of televisions sold and P is the firm's income for all the televisions sold

In this problem we know the equation r(x).

Then P(x) will be:

[tex]P(x) = x*r(x)[/tex]

Therefore if [tex]r(x)=75x^2-5x^{3/2}[/tex] then

[tex]P(x) = x*(75x^2-5x^{3/2})[/tex]

[tex]P(x) = 75x^{2+1}-5x^{\frac{3}{2}+1}\\\\P(x) = 75x^3-5x^{\frac{5}{2}}[/tex]

Answer:

Px =75x^3-5x^5/2

Step-by-step explanation:

Answer:

5 factories closed

Step-by-step explanation:

In 2014 there were 15 operating factories.

We know that of those 15 factories only 2/3 remain operative.

If only 2/3 remain operational this means that 1/3 of them closed.

To calculate the number of factories that closed we must multiply the initial number of operative factories by 1/3.

This is:

[tex]15 * \frac{1}{3} = \frac{15}{3} = 5[/tex].

5 factories closed

The 7 feet of fabric were remaining.

To solve this problem step by step:

1. Convert the length of the roll of fabric from inches to feet.

  - 120 inches ÷ 12 inches/foot = 10 feet

2. Subtract the length purchased by the customer from the total length of the roll.

  - 10 feet - 3 feet = 7 feet

So, the customer bought 3 feet of fabric, leaving 7 feet remaining.

1. To convert inches to feet, we know that there are 12 inches in a foot. So, we divide the length of the fabric in inches by 12 to get the length in feet.

  - 120 inches ÷ 12 inches/foot = 10 feet

2. Next, we subtract the length purchased by the customer (3 feet) from the total length of the roll (10 feet) to find out how much fabric remains.

  - 10 feet - 3 feet = 7 feet

Therefore, the customer bought 3 feet of fabric, leaving 7 feet remaining.

Complete question:

A roll of fabric was 120 inches long. A customer bought 3 feet of the fabric.

How many feet of fabric were remaining?

Answer:

Step-by-step explanation:

If the triangle is equilateral :

2x +y/2 =  5x/3+y + ½  = 2/3x +2y +5/2

so the perimeter is : P = 3(2x +y/2) or 3(5x/3+y + ½) or 3(2/3x +2y +5/2)

the simplest is :  P = 3(2x +y/2)

                            P = 6x + (3y)/2

Answer: v = 1

1v + 6v = 7             Combine like terms

7v = 7                    Divide both sides by 7

v = 1                       Answer!

Answer:

v=1

Step-by-step explanation:

You can add the similar variables (1v and 6v) to get 7v. now your equation should be 7v=7. divide each side by 7 so that the variable stands alone. 7/7 = 1, so v=1.

Answer:

Option D. $2273.13

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=7\ years\\ P=\$1,685\\ r=0.043\\n=4[/tex]  

substitute in the formula above  

[tex]A=\$1,685 (1+\frac{0.043}{4})^{4*7}=\$2,273.13[/tex]  

3.5-2.6=0.9

0.9÷3=0.3

2.6+0.3=2.9

answer is 2.9

Answer:

55

Step-by-step explanation:

The number that when added to 43, would give the result of 112 can be found to be 69.

To find the number that, when added to 43, equals 112, you can use algebraic reasoning.

Let's represent the unknown number with the variable "x". The equation can be set up as:

43 + x = 112

To solve for "x," we need to isolate it on one side of the equation.

First, subtract 43 from both sides of the equation:

43 + x - 43 = 112 - 43

The 43 on the left side cancels out:

x = 112 - 43

Simplifying the right side of the equation:

x = 69

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To solve the equation 43 + x = 112, subtract 43 from both sides to isolate 'x'. The value of 'x' is 69.

To find the number that, when added to 43, equals 112, we can use algebra. Let's use the variable 'x' to represent the unknown number. So, the equation is 43 + x = 112.

To isolate 'x', we need to move 43 to the other side of the equation.

By subtracting 43 from both sides, we get x = 112 - 43. Evaluating the subtraction, we find that x = 69.

Answer:

Maximum number of relative extremes contained in the graph of this function = 3.

Step-by-step explanation:

We have been given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Now we need to find about what is the maximum number of relative extremes contained in the graph of the given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Degree of the given function = 4.

Because degree is the highest power of variable.

Then relative number of extrema = degree - 1 = 4 - 1 = 3

Hence final answer is 3.

should be 20%

Hope this helps

Answer:it's 12.20

Step-by-step explanation:

Answer:

- 2

Step-by-step explanation:

Given

9x + 3xy - 2

Substitute x = 3 and y = - 3 into the expression

= 9(3) + 3(3)(- 3) - 2

= 27 - 27 - 2 = - 2

Answer:

C

Step-by-step explanation:

Just did it on edg

Answer:13

Step-by-step explanation:

5x+15=7x-11

7x. 7x

2x+15=11

+15 +15

2x =26

———

2

x = 13

A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal. The value of x is 13.

A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.

In an isosceles trapezoid, the angles formed at the ends of any one of the parallel lines are congruent. Therefore, we can write,

5x+15 =7x-11

15+11=7x-5x

26=2x

x = 13

Hence, the value of x is 13.

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Answer:

(-2,-8)

Step-by-step explanation:

y=4x

3x+5y=-46

3x+5(4x)=-46

3x+20x=-46

23x=-46

x=-2

y=4(-2)

y=-8

Answer:

Yes

Step-by-step explanation:

The standard form for a quadratic equation in the US has the terms in decreasing order by power on the left of the equal sign, and the right side zero. Preferably, the leading coefficient is positive. This might also be called "general form." Elsewhere, the "standard form" may be different.

Answer:

Volume: 8x1x12=96 inches^3

Surface area: 8x1x2=16

1x12x2=24

8x12x2=192

the total surface is: 16+24+192=232 inches^2

12 in tall * 8 in wide = 96 in area. You need a third value to find a volume.

Answer:

The original price was $85

She spent $72.25

Step-by-step explanation:

When x equals the price of the chair:

12.75/15 = x/100

15 x = 1275

x = $85

To find the price she paid:

85 - 12.75 = $72.25

Answer:

x=20

Step-by-step explanation:

20-10=10

Answer:

x = 20

Step-by-step explanation:

x - 10 = 10

   +10

cancel out the 10 and do the same thing to both sides

x = 20

very simple

Answer:

No!

The answer is 30 + 45x   See below. Very important question.

Step-by-step explanation:

No!

If you do that, you are violating the properties of the distributive property.

You must multiply both sides of the plus sign by 3

3(10 + 15x) = 3*10 + 3*15x

3(10 + 15x) = 30 + 45x

Answer:

y = 3/2x - 14.

Step-by-step explanation:

The slope of the perpendicular line  is - 1 / -2/3

= 3/2.

Using the point slope form y-y1 = m(x-x1):

y - (-8) = 3/2(x - 4)

y + 8 = 3/2x - 6

y = 3/2x - 14.

Answer:

y = [tex]\frac{3}{2}[/tex] x - 14

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{2}{3}[/tex] x ← is in this form

with slope m = - [tex]\frac{2}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex], hence

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (4, - 8) into the partial equation

- 8 = 6 + c ⇒ c = - 8 - 6 = - 14, so

y = [tex]\frac{3}{2}[/tex] x - 14 ← equation of perpendicular line

Answer:

A = 55 cm²

Step-by-step explanation:

Here, L = W + 6 cm, and P = 2W + 2L = 2W + 2(W + 6 cm) = 32 cm

Then 2W + 2(W + 6 cm) = 32 cm becomes:

         2W + 2W + 12 cm = 32 cm, or

               4W                   = 20 cm.

Therefore, W = 20 cm / 4  =  5 cm

The area of this rectangle is A = L · W = (5 cm + 6 cm) · (5 cm), or

                                                             A = (11 cm)(5 cm), or A = 55 cm²

Final answer:

The area of the rectangle is calculated by solving for the width using the given perimeter, then finding the length, and finally multiplying the two. The width is 5 cm, the length is 11 cm, and the area is 55 cm².

Explanation:

Let's denote the width of the rectangle as w centimeters. According to the problem, the length of the rectangle is 6 cm longer than its width, so we can express the length as w + 6 cm.

The perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given the perimeter is 32 cm, we can write the equation 2(w + 6) + 2w = 32.

Solving this equation:

2w + 12 + 2w = 32

4w = 32 - 12

4w = 20

w = 5 cm

Now that we have the width, we can find the length:

l = w + 6

l = 5 + 6

l = 11 cm

The area of the rectangle is found by multiplying the length by the width, A =[tex]l \(\times\) w[/tex], which gives us:

A = [tex]11 \(\times\) 5[/tex]

A = 55 cm²

Answer:

C

Step-by-step explanation:

The volume (V) of a cone is calculated using the formula

V = [tex]\frac{1}{3}[/tex] πr² h

where r is the radius and h the perpendicular height

here r = 5 and h = 6, hence

V = [tex]\frac{1}{3}[/tex] × π × 5² × 6

   = 2π × 25 = 50π m³ → C

The volume of the cone is [tex]\( 50\pi \, \text{m}^3 \).[/tex]

How to get the volume of the cone

The formula for the volume v of a cone is given by:

[tex]\[ V = \frac{1}{3} \times \pi \times r^2 \times h \][/tex]

The variables in the formula are:

r is the radius of the base of the cone.

his the height of the cone.

Given a cone with radius r = 5 meters and height h = 6 meters, substitute these values into the formula:

[tex]\[ V = \frac{1}{3} \times \pi \times (5^2) \times 6 \]\[ V = \frac{1}{3} \times \pi \times 25 \times 6 \]\[ V = \frac{1}{3} \times \pi \times 150 \]\[ V = 50 \pi \][/tex]

Therefore, the volume of the cone is [tex]\( 50\pi \, \text{m}^3 \).[/tex]

Answer:

x=1 and y = 9

Step-by-step explanation:

Solving using elimination method:

In elimination method we solve equations such that one variable cancels out and we find the value of other variable.

x + 7y = 64

x + 3y = 28

Subtracting both equations:

x + 7y = 64

x + 3y = 28

-   -       -

___________

0 +4y = 36

y= 36/4

y=9

Putting value of y in one of the equation,

x+7y = 64

x + 7(9) = 64

x + 63 = 64

x = 64-63

x = 1

So, x=1 and y=9

Solving using substitution method:

In substitution method, we substitute value of one variable into other value

x + 7y = 64   (1)

x + 3y = 28   (2)

From 1

x = 64 -7y

Putting value of x in eq(2)

(64 -7y) + 3y = 28

64 -7y +3y =28

64 - 4y = 28

-4y = 28 -64

-4y = -36

y = -36/-4

y = 9

Putting value of y in eq (1)

x + 7y = 64

x + 7(9) = 64

x + 63 = 64

x = 64 - 63

x = 1

So, x=1 and y = 9.

Wym is this multiplication

Answer:

13

Step-by-step explanation:

First find the average the numbers (40 / 4 = 10)

2 are more and 2 are less

7, 9, 11, 13

An odd number can be written as 2n+1, where n is an integer. Four consecutive odd numbers can be written as 2n-3, 2n - 1, 2n + 1 and 2n + 3. Adding these together gives you 8n, which we are told is 40. So n is 5 and the four consecutive odd numbers are 7, 9, 11 and 13.

Factor out the common term; 3

(3(x + 1))^2 = 36

Use the Multiplication Distributive Property; (xy)^a = x^ay^a

3^2(x + 1)^2 = 36

Simplify 3^2 to 9

9(x + 1)^2 = 36

Divide both sides by 9

(x + 1)^2 = 36/9

Simplify 36/9 to 4

(x + 1)^2 = 4

Take the square root of both sides

x + 1 = √4

Since 2 * 2 = 4, the square root of 2 is 2

x + 1 = 2

Break down the problem into these 2 equations

x + 1 = 2

x + 1 = -2

Solve the first equation; x + 1 = 2

x = 1

Solve the second equation; x + 1 = -2

x = -3

Collect all solutions;

x = 1, -3

is this the full question?

Answer: N=8

Step-by-step explanation: So 1/2*4=2 then you know that you need 4 to get to six because you already have two. Then 8/2=4 so N=8.

1/2(8+4)=6

4+2=6

6=6

Hope this helped!!!!!

Final answer:

To find the value of n that satisfies the equation 1/2 (n+4)=6, multiply both sides by 2 and subtract 4 from both sides to get n=8.

Explanation:

The student's question asks for the solution to the algebraic equation: 1/2 (n+4)=6. To solve for n, follow these steps:

Therefore, the value of n that makes the equation true is 8.

Answer:

They averaged 79 km per hour

Step-by-step explanation:

To find the average distance, take the kilometers and divide by the hours

1106 km/  14 hours

79 km / hours

They averaged 79 km per hour

79

79x14 is 1106. hope this helps

Answer:

2. 1- Experimental probability of rolling a 4 = 40%

3. 2- Theoretical probability is 3%  greater than experimental probability.

Step-by-step explanation:

Experimental probability of rolling a 4 = 100 × [tex]\frac{8}{20}[/tex]

                                                                  = 100 × 0.4

                                                                  = 40%

Experimental probability of getting at least one tail  = [tex]\frac{72}{100}[/tex]

                                                                                    = 0.72

Theoretical probability of getting at least one tail  = [tex]\frac{3}{4}[/tex]

                                                                                  = 0.75

Theoretical probability is 3%  greater than experimental probability.