bz is tangent to circle o. ac is a diameter. mbc=90. mcd=30. mde=20.

state the theorem(s) that you used to find the measures of angles 1-10.

Answers

Answer 1

Answer:

1. Arc angle

2. Angle at circumference

3. Base angle of an isosceles triangle

4. Sum interior of angles in a triangle

5. Sum interior of angles in a triangle

6. The sum of angles on a straight line

7. Sum interior of angles in a triangle

8. Sum interior of angles in a triangle

9. Angle from a tangent to the radius of a circle

10. Alternate angles of line crossing two parallel lines

Step-by-step explanation:

Here, we note that, the angles where derived as follows;

1. mBC = 90°, therefore, angle subtended by the arc BC at the center of the circle = 1 = 90°

2. 90° The angle at the center which is the straight line diameter with angle 180° = 2 × angle at the circumference

∴ The angle at the circumference, angle 2 = 180°/2 = 90°

3.  Angle subtended by the sum of arcs CD + DE at the center = 50°, therefore, ∡EOC = 50° and ∡EOA = 180° - 50° = 130° (the sum of angles on a straight line), since ΔAOE is an isosceles triangle, therefore, ∡OAE = ∡OEA = (180° - 130°)/2 = 25°

4. ∡A + ∡E + ∡C = 180° (Sum interior of angles in a triangle)

∴ 25° + 90° + ∡C = 180°

Hence ∡C = 180° - (90° + 25°) = 65°

5. From arc CD = 30°, ∡COD = 30°, ∴ ∡OBD = 30° = base angle of isosceles triangle with sides equal to the radius

Hence ∡8 = 30° from ∡8 + ∡1 + ∡OBD = 180° which gives

∡8 + 90° + 30° = 180°, hence;

∡8 = 180° - (90° + 30°) = 60°

∡8 = opposite ∡8 = 60°

Opposite ∡8 + ∡C + ∡5 = 180° (Sum interior of angles in a triangle)

Therefore ∡5  = 180° - (opposite ∡8 + ∡C) = 180° - (60° + 65°) = 55°

6. Angles 6 plus angle 5 = 180° (The sum of angles on a straight line)

Therefore, ∡6 = 180° - ∡5 = 180° - 55° = 125°

7. ∡7 + opposite ∡5 + ∡E = 180° (Sum interior of angles in a triangle)

∡E + ∡2 = 180° (The sum of angles on a straight line)

∴ ∡E = 180° - ∡2 = 180° - 90° = 90°

Hence, ∡7 + opposite ∡5 + ∡E = 180° = ∡7 + 55° + 90° = 180°

∴ ∡7 = 35°

8. ∡8 = 60° as found above

9. ∡9 = 90° (Angle from a tangent to the radius of a circle)

10. ∡10 = ∡8 = 60° (Alternate angles).


Related Questions

there are 12 inches in 1 foot
write an equation to find the number of inches in any number of feet

Answers

Answer:

divide the number of inches by 12

Step-by-step explanation:

1/12=x/12 then you would cross multiply it

Apollo does 240 push-ups in 5 minutes. How many push-ups can Apollo do in 1 minute

Answers

Answer:

48

Step-by-step explanation:

240/5 = 48

Answer:

48 push ups in 1 minute

Step-by-step explanation:

We can use a ratio to solve

240 pushups

-----------------------

5 minutes

Divide each by 5

48 pushups

--------------------

1 minutes

Need help with this

Answers

Answer:

5 to the power of -2

Step by Step explanation:

Because you are diving, you need to subtract the powers.

For example, you subtract 10 from 12 to get -2

The 5 remains the same so the answer should be 5 to the power of -2

Hope this helps

2. The length of the side of a square is
represented by the expression 2a²b. Which
term represents the area of this square?
A. 8a3b
B. 4a3b
C. 4a4b2
D. 2a6b2

Answers

B!!! Explanation: just took the test

Please help with question off algebra nation

Answers

Answer:I’m on that same question and I need help to

Step-by-step explanation:

Answer:

Table C is a linear function. Table A is an exponential function. And lastly table B is a quadratic function.

Step-by-step explanation:

I know that table C is linear because it has a constant rate of change the whole entire time.

I know table A is exponential because of the way it drastically increases at the end.

And lastly I know that table B is quadratic because if I were to graph it and keep on placing points, it would make a parabola.

I hope I helped.

Which is the longest length?
a 1 yd. 20 in.
b 1yd. 1 ft.
С
40 in.
d 3 ft.

Answers

Answer:

a-1yd20in

Step-by-step explanation:

a-4ft 8in

b-4ft

c-3ft 4in

d-3ft

Answer:

it's A, one yard and 20 inches

Step-by-step explanation:

If you convert them all to inches,  a yard and a 20 inches are equal to 56 inches, so you can rule out the 40 inches answer. a yard and a foot are equal to 48 inches, so we can rule out that also. 3 feet is equal to 36 inches, because we know that a foot is equal to 12 inches. so you are left with A. 1 yard and 20 inches.

|n|=5 what is the value for n.

A -5or5
B 0 and 5
C -5 only
D 5 only

Answers

Answer:

A -5or5

Step-by-step explanation:

|n|=5

Absolute value means take the positive value of the number

|5|=5

|-5|=5

so positive 5 and -5

What is the solution to this system of equations?

Negative 3 x + 5 y = negative 2. 3 x + 7 y = 26.
(4, 2)
(2, 3 and one-third)
no solution
infinitely many solutions

Answers

Answer:

4,2

Step-by-step explanation:

did the test

The solution of the system of equation is (4, 2) which is correct option(A).

What is equation?

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Given the two systems of equations,

-3x + 5y = -2

3x + 7y = 26

Adding the both equations

-3x + 5y + 3x + 7y = -2+26

12y = 24

y = 2

Substitute the value of y in any one of the equations,

3x + 7 y = 26

3x + 7(2) = 26

3x = 26-14

3x = 12

x = 4

Hence, the solution of the system of equation is (4, 2).

Learn more about equation here:

brainly.com/question/10413253

#SPJ2

Find the volume of the following solid figure. Use = 3.14.
V = 4/31tr3. A sphere has a radius of 4.5 inches.
Volume (to the nearest tenth) =
cubic inches.
381.5
56.5
84.8

Answers

381.5 because it is......

I NEED HELPPPPP!!!! PLZZZ

Answers

Answer:

13.5

Step-by-step explanation:

What I want you to do is think of yourself as a tourist who just landed in Nebraska. You've decided to take a road trip across the northwestern US (as presented in the states shown on the map) and you want to cross each state border exactly once. So for example, you want to make sure that you cross the border between SD-ND, SD-NE, SD-WY, SD-MT. You don't just want to visit South Dakota, but you want to cross all of the borders as well... but only once! You can visit each state as many times as you wish, but you can only cross each border once. Can you think of a way to cross ALL of the state borders in the map exactly once, while ending back where you started in Nebraska?

Answers

Answer: up, left, down, right

Step-by-step explanation:

because

Which values are solutions to the inequality below
Check all that apply

Answers

I honestly don’t know

The table shows the cost in dollars, y, for renting a pair of snow skis or renting a snowboard for x days. Which function shows the combined cost in dollars, y, for renting two pairs of snow skis and two snowboards for x days? y = 45x + 60 y = 90x + 120 y = 25x + 25 y = 20x + 35

Answers

Answer: this is the right answer y = 90x + 120

Step-by-step explanation:

HURRY PLEASE!! WILL MARK THE BRAINLIEST

Which of the following are factors of the
polynomial?

Answers

Answer:

All of the above

Step-by-step explanation:

In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Since, they all have a degree of 1 they are all polynomials.

A sports stadium holds 14,600 people. There are eight home games in
a season. Find the total number of people who could attend home
games in one season.

Answers

Answer:

116800

Step-by-step explanation:

14600x8

166800

Answer:

b

Step-by-step explanation:

hope this helps you

What is the volume of the cone to the nearest cubic millimeter? (Use ​π = 3.14)

A) 52 mm3

B) 157 mm3

C) 209 mm3

D) 628 mm3

Answers

Answer:

209

Step-by-step explanation:

The volume of the cone, to the nearest cubic millimeters is: C. 209 mm³.

What is a Cone's Volume?

Volume of a cone = 1/3πr²h

Where, r = radius of the cone, and h = height of the cone.

Given:

​π = 3.14Radius (r) = 5 mmHeight (h) = 8 mm

Thus:

Volume of a cone = 1/3(3.14)(5²)(8)

Volume of a cone = 209 mm³

Thus, the volume of the cone, to the nearest cubic millimeters is: C. 209 mm³.

Learn more about volume of cone on:

https://brainly.com/question/14278632

help quick!!!!?????​

Answers

Omg I’m so sorry to interrupt but I really need help on my homework :( it’s two questions for 20 points||| can someone please help

Answer:

none

Step-by-step explanation:

57+75+95= 227

24+70+75= 169

48+64+80= 192

19+27+80=73

A right triangle equals 180 degrees.

The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students. General High rented and filled 14 vans and 12 buses with 738 students. How many students would fill 2 buses and 3 vans?

Answers

Answer:

133 students would fill 2 buses and 3 vans

Step-by-step explanation:

Let x be the no. of students in each van

No. of students in 12 vans = 12x

No. of students in 14 vans = 14x

Let y be the no. of students in each bus

No. of students in 14 buses = 14y

No. of students in 12 buses = 12y

We are given that The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students.

12x+14y=796 ---1

We are also given that General High rented and filled 14 vans and 12 buses with 738 students.

14x+12y=738 ---2

Plot 1 and 2 on graph

12x+14y=796 --- Green line

14x+12y=738 --- Purple line

Intersection point gives the solution

Intersection point=(x,y)=(15,44)

No. of students in 1 van = 15

No. of students in 3 vans = [tex]15 \times 3 = 45[/tex]

No. of students in 1 bus = 44

No. of students in 2 buses =[tex]44 \times 2 = 88[/tex]

So,Total no. of students in 3 vans and 2 buses = 45+88=133

Hence 133 students would fill 2 buses and 3 vans

5(x-10)=30-15x
Ox=1
Ox=4
Ox=5
Ox=8

Answers

Answer:

x = 4

Step-by-step explanation:

5x-50=30-15x

5x +15x =30+50

20x= 80

Divide both sides of the equation by 20

x = 4

I hope it helps

AC =
Round your answer to the nearest hundredth.
40°

Answers

This rounded to the nearest hundred is 50°

What is the value of x?
A.2
B.3
C.6
D.7

Answers

Answer:

A

Step-by-step explanation:

Given 2 secants from a point outside the circle.

Then the product of the external part and the entire secant of one secant is equal to the product of the external part and the entire secant of the other secant, that is

(x + 1)(x + 1 + 11) = (x + 4)(x + 4 + 1)

(x + 1)(x + 12) = (x + 4)(x + 5) ← expand both sides

x² + 13x + 12 = x² + 9x + 20 ← subtract x² + 9x from both sides

4x + 12 = 20 ( subtract 12 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2 → A

answer with work pls !!

Answers

19.3 x 9.5 = 183.35 with the correct answer

-3x+1/2=3/8
Whats x? pls someone help step by step

Answers

Answer:

x = -1/24 = -0.042

Step-by-step explanation:

Step  1  :   Simplify  3/8

Step  2 :

Rewriting the whole as an Equivalent Fraction

Step  3  :

Calculating the Least Common Multiple

Equation at the end of step  3  :

 24x + 1

 ———————  = 0  

    8  

Last step:

Solving a Single Variable Equation :

5.2      Solve  :    24x+1 = 0  

Subtract  1  from both sides of the equation :  

                     24x = -1

Divide both sides of the equation by 24:

                    x = -1/24 = -0.042

Hope this helps.

The lowest point of elevation in the United States is at Death Valley National Park in California at 282 feet below sea level. The Dead Sea in Israel is 1,360 feet below sea level. Write a division expression that could be used to find how many times greater the Dead Sea lies below sea level than Death Valley. Then determine how many times greater. Round to the nearest whole number.

Answers

Answer:437

Step-by-step explanation:I took the test

Simplify the following expression
x^5/x^-2=x^n
A. 8
B. 2
C. 7
D. 10

Answers

Answer:

7

Step-by-step explanation:

x^5/x^-2=x^n

x^5=x^n×x^-2

x^5=x^-2+n

5=-2=n

n=7

this is 100% correct

plzz mark me brainliest

(x*y)*z=144
x = y*3
z = y*2

please help

Answers

Answer:

whats the question that u need help with

Students in grade 7 and 8 were asked which food they liked best the results are shown in the table below?

Answers

Answer:

55% if the students like hotdods

Answer:

55%

Step-by-step explanation:

Factor the expression below.
x2 - 6x + 9
A.
(x + 3)(x + 3)
B.
3(x2 - 2x + 3)
OC. (x-3)(x-3)
OD.
(x - 3)(x + 3)
HELP

Answers

Answer:  (x-3)(x-3)

This is a perfect square trinomial in the form a^2 - 2ab + b^2 = (a-b)^2. In this case, a = x and b = -3.

Another way you can look at it is to ask yourself "what two numbers multiply to 9 (last term) and add to -6 (middle coefficient)?". Those two numbers are -3 and -3

-3 plus -3 = -6

-3 times -3 = 9

So this is why x^2-6x+9 = (x-3)(x-3)

We can expand (x-3)(x-3) back out to get x^2-6x+9 again using the FOIL rule, distributive property, or the box method.

Answer:

C. (x-3)(x-3)

Step-by-step explanation:

x² - 6x + 9 = 0

x² - 3x - 3x + 9 = 0

x(x - 3) - 3(x - 3) = 0

(x - 3) (x - 3) = 0

If you save $3,000 at an interest rate of 14 percent per year, how much will you have at the end of six years? The interest should be compounded. A. $5,805.96 B. $6,502.34 C. $6,584.91

Answers

Answer:

C.) $6,584.91

Step-by-step explanation:

Amount earned in compound interest = P(1 + r)^n;

where P is the principal,

r is the rate and n is the number of periods.

Amount = 3,000(1 + 14%)^6 = 3,000(1 + 0.14)^6 = 3,000(1.14)^6 = $6,584.91

Answer:

C) 6584.91

Step-by-step explanation:

plato

A Bowling ball is rolled down the alley with the constant velocity of 1.6 m/sec at an angle of 85° to the starting line, the position of the person throwing a bowling ball can be represented by the point (0,0). where is the ball after six seconds?

Answers

We have been given that a Bowling ball is rolled down the alley with the constant velocity of 1.6 m/sec at an angle of 85° to the starting line, the position of the person throwing a bowling ball can be represented by the point (0,0).

We are asked to find the position of ball after 6 seconds.

We will use horizontal position and vertical position formula to solve our given problem.

Horizontal position is given by formula: [tex]x=v\cdot \text{cos}(\theta)\cdot t[/tex] and vertical position is given by formula: [tex]y=v\cdot \text{sin}(\theta)\cdot t[/tex],where,

v = Velocity,

t = Time,

[tex]\theta[/tex] = Angle to the starting line.

For our given problem [tex]v=1.6[/tex], [tex]t=6[/tex] and [tex]\theta=85^{\circ}[/tex].

[tex]x=1.8\cdot \text{cos}(85^{\circ})\cdot 6[/tex]

[tex]x=10.8 \cdot 0.087155742748[/tex]

[tex]x=0.9412820216784\approx 0.94[/tex]

[tex]y=1.8\cdot \text{sin}(85^{\circ})\cdot 6[/tex]

[tex]y=10.8\cdot 0.996194698092[/tex]

[tex]y=10.7589027\approx 10.76[/tex]

Therefore, the position of ball after 6 seconds would be [tex](0.94,10.76)[/tex].

Answer:

(0.8,9.6)

Step-by-step explanation:

x=1.6*cos85* 6=0.8

y=1.6*sin85 *6=9.6

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