25points for this question Given: AB ≅ BC and AO ≅ OC OK − angle bisector of ∠BOC Find: m∠AOK

25points For This Question Given: AB BC And AO OC OK Angle Bisector Of BOC Find: MAOK

Answers

Answer 1
AB and BC are congruent (given)AO and OC are congruent (given)BO is congruent with itself (reflexivity)

Taken together, these three facts imply that triangles AOB and COB are congruent (side-side-side congruence postulate).

Now, it's not exactly clear whether A and C lie on the same line (it's possible that the figure is not drawn to scale). If they do, then both angles AOB and COB are right angles, so angle BOK has measure 45º, and so [tex]m\angle AOK=135^\circ[/tex].

Answer 2

By applying the theorems of an isosceles triangle and an angle bisector, m<AOK = 135 degrees.

Recall the Theorem of Isosceles Triangle:

A triangle having two equal sides is an isosceles triangle.If a line segment from a vertex of the isosceles triangle meets intersects the base of the isosceles triangle at the midpoint, the line segment is therefore perpendicular to its base.The angles formed on both sides of the line segment that bisects the base are each 90 degrees.

We would apply the above stated to solve the problem given.

We know the following:

AB ≅ BC (given)AO ≅ OC (given)OK bisects angle BOC (given)

We can deduce that:

Triangle ABC is an isosceles triangle (it has two equal sides, AB and BC).m<AOB = 90 degrees (BO is perpendicular to AC)m<BOC = 90 degrees (BO is perpendicular to AC)m<BOK = 45 degrees (OK bisects angle BOC)

Thus:

m<AOK = m<AOB + m<BOK

Substitute

m<AOK = 90 + 45

m<AOK = 135 degrees.

Therefore, by applying the theorems of an isosceles triangle and an angle bisector, m<AOK = 135 degrees.

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Related Questions

a penny is dropped from the top of the statue of liberty which is 305 feet tall . the height of the penny, (h,) at time (t) seconds can be repesented by the equation h(t) = -16t^2 + 305. After 4 seconds how much further does the penny need to travel before it hits the ground.

Answers

Answer: Penny need to travel 49 feet before it hits the ground.

Step-by-step explanation:

Since we have given that

[tex]h(t)=-16t^2+305[/tex]

Here, h denotes the height of the penny

t denotes the time in seconds.

Now, t = 4 seconds

So, the penny needs to travel before it hits the ground is given by

[tex]h(4)=-16(4)^2+305\\\\h(4)=-16\times 16+305\\\\h(4)=256-+305\\\\h(4)=49\ feet[/tex]

Hence, Penny need to travel 49 feet before it hits the ground.

Final answer:

After 4 seconds, the penny needs to travel an additional 49 feet before it hits the ground.

Explanation:

The equation h(t) = -16t^2 + 305 represents the height of the penny at time t seconds. To find out how much further the penny needs to travel before it hits the ground after 4 seconds, we need to substitute t = 4 into the equation and solve for h.

h(4) = -16(4)^2 + 305

h(4) = -256 + 305

h(4) = 49 feet.

Therefore, the penny needs to travel an additional 49 feet before it hits the ground.

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What is the value of x?

Answers

x = 16.

Hope this helps!

Answer:

x = 16

Step-by-step explanation:

Since the triangles are similar then the ratio of corresponding sides are equal, that is

[tex]\frac{x}{4}[/tex] = [tex]\frac{20}{5}[/tex] ( cross- multiply )

5x = 80 ( divide both sides by 5 )

x = 16

what is the difference r+2/r+4-3/r+1

Answers

Answer:

[tex]\frac{r^2-10}{(r+4)(r+1)}[/tex]

Step-by-step explanation:

We want to evaluate:

[tex]\frac{r+2}{r+4}-\frac{3}{r+1}[/tex]

We collect the least common multiple of the denominators to get:

[tex]\frac{(r+2)(r+1)-3(r+4)}{(r+4)(r+1)}[/tex]

Expand the numerator:

[tex]\frac{r^2+3r+2-3r-12}{(r+4)(r+1)}[/tex]

[tex]\frac{r^2-3r+3r+2-12}{(r+4)(r+1)}[/tex]

[tex]\frac{r^2-10}{(r+4)(r+1)}[/tex]

Answer:

[tex]\frac{ r^2-10}{(r+4)(r+1)}[/tex]

Step-by-step explanation:

[tex]\frac{r+2}{r+4} - \frac{3}{r+1}[/tex]

To simplify the fractions we take common denominator

LCD is (r+4)(r+1)

we try to get same denominator on both fraction

multiply the first fraction by r+1 and second fraction by r+4

[tex]\frac{(r+2)(r+1)}{(r+4)(r+1)} - \frac{3(r+4)}{(r+1)(r+4)}[/tex]

(r+2)(r+1) becomes r^2 +3r+2

3(r+4) becomes 3r+12

[tex]\frac{ r^2 +3r+2}{(r+4)(r+1)} - \frac{3r+12)}{(r+1)(r+4)}[/tex]

[tex]\frac{ r^2 +3r+2-3r-12}{(r+4)(r+1)}[/tex]

combine like terms

[tex]\frac{ r^2-10}{(r+4)(r+1)}[/tex]

Carly wins 1282 tickets at a arcade. For each group of 65 tickets she will receive a prize. Carl solve the problem 1282÷65 and determines that she has enough tickets right now for 19 prices. What is the least number of additional tickets that current needs to win to have enough tickets for a 20th prize?

Answers

18 is correct because 1300/65=20 1300-1282=18.

The manager of a company that sells movie tickets online releases a report. The report states that the company's customers do not want the option of reserving a seat when they buy tickets. The report was based on a survey of 200 customers chosen at random from the company's database. Participants were asked the question, "Are you willing to spend the extra time and effort to reserve a seat when you buy tickets?" Select all statements that correctly evaluate the report. The question is biased toward a Yes response.

A) The sample is biased because it does not represent the population.

B) The question is biased toward a No response.

C)The question is not biased.

D) The sample is not biased.

Answers

Answer:

the question is biased towards a no response, because they're asking participants "are you willing to spend the extra time to blah blah" obviously they're going to say no, and the second answer is the sample is not biased because they're not giving the consumers any reason to want the product they're selling.

Step-by-step explanation:

Answer:

The sample is not biased.

The question is biased toward a No response

Step-by-step explanation:

I took the test!

caleb made 6 quarts of trail mix for his camping trip. Each week he consumed 4 pints of the trail mix. How many weeks did Caleb have trail mix? ​

Answers

Answer:

3 weeks

Step-by-step explanation:

1 quart = 2 pints

6 quarts = 12 pints,

so 4 pints each week would take 3 weeks (4pints x 3weeks =12pints)

If the mean of this distribution is 7, which could be the median? A) 1.5 B) 5 C) 8 D) 10


PLEASE HELP

Answers

Answer:

Tationia Rolon

Step-by-step explanation:

I think its C because the median is the number in the middle

Answer

6

Step-by-step explanation:

I got is correct on usatestprep

Which of the following statements is false regarding randomization

Answers

Answer:

Randomization can be replaced by accurately matching the sample to the population

You should never replace Randomization, its important. Thats why this is false (I just took this quiz)

write the equation for an exponential function, in the form axb^x, whose graph passes through the coordinates points (1, 7.5) ( 3, 16.875)

Answers

Answer:

see explanation

Step-by-step explanation:

The equation of the exponential function in the form

y = a[tex]b^{x}[/tex]

Substitute the given points into the equation and solve for a and b

Using (1, 7.5), then

7.5 = ab → (1)

Using (3, 16.875), then

16.875 = ab³ → (2)

Divide (2) by (1)

[tex]\frac{ab^3}{ab}[/tex] = [tex]\frac{16.875}{7.5}[/tex], hence

b² = 2.25 ( take the square root of both sides )

b = 1.5

Substitute b = 1.5 into (1)

1.5a = 7.5 ⇒ a = 5

The exponential function is y = 5[tex](1.5)^{x}[/tex]

john is asked to roll a fair numver cube, numbered 1 to 6, and tossed a balanced quarter simultaneously. What is the probability that he will roll a 2 and the quarter will come up tails? A.) 1/2 B.) 2/3 C.) 1/6 D) 1/12​

Answers

Answer: B 2/3

Step-by-step explanation:

1/6 + 1/2

15. Cody and his wife are purchasing a home. The cost
of the home is $145,900. They will be required to
pay a down payment of 5% of the purchase price
and to pay closing costs of 6% of the purchase
price. How much cash will they need for the down
payment and closing costs?
$16,049
$8,754
$7,295
$145,900
$161,949​

Answers

They would need $16,049!

Price of the home is $145,900.

Percentage of the down payment is 5%

Subtract 5% from $145,900 = $138,605

That mean 5% of $145,900 is $7,295

Percentage of the closing cost is 6%.

Subtract 6% from $145,900 = 137,146

That mean 6% of 145,900 is $8,754

Add the down payment ($7,925) and closing cost ($8,745)

$16,049!

Mark me Brainliest!! Please!

they will need to pay $16,049

multiply $145,900 by 5%

multiply $145,900 by 6%

now add the totals to get $16,049

y = 3x-5
6x + 3y= 15

Answers

y = 3x - 5

So substitute 3x-5 for y:

6x + 3(3x-5) = 15

Simplify:

6x + 9x - 15 = 15

15x - 15 = 15

x - 15 = 1

x = 16

THEN find y by plugging the value of x back into the first equation:

y = 3(16) - 5

y = 48 - 5

y = 43

Find the perimeter of the polygon ??

Answers

Answer:

35.5 m

Step-by-step explanation:

The perimeter of the polygon is the sum of all the sides of the polygon. The sides are given as

11 m , 5 m ,7.5 m , 5m and 7m

Hence the perimeter would be,

11+5+7.5+5+7

= 35.50 m

Brainliest + Points Please help!!!

A force of 100 newtons will stretch a spring 0.25 meters. How far will a force of 80 newtons stretch it?

Use Hooke's law F = kx.

A.
0.04 meters

B.
0.2 meters

C.
0.4 meters

D.
2 meters

Answers

Answer:Your Answer would be  B 0.2 meters

Step-by-step explanation:

Convert 7pi/5 to degrees.

Answers

Answer: 252 degrees!

7pi/5 is 252degrees.

What is radians?

The standard unit of angular measure used in many branches of mathematics is the radian, indicated by the symbol rad. The radian is the SI unit for measuring angles. The radian has replaced the unit as a SI derived unit, which was previously a SI supplementary unit.

Given

To convert radians to degrees, multiply by 180/π, since a full circle is

360° or 2π radians.

(7π/5)⋅180°/π

Cancel the common factor of π.

Rewrite the expression.7/5⋅180

7⋅36

Multiply 7 by 36.

252

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Tell whether each equation represents a direct proportion. If so, identify the
constant of proportionality.

1. 0.4y = x

2. x = 1 - 2y

Answers

Answer:

Step-by-step explanation:

1. 0.4y = x is a direct proportion.  It'd be more appropriate to write this as

   y =  x / 0.4, or y = 2.5x, in which case 2.5 is the constant of proportionality.

2. x = 1 - 2y is not a direct proportion because of the offset (1).  A line representing a direct proportion must go through the origin (0, 0); this particular line does not do that.

The first equation, 0.4y = x, represents a direct proportion with the constant of proportionality being 2.5. The second equation, x = 1 - 2y, does not represent a direct proportion since it does not have the form y = kx.

When we talk about two quantities being directly proportional, we mean that as one quantity increases, the other increases by a constant rate, and vice versa. This relationship can be represented by the equation y = kx, where k is the constant of proportionality.

For the first equation, 0.4y = x, this is rearranged as y = (1/0.4)x or y = 2.5x. This is indeed a directly proportional relationship, with the constant of proportionality being 2.5.

The second equation x = 1 - 2y does not describe a directly proportional relationship because it is not of the form y = kx. Instead, it shows that x decreases as y increases, which is suggestive of an inverse relationship, rather than a direct one.

Find the value of X in the circle

Answers

Answer:

x=7 units

Step-by-step explanation:

see the attached figure with letters to better understand the problem

we know that

The triangles AMN and APQ are congruent by SAS similarity postulate

The include angle

∠MAN=∠PAQ

Because

Arc MN=Arc PQ

therefore

MN=PQ

substitute the values

38=4x+10

solve for x

4x=38-10

4x=28

x=7 units

x would be 7 units because 4 × 7 = 28 And 28 + 10 = 38

A ________ is a transformation of a figure by turning it around a given point.

A. dilation

B. reflection

C. rotation

D. translation

Answers

Answer:

Translation

Step-by-step explanation:

How many terms are in the arithmetic sequence 7, 1, −5, …, −161?

Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference

27
28
29
30

Answers

Answer:

29

Step-by-step explanation:

The n th term of an arithmetic sequence is

• [tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

d = 1 - 7 = - 5 - 1 = - 6 and a₁ = 7, [tex]a_{n}[/tex] = - 161, hence

7 - 6(n - 1) = - 161 ← solve for n

7 - 6n + 6 = - 161

13 - 6n = - 161 ( subtract 13 from both sides )

- 6n = - 174 ( divide both sides by - 6 )

n = 29

There are 29 terms in the sequence

For the z-score for the 11.6 data point

Answers

Answer:

z = 1.3345

Step-by-step explanation:

The z-score for a given data point, say x, from a normal distribution with a given mean and population standard deviation is usually calculated using the formula;

[tex]z=\frac{x-mean}{standard deviation}[/tex]

The following information is available;

mean = 7

population standard deviation = 3.522

x = 11.7

We simply employ the above formula to determine the z-score associated with the 11.7 data point;

[tex]z=\frac{11.7-7}{3.522}=1.3345[/tex]

Find the value of h in the parallelogram. Round your answer to the nearest tenth​

Answers

Answer:

h=7.5 in

Step-by-step explanation:

see the attached figure with letters to better understand the problem

In the right triangle ABC

sin(CAB)=15/18 ----> opposite side divided by the hypotenuse

In the right triangle CDE

sin(DCE)=h/9 ----> opposite side divided by the hypotenuse

In this problem

∠CAB=∠DCE ------> by corresponding angles

therefore

sin(CAB)=sin(DCE)

15/18=h/9

solve for h

h=15*9/18

h=7.5 in

Answer:

Step-by-step explanation:

7.5 inches is correct

Which of the following is the solution to the inequality below?

Answers

Answer:

C.

Step-by-step explanation:

distribute.

-3x+9 > 5-5x

put the x's to one side.

2x+9 > 5

put the number to the other side.

2x > -4

x > -2

To the nearest hundred what is the value of X

Answers

Answer:

41.51

Step-by-step explanation:

We can find the value of x using the trigonometry identify.

Cos (41) = x/55

x = 55cos (41)

x = 41.51

ANSWER

[tex]x = 41.51[/tex]

EXPLANATION

The given triangle has a right angle.

We were given an acute angle that measures 41°

The hypotenuse of the given right triangle is 55.

Since x is adjacent to the given angle and we also know the hypotenuse, we use the cosine ratio to find x.

[tex] \cos(41 \degree) = \frac{x}{55} [/tex]

Therefore

[tex]x = 55 \cos(41 \degree) [/tex]

[tex]x = 41.509[/tex]

We round to the nearest hundredth to obtain,

[tex]x = 41.51[/tex]

The probability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1. The events are not independent because the .

Answers

Answer:

The events are not independent because the product of their marginal probabilities is not equal to their joint probability

Step-by-step explanation:

Two events A and B are said to be independent with respect to probability if the product of their marginal probabilities is equal to their joint probability. In the question presented we have;

Pr(A) = 0.4

Pr(B) = 0.2

Pr(A n B) = 0.1

The product of their marginal probabilities is;

Pr(A) * Pr(B) = 0.4 * 0.2 = 0.08

Their joint probability is given as;

Pr(A n B) = 0.1

Clearly, Pr(A) * Pr(B) ≠ Pr(A n B) and thus the events are not independent.

Answer:

Product of P(A) and P(B) is not equal to P(A and B)

Step-by-step explanation:

it would be option C on E2020

A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?

22 feet

26 feet

33 feet

44 feet​

Answers

22 feet is the answer I hope this helps

Answer:

Longest rope is 44 feet. 1 piece is 1/2(44)=22. 22+44=66

Step-by-step explanation:

given f(x)=x+2 and h(x)=1/x-1 evaluate the following function at x=2​

[h(x)]^2/f(x)

Answers

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Substitute x = 2 into both h(x) and f(x)

h(2) = [tex]\frac{1}{2-1}[/tex] = 1 ⇒ (h(2))² = 1

f(2) = 2 + 2 = 4

Hence

[tex]\frac{h(x)^2}{f(x)}[/tex] when x = 2

= [tex]\frac{1}{4}[/tex]

1/4 is the following function at x=2​

What are functions?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and co domain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Given

Substituting x = 2 into both h(x) and f(x)

h(2) = 1(2-1) = 1 ⇒ (h(2))² = 1

f(2) = 2 + 2 = 4

Hence

h(x)²/f(x)  when x = 2

=1/4

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The ratio of red cars to blue cars in a parking lot was 5:3.if there were 40 red cars, how many blue cars were there??

Answers

Every 5 red cars there are 3 Blue cars,

So if there are 40 red cars,

there are going to be 24 Blue cars

40 divided by 5 which is 8

Multiply 3 × 8 which is ( 24 blue cars )

Answer:

24

Step-by-step explanation:

The 5 part of the ratio represents 40 cars, thus

40 ÷ 5 = 8 cars ← value of 1 part of the ratio

3 parts = 3 × 8 = 24 ← number of blue cars

Can someone help me on 8,12 please

Answers

Step-by-step explanation:

8.

[tex]\triangle CHF\sim\triangle YWS\\\\\angle C\cong\angle Y\\\angle H\cong\angle W\\\angle F\cong\angle S\\\\\dfrac{CH}{YW}=\dfrac{HF}{WS}=\dfrac{CF}{YS}[/tex]

Although it does not look like the picture.

From the picture ∠F ≅ ∠Y...

We must stick to the correct writing:

Δ → Δ

C → Y

H → W

F → S

12.

ΔMLK and ΔYWZ are not similar because they have different angles (different shape).

What is the answer to this?

Answers

Answer:

90°

Step-by-step explanation:

The angles at the intersection of a kite will always be 90°

What is the surface area of the cylinder in term of pi? Radius of 11 and height of 23

Answers

Answer:

The surface area of the cylinder is [tex]748\pi[/tex].

Step-by-step explanation:

Given : Radius of the cylinder is 11 unit and height of the cylinder is 23 unit.

To find : What is the surface area of the cylinder in term of pi?

Solution :  

The formula of surface area of cylinder is

[tex]A=2 \pi r^2+2\pi rh[/tex]

Where, r is the radius of the cylinder r=11 unit.

h is the height of the cylinder h=23 unit.

Substitute the value in the formula,

[tex]A=2 \pi r^2+2\pi rh[/tex]

[tex]A=2\pi(r^2+rh)[/tex]

[tex]A=2\pi(11^2+11(23))[/tex]

[tex]A=2\pi(121+253)[/tex]

[tex]A=2\pi(374)[/tex]

[tex]A=748\pi[/tex]

Therefore, The surface area of the cylinder is [tex]748\pi[/tex].

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