In a 30°-60°-90° triangle, what is the length of the longer leg when the length of the hypotenuse is 18 inches?
9✓2 in.
9✓3in.
18✓2 in.
18✓3in.​

Answers

Answer 1

Answer:

9sqrt(3) in.

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is:

short leg : long leg : hypotenuse

      1        :   sqrt(3)  :          2

If the short leg measures 1, then the hypotenuse measures 2.

The length of the hypotenuse is twice the length of the short leg.

The length of the long leg is sqrt(3) times the length of the short leg.

If the hypotenuse measures 18 in., then the short leg measures 9 in.

Then the long leg measures 9sqrt(3) in.

Answer 2

The length of the longer leg is 9√3 inches.

What is a Ratio?

A ratio indicates the number of times one number contains another.

Given that, the length of the hypotenuse is 18 inches.

The ratio of the lengths of the sides of a 30°-60°-90° triangle is:

Short leg: long leg: hypotenuse = 1 : √3 : 2

Since the hypotenuse is 18 inches, it follows that the value of 2 is 18:

2 = 18

1= 9

√3 = 9√3

Hence, the length of the longer leg is 9√3 inches.

To learn more about ratios, click here:

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Related Questions

Please help math experts need your help 15 points !

For number 2 the Awnser choices are

3
-3
5
-5

Answers

Answer:

12 = -3 - 3x

Step-by-step explanation:

Same concept as the last question I answered. First, let's derive a formula from the given model. So we have 3 negative x and 3 negative 1 which equal to 12 positive ones, this can be written as:

-3x - 3 = 12

which can be rewritten as

12 = -3 - 3x

Which is an equivalent equation solved for the slope, m? m = yx + b m = m equals StartFraction y minus b Over x EndFraction. m = m equals StartFraction y Over x EndFraction minus b. – b m = y – m equals y minus StartFraction b Over x EndFraction.

Answers

Answer:

m equals StartFraction y minus b Over x EndFraction

Step-by-step explanation:

The standard equation of a line is expressed as;

y = MX+b where;

m is the slope

cmb is the intercept

We are to get the equivalent expression for finding the slope.

Make m the subject of the formula to get this as shown;

From the equation;

y =MX+b

Subtract c from both sides;

y-b = MX+b-b

MX = y-b

Divide through by x;

mx/x = (y-b)/x

m = (y-b)/x

Heme the required expression is m = (y-b)/x OR m equals StartFraction y minus b Over x EndFraction

Answer:

Answer B. ( I hope)

Step-by-step explanation:

You made 15 t-shirts for beta club. A t-shirt box will hold 5 t-shirts. How many boxes do you need for all the shirts? 10 points A) 5 B) 15 C) 20 D) 3

Answers

Answer:

D) 3

Step-by-step explanation:

15 divided by 5 equals 3.. brainliest plz

If there’s 15 shirts and a box holds 5, there’s 3 boxes. 15:5=3. So the answer is D.

I need help again please

Answers

Answer:

6. Would be Sports City

Step-by-step explanation:

Take 180*.15= 27

Subtract 27 from 180 and you get 153.

200*.20=40

Subtract 40 from 200 and you get 160.

For 5 just multiply the discounted price by 2.

I hope I answered your question.

Please help! I’ll give brainliest!

Answers

Answer:

27 degrees withI think angle sum postulate

Step-by-step explanation:

Answer:

27 degrees The postulates used are FGT and FGH

Step-by-step explanation:

FGH is 180 degrees. FGT is 153 degrees. So 180-153 is 27. plz make due on yuor brainliest promise thank you

Jamal hiked on two trails. The first trail was 8 1 3 miles long, and the second trail was 1 3 5 times as long as the first trail. How many miles did Jamal hike? Enter your answer as a mixed number in simplest form.

Answers

Answer:Total distance( miles ) covered by Jamal =21 2/3 miles

Step-by-step explanation:

Step 1

first trail = 8 1/3 miles long

2nd trail = 1 3/5 times as long as the first

Therefore the  distance walked in the  2nd trail is  1 3/5  x 8 1/3

changing to improper fraction and solving  

=8/5 x 25/3= 40/3

The distance hiked by Jamal in the second trail = 40/3=13 1/3

Step 2

Total distance( miles ) covered by Jamal = first trail +2nd trail

= 8 1/3 + 13 1/3 =21 2/3 miles

Answer:

21 2/3 miles

Step-by-step explanation:

First trail = 8 1/3 miles long

Second trail = 1 3/5 times as long as the first trail

= 1 3/5 × 8 1/3

= 8/5 × 25/3

= 40 / 3

= 13 1/3 miles

How many miles did Jamal hike?

Total miles hiked = First trail + Second trail

= 8 1/3 miles + 13 1/3 miles

= 25/3 + 40/3

= 25+40/3

= 65/3

= 21 2/3 miles

Jamal hiked 21 2/3 miles

Aimee is in charge of buying tickets for a trip to the movies. She can buy tickets at the theater or online. At the theater, 8 tickets cost $60. Online, 6 tickets cost $51. Aimee needs to buy 24 tickets. How much money can Aimee save by buying tickets at the lower price? Show your work

Answers

Answer:

Aimee can save $24 by buying tickets at the lower price that is at the theater.

Step-by-step explanation:

First, you need to find the amount she would spent by buying tickets at the theater and online by using a rule of three:

Theater:

60→8

x  ←24

x=(60*24)/8=180

Online:

51→6

x ←24

x=(51*24)/6=204

Now, you need to calculate the difference:

$204-$180=$24

According to this, the answer is that Aimee can save $24 by buying tickets at the lower price that is at the theater.

Answer:

Aimee can save $24 by buying tickets at the lower price that is at the theater.

a triangle has side lengths of 14, 23, and 27. Is it a right angle ?

Answers

Answer:

No, it is not

Step-by-step explanation:

Here, we want to check if the lenghts given is that of a right angle triangle

For a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the two other sides

The hypotenuse represents the longest side

So 27^2 = 14^2 + 23^2

The difference between these is 4, and as such the triangle is not a right angled

The solutions to the equation f(x) = g(x) are -2 and 1. Iff and g are graphed on the same coordinate plane, which statement must be true?
The functions will intersect at x = -2 and x = 1.
The functions will intersect at y = -2 and y = 1.
Both functions will have y-intercepts at 2 and 1.
Both functions will have x-intercepts at -2 and 1.

Answers

Answer:

The correct option is;

The function will intersect at x = -2 and x = 1

Step-by-step explanation:

The question parameters are

The functions in the question are f(x) and g(x)

The solution to the equation f(x) = g(x) are -2, and 1

Given that the equations, f(x) and g(x), are both given in values of x, their solution will be the x values that satisfies both functions

Therefore, the functions will intersect (have the same values of f(x) and g(x)) at the points of the solutions, which are given as x = -2, and x = 1

The statement that should be true is the function will intersect at x = -2 and x = 1.

Given that,

The solutions to the equation f(x) = g(x) are -2 and 1. If f and g are graphed on the same coordinate plane.

Based on the above information, the following information should be considered:

As the solutions represent x values that satisfied the both functions. Also, the functions should intersect that contains the same value i.e. x = -2 and x = 1.

Therefore, we can conclude that the first option is correct.

Learn more: brainly.com/question/24169758

 

!!!Help!!!
Including scholarships and financial aid, Madeline has $41,000 to spend on college. If the total cost of her college education is __________, she will have enough resources to pay.
A.$44,000
B.$47,000
C.$50,000
D.$38,000

Answers

Answer:

D

Step-by-step explanation:

The answer is D. That’s the only answer where she will have remaining money.

Just want a friend
Hi

Answers

Answer:

Meeeeeeee, I want to be your FRIEND!!! I don't have any.

I love friends and it's always nice to have someone that has your back at all times. It's also nice to have someone who shares the greatest moments with you and someone who truly cares for you. I can be your friend if you want to, but you don't have to accept me as a friend if you don't want to, but either way please don't judge this message. I didn't do it because I like you, I did it to be a nice person. Hope you're having a wonderful afternoon and have fun. Enjoy the last day of your Thanksgiving Break!!! ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️

The domain, range, and intercepts of a function are shown. Which set of information could be characteristics of the function's inverse? domain: x ≥ -1 range: y ≥ -2 y-intercept: (0,-1) x-intercept: (1,0)

Answers

Just took the test so ik it's right

Domain: x is greater than or = to -2

Range: y is greater than or = to -1

Y-int: (0-1)

X-int: (-1,0)

Basically you just flip everything

Answer:look at explanation

Step-by-step explanation:

Harmon’s Jewelry Store receives a shipment of 500 jewelry pieces, but 15 pieces are damaged. At this rate, if Mrs. Harmon places an order for 5,500 jewelry pieces, how many should she expect to be damaged?

Answers

Answer:

She should expect 165 jewelry pieces to be damaged.

Step-by-step explanation:

5,500/500 = 11

11 x 15 = 165

X-8=3x
A) -6
B)-5
C) -4
D)-3

Answers

Answer

The answer is C) -4





[tex] {x}^{4} - 6 {x}^{3} + 22 {x}^{2} - 48x + 40[/tex]
find the zeros​

Answers

Answer:

x = 2, 1 + 3i, 1 − 3i

Step-by-step explanation:

Find the Roots (Zeros)

x^4 − 6x^3 + 22x^2 − 48x + 40

Set x^4 − 6x^3 + 22x^2 − 48x + 40 equal to 0. x^4 − 6x^3 + 22x^2 − 48x + 40 = 0

Solve for x.

Factor the left side of the equation.

Factor x^4 − 6x^3 + 22x^2 − 48x + 40 using the rational roots test.

(x − 2) (x^3 − 4x^2 + 14x − 20) = 0

 Factor x^3 − 4x^2 + 14x − 20 using the rational roots test.

(x − 2) (x − 2) (x2 − 2x + 10) = 0

 Combine like factors.

(x − 2)2 (x^2 − 2x + 10) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

(x − 2)^2 = 0

x^2 − 2x + 10 = 0

 Set (x − 2)^2 equal to 0 and solve for x.

Set (x − 2)^2 equal to 0.

 (x − 2)^2 = 0

Solve (x − 2)^2 = 0 for x.

x = 2

 Set x^2 − 2x + 10 equal to 0 and solve for x.

Set x^2 − 2x + 10 equal to 0. x^2 − 2x + 10 = 0

Solve x^2 − 2x + 10 = 0 for x.

Use the quadratic formula to find the solutions.

−b ± (√b^2 − 4 (ac) )/2a

Substitute the values a = 1, b = −2, and c = 10 into the quadratic formula and solve for x.

2 ± (√(−2)^2 − 4 ⋅ (1 ⋅ 10))/2 ⋅ 1

Simplify.

Simplify the numerator.

  x =    2 ± 6i/ 2.1

Multiply 2 by 1

 x =  2 ± 6i/2⋅1

 Simplify

  2 ± 6i/2  

   x = 1 ± 3i

The final answer is the combination of both solutions.

x = 1 + 3i, 1 − 3i

The final solution is all the values that make (x − 2)2 (x2 − 2x + 10) = 0 true.

x = 2, 1 + 3i, 1 − 3i

The area of a circle is 36n units squared.
What is the radius?

Answers

Answer:

3.385137501

OR it is 1.909859317

Step-by-step explanation:

for the first one:

36/pi which is 11.4591559, then you take the square root of 11.4591559 to get 3.385137501

For the second:

you take the square root of 36 which is 6, then you divide 6 by pi which gets you 1.909859317

BUT NOT 100% SURE THIS IS CORRECT!

HELP JUST LOOK AT PICTURE

Answers

It should be A and C

Helppppppppppppppppp

Answers

Answer:

same

Step-by-step explanation:

1. One number added to three times another number is 24. Five times the first num
three times the other number is 36. Find the numbers.

Answers

Answer:

Let x equal the one number.

Let y equal the other number.

x + 3y = 24

5x +3y = 36

Subtract the first equation from the second equation.

4x = 12

x = 3

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A 2-column table with 4 rows. Column 1 is labeled Gallons with entries 2, 4, b, 10. Column 2 is labeled miles with entries 56, a, 168, c.
Alexa is planning to drive across the United States in her car. She started making a table to represent the proportional relationship between gallons of gas and miles driven. The table shows how far she can travel for each gallon of gas that she uses.

