Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of pi (no approximations)

Given:

QR is parallel to RS.

To find:

The value of x.

Solution:

In the given figure, we have,

[tex]PR=12[/tex]

[tex]RT=2x-2 [/tex]

[tex]QS=21[/tex]

[tex]ST=3x-1[/tex]

Using basic proportionality theorem (BPT), we get

[tex]\dfrac{PR}{RT}=\dfrac{QS}{ST}[/tex]

[tex]\dfrac{12}{2x-2}=\dfrac{21}{3x-1}[/tex]

On cross multiplication, we get

[tex]12(3x-1)=21(2x-2)[/tex]

[tex]36x-12=42x-42[/tex]

[tex]36x-42x=12-42[/tex]

[tex]-6x=-30[/tex]

Divide both sides by -6.

[tex]x=\dfrac{-30}{-6}[/tex]

[tex]x=5[/tex]

Therefore, the value of x is 5.

Answer:

calculator

Step-by-step explanation:

calculator

Answer:Set it up as two equations.  Start off by stating that x= the number of adult tickets, and y= the number of student tickets.

6x+4.5y=2175

x+y=430

State that y = 430-x, and substitute it into the second equation 6x +4.5(430-x)= 2175.

Solve for x.  Then plug in what you get for x into the x+y=430 equation and solve for y.  Your number of adult tickets should equal 160, and your number of child tickets should equal 270.

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

The sign on the 'x' changes, this implies a reflection.

g(x) = -f(x) = -(x+1) = -x -1

Now apply a vertical translation 'up 5' to f(x)

g(x) = -f(x) + 5 = (-x-1) +5 = -x +4

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

use formula

P(x,)=P'(-x,y)

A(5,8)=A'(-5,8)

Answer:

f. for the x values I think its -1 & 5

Blueberry pies sold each day So, Least: 1, Greatest:8, Median(02):4,

Lower quartile(q1):3, Upper quartile(03):5.

When we get data that can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each group approximately possessing 25% of the data.

The lower quartile, also called the first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.

Left to right is said in the assumption that data were arranged increasingly from left to right.

From the given data

The Least number is  1.

The greatest number is 8.

The Median(02) is  4.

Lower Quartile (Q1): 3

Upper Quartile (03): 5

Learn more about quartiles here:

brainly.com/question/9260741

#SPJ2

Answer:

[tex]840[/tex]

Step-by-step explanation:

This is a good example of permutations. For the first slot on his shelf, Dylan has 7 trophies to choose from. Then 6, 5, and so on. Since he is only fitting 4 trophies on his shelf, we only continue until we have the slots filled. Thus, we have [tex]7\cdot 6 \cdot 5\cdot 4=\boxed{840\:\text{ways}}[/tex] to do so.

*Note: We do not divide by [tex]4![/tex] because in this case, order matters. A different order of the same four books still produces different arrangements, so the order matters.

Answer: [tex](c)[/tex]

Step-by-step explanation:

Given

Fractions are[tex]\dfrac{x^2-5x+6}{x-5}[/tex] and [tex]\dfrac{x^2-1}{3(x-5)}[/tex]

LCD of the two fractions is the least common denominator

[tex]\text{LCD}\{x-5,3(x-5)\}=3(x-5)[/tex]

Thus, option (c) is correct.

Answer:

the answer is probably C

Answer:

the answer is B

Step-by-step explanation:

because the minimum score is 5

refer to the attachment

Answer:

16 ^3/2

Step-by-step explanation:

16 ^3/2 = 64, while all other choices are equal to 16.

Answer:

47.50 per calculator

Step-by-step explanation:

Take the total cost and divide by the number of calculators to get the cost of one calculator

190/4 =47.50

Answer:

[tex]4+c=2\frac{1}{4}+2\frac{1}{3},\\\\\frac{7}{12}\:\text{more cups of flour}[/tex]

Step-by-step explanation:

The total amount of flour, in cups, Matthew needs is equal to [tex]2\frac{1}{4}+2\frac{1}{3}=4\frac{7}{12}[/tex]. Because he only has 4 cups, we can write the following expression to determine how many additional cups of flour he needs:

[tex]4+c=2\frac{1}{4}+2\frac{1}{3},\\\\4+c=\frac{7}{12}, \\\\c=\boxed{\frac{7}{12}\:\text{more cups of flour}}[/tex]

Answer:

59°

Step-by-step explanation:

½×(175-57) = ½×118 = 59°

Answer:

mr hill: 9

mr chang: 12

Step-by-step explanation:

mr hill can have 3 teams of 9 and

mr chang can have 2 teams of 12

Answer:

3 Teams of 25

Step-by-step explanation:

27+ 24= 51

51/3 = 17

Therfore it has to be 3 teams of 17

The answer is A, 13

Step-by-step explanation:

The easy way to solve it was to plug in every answer to see which was equal to 32 since both sides were identical.

Answer:

what is the question?

Step-by-step explanation:

Answer:

i answered

Step-by-step explanation:

Answer:

y = 3x + 4

Step-by-step explanation:

y = mx + b

b = y-intercept so:

b = 4

Since 4 is the y-intercept that means (0, 4).

To find slope:

m=(y2-y1)/(x2-x1)

m=(4 - 10)/(0 - 2)

m= (-6)/(-2)

m= 3

Slope-intercept:

y - y1 = m(x - x1)

y - 10 = 3(x - 2)

y - 10 = 3x - 6

y = 3x + 4

Answer: 4

Step-by-step explanation:

Just add

Answer:

4

Step-by-step explanation:

just add or if you can't then use a calculator

Answer:

Apples

Step-by-step explanation:

For each probability, transform the normal random variable X with mean 19 and s.d. 4.04 to a standard normal random variable Z with mean 0 and s.d. 1, using the rule

Z = (X - 19) / 4.04

(a) Pr[15 ≤ X ≤ 20] = Pr[(15 - 19)/4.04 ≤ (X - 19)/4.04 ≤ (20 - 19)/4.04]

… ≈ Pr[-0.9901 ≤ Z ≤ 0.2475]

… ≈ Pr[Z ≤ 0.2475] - Pr[Z ≤ -0.9901]

(since Z is a continuous random variable)

… ≈ 0.4367

(b) Pr[X > 20] = Pr[(X - 19)/4.04 > (20 - 19)/4.04]

… ≈ Pr[Z > 0.2475]

… ≈ 1 - P[Z ≤ 0.2475]

(taking the complement probability)

… ≈ 0.4023

(c) Pr[X < 15] = 1 - Pr[15 ≤ X ≤ 20] - Pr[X > 20]

(also taking the complement)

… ≈ 0.1611

Answer:

Step-by-step explanation:

Properties

Center:(7,0)

The center of a circle is a point from which all points on a circle are the same distance.

Radius:4

The radius of a circle is the length of a line segment from its center to its perimeter.

The radius is typically denoted as "r" or "R".

Diameter:8

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle.

Circumference or (or Permieter) = 2*π*R = 2*3.14*4 = 25.1327412287183

The circumference of a circle is the distance around it.

Area:50.2654824574367

Area of a Circle is the amount of space occupied by the circle.The area of a circle is p times the radius squared, which is written: A = π*R2.

Equation

Standard Form

The standard form for the equation oif a circle is

(x-a)2+(y-b)2=r2

And in our particular case:

(x-7)2+(y-0)2=42

(x-7)2+(y-0)2=16

General Form

The general form for the equation of a circle is

x2 + y2 + Ax + By + c = 0

We can get the general form by expanding the equation of the standard form

(x-a)2+(y-b)2=r2

(x-7)2+(y-0)2=42

(x-7)2+(y-0)2=16

x2-14x+49+y20y+0=16

x2+y2-14x+0y+33=0 Referenced definitions

Chord A chord of a circle a line segment that joins two points on the circumference of a circle.

π The ratio of a circle's circumference to its diameter. Equal to 3.1415926535... (the digits go on indefinitely without repeating)

Circle a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre).

The required equation of a circle will be (x - 7)² + y² = 16 with a center at (7, 0) and a radius of 4.

The equation of a circle with center (h,k) and radius r is :

r² = (x−h)² + (y−k)²

The center of the circle is given as (h,k) = (7, 0) which is given in the question

And radius r = 4

Substituting the given values into this equation gives us an equation of a circle with a center at (7, 0) and a radius 4:

(x - 7)² + (y - 0)²  = 4²

Simplifying this equation gives us:

(x - 7)² + y² = 16

This is the equation of a circle with a center at (7, 0) and a radius of 4.

Learn more about the equation of a circle here:

brainly.com/question/1554214

#SPJ2

Answer:

Charlotte has 23 of her book left to read. She can read 29 of it each day.

Step-by-step explanation:

Answer:

66.6666666667%

Step-by-step explanation:

12/18 = x/100

cross product

18x = 12(100)

18x = 1200

18× = 1200

__ _____

18 18

x=66.6666666667%

Answer:

True

Step-by-step explanation:

The largest animal phylum is also included within invertebrates

Answer:

Step-by-step explanation:

✓(x-5) - 5 = 3

✓(x-5) - 8 = 0

(✓(x-5))² - 8² = 0

x-5 - 64 = 0

x - 69 = 0

x = 69

Answer:

1/6

Step-by-step explanation: