if a round cake has 30 slices how many slices will represent an angle of 216°?​

The expression for the area within the circle but outside the triangle as a function of the length 3x of the side of the triangle is [tex]\frac{88r^2}{7}-\frac{9\sqrt{3} }{2}x^2[/tex].

It is given that:-

Radius of circle = 2r

Length of side of equilateral triangle = 3x

We have to find the expression for the area within the circle but outside the triangle as a function of the length 3x of the side of the triangle.

We know that,

Area of circle = [tex]\pi R^2[/tex]

Where R is the radius of the circle.

We have R = 2r

Area of an equilateral triangle = [tex]\frac{\sqrt{3} }{2}a^2[/tex]

Where, a is the length of side of equilateral triangle.

a = 3x

Hence,

Expression = [tex]\pi R^2-\frac{\sqrt{3} }{2}a^2[/tex]

Expression = [tex]\frac{22}{7}*(2r)^2-\frac{\sqrt{3} }{2}*(3x)^2 = \frac{88r^2}{7}-\frac{9\sqrt{3} }{2}x^2[/tex].

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Beginning with the graph of f(x) = x2, The transformations that are needed to form  [tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex] is

The graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units

This is further explained below.

Generally, A point, a line, or a geometric figure may undergo one of these four distinct transformations in order for the point's, line's, or figure's shape and/or location to be altered.

The shape of the item as it was before the transformation is referred to as the Pre-Image, while the shape and location of the object after the change make up the Image.

In conclusion, The necessary transformations may be found by beginning with the graph of the function f(x) = x2.

[tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex]

The graph of g(x) is bigger than the graph of f(x), and it is displaced 3 units to the left and 3 units down from its original position.

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Answer:

The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.

Step-by-step explanation:

I got it right.

Answer: Marie ran 4.5 miles on Monday.

Step-by-step explanation: 5.7

                                            +1.2

                                             6.9      

Answer:

Step-by-step explanation: Well €550 Euros is equal to $547.42 US dollars in currency. But since this is approximately, (D) should be correct.

The expression to show the stock's value is -$138 x 13

Given that the price of a stock is steadily decreasing.

Decreasing values are usually represented along with a negative sign.

The decreased price = $138

This means the decrease is of -$138.

Number of months = 13 years

That is $138 is decreased over 13 years.

Then The expression to show the stock's value is -$138 x 13

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False, If we know the distance of an object from earth, we can determine the size of the object by measuring its parallax.

What is parallax explain?

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Answer:

1204.7 in

Explanation:

The steps that you should take to approximate the total amount that Gwinnett County must pay teachers for the whole year are:

The approximate amount that is paid to teachers in will be based on the average wages that is paid to teachers in Gwinnett County. You can find this out by conducting an anonymous survey of different levels of teacher salaries in Gwinnett County or you can find it from the relevant Gwinnett County government department.

Then, look for records to show the number of teachers in Gwinnett County.

Multiply these two figures and you will then get the approximate the total amount that Gwinnett County needs to pay its teachers.

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Answer:

9

Step-by-step explanation:

→ Substitute in the values

2³ +√64 ÷ 8

→ Simplify

8 + 8 ÷ 8

→ Calculate

8 + 1 = 9

Answer:

9

Step-by-step explanation:

2 to the power of 3 is 8

8 + 64 = 72

72 ÷ 8 = 9

The average fraction of students in the two classes who went on the field trip is 11/16

The given parameters are:

Class 1 = 3/4

Class 2 = 5/8

The average is calculated as

Average = 1/2 * (Class 1 + Class 2)

So, we have

Average = 1/2 * (3/4 + 5/8)

Evaluate

Average = 11/16

Hence, the average fraction of students in the two classes who went on the field trip is 11/16

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Answer:

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

2. (3y +2 ) (y + 1)

3. (w - 3) (3w + 5)

4. (4s - 1) (s + 7)

5. (x + 5) (2x - 3)

Step-by-step explanation:

Lots of good articles on factoring quadratics - that is what this is called.

Answer:

1. (2x + 1) (x - 4) 

2. (3y +2 ) (y + 1)

3. (w - 3) (3w + 5)

4. (4s - 1) (s + 7)

5. (x + 5) (2x - 3)

Step-by-step explanation:

a) If the [tex]n[/tex]-th term is [tex]x_n = cn+d[/tex], then

[tex]x_1 = c + d = 16[/tex]

[tex]x_2 = 2c + d = 19[/tex]

Eliminating [tex]d[/tex],

[tex](2c+d) - (c+d) = 19-16 \implies c = 3[/tex]

Solving for [tex]d[/tex],

[tex]3 + d = 16 \implies d = 13[/tex]

Then

[tex]\boxed{x_n = 3n + 13}[/tex]

b) When [tex]n=11[/tex], we get

[tex]x_{11} = 3\cdot11 + 13 = \boxed{46}[/tex]

Answer:

27

Step-by-step explanation:

4.5*3*2 = 27

hi,

You just have to multiply the three measures.  

So :  

2*3*4.5 =  27 cm³

Easy, is it not ?  

Answer:11

Step-by-step explanation:

Answer: 0

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer:

let the number be x

3×(x+11)

3x+33

The price of the perpetuity is $2200

The present value of a perpetuity is determined by simply dividing the amount of the regular cash flows by the discount rate. A growing perpetuity includes a growth rate that increases the cash flows received each period going forward.

Given:

coupon=$55

yield to maturity=2.5%

As, we know price of the perpetuity is determined by dividing the coupon by the yield to maturity.

So,

price=coupon/yield to maturity

price=$55/2.5%

price=$2200

Hence, the price of the perpetuity is $2200

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Answer:

See the picture below.

Step-by-step explanation:

Answer:

[tex]\sqrt{-63}=3i\sqrt{7}[/tex]

[tex]\sqrt{-156}=2i\sqrt{39}[/tex]

[tex]6\sqrt{-12}=12i\sqrt{3}[/tex]

[tex]-5\sqrt{-75}=-25i\sqrt{3}[/tex]

Step-by-step explanation:

An imaginary number is a non-zero real number multiplied by the imaginary unit [tex]i[/tex].

[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Imaginary Number Rule}\end{center}\\\begin{center}$\sqrt{-1}=i$\end{center}\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Radical Rule}\end{center}\\\begin{center}$\sqrt{a \cdot b}=\sqrt{a} \sqrt{b}$\end{center}\end{minipage}}[/tex]

[tex]\begin{aligned}\sqrt{-63} & = \sqrt{9 \cdot -1 \cdot 7}\\& = \sqrt{9}\sqrt{-1}\sqrt{7}\\& = 3i\sqrt{7}\end{aligned}[/tex]

[tex]\begin{aligned}\sqrt{-156} & = \sqrt{4 \cdot -1 \cdot -39}\\& = \sqrt{4} \sqrt{-1} \sqrt{39}\\& = 2i\sqrt{39}\end{aligned}[/tex]

[tex]\begin{aligned}6 \sqrt{-12} & = 6 \sqrt{4 \cdot -1 \cdot -3} \\& = 6 \sqrt{4} \sqrt{-1} \sqrt{3} \\& = 6 \cdot 2 i \sqrt{3} \\& = 12i \sqrt{3}\end{aligned}[/tex]

[tex]\begin{aligned}-5 \sqrt{-75} & = -5 \sqrt{25 \cdot -1 \cdot -3} \\& = -5 \sqrt{25} \sqrt{ -1 } \sqrt{3} \\& = -5 \cdot 5i \sqrt{3} \\& = -25i \sqrt{3}\end{aligned}[/tex]

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It would cost $70 to buy 40 ft of crown molding.

What is cost explain?

8 ft length costs $14

To find the cost of 1 ft length,

Divide through by 8

8ft/8 length costs $14/8

1ft costs $1.75

Now, to find the cost of 40 ft length

1ft costs $1.75

1 ft x 40 would cost $1.75

40 ft would cost $70

Therefore, it would cost $70 to buy 40 ft of crown molding.

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The value of expression |-4 + 3| · 8 is 8.

What is Modulus function?

A modulus function is a function which gives the absolute value of numbers or variable.

The expression is given as;

| -4 + 3 | * 8

Now, Solve the expression as;

⇒ | -4 + 3 | * 8

⇒ | - 1 | * 8

⇒ 1 * 8

⇒ 8

Since, Modulus of a negative number gives the positive of that number.

Hence, The value of expression |-4 + 3| · 8 is 8.

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Answer:

[tex]m^8-4[/tex]

Step-by-step explanation:

[tex]Rule: a^b\cdot \:a^c=a^{b+c}\\=m^7m=m^{7+1}\\=m^{7+1}-4\\=m^8-4[/tex]

The difference quotient of the function that has been presented to us will turn out to be 5.

In this step, we wish to determine the difference quotient for the function that was supplied.

To begin, keep in mind that the difference quotient may be calculated by:

Lim h->0 [tex]\frac{f(x+h)-f(x)}{h}[/tex]

Now, for the purpose of the function, we need this:

Then we will have:

[tex]$$\begin{aligned}&\lim _{h \rightarrow 0} \frac{j(x+h)-j(x)}{h} \\&\lim _{h \rightarrow 0} \frac{5 *(x+h)-3-5 * x+3}{h} \\&\lim _{h \rightarrow 0} \frac{5 x+5 h-3-5 x+3}{h} \\&\lim _{h \rightarrow 0} \frac{5 h}{h}=5\end{aligned}$$[/tex]

j(x) = 5x - 3

Then the following will be true:

Therefore, 5 is the value of the difference quotient for j(x) is %

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There are 3 computer games she can brought at $75.

Unitary method

Unitary method is defined as the process of finding the value of a unit and then the value of a required number of units.

Given,

Arianna buys computer games from an online store.

Each game she orders costs $22 and shipping for her total is $9.

Arianna can spend no more than $75.

Here we need to find how many computer games did Arianna Brought.

Let x be the number of computer games she brought.

We know that,

Cost for one game = $22

Shipping cost = $9.

She spent = $75.

So, it can be written as,

=> 22x + 9 = 75

=> 22x = 75 - 9

=> 22x = 66

=> x = 66/22

=> x = 3.

So, she can brought 3 computer games at $75.

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since you said please: 127*

If we select -9 in the number line, then we need to add 6. Because 6 is positive, we need to move 6 units to the right of -9, it will give:

-9 + 6 = -3

When we have two values A and B and we want to add them using the number line, the first thing we need to do is select one of these two, and locate it on the number line.

Once we did that, the other number will tell us how many units we need to move to the left (if B is negative) or to the right (if B is positive).

In this case the two numbers are -9 and 6.

If we select -9 in the number line, then we need to add 6. Because 6 is positive, we need to move 6 units to the right of -9, it will give:

-9 + 6 = -3

We will get the exact same thing if we first step on the number 6 on the number line, and then move 9 units to the left, we will got -3.

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The coordinates of point T is (9,-2)

Given that A is the midpoint of segment ST. midpoint A has coordinates (7,-1) and point S has coordinates ( 5,0 ) and asked to find the coordinates of the point T

Let's assume the  coordinates of the point T as(a,b)

Midpoint formula for a line segment having endpoints (x1,y1) and (x2,y2)

Let's assume the midpoint as (X,Y)

(X,Y)=([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])

Here the endpoints of the linesegment ST are S(5,0) and T(a,b) and the midpoint of the linesegment ST is A and has coordinates (7,-1).

⇒(7,-1)=([tex]\frac{5+a}{2}[/tex],[tex]\frac{b}{2}[/tex])

⇒7=[tex]\frac{5+a}{2}[/tex]⇒14=5+a⇒a=9

⇒-1=[tex]\frac{b}{2}[/tex]⇒b=-2

Therefore,The coordinates of point T is (9,-2)

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Answer:

If there are dotted lines available then use dotted lines for the range where its only greater than or less than, when there is no equals to sign then you use dotted lines

Step-by-step explanation: