Consider circle O, in which arc XY measures 16π cm. The length of a radius of the circle is 32 cm.
What is the circumference of the circle?
π units
What is the ratio of the arc length to the circumference?


What is the measure of central angle XOY?

Answer:

L = 8

Step-by-step explanation:

The volume of a rectangular prism is found by V = L*h*w. Substitute V = 120, w = 5 and h =3 then solve for the length.

120 = L*3*5

120 = 15L

8 = L

Answer:

[tex]\large\boxed{y=(x+5)^2-64}[/tex]

Step-by-step explanation:

[tex]\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\h=\dfrac{-b}{2a},\ k=f(h)\\\\\text{We have the equation:}\ y=x^2+10x-39\to x=1,\ b=10,\ c=-39.\\\\\text{Substitute:}\\\\h=\dfrac{-10}{2(1)}=\dfrac{-10}{2}=-5\\\\k=f(-5)=(-5)^2+10(-5)-39=25-50-39=-64\\\\\text{Finally:}\\\\y=1(x-(-5))^2-64=(x+5)^2-64[/tex]

Answer:

1.047

Step-by-step explanation:

60° × π/180 = 1.047rad

or

From the standard conversion factor

360∘ = 2 π r a d

we may use ratio and proportion to obtain that

60 ∘ = π 3 r a d

Answer:

pi/3

Step-by-step explanation:

To convert from degrees to radians, we multiply by pi/180

60 degress * pi/180 =  pi/3

60 degrees is pi/3 radians

[tex]\bf \cfrac{Zak}{Fred}\qquad \cfrac{1.86}{1.6}\implies \cfrac{~~\frac{186}{100}~~}{\frac{16}{10}}\implies \cfrac{186}{100}\cdot \cfrac{10}{16}\implies \cfrac{186}{16}\cdot \cfrac{10}{100}\implies \cfrac{93}{8}\cdot \cfrac{1}{10} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{93}{80}~\hfill[/tex]

To express Zak's height as a fraction of Fred's, divide Zak's height by Fred's height. This will yield a fraction that represents how Zak's height compares to Fred's. The heights need to be provided to calculate the actual fraction.

To write the height of Zak as a fraction of the height of Fred, we need to know both Zak's height and Fred's height. For instance, if Zak's height is 4 feet and Fred's height is 6 feet, the fraction representing Zak's height in relation to Fred's height would be ⅓ (Zak's height) over ⅔ (Fred's height). This is simplified by dividing both the numerator and the denominator by the GCD (Greatest Common Divisor) of Zak's and Fred's height if they are not already in simplest form.

If Zak is shorter than Fred, the fraction will be less than 1, indicating that Zak is shorter than Fred. Conversely, if Zak is taller than Fred, the fraction will be greater than 1, indicating Zak's greater height. In your specific question, it seems the heights are not provided, so please provide them in order to calculate the exact fraction.

Answer:

she thought the chair's orginal price was fourty instead it is 72

Step-by-step explanation:

the area is 164. You multiply 6x4=24 and then u do 10x8=80 and then u add and get 164

Answer:

12 patties

Step-by-step explanation:

4 ÷ 1/3 = 12

Answer: 8

[tex]{10}^{2} = 100 \\ {6}^{2} = 36 \\ 100 - 36 = 64 \\ \sqrt{64} = 8[/tex]

Answer:

8

Step-by-step explanation:

6² + x² = 10²

36 + x² = 100

x² = 64

x² = √64

x = 8

Julia ate 1/8

Ellen and Jenny ate 3/8

1/8 + 3/8 = 4/8

No they didn't eat the whole pizza, they only ate half of the pizza.

Julie, Ellen, and Jenny together ate [tex]\frac{1}{8}[/tex]+ [tex]\frac{3}{8}[/tex] = [tex]\frac{4}{8}[/tex] or [tex]\frac{1}{2}[/tex]of the pizza, which means they ate only half of it, not the entire pizza.

The question involves the mathematical concept of fractions and their addition. Julie ate [tex]\frac{1}{8}[/tex] of the pizza, while Ellen and Jenny together ate [tex]\frac{3}{8}[/tex]of the pizza. To determine if they ate the whole pizza, we need to add these fractions.

[tex]\frac{1}{8}[/tex] (Julie's portion) + [tex]\frac{3}{8}[/tex] (Ellen and Jenny's portion) =  [tex]\frac{4}{8}[/tex]or [tex]\frac{1}{2}[/tex] after simplifying.

Since [tex]\frac{1}{2}[/tex] is less than a whole, Julie, Ellen, and Jenny did not eat the entire pizza. They ate only half of it.

Answer: The identity is verified. See the explanation.

Step-by-step explanation:

You must keep on mind the following identities:

[tex]csc\theta=\frac{cos\theta}{sin\theta}\\\\csc\theta=\frac{1}{sin\theta}\\\\sin^2\theta+cos^2\theta=1[/tex]

Therefore, by substitution, you can rewrite the identity as shown below:

[tex]1+cot^2\theta=csc^2\theta\\\\1+\frac{cos^2\theta}{sin^2\theta}=csc^2\theta[/tex]

Simpliying, you obtain:

[tex]\frac{sin^2\theta+cos^2\theta}{sin^2\theta}=csc^2\theta\\\\\frac{1}{sin^2\theta}=csc^2\theta\\\\csc^2\theta=csc^2\theta[/tex]

The identity is verified.

3/4(2(2+4k)+2(3+3/2k))

Use the distributive property inside the parenthesis first:

3/4(4+8k + 6 + 3k)

Simplify:

3/4(11k + 10)

Distributive property again:

3/4(11k) + 3/4(10)

33/4k + 15/2

Rearrange to get A. 15/2 + 33/4k

Answer:

[tex]x=53[/tex]

Step-by-step explanation:

step 1

Find the measure of arc DF

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m<OEF=\frac{1}{2}(arc\ DF)[/tex]

we have

[tex]m<OEF=32\°[/tex]

substitute

[tex]32\°=\frac{1}{2}(arc\ DF)[/tex]

[tex]arc\ DF=64\°[/tex]

step 2

Find the measure of x

we know that

[tex]arc\ DF+arc\ EF=180\°[/tex] ---> is half the circle

we have

[tex]arc\ DF=64\°[/tex]

[tex]arc\ EF=(2x+10)\°[/tex]

substitute

[tex]64\°+(2x+10)\°=180\°[/tex]

[tex]2x\°=180\°-74\°[/tex]

[tex]2x\°=106\°[/tex]

[tex]x=53[/tex]

The value of x for the angles of the inscribed circle is gotten as; x = 53°

Let us first find the angle subtended by the arc DF

From inscribed angle theorem, we know that the measure of an inscribed angle is half the measure of the intercepted arc. Thus;

m∠EOF = ¹/₂(arc DF)

Thus;

¹/₂(arc DF) = 32°

arc DF = 64°

From half circle theorem, we can say that;

arc DF + arc EF = 180°

Thus;

64 + 2x + 10 = 180

2x = 180 - 74

2x = 106

x = 53°

Read more about inscribed angles at; https://brainly.com/question/13110384

Answer:

* The degree of the function is 4 and the leading coefficient is positive

 f(x) = (x + 6)(2x - 3)(x - 1)²

* The degree of the function is 5 and the leading coefficient is negative

 f(x) = (x - 2)²(-2x - 1)²(-x + 1)

* The degree of the function is 6 and the leading coefficient is negative

 f(x) = (-x + 1)³(x + 2)²(x - 3)

* The degree of the function is 5 and the leading coefficient is positive

 f(x) = (-2x + 1)²(x - 3)²(x + 1)

Step-by-step explanation:

∵ f(x) = (x + 6)(2x - 3)(x - 1)²

∵  (x)(2x)(x²) = 2x^4

∴ The degree of the function is 4

∴ The leading coefficient is positive ⇒ (2)

∵ f(x) = (x - 2)²(-2x - 1)²(-x + 1)

∵ (x)²(-2x)²(-x) = (x²)(4x²)(-x) = -4x^5 ⇒ (neglect -ve with even power)

∴ The degree of the function is 5

∴ The leading coefficient is negative ⇒ (-4)

∵ f(x) = (-x + 1)³(x + 2)²(x - 3)

∵ (-x)³(x)²(x) = (-x³)(x²)(x) = -x^6

∴ The degree of the function is 6

∴ The leading coefficient is negative ⇒ (-1)

∵ f(x) = (-2x + 1)²(x - 3)²(x + 1)

∵ (-2x)²(x)²(x) = (4x²)(x²)(x) = 4x^5

∴ The degree of the function is 5

∴ The leading coefficient is positive ⇒ (4)

Answer:

The x-intercepts will be, x= 7 or x =9

Step-by-step explanation:

f(x)= x^2 -16x+63

At the x-intercept, f(x) is zero.

Therefore;

x² - 16x + 63 = 0

solving it quadratically;

product = 63

Sum       = -16

x² - 9x - 7x + 63 = 0

x(x-9) - 7( x-9) = 0

(x-7) (x-9) = 0

x = 7 or x = 9

Therefore;

The x-intercepts will be, x= 7 or x =9

Answer:

(7, 0) and (9, 0)

Step-by-step explanation:

The x-intercepts refers to the points where the graph of the function crosses the x-axis, or simply the zeroes of the function. In this case, we can determine these points analytically or graphically. We simply graph the function;

y = x^2 -16x +63 then determine where the function crosses the x-axis; see the attachment below;

The x-intercepts of this function are;

(7, 0) and (9, 0)

Answer:

tn = 7 + (n - 1)*(-2) or

tn = 9 - 2n

Step-by-step explanation:

You are (beginning with 7) subtracting 2 from the term to the left.

a = 7

d = -2

tn = a1 + (n - 1)*d

tn = 7 + (n - 1)*(-2)

Try this out on n = 4

t4 = 7 + (4 - 1)*-2

t4 = 7 +  (3) (-2)

t4 = 7 - 6

t4 = 1 just as it says.

More generally

tn = 7 + (n - 1)*-2

tn = 7 + (-2n) + 2

tn = 9 - 2n

Answer:

AM = 6

Step-by-step explanation:

Using the property of a parallelogram

• The diagonals bisect each other

MO is a diagonal, hence

AM = AO = 6

Answer:

A. -6

Step-by-step explanation:

(2,-2) reflected over X would be (-2,2). Then dilate by 3 which you multiply by 3. So -2 x 3 = -6.  

Answer:

The slope is 5/4

Step-by-step explanation:

This equation is written in slope intercept form

y = mx+b, where m is the slope and b is the y intercept

y = 5/4x -7/4

5/4 is the slope and -7/4 is the y intercept

total 5 friends ate 5 half pieces of pizza

so we will add all 5 pieces togther.

total pizza = 1/2 +1/2+1/2+1/2+1/2 = 5/2

so option C is answer

Answer:

C

Step-by-step explanation:

Now there are 6+4+8+1+1=20 dads in the Dads Club.

Fewer than 3 children have

So, 6+4=10 dads have fewer than 3 children.

The probability that the dad of Dads Club has fewer than 3 children is

[tex]Pr=\dfrac{10}{20}=0.5 \text{ or } 50\%.[/tex]

The probability that the next dad to join Dads Club has fewer than 3 children is reasonable to be 50%.

Option: C is the correct answer.

           C.  50%

Let P denotes the probability of an event.

and A denote the event that the next dad has fewer than 3 children.

From the table the total number of dads are: 6+4+8+1+1=20

The number of dad who have less than 3 children are: 6+4=10

Hence, we have

[tex]P(A)=\dfrac{\text{Number\ of\ dad\ with\ less\ than\ 3\ children}}{\text{Total\ number\ of dad}}[/tex]

Hence, we have:

[tex]P(A)=\dfrac{10}{20}=\dfrac{1}{2}[/tex]

which in percentage is given by:

     [tex]P(A)=50\%\\\\(Since,\\\\\dfrac{1}{2}\times 100=50\%)[/tex]

Answer:

See explanation below, and see attached photo for graphs

Step-by-step explanation:

To graph 3x + y = 6, find the x and y intercepts.  

