Two straight edges of a pizza slice meet at an angle of 30°. If the pizza has a radius of 12
inches, what is the area of the slice and how long is its crust? Show how you got your answer step-by-step.

Answer:

Step-by-step explanation:

Diameter ( d ) = 21 cm

Radius is just half of the diameter

Radius ( r ) = [tex] \sf{ \frac{21}{2} }[/tex] = 10.5 cm

Now, let's find the perimeter of a semi - circle :

[tex] \sf \frac{1}{2} \pi \: r \: [/tex]

Plug the values

⇒[tex] \sf{ \frac{1}{2} \times 3.14 \times 10.5}[/tex]

Calculate

⇒[tex] \sf{16.485 \: cm}[/tex]

Hope I helped!

Best regards!

Answer:

61

Step-by-step explanation:

7n+5

Let n=8

7*8 +5

56+5

61

Answer:

[tex]\Huge \boxed{61}[/tex]

Step-by-step explanation:

[tex]7n+5 \\ \\ \\ n=8[/tex]

Replace n with 8.

[tex]7(8)+5[/tex]

Evaluate the expression.

[tex]56+5[/tex]

[tex]=61[/tex]

Answer:

So the sequence of the five numbers are;

10,26,74,218,650

Step-by-step explanation:

In this question, we are interested in building a sequence of 5 numbers given the initial term.

Okay, to build this sequence, we will need to look at the rule that guides the building of the new sequence:

The rule is that the next term is 4 less than 3 times the previous term.

Okay, let’s call the next term y, while the previous term is x.

Following what was specified in the question;

y = 3x -4

Recall; the next term(y) is 4 less (-4) than 3 times (3 multiplied by) the previous term (x)

So let’s start with the initial term of 10.

The next term will be;

y = 3(10) -4 = 30-4 = 26

The next term after 26 will be ;

y = 3(26) -4 = 78-4 = 74

The next term after 74 will be;

y = 3(74) -4 = 222-4 = 218

The next term after 218 will be;

y = 3(218) -4 = 650

Answer:

a and e jfdjjxjccjddjdjdjdjdjjdjdidie

Hey There!!

∠ABC ≅ ∠DEC

∠DEC = ∠GEF

thus:

∠ABC = ∠GEF

∠GFE ≅ ∠DCE

∠DCE = ∠ACB

thus:

∠ACB = ∠GFE

If two of their angles are equal, then the third angle must also be equal, because angles of a triangle always add to make 180°.

Thus: ΔABC ∼ ΔGEF by AA similar triangle postulate.

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer:

x = 40

Step-by-step explanation:

x/8 - 5/2 =5/2

x/8 = 10/2

x/8 = 5

x  = 40

Answer:

[tex]\Huge \boxed{x = 40}[/tex]

Step-by-step explanation:

x/8 - 5/2 = 5/2

Add 5/2 to both sides of the equation.

x/8 - 5/2 + 5/2 = 5/2 + 5/2

Simplify the equation.

x/8 = 10/2

x/8 = 5

Multiply both sides of the equation by 8.

(8)x/8 = (8)5

x = 40

Answer:

6/17

Step-by-step explanation:

Given the following :

Number of caramel = 12

Number of dark chocolate = 16

Number of mint = 7

probability fraction of "selecting a caramel" after selecting a dark chocolate and eating it.

After eating means : picking without replacement.

Probability = (Number of required outcomes / total possible outcomes)

Total number of items = ( 7 + 12 + 16) = 35

After first picking a dark chocolate and eating it, total number of items left in the jar becomes:

(35 - 1) = 34

Then,

P(picking a caramel) = (number of caramels / total number of items)

P(picking a caramel) = 12 / 34 = 6/17

Answer:

a) 24

b) Bowtown and Dovebury

c) 57

Answer:

Slope = 1/4

Step-by-step explanation:

Slope = rise/ run

=> slope= 1 = rise / 4 = run

=> Slope = 1/4

Answer:

41.

Step-by-step explanation:

The range = highest - lowest value

= 65 - 24

= 41.

Answer:

Step-by-step explanation: use the calculatrr

Answer:

11/12

Step-by-step explanation:

Nesta questão, estamos interessados ​​em saber em que fração do álbum de figurinhas ambos contribuíram.

Pela pergunta, ficamos sabendo que Karina contribuiu com 1/6 enquanto Cristina contribuiu com 3/4.

Portanto, para encontrar a fração com a qual ambos contribuem, simplesmente adicionamos as duas frações.

Matematicamente, isso seria 1/6 + 3/4 = (2 + 9) / 12 = 11/12

Answer:

K = 12

Step-by-step explanation:

10 Cos 30° – 3 Tan 60°

The above expression can be simplified as follow:

10 Cos 30° – 3 Tan 60°

Recall:

Cos 30° = √3/2

Tan 60° = √3

Therefore,

10 Cos 30° – 3 Tan 60°

10 (√3/2) – 3(√3)

5√3 – 3√3

(5 – 3) √3

2√3

To write the above expression 2√3 in the form √K, we simply do the following:

2√3

Find a number, such that the square root of the number will result to 2. The number is 4 as shown below

√4 = 2

Next, replace 2 with √4 in the expression above

2√3

= √4 × √3

= √(4 × 3)

= √12

Therefore,

2√3 = √12

Comparing √12 with √K,

√12 = √K

K = 12

Answer:

Step-by-step explanation:

Given the volume of the cylindrical soup expressed as V = πr³+ 7πr²

From V = πr³ + 7πr²;

factor out the common variable

V = πr³ + 7πr²

V = πr²(r+7) ... 1

The original volume of a cylinder V =  πr²h .... 2 where;

r is the radius of the cylinder

h is the height of the cylinder

Equating equation 1 and 2, we will have;

πr²(r+7)  =  πr²h

Divide both sides by  πr²

πr²(r+7)/ πr² = πr²h/ πr²

r+7 = h

h = r+7

Hence the factor in the context given is equivalent to the height of the cylinder written as a function of its radius r. The statement means that the height of the cylindrical soup is 7 more than its radius.

Answer:

Step-by-step explanation:

the height of the cylendar is 7 units greater than the radaius

Evin is walking home from the museum. She starts 38 blocks from home and walks 2 blocks each minute. Evin's distance from home is a function of the number of minutes she has been walking.

(a) which variable is independent and which variable is dependent in this scenario?

(b) Fill  in the table below for a variety of time values.

Time, t, in minutes                                0               1            5          10

Distance from home, D, in blocks  

Answer:

Step-by-step explanation:

From the given information:

(a) which variable is independent and which variable is dependent in this scenario?

An independent variable is a variable that when two variable occurs in a particular event, one variable does not in any way affect the event of the other variable.

A dependent variable is a variable where on variable is dependent on the other variable.

From the question given;

time (t) in minutes is the independent variable

Distance D from home is the dependent variable

(b) Fill  in the table below for a variety of time values.

Time, t, in minutes                                0               1            5          10

Distance from home, D, in blocks      

We are being told that Evin starts 38 blocks from home,

Then she is just starting, i.e from rest

Then; at time t = 0 , she is 38 block distance from home

However, if she walks 2 blocks each minute,

then after 1 minute , that will be 38 blocks - 2 blocks = 36 blocks distance from home.

If she walks for 5  minutes,

then she will be (38 - 2(5) ) blocks away from home

= 38 - 10

= 28 blocks away from home

If she walks for 10 minutes,

then she will be (38 -2(10)blocks away from home

= 38 - 20

= 18 blocks away from home.

Time, t, in minutes                                0               1            5          10

Distance from home, D, in blocks      38              36         28        18

Answer:

  D. a = cost of apples O = cost of oranges

Step-by-step explanation:

The only choice that actually shows a definition of the variables is choice D.

Answer:

Step-by-step explanation:

Given the expression − 6 + 3 ( 2 + ( − 4 t ) ), to get the equivalent expression, the following steps must be followed;

Step 1: Multiply the signs inside the parenthesis

= − 6 + 3 ( 2 + ( − 4 t ) )

= -6+3(2-4t)

Step 2: Open up the parenthesis

= -6 + 3(2)+3(-4t)

= -6 + 6 - 12t

Step 3: Simplify the resulting expression by taking the diffrence between -6 and 6:

= 0 - 12t

= -12t

Hence the equivalent expression is -12t

Answer:

-12t

Step-by-step explanation:

Answer:

81.64 inches.

Step-by-step explanation:

You're looking for circumference here.

d = diameter of the wheel

d = 26 inches.

Input your values:

C = π * d

C = 3.14 * d

C = 3.14 * 26 inches

C = 81.64 inches.

Answer:

C≈81.68 in. thus B is the answer (I used more digits for π).

Step-by-step explanation:

Formula C=2πr

Answer:

-2(x - 5)(x + 1)

Step-by-step explanation:

-2x² + 8x + 10

-2(x² - 4x - 5)

-2(x - 5)(x + 1)

Step-by-step explanation:

Hey, there!!

Let's do it simply, ok.

Given that,

[tex] = - 2 {x}^{2} + 8x + 10[/tex]

Take (-2) common to make it easy.

[tex] = -2( 2 {x}^{2} - 8x - 10)[/tex]

= -2{ x^2-(5-1)x -5}

Multily with x,

= -2 {x^2-5x+x-5}

Taking common,

= -2{x(x-5) +1(x-5)

= -2{(x+1)(x-5)}...is your required answer.

Hope it helps...

Answer:

 (0 + m)/2, (0 + n)/2.

Step-by-step explanation:

The  x coordinate of the  midpoint must be halfway  between the x coordinates of  A and B, and the y coordinate must be  found in the same way.

So the midpoint is  (0 + m)/2, (0 + n)/2.

Answer:

0.44 seconds

Step-by-step explanation:

Time period is the time duration for completing one oscillation:

Answer is 0.44 seconds

Step-by-step explanation:

The Time period of pendulum (T) is

T=46/20

T=2.3s

Answer:

1587.57 grams

Step-by-step explanation:

1 pound = 453.592 grams.

so multipy that by 3.5

Answer:

Justin's displacement is 12.65 km.

