Find the missing side lengths of the special right triangle. Leave your answers as radicals in simplest form.

Find The Missing Side Lengths Of The Special Right Triangle. Leave Your Answers As Radicals In Simplest

Answers

Answer 1

We have been a right triangle. We are asked to find the missing length of the given triangle.

We can see that our given triangle is 30-60-90 triangle.

We know that the lengths of the sides of a 30-60-90 triangle are in the ratio [tex]1:\sqrt{3}:2[/tex].

If the side opposite to 30 degree is [tex]n[/tex], then the side opposite to 60 degree angle will be [tex]\sqrt{3}n[/tex] and side opposite to hypotenuse will be [tex]2n[/tex].

We can see that side corresponding to hypotenuse is 6 that is [tex]2n=6[/tex].

Let us solve for n.

[tex]\frac{2n}{2}=\frac{6}{2}[/tex]

[tex]n=3[/tex]

The side corresponding to 30 degree angle will be half of 6 that is 3. Therefore, the value of y is 3.

The value of x will be [tex]3\sqrt{3}[/tex] as it is side corresponding to 60 degree angle.


Related Questions

The Vega family must pay $1776 each year in property taxes for their home they pay the tax and equal monthly payments your house payment is $948 a month before the text what is your house payment each month with the tax

Answers

Answer:

$1,096.00 per month        

Step-by-step explanation:

Divide 1776 by 12 for one payment per month equals 148.

Add the monthly house payment $948 to the monthly tax payment $148. The total monthly payment due is $1,096.00.

An internet company Randomly selected 50 of his customers and ask them how many hours per week to use the Internet of those surveyed 28 use the Internet more than 15 hours per week based on the data if the company has 800 subscribers how many use more than 15 hours per week

Answers

Answer:

448 subscribers use more than 15 hours per week

Step-by-step explanation:

In this question, we shall be using the proportion of what was gotten from a survey to estimate the number of subscribers that use more than 15 hours per week

From the question, we can see that out of the 50 people surveyed, 28 use more than 15-hours per week based on data

The proportion that thus use 15-hours per week based on data is 28/50

Now to know the number of subscribers out of 800 that use more than 15-hours per week based on data we have ; 28/50 * 800 = 28 * 16 = 448 subscribers

Randall buys 3 tickets for a concert for 14.50 each. He gives the cashier a $50 bill. How much change does he get?​

Answers

The answer will be $6.50
The answer will be $6.50 because 3 tickets are 14.50

5g - 10 = -25
please help!​

Answers

Answer:

g = -3

Step-by-step explanation:

5g - 10 = -25

5g = -25 + 10

5g = -15

g = -15/5

g = -3

hope it helps!

Answer:

g = - 3

Step-by-step explanation:

5g - 10 = - 25

5g = - 25 + 10

5g = - 15

g = - 15 : 5

g = - 3

A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?

Answers

Answer:

Step-by-step explanation:

Given that,

The company makes 4 different sweat shirts

Each year they make 60,000 of each kind.

So, if they will make 60,000 sweat shirt for each brand and the company design 4 different brand.

So, number of brand is 4

n = 4.

Then,

1 brand = 60,000

Therefore, 4 brand = 60,000 × 4

4brand = 240,000 sweat shirts.

So, in a year the company will make 240,000 sweat shirts.

The company makes a total of 240,000 sweatshirts each year by producing 60,000 of each of the 4 different kinds.

The question asks for the total number of sweatshirts produced by a company each year if it makes 60,000 of each kind and there are 4 different kinds of sweatshirts.

Identify the number of different kinds of sweatshirts: 4.Determine the number of each kind of sweatshirt made annually: 60,000.Multiply the number of kinds by the number of each kind: 4 x 60,000 = 240,000.

Therefore, the company makes a total of 240,000 sweatshirts each year.

A circle of a certain radius has an area which is numerically 5 times the value of the circumference. What is the radius of the circle?

Answers

We have been given that a circle of a certain radius has an area which is numerically 5 times the value of the circumference. We are asked to find the radius of the circle.

We know that area of circle with a radius of r units is [tex]\pi r^2[/tex].

We know that circumference of a circle is [tex]2\pi r[/tex].

5 times the value of circumference would be [tex]5(2\pi r)=10\pi r[/tex].

Now we will equate 5 times circumference with area as:

[tex]\pi r^2 = 10\pi r[/tex]

Let us solve for r.

[tex]\pi r\cdot r = 10\pi r[/tex]

[tex]\frac{\pi r\cdot r}{\pi r}=\frac{10\pi r}{\pi r}[/tex]

[tex]r=10[/tex]

Therefore, the radius of the circle would be 10 units.

What are all the simplified form of the equation 3(4x - 2) = 9 + 2x + 5

Answers

Step-by-step explanation:

Step 1:  Distribute

[tex]3(4x - 2) = 9 + 2x + 5[/tex]

[tex](3 * 4x) + (3 * -2) = 14 + 2x[/tex]

[tex]12x - 6 = 14 + 2x[/tex]

Step 2:  Add 6 to both sides

[tex]12x - 6 + 6 = 14 + 6 + 2x[/tex]

[tex]12x = 20 + 2x[/tex]

Step 3:  Subtract 2x from both sides

[tex]12x - 2x = 20 + 2x - 2x[/tex]

[tex]10x = 20[/tex]

Step 4:  Divide both sides by 10

[tex]10x / 10 = 20 / 10[/tex]

[tex]x = 2[/tex]

Answer:  [tex]x = 2[/tex]

Highest common factor of 32,48 and 72

Answers

Answer:

the hcf of 32 48 and 72 is 8

Step-by-step explanation:

We have ,

32 = 2×2×2×2×2 = 2^{5}

48 = 2×2×2×2×3 = 2⁴×3¹

72 = 2×2×2×3×3 = 2³×3²

Now,

HCF(32,48,72) = 2³ = 8

/* Product of the smallest power of each common prime factors of the numbers */

The highest common factor of 3248 and 72 is 8.

What are LCM and HCF?

The LCM of two or more numbers is the least common multiple of them.

The HCF of two or than two given numbers are the highest number that divides them completely.

Given, Are two numbers 3248 and 72.

Let us see is 3248 is completely divisible by 72, it is not.

Now, Check if 3248 is completely divisible by 36, it is not.

Other factors of 72 are 18, and 18 also does not divide 3248.

8 divides 328 complete so the HCF of 3248 and 72 is 8.

learn more about HCF here :

https://brainly.com/question/29114178

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(e) The number of bees spotted in Amelie's garden can also be modeled by the function B(x) = 50√ k + 2x where x is the daily high temperature, in degrees Fahrenheit, and k is a positive constant. When the number of bees spotted is 100, the daily high temperature is increasing at a rate of 2 ◦F per day. According to this model, how quickly is the number of bees changing with respect to time when 100 bees are spotted?

Answers

Answer:

[tex]\frac{dB}{dt}=4[/tex]

Step-by-step explanation:

Derivative indicates rate of change of dependent variable with respect to independent variables. It indicates the slope of a line that is tangent to the curve at the specific point.

Given:

Number of bees is modeled by the function [tex]B(x)=50\sqrt{k}+2x[/tex]

The daily high temperature is increasing at a rate of 2 °F per day when  the number of bees spotted is 100.

To find:

rate of change of number of bees when 100 bees are spotted

Solution:

[tex]B(x)=50\sqrt{k}+2x[/tex]

Differentiate with respect to t,

[tex]\frac{dB}{dt}=0+2(\frac{dx}{dt}) \\\frac{dB}{dt}=2(\frac{dx}{dt}) \\[/tex]

Put [tex](\frac{dx}{dt}) =2[/tex]

[tex]\frac{dB}{dt}=2(2)=4[/tex]

At x = 100, [tex]\frac{dB}{dt}=4[/tex]

On his last three tests, Mark scored 85, 95, 80. What grade must he get on his next test to have an average of 90 for all four tests

Answers

Answer: 100

Step-by-step explanation:

85+95+80=260 divided by 3 is 86.6 repeating and getting 100 on his next test would add up to 360 and 360/4 is 90

Please help me now plz
I will mark you brainliest

Answers

Answer:

theta = 24.4 degrees

Step-by-step explanation:

This is a right triangle.

sin theta = opp/ hyp

sin theta = 33/80

Take the inverse of each side

sin^-1 sin(theta) = sin^-1 (33/80)

theta =24.36197794

To the nearest tenth

theta = 24.4 degrees

PLEASE HELP WITH THIS QUESTION!!

Answers

Answer:

y = 2 * 3^x

Step-by-step explanation:

y = a b^x

a is the initial value ( when x = 0)

The initial value is 2

y = 2 b^x

Pick a value  (1,6) and substitute it in

6 = 2 * b^1

6 = 2 * b

Divide by 2

6/2 = 2/2 b

3 =b

y = 2 * 3^x

In a new lottery game, contestants pick 5 numbers (1-9 inclusive) and must guess exactly 3 correct in order to win. What’s the probability of winning this lottery?

Answers

Answer: 0.6%

Step-by-step explanation:

We have a selection of 5 numbers, in those selection we have 3 combinations of 3 consecuitve numbers (because the numbers must be in correct order).

The first 3

The 3 in the middle

the last 3.

So a contestant has 3 combinations were he wins.

Now, the number of possible combinations of the 9 numbers given is:

For the first number we have 9 options.

For the second number we have 8 options (because we already selected one)

For the last number we have 7 options (because we already selected 2 numbers)

Then the number of possible combinations is

10*9*8 = 504

The probabilty of winning will be equal to the number of combinations that the contestant has (3) divided by the total number of combinations, this is:

p = 3/504 = 0.006 or 0.006*100% = 0.6%

7.142857142857143‬ to the next whole number

Answers

Answer:

the answer is 7

Step-by-step explanation:

PLEASE HELP!! 25 POINTS!!!


Agnes and Jamie left the apartment at the
same time traveling in the same direction
(along the same road). Agnes is traveling
at 54 mph and Jamie at 60 mph. How
many hours will it be before Jamie is 12
miles ahead of Agnes?

Answers

Answer:

2 Hours

Step-by-step explanation:

If Jamie is going 6 miles per hour faster than Agnes, then in 2 hour Jamie should be 12 miles ahead of Agnes

Suppose you have the same box with a volume of 400 in^3. And a height of 5 in. You now also know that the box is 8 in. Wide. What is the length of the box?

Answers

Answer:

Step-by-step explanation:

Volume of the box = 400 cubic inches

length * width * height = 400

length * 8 * 5 = 400

length * 40 = 400

length = 400/40

length = 10 inches

Answer:

Step-by-step explanatio

it is C

Find the whole.
25​% of what number is 70​?

Answers

Answer:280

Step-by-step explanation:

25% of x = 70

x= 280

The answer should be 280

Elena bought a backpacking tent to take with her on hiking trips.
She needs to buy a rain proof tarp for the tent that will cover all 4 sides, as well as protect the ground underneath. Which size tarp should she purchase? *
1 point
a) X-Small: 16 ft²
b) Small: 34 ft²
c) Medium: 88 ft²
d) Large: 104 ft²
e) X-Large: 144 ft²

If the tarp that she buys does not work and the tent fills up completely with water, how much water would it take to fill the tent, if the tent is 8.75 ft tall? *
1 point
a) 140 ft³
b) 144 ft³
c) 48 ft³
d) 46.7 ft³
e) 36 ft³

Answers

Answer:

Question 1 = c) Medium: 88 ft²

Question 2 = d) 46.7 ft³

Step-by-step explanation:

Question 1

We would be solving this question by finding the surface area of the tent. The shape of the tent is a square based pyramid.

The surface area of a square based pyramid(tent) =

a² + 2ah

Where in the diagram,

a = base length = 4 ft

h = height of the pyramid (tent ) = 9ft

Surface area = 4² + 2 × 4 × 9

= 16 + 72

= 88ft²

Therefore, the size tarp should she purchase is Medium: 88 ft²

Question 2

For question 2, from the attached diagram, we can see that the diagram is a square based pyramid.

To calculate the amount of water that would fill the square based pyramid, we would have to find the Volume of the tent(square based pyramid).

The formula for the Volume of the tent(square based pyramid) = 1/3(a²h)

Where a = base edge

h = height of the pyramid.

From the diagram,

a = base edge => 4ft.

From the question,

h = height of the tent is given as how tall the tent is = 8.75ft.

Therefore, 1/3(a²h)

1/3 × (4ft)²× 8.75ft

= 46.67ft³

Approximately = 46.7ft³

Therefore, the amount of water it would it take to fill the tent, if the tent is 8.75 ft tall is 46.7ft³

What’s the distance between 120 and -50 on a number line ?

Answers

Answer:

170

Step-by-step explanation:

The distance between 120 and -50 on a number line is equal to 170.

What is a number line?

In Mathematics and Euclidean Geometry, a number line is a type of graph that is composed of a graduated straight line, which typically comprises both negative and positive numerical values that are located at equal intervals along its length.

This ultimately implies that, every number line would primarily increase in numerical value towards the right from zero (0) and decrease in numerical value towards the left from zero (0).

Based on the information provided above, we would determine the distance between the two numerical values 120 and -50 by using the number line as follows:

x = 120 - (-50)

x = 120 + 50

x = 170.

Read more on number line here: brainly.com/question/22515080

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Line d has a slope of –7 4 . Line e is perpendicular to d . What is the slope of line e ? Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Final answer:

The slope of line e, which is perpendicular to line d with a slope of -7/4, is 4/7.

Explanation:

The slope of line d is -7/4. To find the slope of a line perpendicular to d, we use the property that the product of the slopes of two perpendicular lines is -1. So, the slope of line e is the negative reciprocal of -7/4.

To find the negative reciprocal, we find the reciprocal by flipping the fraction and then negate it by changing the sign. Therefore, the slope of line e is 4/7.

Ella bought 11/12 of a pound of green grapes and 3/4 of a pound of red grapes. How much more did the green grapes weigh than the red grapes?

Answers

Answer:

1/6

Step-by-step explanation:

11/12-3/4

=11/12-9/12

=2/12

=1/6

Answer:

2/12 or 1/6

Step-by-step explanation:

11/12-3/4

First convert the 3/4 to 9/12 becase the numbers have to have the same denominater.

3/4=9/12

11/12-9/12=2/12

Simplified would be 1/6

Which expressions are equivalent to -56z + 28.
A. 1/2 *(-28z + 14
B. (-1.4z+0.7) *40
C. (14 -7z) *(-4)
D.(8z - 4) (-7)
E. -2(-28z-14)

There are 2 right answers. Plz help!

Answers

The expressions that are equivalent to -56z + 28 are B. (-1.4z+0.7) * 40 and D.(8z - 4) * (-7), as they both simplify the given expression.

You are looking to find expressions that are equivalent to -56z + 28. Let's simplify each of the given options:

A. 1/2 *(-28z + 14) simplifies to -14z + 7, so this is not equivalent to -56z + 28.

B. (-1.4z+0.7) * 40 simplifies to -56z + 28, which is equivalent.

C. (14 -7z) *(-4) simplifies to -56z + 56, which is not equivalent to -56z + 28.

D.(8z - 4) * (-7) simplifies to -56z + 28, which is equivalent.

E. -2(-28z-14) simplifies to 56z + 28, which is not equivalent since the terms have opposite signs.

The equivalent expressions to -56z + 28 are options B and D.

since 2010 the town of fall river has been experiencing a growth in population according to the model what will the population of fall river be in 2020

Answers

Answer:

the population of fall river will be 48558

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Since 2010, the town of Fall River has been experiencing a growth in population. The relationship between the elapsed time, t, in years, since 2010 and the town's population, P(t left parenthesis, t, right parenthesis, is modeled by the following function. P(t)=36,800⋅[tex]2^{\frac{t}{25} }[/tex] According to the model, what will the population of Fall River be in 2020? Round your answer, if necessary, to the nearest whole number.

My answer:

Given the exponential function:

P(t)=36,800⋅[tex]2^{\frac{t}{25} }[/tex]  where:

t in years, since 2010 the town's population, P(t)

As we know, from 2010 to 2010 are 10 years

Hence, to find the population of fall river be in 2020, we substitute t =10 into the given function:

[tex]P(10)=36800\cdot2^{^\dfrac{10}{25}}}\\=48557.9\\\approx 48558[/tex]

So in 2020, the population of fall river will be 48558

Hope it will find you well.

Answer:

By 2020 the population of Fall River will be 48558

Step-by-step explanation:

Here, we note that the equation for the model is p(t) = 36,800×2^(t/25)

That is the format;

[tex]p(t) = 36,800 \times 2^{\frac{t}{25}[/tex]

Where:

t = Number of years since 2010

Therefore, the population of the town in 2020 can be found by first finding the number of years between 220 and 2010 and plugging the value into the equation as follows;

Number of years, t = 2020 - 2010 = 10 years

Hence;

[tex]p(t) = 36,800 \times 2^{\frac{10}{25}} = 48557.89 \approx 48558[/tex]

Therefore, according to the model, by 2020 the population of Fall River will be 48558.

A car is traveling at 65 miles per hour. What happens to the number of miles when the number of hours changes?
VX
O When the number of hours increases, the number of miles decreases.
O When the number of hours increases, the number of miles increases.
O When the number of hours decreases, the number of miles increases
O When the number of hours decreases, the number of miles stays the same.
Mark this and return
Save and Exit
Next
Submit

Answers

Answer: The answer is the second one Letter B.

when the number of hours increases, the number of miles increases

Hope this help You Yo.

Find the circumference of a circle with radius, r = 19.5m.
Give your answer in terms of pie

Answers

Answer:

39π cm

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = 2πr ( r is the radius )

Here r = 19.5, thus

C = 2π × 19.5 = 39π cm

PLEASEEEEEEEEE HELP 15 POINTS

Answers

Answer:

If I remember correctly,

P x 9 = $60.75 and 6 x(times) $1.25=c

Step-by-step explanation:

First problem:

Since the total price of all 9 sandwiches is $60.75, that means that the price of one sandwich nine times will equal the total price.

Second problem:

Rather than giving you the total price, it gives you the price of one drink, so to find the total price you would need to multiply the price of one drink by the number of drinks to get the total (the total being c in this case)

what is the factorization of x2 + 2x − 63

Answers

Answer:

(x+9) (x-7)

Step-by-step explanation:

x^2 + 2x − 63

What 2 numbers multiply to -63 and add to 2

9* -7 = -63

9+-7 = 2

(x+9) (x-7)

if a bicycle wheel has a diameter of 21 inches what the exact circumference?

Answers

Answer:

Circumference = 65.97344573

Step-by-step explanation:

Given the diameter of a circle, we can use the formula C = πd to find the circumference.

C = circumference

π = pi

d = diamater

Equation: 21(π) = 65.97344573

Make sure to round to whatever decimal place is asked for!

need help
What is the volume of this rectangular prism?
What is the volume of this rectangular prism?

A rectangular prism with a length of 6 and one-fourth foot, width of 14 feet, and height of 3 feet.
A:87 and one-half feet cubed
B:131 and one-fourth feet cubed
C:252 feet cubed
D:262 and one-half feet cubed

Answers

Answer:

252 feet cubed

hope this helps!

Step-by-step explanation:

answer : 252 feet





explaination : i just did this and got it right

ahhhhhhhhhh to lazy :(​

Answers

Answer:

28

Step-by-step explanation:

10 - 12^2 ÷(-2)^3

PEMDAS

Exponents first

10-144÷(-8)

Then multiplication and division

10- (-18)

Then add and subtract

10+18

28

Answer:

why don't you answer mine

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