We get the x intercept when y = 0, so plug in 0 for y and solve...

3x + 0 = 6

   3x = 6

    x = 2, so the x intercept is at (2, 0)

We get the y intercept when x = 0, so plug in 0 for x and solve...

3(0) + y = 6

   y = 6, so the y intercept is at (0, 6)

Plot those two points and draw a line through them

To graph -3x - 4y = 12, find the x and y intercepts.  

We get the x intercept when y = 0, so plug in 0 for y and solve...

-3x - 4(0) = 12

   -3x = 12

    x = -4, so the x intercept is at (-4, 0)

We get the y intercept when x = 0, so plug in 0 for x and solve...

-3(0) - 4y = 12

       -4y = 12

           y = -3, so the y intercept is at (0, -3)

Plot those two points and draw a line through them

The system of equations 3x + y = 6 and -3x - 4y = 12 is graphed by converting each to slope-intercept form, plotting points, and drawing lines. Intersection is found by solving the equations simultaneously, resulting in the intersecting point (4, -6).

To graph the system of equations consisting of 3x + y = 6 and -3x - 4y = 12, we first need to solve each equation for y to get them into slope-intercept form (y = mx + b). Here are the steps:

Next, we plot the lines on a coordinate plane by finding at least two points for each line based on the equations we've just derived:

After plotting these points for each line, draw straight lines through the points to complete the graph. The coordinates of the intersection of the two lines can be found by setting the two equations for y equal to each other and solving for x:

Therefore, the intersection point is at (4, -6).

Answer:

5400 cm^3

Step-by-step explanation:

Volume = Base Area * H

Base area is the area of a square with one side = 30 cm

H = 6cm

Base Area = s^2

Base Area = 30^2 = 900

Volume  =  900 * 6

Volume = 5400 cm^3

Answer:

1800 cm³

Step-by-step explanation:

Recall that the formula for the area of a square is A = s², where s is the side length.

Here, that area is A = (30 cm)²2.

The formula for the volume of a square pyramid is:

V = (1/3)(base area)(height)

   = (1/3)(30 cm)²2*(6 cm)

   = (1/3)(900 cm²)(6 cm) = 1800 cm³

The volume of this pyramid is 1800 cm³.

Answer:

x = [tex]\frac{20}{3}[/tex]

Step-by-step explanation:

ΔABC and ΔEDC are similar triangles ( AA ), hence the ratios of corresponding sides are equal, that is

[tex]\frac{AB}{ED}[/tex] = [tex]\frac{BC}{DC}[/tex], substitute values

[tex]\frac{x}{4}[/tex] = [tex]\frac{5}{3}[/tex] ( cross- multiply )

3x = 20 ( divide both sides by 3 )

x = [tex]\frac{20}{3}[/tex]

Answer: one hundred and twenty five million

Answer:

125,000,000

Step-by-step explanation:

3 billion has 9 0's so you take that and divide it by 24 to get:

3,000,000,000/24=125,000,000 as your answer

Answer:

9.22×10^9

Step-by-step explanation:

The number must be written with

- a number between 1-10

- multiplied by a power of 10

The power of 10 tells you how many times you moved the decimal.

Yes it is called a right angled triangle

To model Orlando's population growth, an equation in slope-intercept form is y = 2000x + 175000. The year 2010 is 15 years after 1995, so substituting 15 in for x gives a population of approximately 205,000 residents for Orlando in 2010.

To answer the student's question, first we need to write an equation in slope-intercept form to find Orlando's population for any year. The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the starting value when x=0). In this case, the variable y represents Orlando's population, m represents the annual growth rate (2000 people per year), and x represents the number of years since 1995.

Using these variables, our equation becomes y = 2000x + 175000, where x is the number of years since 1995. To find Orlando's population in 2010, we must substitute x with 15, since 2010 is 15 years after 1995.

The calculation would be: y = 2000(15) + 175000, which simplifies to y = 205000.

Therefore, Orlando's population in 2010 was approximately 205,000 residents.

Answer:

Graph 3

Step-by-step explanation:

Answer:

i forgot to

Step-by-step explanation: