In a 30-60-90 triangle, if the the side opposite 30 degrees has a length
of 5, what is the length of the hypotenuse?

Answers

Answer 1

Might Want to draw this and Its very long but Hope it helped :)

Answer:

The sides are all of the same length - let's say a. The angles are all the same too, and since the angles must add up to 180∘, we conclude that the three angles in the equilateral triangle are equal to 180∘/3=60∘.

Now we do something sneaky. We draw a line all the way down from the top vertex of the triangle to the midpoint of the bottom line.

This new line cuts our equilateral triangle in half. What are the angles in one half?

The angle at the bottom is 90∘.

One of the angles is the same as one of the angles in the original equilateral triangle, so it is 60∘.

So the third angle must be 180∘−90∘−60∘=30∘.

Now the hypotenuse of this new triangle is a, the side length of the equilateral triangle. And the length of the shortest side is a/2, since the line we drew cut the bottom line in half.


Related Questions

In 2002, the average price of a new domestic car was $19,126. In 2008, the average price was $28,715. Based on a linear model, what is the predicted average price for 2014? Ston Down​

Answers

Answer:

The predicted average price for 2014 is of $38,304.

Step-by-step explanation:

Linear model:

In a linear model, the average price increases by the same amount during each period.

In 2002, the average price of a new domestic car was $19,126. In 2008, the average price was $28,715.

In a period of 6 years, the increase was of:

28715 - 19126 = $9,589

Based on a linear model, what is the predicted average price for 2014?

Another period of 6 years, so it will increase by 9589 more. Than

28715 + 9589 = 38304

The predicted average price for 2014 is of $38,304.

what is 381.7 rounded to the nearest tenth?

Answers

i need more information in order to help you

1. (20 points) One step in the manufacture of a certain metal clamp involves the drilling of four holes. In a sample of 150 clamps, the average time needed to complete this step was 72 seconds and standard deviation was 10 seconds. (a) Find a 99.5% confidence interval for the mean time needed to complete the step. (b) What is the confidence level of the interval (71, 73)? (c) How many clamps must be sampled so that 99.5% confidence interval specifies the mean to within ±1.5 seconds? (d) Can you conclude that the mean time needed to complete the step is greater than 73 seconds? i. State hypothesis. ii. Compute P-value. iii. What is your conclusion?

Answers

Answer:

(69.708 ; 74.292) ; 78% ; 350 ;

H0 : μ = 72

H0 : μ > 72

Pvalue = 0.8897

there is not enough evidence to support the claim that the mean time needed to complete the step is greater than 73.

Step-by-step explanation:

99.5% confidence level, = 2.807

Sample size, n = 150

xbar = 72

Standard deviation, s = 10

Xbar ± Margin of error

Margin of Error = Zcritical * s/sqrt(n)

Margin of Error = 2.807 * 10/sqrt(150)

Margin of Error = 2.292

Lower boundary = 72 - 2.292 = 69.708

Upper boundary = 72 + 2.292 = 74.292

(69.708 ; 74.292)

B.)

Confidence level of the interval (71, 73)

(72 - 71 ) or (73 - 72)

Margin of Error = 1

Margin of Error = Zcritical * s/sqrt(n)

1 = Zcritical * 10/sqrt(150)

1 = Zcritical * 0.8164965

Zcritical = 1 / 0.8164965

Zcritical = 1.2247

α = 0.22 = 1 - 0.22 = 0.78 = 78%

C.)

Margin of Error = ±1.5

1.5 = Zcritical * s/sqrt(n)

99.5% confidence level, = 2.807

1.5 = 2.807 * 10/sqrt(n)

1.5 = 28.07 / sqrt(n)

Square both sides

1.5² = 28.08² / n

2.25n = 788.4864

n = 788.4864 / 2.25

n = 350.4384

n = 350 samples

D.)

H0 : μ = 72

H0 : μ > 72

Test statistic :

(xbar - μ) ÷ s/sqrt(n)

(73 - 72) ÷ 10/sqrt(150)

Test statistic = 1.2247

Pvalue :

P(Z < 1.2247) = 0.8897

Pvalue > α

0.8897 > 0.005

We fail to reject the Null ; Hence there is not enough evidence to support the claim that the mean time needed to complete the step is greater than 73.

If Quamie purchased 5 pencils for 20¢, how much will 20 pencils cost?

Answers

Answer:

80 cents

Step-by-step explanation:

Answer:

80 cents

Step-by-step explanation:

if you multiply 5 by 20 cents, you will get 100, now, if you know where I'm going, every time she buys 5 pencils she pays 20 cents, so if she buys 20 pencils, it will cost her 80 cents, Hope this helped! mark me brainiest if you can!

Find the area of the sector.

Answers

Answer:

D. 158.4 km²

Step-by-step explanation:

Area of sector = θ/360 * πr²

Where,

θ = 150°

r = 11 km

Substitute

Area = 150/360 * π * 11²

Area = 158.38863 ≈ 158.4 km² (nearest tenth)

Someone please help me with this math problem

Answers

Answer: 27,600

Step-by-step explanation:

Ok, there could be two answers to this question. If the question is asking how much he would make if it was .15% more, the total would be 27,600/a year

However, if it's asking .15% of 24,000, your answer would be 3,600 ( as in the extra he would be making)

To find the answer, you would have to multiply 24,000*.15 (your starting value times how much you would like to multiply it by)

elliaarteaga14
hey ik u dont know me,but i found u and i need a lot of help. Please and thank you If Mrs. Allan’s car uses 8 gallons of gas for a 224-mile trip, then, at that rate, how many gallons of gas would the car use for a 560-mile trip?

Answers

Answer:20 gallons

Step-by-step explanation:


A recipe calls for one egg to serve every four people. It also requires two tbsp of salt for every five eggs used. If you are cooking a
banquet for 300 people, how many tbsp of salt will you need?


a. 7.5 tsp
b. 30 tsp
c. 15 tsp
d. 60 tsp
I
No calculator is allowed on this question.

Answers

Answer:

30

Step-by-step explanation:

300/4=75

75/5=15

15*2=30

Place the indicated product in the proper location on the grid.

(2x - )2

Answers

Answer: it will be (4x-)

explanation: because the 2 that is outside the bracket will affect the 2 that is inside so it will be (4x-)

Answer:

Hope it helps u

Step-by-step explanation:

FOLLOW MY ACCOUNT PLS PLS

Photo for the question I asked a few seconds ago please help

Answers

Answer:

9160.88

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

Answer:

A≈9160.88

Step-by-step explanation:

A=πr^2=π·54^2≈9160.88418

Which is larger, a pound or a kilogram?

Answers

Answer:

Pounds

Step-by-step explanation:

1 kilogram= about 2.2 pounds

Answer:

kilgoram

Step-by-step explanation:

1 kg= 2.2lb

Evaluate the expression : (4 x 5)2 – 6 + 3 II
help I'm doing a test online​

Answers

Answer:

8x5−3

Step-by-step explanation:

(4 x 5)2 - 6 + 3 = 397 , I’m pretty sure

Find the radius of circle G below.

Answers

The answer is going to be A

If you can buy 48 plantains for $24, then how many can you buy with $4?​

Answers

Answer:

Step-by-step explanation:

I believe the answer is 8 plantains. For $12 you can buy 24 plantains, for $24 you can buy 48 plantains. Now we know that it is going to be times 2. This means you could get 8 plantains.      

Hope this helps!

(1 point) An open-top box is to be constructed from a 8 \ \mbox{in} by 14 \ \mbox{in} rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let x denote the length of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume, V, of the box as a function of x. \ \ V(x)

Answers

Answer:

Volume=[tex]4x^3-44x^2+112x[/tex]

Step-by-step explanation:

Let x denotes the length of the side of each cut

After Cutting square length will be=8-2x (where 2x for 2 squares as on each side two corners are there thus 2 squares will be cut down)

After cutting square width will be=14-2x (where 2x for 2 squares as on each side two corners are there thus 2 squares will be cut down)

Height = x

Volume=Length*width*Height

Volume=(8-2x)*(14-2x)*x

On solving we will get:

Volume=[tex]4x^3-44x^2+112x[/tex]

Can someone plz help me

Answers

Answer:

47.5 in²

Step-by-step explanation:

Answer:

47.5 in²

Step-by-step explanation:

A = a+b

/2h = 7+12

/2·5 = 47.5

The base of an ice cream cone has a radius of 4cm and the cones height is 12cm

Answers

Answer:

V=201.06

Step-by-step explanation:

V=πr2h

3=π·42·12

3≈201.06193

help please i need it asap

Answers

The correct answer would be 6

-6y+15= -27 what is y?

Answers

Answer:

y=7

Step-by-step explanation:

-6y= -27-15

-6y= -42

y=7

Answer:

‐6y= ‐27‐15

‐6y= ‐42

y= ‐42/‐6 minus minus sign will be cut

y=7

Need help with this question.

Answers

9514 1404 393

Answer:

  643.72 m²

Step-by-step explanation:

The area is the sum of the areas of the parts. The figure can be divided into a triangle and a semicircle.

The formula for the area of the triangle is ...

  A = 1/2bh

For the given base of 28 m and height of 24 m, the area is ...

  A = 1/2(28 m)(24 m) = 336 m²

__

The area of a semicircle is given by the formula ...

  A = (π/8)d² . . . . for diameter d

The given diameter is 28 m, so the area is about ...

  A = (3.14/8)(28 m)² = 307.72 m²

__

Then the total area of the figure is ...

   total area = triangle area + semicircle area

   total area = 336 m² +307.72 m² = 643.72 m²

Could I get some help with this question? Thanks

Answers

Answer:

I am unable to see the picture if you type it i can possibly help

Step-by-step explanation:

can someone help me ​ please

Answers

9514 1404 393

Answer:

  1. 5000

  2. the year is 2003

  3. > 1000; evaluate the function

Step-by-step explanation:

1. The value of t is "years since 2005." In 2005, the value of t is zero. To find the model's prediction for 2005, substitute t=0.

  p = 5000·2^0 = 5000·1

  p = 5000 . . . . in 2005

__

2. When t=-2, it means you're concerned with the population 2 years before 2005. That is, you are modeling the population in 2003.

__

3. Evaluate the function for t=-2:

  p = 5000·2^(-2) = 5000·1/4 = 1250

For t=-2, the fish population is 1250, which is more than 1000.


What is the area of the square? It has a side of 5 mm.

Please help i give brainliest

Answers

Answer:
25



Exp: bh so 5x5

giving out brainliest answer !!!!! help me out ASAP !!!

Answers

Answer:

0.7880

Step-by-step explanation:

0.7883

Hope it helps!

please help me ASAP!!!​

Answers

Answer: 8

Because 8 - 11 = -3

Hope it helps.

Answer:

add a positive 8

Step-by-step explanation:

if you add a positive 8 so you will minus by 8 and you get -3 cause negative -11 is bigger then positive +8

Find all solutions to 2sin(θ)=√3 on the interval 0≤θ<2π

Answers

Answer:

2sin(3θ) - √3 = 0

Step-by-step explanation:

 sin(3θ) = √3/2

 

3θ = π/3 + 2kπ or 2π/3 + 2kπ, k = 0, ±1, ±2, ±3,...

 

θ = π/9 + 2kπ/3, 2π/9 + 2kπ/3

 

If k = 0, we get θ = π/9, 2π/9

If k = 1, we get θ = 7π/9, 8π/9

If k = 2, we get θ = 13π/9, 14π/9

 

Other values of k give values of θ lying outside of the interval [0, 2π).

We want to find all the solutions of 2sin(θ) = √3 on the interval 0 ≤ θ ≤ 2π. The only solution is θ = 1.05

So we want to solve the equation: 2sin(θ) = √3

First, we divide both sides by 2 to get:

sin(θ) = (√3)/2

Now remember the inverse sine function, it acts as follows:

Asin(sin(x)) = xsin(Asin(x)) = x

So we can apply this to both sides to get:

Asin(sin(θ)) = Asin((√3)/2)θ = Asin((√3)/2) = 1.05

And because we know that the period of the sine function is 2π, we know that there is only one solution on the range between 0 and 2π, then the only solution in the interval is:

θ = 1.05

If you want to learn more, you can read:

https://brainly.com/question/12015707

How to find the smallest integer k such that 60k is a perfect square

Answers

9514 1404 393

Answer:

  k = 15

Step-by-step explanation:

Look for the missing factors that make all of the factors of 60k be squares.

  60 = 2² × 3 × 5

The factors 3 and 5 each have an odd exponent (1), so those two factors must be part of k.

  60k = 2² × 3 × 5 × k

is a perfect square when ...

  3 × 5 = k = 15

For k = 15, 60k = 900 = 30²

THIS IS DUE NOW wiil give crown if right Winston bought an encyclopedia priced at $42. Shipping and handling cost anadditional 30% of the price. What was the total cost of the encyclopedia, in cluding shipping and handling?

Answers

Answer:$52.60

Step-by-step explanation: You have a initial cost of $42 and you have to add 30 %. When you add the 30 % you get 12.60 more dollars added to the amount. This will then give you an answer of $52.16.

hi can anyone help me with this

Answers

Answer:

i think you should multiply 6cm by 8 cm by 10 cm ..sorry if it was not vlear but i try:)

State of the given functions are inverses

Answers

Answer:

1) They are not inverses

2) They are inverses

Step-by-step explanation:

We need to find the composition function between these functions to verify if these functions are inverses. If f[g(x)] and g[f(x)] are equal to x they are inverses.

1)

Let's find f[g(x)] and simplify.

[tex]f[g(x)]=\frac{1}{2}g(x)+\frac{3}{2}[/tex]

[tex]f[g(x)]=\frac{1}{2}(4-\frac{3}{2}x)+\frac{3}{2}[/tex]    

[tex]f[g(x)]=\frac{7}{2}-\frac{3}{4}x[/tex]

As f[g(x)] is not equal to x, these functions are not inverses.

2)

Let's find f[g(x)] and simplify.

[tex]f[g(n)]=\frac{-16+(4n+16)}{4}[/tex]

[tex]f[g(n)]=\frac{-16+4n+16}{4}[/tex]

[tex]f[g(n)]=\frac{4n}{4}[/tex]

[tex]f[g(n)]=n[/tex]

Now, we need to find the other composition function g[f(x)]

Let's find g[f(x)] and simplify.

[tex]g[f(x)]=4(\frac{-16+n}{4})+16[/tex]

[tex]g[f(x)]=-16+n+16[/tex]

[tex]g[f(x)]=n[/tex]

Therefore, as f[g(n)] = g[f(n)] = n, both functions are inverses.

I hope it helps you!  

Other Questions
In 1987, a survey of 1000 young people found that 540 said they smoked cigarettes, whilst460 said they did not. In 2017, a similar survey of another 1000 young people found that125 said they smoked cigarettes, whilst 875 said they did not.Calculate the ratio of smokers to non-smokers in 2017. Give your answer in simplest form:Show your workings.[2 marks] ______ is the movement of sediment from one place to another What is the basic economic problem that happens because people have unlimited wants but resources are limited? *A opportunity cost B sunk cost C needsD scarcity Pilar and Ramesh left a 20% tip after having dinner. The amount of the tip was $5. Pilar's dinner cost $15. Which equation can you use to find x, the cost of Ramesh's dinner? PLZ HELPPP.3+28/z +4s use z=7 and s=5 The equation of the line shown in the graph is y = ?. 1.Why do you think Mrs. Mallard married Brently? Do you think Mrs. Mallard loves herhusband? People leaving a movie theater were randomly sampled and asked their age. Which stem-and-leaf plotcorrectly displays the data for this sample?13, 17, 27, 34, 36, 58, 64, 66, 87, 91 The first five terms in a pattern are shown below. -0.5, -0.25, 0 , 0.25, 0.5, . . . Which equation represents the pattern? Finn has $60 in a savings account. The interest rate is 10% per year and is not compounded. How much interest will he earn in 1 year?Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. Help please :( CROWN ??? Ana: Felipe, quieres ____________ el men?Felipe: Aqu est, sobre la _____________ .Ana: Bueno, qu vamos a comer ___________? .Luisa: Parece que tienen muchos ______________ .Ana: No como __________ . Voy a pedir el ____________ y una _________ de tomate.Felipe: Yo s como carne. Voy a pedir un ____________ con patatas.Luisa: Y yo voy a pedir el pollo y una verdura s, el ____________ .Felipe: Y de _________, pastel de chocolate para los tres!Word Bank:pescadomesacarnepedirplatos principalespostrebrocolibistec ensalada What is the volume of a square pyramid with a base area of 36 and a height of 9 cm?o 36 cmo 108 cmo 18 cmo 324 cm Read this excerpt from "Casey at the Bat" by Ernest Lawrence Thayer. What is the style of this poem? It looked extremely rocky for the Mudville nine that day: The score stood four to six with just an inning left to play; And so, when Cooney died at first, and Burrows did the same, A pallor wreathed the features of the patrons of the game. A. narrative B. limerick C. sonnet D. lyrical What happens to energy when it is consumed? Australia is ranked #25 out of 121 countries in cost of livingTrueFalse Mr. Carson drove his car to visit his brother in Upstate New York. He traveled at a rate of 56 miles per hour for 3.5 hours. Use the formula d = rt to determine how far did Mr. Carson drive his car? Cules son algunos obstculos que necesitas enfrentar para tener un mejor rendimiento acadmico? I need help with this. There are enzymes in the small intestine explain why these are needed