Step-by-step explanation:

Since Justin rides 12 km south, then 4 km west, his displacement can be determined by applying Pythagoras theorem to the sketch of his journey. Let his displacement be represented by s,

[tex]/Hyp/^{2}[/tex] = [tex]/Adj1/^{2}[/tex] + [tex]/Adj2/^{2}[/tex]

[tex]s^{2}[/tex] = [tex]/4/^{2}[/tex] + [tex]/12/^{2}[/tex]

   = 16 + 144

[tex]s^{2}[/tex]  = 160

⇒ s = [tex]\sqrt{160}[/tex]

      = 12.6491

s ≅ 12.65 km

Justin's displacement is 12.65 km.

Answer:

y- intercept (0, -1.2)

x- intercept (-3, 0)

Step-by-step explanation:

Line is given:

Y- intercept:

When x= 0

Point is (0, -1.2)

X- intercept:

When y = 0

Point is (-3, 0)

Answer:

[tex] \frac{25}{39} [/tex]

Step-by-step explanation:

[tex]\frac 13,~\frac 27,~\frac 3{10},~\frac 4{13},~\frac 5{17}~?[/tex]

Convert them to fractions with their L.C.D (lowest common denominator)

[tex]\frac {15470}{46410},~\frac {13260}{46410},~\frac {13923}{46410},~\frac {14280}{46410},~\frac {13650}{46410}~?[/tex]

hence the two largest are

[tex] \frac{1}{3} \: and \: \frac{4}{13} [/tex]

[tex] \frac{1}{3} + \frac{4}{13} = \frac{25}{39} [/tex]

Answer:

Angle= 135°

Step-by-step explanation:

FUZ CIA

Corresponding angles are equal

Answer:

Yes, you have to move because 1 square is one unit.

Answer:

We have to travel 26.93 units from platform B to C.

Step-by-step explanation:

Length of a segment having coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is determined by the formula,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

From the graph attached,

Coordinates of the points B and C are (-25, -20) and (-15, 5) respectively.

Distance between these points B and C Or length of BC will be,

BC = [tex]\sqrt{(-25+15)^2+(-20-5)^2}[/tex]

     = [tex]\sqrt{100+625}[/tex]

     = [tex]\sqrt{725}[/tex]

     = [tex]5\sqrt{29}[/tex]

     = 26.93 units

Therefore, we have to travel 26.93 units from platform B to C.

Answer:

22.4 meters

Step-by-step explanation:

Because the distance and stuff I don't really know sorry

Answer:

2a +ab-9

Step-by-step explanation:

First, write out what you have:

3a-2b-ab-(a-b+ab)+3ab+b-9

Then, distribute the "-" to the "a-b+ab" inside the parenthesis:

3a-2b-ab-a+b-ab+3ab+b-9

Finally, combine like terms and simplify:

3a-a-2b+b+b-ab+3ab-ab-9

2a-2b+2b+3ab-2ab-9

2a+0+ab-9

2a+ab-9 is you equation fully simplified

Answer:

A translation (9 units) to the left will result in a function that is neither even nor odd

Step-by-step explanation:

With horizontal translation to the left, we have;

h(x) = 12(x - 9)⁸ + 49

Which gives;

h(x) = 12(x - 9)⁸ + 49 = 12(x⁸ - 72x⁷ + 2268x⁶ - 40824x⁵ + 459270x⁴ -3306744x³ + 14880348x² - 38263752x + 43046721) + 49

For x = 1, we get;

h(x) = 201326641

When we replace x by -x, we get;

h(x) = 12(-x - 9)⁸ + 49 = 12(x⁸ + 72x⁷ + 2268x⁶ + 40824x⁵ + 459270x⁴ + 3306744x³ + 14880348x² + 38263752x + 43046721) + 49

For x = 1, we get;

h(x) = 1200000049

Therefore a translation 9 units to the left will result in a function that is neither even nor odd.

Answer:

y≤1

y−x>0

Step-by-step explanation:

I just took the quiz

A graph can be used to represent a system of inequality.

The system of inequality, the graph represents is:

[tex]y \ge 1[/tex] and [tex]y - x > 0[/tex]

The attached graph has two lines.

The thick horizontal line

Below this line, is a shaded region; and it passed through [tex]y = 1.[/tex]

This means that the horizontal line represents all values of y starting from 1.

So, the inequality is:

[tex]y \ge 1[/tex]

A dotted slanted line

First, calculate the slope of the line

[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]

The line passes through (0,0) and (1,1).

So, we have:

[tex]m =\frac{1-0}{1-0}[/tex]

[tex]m =1[/tex]

The equation is:

[tex]y = m(x - x_1) + y_1[/tex]

[tex]y = 1(x - 0) + 0[/tex]

[tex]y = x + 0[/tex]

[tex]y = x[/tex]

The left part of the dotted line is shaded. This represents >.

So, we have:

[tex]y> x[/tex]

Subtract x from both sides

[tex]y - x > 0[/tex]

Hence, the system of inequality, the graph represents is:

[tex]y \ge 1[/tex]

[tex]y - x > 0[/tex]

Read more about system of inequalities at:

https://brainly.com/question/19526736