On a certain hot​ summer's day, 269 people used the public swimming pool. The daily prices are 1.50 for children and 2.00 for adults. The receipts for admission totaled 504.50.How many children and how many adults swam at the public pool that​ day?

Given:

Consider the below figure attached with this ques.

To find:

The length of the line segment XZ.

Solution:

According to the tangent-secant theorem, the square of tangent is equal to the product of secant and external segment of secant.

Using tangent-secant theorem, we get

[tex]WZ^2=ZX\times ZY[/tex]

[tex](k+4)^2=(k+12)k[/tex]

[tex]k^2+8k+16=k^2+12k[/tex]

[tex]8k+16=12k[/tex]

Subtract both sides by 8k.

[tex]16=12k-8k[/tex]

[tex]16=4k[/tex]

Divide both sides by 4.

[tex]4=k[/tex]

Now,

[tex]XZ=12+k[/tex]

[tex]XZ=12+4[/tex]

[tex]XZ=16[/tex]

Therefore, the measure of XZ is 16 units.

Answer

LINE OF REFLECTION

Step-by-step explanation:

In geometry, reflection basically just means flipping things over a line.

Answer:

1/12

Steps:

1 - 2/3 = 1/3

1/3 / 4 = 1/3 × 1/4 = 1/12

The simplified expression is: -243v^5

hope this helps ;')

Answer:

27.84 m² , 42.48 m²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Shape A

has b = 9.6 and h = 5.8, then

A = 0.5 × 9.6 × 5.8 = 27.84 m²

Shape B

has b = 11.8 and h = 7.2 , then

A = 0.5 × 11.8 × 7.2 = 42.48 m²

Answer:

Shape A = 55.68

Shape B = 79.2

Step-by-step explanation:

Shape A work : [tex]9.6[/tex] x [tex]5.8[/tex] = 55.68

Shape b work :  11 x 7.2 = 79.2

Hope this helps!

Answer:

(0,12)

Step-by-step explanation:

Answer:

(0,12)

Step-by-step explanation:

Use y=mx+b to answer the equation

Answer:

b

Step-by-step explanation:

the y axis is the axis going up and down, so the reflection would be on the other side of the axis.

Answer:

3.5

Step-by-step explanation:

3.5 + 3.5 = 7

Answer:

2200 baseball cards

Step-by-step explanation:

Answer:

telephone pole height = 480ft

Step-by-step explanation:

Assume that the shadow that an object casts is proportional to the height of the object. Then one can form the ratio:

[tex](shadow : height)[/tex]

Making the assumption that this ratio is proportional for all objects in this given scenario, then one can say that the ratio of the height of the man and his shadow is equal to the ratio of the height of the telephone pole and its shadow:

(man's height) : (man's shadow) = (pole's height) : ( pole's shadow)

Substitute:

6ft : 4ft 6in = (telephone pole hiehgt) : 30ft

Convert to inches (since it is all in the same unit now, one's doesn't need to write the unit anymore):

72 : 54 = (telephone pole height) : 360

Simplify:

4 : 3 = (telephone pole height) : 360

Now solve, use cross products:

3(telephone pole height) = 1440

Inverse operations,

3(telephone pole height) = 1440

/3                                          /3

telephone pole height = 480

Answer:

12

Step-by-step explanation:

12 - 4 = 8

The square of 8 is 64

Answer:

6

Step-by-step explanation:

(n + 4)^2 = n^2 + 64

n^2 + 8n + 16 = n^2 + 64

8n = 48

n = 6

Answer:

3rd one

Step-by-step explanation:

Answer:

Slope of the line 'm' = 5

Step-by-step explanation:

Step(i):-

Given that the straight line

              5 x - y = 20

          ⇒ 5x - 20 = y

               y = 5 x - 20

Step(ii):-

The equation of the straight line having to slope 'm'

               y = m x + c

given that the straight line

              y = 5x +20

comparing   y = m x + c

Slope of the line 'm' = 5

Answer:

22 hens and 78 sheep

Step-by-step explanation:

Let the number of hens = x

Number of sheep = y

Total heads = 100

x +  y = 100      --------------------(I)

 x = 100 - y

Number of legs of 'x' hen = 2*x = 2x

Number of legs of 'y' sheep = 4*y = 4y

total legs = 356

2x + 4y =  356 -----------------------(II)

Substitute x = 100 -y in equation (II)

2(100 - y) + 4y = 356

2*100 - 2*y + 4y = 356

200 - 2y + 4y    = 356 {Combine like terms}

        200  + 2y = 356          {Subtract 200 from both sides}

                   2y = 356 - 200

                  2y = 156       {Divide both sides by 2}

                    y = 156/2

                  y = 78

Plugin  y = 78 in equation (I)

x + 78 = 100

       x = 100 - 78

       x = 22

22 hens and 78 sheep

Answer:

Step-by-step explanation:

The radius of the circle is ( r = 4) so

[tex]p = 2\pi \times r \\ p = 2(3.14)(4) \\ p = 25.12[/tex]

Answer: SHE MADE ANOTHER QUESTION!

Step-by-step explanation:

Step-by-step explanation:

perimeter - 16cm

length - 5cm

find breadth,

perimeter of rectangle = l × b

16cm = 5 × b

b = 16/5

b = 3.2 cm

Step-by-step explanation:

Given

perimeter (P) = 16 cm

Length(L) = 5 cm

breadth (b) = ?

We know

P = 2 (L + b)

16 = 2 ( 5 + b)

16 = 10 + 2b

2b = 16 - 10

2b = 6

b = 6 / 2

b = 3 cm

Hope it will help :)❤

Answer:

I only know the area sorry it is 7.065 ft2

Answer:

Perimeter: 7.712

Area: 3.534

Step-by-step explanation:

A= [tex]\pi*r^{2}/2\\[/tex]

L=[tex]\pi *r/2\\[/tex]

An equation for the pictured graph and the equation for the pictured graph in factored form is: y = rs - r - s + 1.

Let's assume the equation for the graph in factored form is: y = a(x - r)(x - s), where 'a' is a constant and 'r' and 's' are the roots of the equation (x-intercepts of the graph). Since we are given that the graph passes through the points (0, -2) and (1, 0), we can use this information to find the values of 'r' and 's.'

Using the point (0, -2):

When x = 0, y = -2.

We can substitute these values into the equation:

-2 = a(0 - r)(0 - s)

Simplifying, we get: -2 = a(-r)(-s) or -2 = ars.

Using the point (1, 0):

When x = 1, y = 0.

Substituting these values into the equation:

0 = a(1 - r)(1 - s)

Simplifying, we get: 0 = a(1 - r)(1 - s).

Now, we have two equations:

-2 = ars (Equation 1)

0 = a(1 - r)(1 - s) (Equation 2)

From Equation 1, we can solve for 'a' in terms of r and s:

a = -2 / rs.

Now, substitute this value of 'a' into Equation 2:

0 = (-2 / rs)(1 - r)(1 - s).

To make further progress, we can divide both sides by -2:

0 = (1 / rs)(1 - r)(1 - s).

Next, to eliminate the fractions, multiply both sides by rs:

0 = (1 - r)(1 - s).

Finally, expand the right side of the equation:

0 = 1 - s - r + rs.

The equation for the pictured graph in factored form is:

y = rs - r - s + 1.

To know more about graph here

https://brainly.com/question/17267403

#SPJ2

Answer:

31.7 degrees (A)

Step-by-step explanation:

90 degrees (the whole angle) - 58.3 degrees = 31.7 degrees

the angles are complementary

they add up to 90 degrees

brainliest plz

Answer:

31.7

Step-by-step explanation:

pls mark brainliest

58.3 + 31.7 is 90

Answer:

No Solution.

Step-by-step explanation:

x=x+10

x-x=10

0=10

Answer:

456 in³

Step-by-step explanation:

To find the volume of the box, use the volume formula, V = lwh

Plug in the length, width, and height:

V = lwh

V = (9.5)(8)(6)

V = 456

So, the volume of the box is 456 in³

Answer:

Lily earns $225

y represents the amount that Lily earns

x represents the painting's price

Step-by-step explanation:

Answer:

AAS

Step-by-step explanation:

Angle K is congruent to Angle N (given), Angle H is congruent to itself (reflexive property), and side JH is congruent to side MH (given).

Answer:

$50

Step-by-step explanation:

Answer:50

Step-by-step explanation: