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Assuming construction of the dotted lines, complete the following proof.

Given: lines from P tangent to circle R at points A and B



Prove: PA = PB

Answer:

Horizontal distance = 0 m and 6 m

Step-by-step explanation:

Height of a rider in a roller coaster has been defined by the equation,

y = [tex]\frac{1}{3}x^{2}-2x+8[/tex]

Here x = rider's horizontal distance from the start of the ride

i). [tex]y=\frac{1}{3}x^{2}-2x+8[/tex]

      [tex]=\frac{1}{3}(x^{2}-6x+24)[/tex]

      [tex]=\frac{1}{3}[x^{2}-2(3x)+9-9+24][/tex]

      [tex]=\frac{1}{3}[(x^{2}-2(3x)+9)+15][/tex]

      [tex]=\frac{1}{3}[(x-3)^2+15][/tex]

      [tex]=\frac{1}{3}(x-3)^2+5[/tex]

ii). Since, the parabolic graph for the given equation opens upwards,

    Vertex of the parabola will be the lowest point of the rider on the roller coaster.

    From the equation,

    Vertex → (3, 5)

    Therefore, minimum height of the rider will be the y-coordinate of the vertex.

    Minimum height of the rider = 5 m

iii). If h = 8 m,

    [tex]8=\frac{1}{3}(x-3)^2+5[/tex]

    [tex]3=\frac{1}{3}(x-3)^2[/tex]

    (x - 3)² = 9

    x = 3 ± 3

    x = 0, 6 m

    Therefore, at 8 m height of the roller coaster, horizontal distance of the rider will be x = 0 and 6 m

Answer:

no. of consecutive integers--- X, X+1, X+2.

there sum is 60

X+X+1+X+2=60

3X+3=60

X+1=20

X=19

integers are=19, 20, 21

Answer:

8.22899353m

= 8m(round)

Step-by-step explanation:

14 * sin(36 degree) = 8.22899353

Answer:

51.89085

Step-by-step explanation:

area = 49pi

150/360 * 49pi = 64.14085

triangle area = 7 * sin(75 degrees) * 7 * cos(75 degrees) = 12.25

==> white region = 64.14085 - 12.25 = 51.89085

Answer:

Alice owed $5.32

Step-by-step explanation:

Answer:$5.34

Step-by-step explanation:

Answer:

Step-by-step explanation:

These represent the points on the graph with w as the x-axis and l as the y -axis. You only need two pairs to make a line, but it is always best to use a 3rd point as a check.

This is how you would graph y=5x+1

Answer:

Step-by-step explanation:

area of base = π4² = 16π in²

lateral area = 2πrh = 2π·4·6 = 48π in²

surface area = 2×16π + 48π = 80π in² ≅ 251.3 in²

Answer: 100.54 in^2

Step-by-step explanation:

(the area of a circle*2) + (the circumference*the height) = the surface area of the circle

Area of a circle: Pi*r^2

Circumference: 2*Pi*r

Answer:

your answer is D

Step-by-step explanation:

hope it helps

have a great day (:

Answer:

hannah is 47 and Anthony is 45

Step-by-step explanation:

Sum= 92= a+(a+1)

sum= 45+(46+1)

sum= 45+47

sum= 92

Answer:

C≈9.42m

Step-by-step explanation:

C=πd=π·3≈9.42478m

Step-by-step explanation:

9x-7i<3(3x-7u)=

9x-7i<9x-21u=

-7i<-21u=

i<3u

Answer:

a³+b³

Step-by-step explanation:

this is formula. You can also refer to the attachment

Answer:

Step-by-step explanation:

(a + b) (a² - ab + b) = a*(a² - ab + b) + b(a² - ab + b)

                               = a*a² - a*ab +a*b + b*a² - b*ab + b*b

                               = a³ - a²b + ab   + a²b -ab² + b²

                             = a³ - a²b + a²b + ab - a²b + b²

                            = a³  + ab - a²b + b²

Answer: 5r-5s

Step-by-step explanation:

Hope this helps :)

Answer:

10

Step-by-step explanation:

7-(-3)=7+3=10

Answer:

A is 60

AC is 150

BC is 120..........

Answer:

The length of the hypotenuse side is (9 + 2·√7) cm

Step-by-step explanation:

The given parameters of the triangle are;

The type f triangle = Right triangle

The length of the sides 2 cm and 7 cm shorter than the hypotenuse

Let 'h' represent the length of the hypotenuse side of the triangle, in centimeters we have;

The length of one side of the right triangle = (h - 2) cm

The length of the other side of the right triangle = (h - 7) cm

By Pythagoras's theorem, we have;

h² = (h - 2)² + (h - 7)²

Using search function on the internet, we have;

h² = (h - 2)² + (h - 7)² = 2·h² - 18·h + 53

∴ h² = 2·h² - 18·h + 53

∴ 2·h² - 18·h + 53 = h²

h² - 18·h + 53 = 0

53 is a prime number, therefore, by the quadratic formula, we have;

h = (18 ± √((-18)² - 4×1×53))/(2 × 1)

h = 9 + 2·√7 cm ≈ 14.29 cm or h = 9 - 2·√7 ≈ 3.71

However, given that one of the side is 7 cm shorter than the hypotenuse, for all the sides to remain positive, we have h = 9 + 2·√7 cm ≈ 14.29 cm , because for h ≈ 3.71 cm, we have;

The length of the other side = (h - 7) cm ≈ (3.71 - 7) cm ≈ -3.29 cm which is not possible for a real triangle

Therefore, the length of the hypotenuse side, h = 9 + 2·√7 cm ≈ 14.29 cm.

Answer:

[tex]16[/tex]

Step-by-step explanation:

Substituting [tex]a=2[/tex] and [tex]b=3[/tex] into [tex](a^{b}+b^{a})-1[/tex] gives us:

[tex](a^{b}+b^{a})-1[/tex]

[tex]=(2^{3} +3^{2})-1[/tex] (Substitute given values into expression)

[tex]=(8+9)-1[/tex] (Evaluate exponents)

[tex]=17-1[/tex] (Evaluate expression in parentheses)

[tex]=16[/tex] (Simplify)

Hope this helps!

Answer:

16

Step-by-step explanation:

Given

([tex]a^{b}[/tex] + [tex]b^{a}[/tex] ) - 1 ← substitute a = 2, b = 3

= (2³ + 3²) - 1

= (8 + 9) - 1

= 17 - 1

= 16

Answer:

it is 80°

cause it is coming from the same cord AB

O and C will be same

Answer:

x = 40

Step-by-step explanation:

x = 80÷2 = 40

Central angle theorem

the americans scored twice in the last period although the soviet team dominated second period, after that the americans finally took the lead

(this is english not math change your question when you have to do this again)

Answer:

Option A.

Length 16 feet

Width 12 feet

Step-by-step explanation:

2 cm=4 feet to scale

so you have this fraction:

2/4

or:

1/2

so for every cm, it's 2 feet.

6x2=12

8x2=16

so the width is 12 ft, the length is 16 ft. Option A

Answer: I believe it's A

Hope this helped love<3

Answer:

B)7 units

Step-by-step explanation:

Answer:

The proofing is given below:

Step-by-step explanation:

[tex]Sec 5\theta = cosec 7\theta\\\\cosec (90 - 5\theta) = cosec 7\theta\\\\Now\ on\ comparision \\\\90 - 5\theta = 7\theta\\\\90 = 7\theta + 5\theta\\\\90 = 12\theta\\\\\frac{90}{12} = \theta\\\\0.75 = \theta[/tex]

Hence, it is proved

Answer:

9/2 or 4 1/2 or 4.5

Step-by-step explanation:

4+1/2=8/2+1/2=9/2

Answer:

es 4 1/2 creo

Step-by-step explanation:brainliest plis

Answer:

9

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

split it in half u get a subtract sing makes that (8-4=4)

Answer:

x+5

Step-by-step explanation:

15+x-10=x+5

Answer:

I think the answer should be 20