Mathematics Middle School

Given: PK and PE tangents
m∠KPE = 60°,
2KP = PE + 1
Find: EK

Answers

Answer 1

Answer:

EK = 1.

Step-by-step explanation:

Here we have KP = PE (tangents from outside the circle)

Therefore, 2KP = PE + 1 = KP + 1

Hence, 2KP - KP = 1 or KP = 1 = PE

Since KE is the base of triangle KPE, where ∡ KPE = 60, and KP = PE, we have an isosceles triangle such that ∡PKE = ∡PEK

Hence, in ΔKPE, ∡KPE + ∡PKE + ∡PEK = 180

Therefore, 60° + ∡PKE + ∡PEK = 180

Hence, ∡PKE + ∡PEK = 180° - 60° = 120°

Because ∡PKE = ∡PEK, (base angles of isosceles triangle), we have;

∡PKE + ∡PEK = 2·∡PEK = 120° which gives

∡PEK = 60° = ∡PKE

Therefore, ∡KPE = ∡PEK = ∡PKE = 60°

Hence, ΔKPE is an equilateral triangle and KP = PE = EK = 1

EK = 1.

Related Questions

What is the solution to the equation below? Round your answer to two
decimal places
e^x = 5.9

Answers

Answer:.1.77

Step-by-step explanation:

e^x = 5.9

Take the natural logarithm of both sides

x = ln (59/10)

x = 1.77

Answer: x=1.77

Step-by-step explanation:

A P E X

What is the radius of J. A. 24.8
B. 6.2
C. 10.8
D. 12.4

Answers

Answer:

12.4 units

Step-by-step explanation:

The diameter of circle J is represented by KN. Half of KN is KJ and JN which means these represent the radius. Since JN equals 12.4 and JN is the the radius, then the radius of circle J is 12.4 units which is answer choice D.

The radius of the given circle is 6.2 unit. So option B is correct.

What is the radius?

A line segment from a circle's or sphere's center to its perimeter or boundary is known as the radius in geometry. It is a crucial component of spheres and circles and is frequently abbreviated as "r". When discussing multiple radiuses at once, the plural form of radius is "radii". The diameter of a circle or sphere is the longest line segment connecting all points on the opposite side of the centre, and the radius is equal to half of the diameter in length. It can be written as d/2, where d is the circle's or sphere's diameter. Look at the illustration of a circle below that depicts the connection between radius and diameter.

Given that,

A circle,

which contains diameter KN of length 12.4 unit

and chord 10.8 unit.

The radius = ?

It is known that, the length of the radius is half of the diameter of the circle,

R = D/2

= 12.4/2

= 6.2

Therefore, the length of the radius is 6.2 unit.

To know more about radius check:

https://brainly.com/question/13449316

#SPJ7

Mimi earns a 15% commission on any sales she earns.
Based on the information, which equation below represents total commission, c, for any given sale, S.
A c = s(1.5)
B. c = s(0.15)
.
Cc=s-s(0.15)
D. c= 150

Answers

Answer:

Its B

Step-by-step explanation:

Miche found that most helicopters fly at speeds of less than 270 kilometers per hour. Her work is shown below. s > 270 A number line going from 260 to 285. An open circle is at 270. Everything to the right of the circle is shaded. Which mistakes did she make? Check all that apply.

Answers

Answer:

The inequality should be s<270.The number line should be shaded to the left.

Step-by-step explanation:

Miche found that most helicopters fly at speeds of less than 270 kilometers per hour.

If s=speed of the helicopters

Then: s<270

Representing this on a number line:

We have an open circle at 270.Everything to the left of the circle is shaded.

Since the options are not given, I would list the mistakes made by Miche.

The inequality should be s<270.The number line should be shaded to the left.

Answer:

A and D

Step-by-step explanation:

I hope this helped <3 ·ω·

If you answer can you write how you solved it?

Answers

Answer:

[tex]145.3in^2[/tex]

Step-by-step explanation:

[tex]A_{L} =2\pi rh=2*\pi *2.5*9.25\\=145.3in^2[/tex]

What percent is modeled by the grid?
A grid model with 100 squares. 33 squares are shaded.
23%
30%
33%
40%

Answers

Answer:

33%

Step-by-step explanation:

There are 33 squares out of 100 that are shaded

33/100

Percent means out of 100

33%

Answer: 33%

Explanation: A ratio that compares a number to 100 can be written as a percent. So in this problem, since the figure has 33 out of 100 boxes shaded, we have the ratio 33/100 which can be written as 33%.

which one isn’t a function ?

Answers

Answer:

D isn't a function because points intersect vertically on the graph

Step-by-step explanation:

what is the answer for the picture.

Answers

Answer:

Step-by-step explanation:

40-36=4

Answer:

She won by 4 seconds.

Step-by-step explanation:

If Bailey ran the race in approximately 36 seconds and Elena ran it in approximately 40 seconds, Bailey would've completed the race 4 seconds faster than Elena.

Can somebody please help me :(

Answers

Steps:

Boys: 30+40+50+60+60+70+70+70+80+80+80+90+90+100 = 970

Girls: 10+20+50+50+60+70+70+80+80+80+90+100 = 760

THEN Divide the sum of boys and girls but how many numbers you added

970 ÷ 14 = 69.2

910 ÷ 12 = 63.3

what is the excluded value of this?

Answers

The value of this would be x+1.5. I have got this because 8/8=1 and 12/8=1.5.

Aisha is playing a game in which she can gain or lose points on each turn. The table below
shows the points she scores on each of four turns in the game.
Aisha states that her highest score is on Turn 3, because 16 is greater than 3, 10, or 9. Use the
drop-down menus to explain Aisha's mistake.

Answers

Answer:

A score of -16 represents the lowest of points for these four turns.

The number for Aisha's highest score will be turn 2 on the number line.

That number is 10.

Step-by-step explanation:

Since the options of the drop down menu are not included, you should choose any option similar to lowest.

Aisha's highest score was obtained in turn 2 and that is 10.

Aisha is comparing absolute terms, that is why she believes that -16 represents a good score, while in reality is the worst she got.

A $135.00 item is marked down by 30%.
What is the new cost of the item?
Round to two decimals if needed.

Answers

Answer:

135.00 multiplied by .30% will be 40.5

Answer:

You can also calculate how much you save by simply moving the period in 30.00 percent two spaces to the left, and then multiply the result by $135 as follows: $135 x . 30 = $40.50 savings. Furthermore, you can get the final price by simply deducting .

Step-by-step explanation:

A mayor wants to determine if the people in his city think that he is doing a good job. Which choice BEST represents the population? A) Voters age 21 to 35. B) All the local business owners. C) The people who voted for him. D) All the residents of the city. Eliminate

Answers

Answer:

Step-by-step explanation:

D is the best choice. A excludes voters age 18-20 and 36+. B excludes everyone who doesn't own a business, and C excludes those who didn't vote for him. For the most honest results, D - everyone - is the best choice.

Ellie’s eats 1/4 cups of raisins everyday. If she buys a package that has 6 cups of raisins,how many days of raisins is that ?

Answers

Answer:

Step-by-step explanation:

Answer:

24 days

Step-by-step explanation:

Alright, so you can set an equation where x is the amount of days this package of raisins can last. Your equation would be 6=1/4x. Now, you solve. Bring the 1/4 over by dividing both sides by it. You get x=24, which is the answer.

Choose the right answer.

Which year had a decrease in profit between months 3 and 4?
Last year
This year

Answers

Step-by-step explanation: last year

Answer:

Last Year

Step-by-step explanation:

If you take a look at the red and blue lines in between the numbers 3 and 4 at the bottom of the graph, you can see that the profit for the red line (last year) is decreasing while the profit for the blue line (this year) is increasing. Last year (red line) had a decrease in profit between months 3 and 4.

A polygon is shown:

The area of polygon MNOPQR = Area of a rectangle that is 9 square units + Area of a rectangle that is ___ square units. (Input whole numbers only, such as 8.) (5 points)

Answers

Answer: 4

We're talking about the right part.

OP = RQ - NM = 7 - 3 = 4

PQ = MR - NO = 3 - 2 = 1

Area(OPQ?) = 4×1 = 4

Answer: 4

The area of polygon MNOPQR = Area of a rectangle that is 9 square units + Area of a rectangle that is 4 square units.

What is the area of the rectangle?

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

A polygon is given in the question, as shown

The area of polygon MNOPQR = Area of a rectangle that is 9 square units + Area of a rectangle that is ___ square units.

We have to determine the fill-in-the-blank.

As per the given figure, we can see that

OP = RQ - NM = 7 - 3 = 4

PQ = MR - NO = 3 - 2 = 1

Required area of rectangle = 4 × 1 = 4

Hence, the required fill-in blank will be "4".

Learn more about the Area of the rectangle here:

brainly.com/question/20693059

#SPJ2

What is the solution to the equation?
2/3a - 1/6 = 1/3

Answers

Answer:

a in this equation would be 3/4 because...

Step-by-step explanation:

2/3a−1/6=1/3

2/3a+−1/6=1/3

2/3a+−1/6+1/6=1/3+1/6

2/3a=1/2

Multiply both sides by 3/2.

(3/2)*(2/3a)=(3/2)*(1/2)

a=3/4

Hope this helps!

the correct answer is 3/4

Which is the angle measure represented by 2 rotations counterclockwise?
a. -1080°
C. 1080°
b. -720°
d. 720°

Answers

-720 because counter clockwise it would be 720 which is 360 times 2 but since it is backwards it’s -720.

I think it is a

Explanation is counterclockwise means going bakwards so that might be right

What is the output or waste of the cellular respiration cycle?

Answers

Answer: The outputs, or products, of cellular respiration are water and carbon dioxide

Explanation: The inputs, or reactants, of cellular respiration are glucose and oxygen. The outputs, or products, of cellular respiration are water, carbon dioxide

(x+4)−(x−1)
HELPPPP
5edrfytguyhidiftougyih;fygvjbmncifyykgvjb mnr6o7ftuglh.bjnhugiyfltudkrysi6d7tfugiy;h/junk;lk

Answers

Answer:

There is no plug-in for x.

X=0.

(0+4) - (0-1) = [(4 - (-1)] = 5.

Answer:

Step-by-step explanation:

(x+4) -x +1

x - x = 0

−8⋅f(0)+4⋅g(−8)=
Please help

Answers

Answer:

-32

Step-by-step explanation:

Look at the attachment

Functions can be represented as equations and graphs.

The value of [tex]\mathbf{-8\cdot f(0)+4\cdot g(-8)}[/tex] is -32

From the graph, we have the following values.

[tex]\mathbf{f(0)= 1}[/tex]

[tex]\mathbf{g(-8)= -6}[/tex]

So, we have:

[tex]\mathbf{-8\cdot f(0)+4\cdot g(-8)= -8 \times 1 + 4 \times -6}[/tex]

Simplify

[tex]\mathbf{-8\cdot f(0)+4\cdot g(-8)= -8 -24 }[/tex]

[tex]\mathbf{-8\cdot f(0)+4\cdot g(-8)= -32 }[/tex]

Hence, the value of [tex]\mathbf{-8\cdot f(0)+4\cdot g(-8)}[/tex] is -32

Read more about functions and equations at:

https://brainly.com/question/3468890

The triangles are congruent by the SSS congruence
theorem.
Which transformation(s) can map ALMN onto
AL'M'N'?
M
translation only
O reflection only
L'
O rotation then translation
M
O reflection then translation
N'
N

Answers

Answer: rotation then translation

Step-by-step explanation:

The transformation(s) can map triangle LMN onto triangle L'M'N' are (c) rotation then translation

The SSS congruence theorem means that the triangles LMN and L'M'N' are congruent by sides and the angles are also congruent.

So, the triangles can be transformed by

TranslationReflectionRotation

From the complete question, the triangles and rotated and translated

Hence, the transformation(s) can map triangle LMN onto triangle L'M'N' are (c) rotation then translation

Answers

Answer:

131

Step-by-step explanation:

25+24=49

180-49=131

1. What side in the second trapezoid corresponds to CD?
choices:
RU
ST
TU
RS

2. What angle in the second trapezoid corresponds to B?

choices:
T
S
U
R

Answers

Answer:

1...ut

2..s

Step-by-step explanation:

you can see that the trapezium ABCD is talented than you are St trapezium so then from the ABCD trapezium Appa what then you can see a De is parallel to you are and ab is parallel to AC and DC is parallel parallel to T s and a De is parallel to ur

Answer:

1. UT

2. S

Step-by-step explanation:

1. parallel sides of the first trapezoid are DC and AB, the last being the longest

so the answer is

UT, which is shorter base

2. B is the right angle

so S is the one on the second trapezoid

HELP ME PLEASE!!

I don't understand the question...
If possible, please explain!

Answers

Answer:

SSS

Step-by-step explanation:

We know 2 of the sides are equal

The thirds side is the same length by the reflexive property since it is the same side

The triangles are congruent by SSS or the side side side postulate

What is the probability of rolling an even an a die and drawing a face card from a standard deck of cards

Answers

Answer:

3/26

Step-by-step explanation:

Assuming this is a six-sided die, the probability of rolling an even number is 3/6 or 1/2. Then the probability of drawing a face card is 12/52 or 3/13. To find the probability of both you need to multiply them by one another an you get 3/26 or 11.5 percent.

answer with work pls!!

Answers

The reflected coordinates will be ( 15,7)

PLS HELP!!!!!! In a survey of 4530 U.S. adults, 87% said that they would like to donate more to charity. What is the margin of error for the survey? Round to the nearest tenth of a percent

Answers

Answer:

Margin of Error = 1.0% to the nearest tenth of a percent.

Step-by-step explanation:

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value is obtained from the z-tables at the popular confidence level of 95% and z-tables is used because the sample size, 4530, is large enough to approximate the population properties.

Critical value = 1.960

Standard error = σₓ = √[p(1-p)/n]

p = 87% = 0.87

n = sample size = 4530

σₓ = √[0.87×0.13)/4530]

= 0.0049966876

Margin of Error = 1.96 × 0.0049966876 = 0.0097935078 = 0.00979 = 0.979% = 1.0% to the nearest tenth of a percent.

Hope this Helps!!!

30 POINTS PLEASE ANSWER CORRECTLY AND CLEARLY THANK YOU!
Which expression represents the growth of an investment of $1,500 at 12% per year for a period of t years?

A. 1500(12)t
B. 1500(0.12)t
C. 1500t1.12
D. 1500(1.12)t

Answers

Answer:

Step-by-step explanation:

The investment grows by 12 percent every year. Therefore, if you multiply the 1500 by 0.12 you should get the value of the amount of extra money made in one year. If you substitute 2 into t you get the value increased by year 2 and so on.

Answer:

the correct answer is b

Step-by-step explanation:

just got it right on egduniuty

I really need help with this

Answers

Answer:

Step-by-step explanation:

In the first case the function could become undefined as x approaches -3 or 3 from either direction. The vertical asymptotes are x = -3 and x = +3.

In the second case, there's only one vertical asymptote, because the denominator can be zero (0) only at x = 0.

Other Questions

Determine if Ginny factored correctly. If not, explainwhere she made an error. Your drawer contains seven red socks and five green socks. It's too dark to see which are which. What is theprobability that the two socks that you pick are both red if you don't replace the first sock after you draw it?7/247/127/1514/35 Analyze the map below and answer the question that follows. A satellite map of the Caribbean. Areas of the map are labeled 1, 2, 3, 4, and 5. Arrow 1 points to a large island south of Florida. Arrow 2 points to a small island south of Cuba. Arrow 3 points to an island southeast of Cuba shared by 2 countries, the Dominican Republic and Haiti. Arrow 4 points to a U S territory east of Haiti. 5 is a group of islands northeast of Cuba. Image courtesy of NASA Which island group is located at number 5 on the map above? A. the Greater Antilles B. the Lesser Antilles C. Trinidad and Tobago D. the Bahamas Please select the best answer from the choices provided A B C D What is the probability of rolling a die 6 times and getting the numbers 1, 2, 3, 4, 5, 6 in that order? Select the best answer from the choices provided. A. 0.001389 B. 0.000129 C. 0.000021 D. 0.0000038 Draw an inference from the text to support the idea that the pigs don't believe all animals are equal. PLZ HURRY I'M GOING TO GET A LOT OF QUESTION SWhat is the surface area of the composite figure shown? 107 square feet 172 square feet 279 square feet 321 square feet Mrs. Dominguez asked her students to plot the number of books they read over the summer.Using the dot plot, how many students read two books?1236 One result of a trade war is _____. A.businesses closing B.workers getting laid off C.higher prices for consumers D.lower prices for consumers The slope intercept equation Math question down below Because the song was sung by Jacksonsupporters, you can infer that they how did Brown v. Board of Education impact sergregation in the United States? Please help No Explanation needed. Its science please need help asap will mark brainliest DON'T WANT TO FAIL!!!What was the political outcome of the Vietnam War? *10 points-Vietnam remains divided at the 17th parallel.-Vietnam was united under one communist rule.-Vietnam remains divided at the 38th parallel.-Vietnam was united under one democratic rule. escoge la conjugacion en el presente perfecto del verbo entre parentesistu no (pensar) en el dinero que debes A person standing on level ground is 2000 feet away from the foot of a 420-foot-tall building, as shown in the accompanying diagram. To the nearest degree, what is the value of X? can someone please help with these sat questions The difference between the most hours of sleep and the least of these students was 2.5 hours. True or false? Which number is equal to 10 Superscript 4?401,00010,00040,000

Given: PK and PE tangents m∠KPE = 60°, 2KP = PE + 1 Find: EK

Answers

Related Questions

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Given: PK and PE tangents
m∠KPE = 60°,
2KP = PE + 1
Find: EK