What is the constant of proportionality?
miles per gallon

Answers

Gallons | Miles
2 | 56
4 | a
B | 168
10 | c

If he can go 56 miles with 2 gallons then he can travel 28 miles with 1 gallon.
4 • 28 = a = 112
168/28=b=6
10 • 28 = c = 280
The constant of proportionality of miles per gallon is 28
Can I get brainliest pls

Answer:

Gallons | Miles

2 | 56

4 | a

B | 168

10 | c

Step-by-step explanation:

A rocking horse has a weight limit of 60 pounds.

What percentage of the weight limit is 33 pounds?
What percentage of the weight limit is 114 pounds?
What weight is 95% of the limit?

Answers

Answer:

(I am not sure what the question means but according to what I understood I got these as my answers)

33 pounds = 55%

114 = 240 %

95% = 57 pounds


Solve each system of equations.
1. Solve:
X-y=1
2x + y = 8
Solution
* write your answer as an ordered pair (X,Y)

Answers

Answer: {x,y} = {10,-2}

Step-by-step explanation: {x,y} = {10,-2}

angle 9 and angle 10 are corresponding and complementary angles formed by two parallel lines cut by a transversal. Find the measure of angle 9.​

Answers

Answer:

45 Degrees

Step-by-step explanation:

9 and 10 are corresponding meaning that they will be the same. They are also complementary, so they equal 90 degrees when added. 90/2 is 45.

Which describes the correlation shown in the scatterplot?

A. There is a positive linear correlation.
B. There is a negative linear correlation.
C. There is no positive or negative correlation.
D. There is a nonlinear correlation.

Answers

Answer:

C.There is no positive or negative correlation.

Step-by-step explanation:

finished Unit Test and got it correct

Answer:

C. There is no positive or negative correlation.

Step-by-step explanation:

as you can see, it is straight up and down :))

Katherine has $140 in the bank and is saving $6 per week. Abbie has $462 in the bank, but spending at a rate of $10m per week. Which equation will determine when they will have the same amount of money in the bank?
A). 140+6x=462+10x
B). 140+6x=462-10x
C). 140+10x=462-6x
D). 140-6x=462+10x

Answers

140 + 6x = 462 - 10x

Hope I helped

Have a great day

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Answers

yes

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50 POINTS!!! WILL MARK BRAINLIEST!!!
solve numbers 16 and 18
show work please

Answers

Answer:

16) 102°18) 75°

Step-by-step explanation:

16)

∠QPR = 1/2(QR + SV)

26x - 2 = 1/2(131 + 18x + 1)26x - 2 = 66 + 9x26x - 9x = 66 + 217x = 68x = 68/17x = 4

∠QPR = 26*4 - 2 = 102°

18)

mBC = ?

∠BAC = 1/2(mBC + mFD)

8x + 6 = 1/2(8x + 11 + 9x - 7)8x + 6 = 1/2(17x + 4)16x + 12 = 17x + 417x - 16x = 12 - 4x = 8

mBC = 8*8 + 11 = 75°

Which statement describes a unit rate? * 5 points Mary paid $2.50 for 3 bottles of water. Ricardo paid $17.00 for 3 pumpkins. Katherine paid $1.25 for 1 bottle of water. Joshua paid $6.00 for 3 masks.

Answers

Answer:

Katherine paid $1.25 for 1 bottle of water.

Step-by-step explanation:

What is the unit rate?

In this context, a unit rate is defined as the amount in dollars paid for one unit of a commodity.

In the given options, all the items are above one except

option C( Katherine paid $1.25 for 1 bottle of water.)

hence all the other amount does not correspond to the unit rate

Mary paid $2.50 for 3 bottles of water. not a aunit rate

Ricardo paid $17.00 for 3 pumpkins.   not a unit rate

Katherine paid $1.25 for 1 bottle of water. a unit rate

Joshua paid $6.00 for 3 masks. not a unit rate

What is the slope of the line that passes through the points ( -9, -8 ) and ( -15, - 16 ) In simplest form please

Answers

Answer:

4/3

Step-by-step explanation:

The slope formula is y2-y1/x2-x1

take the y from one of the points and subtract the y from the other point, the divide that by the x of the first y you picked and subtract the x of the second y

(-16)-(-8)/(-15)-(-9)

-8/-6

simplify

4/3

the slope is 4/3

Teresa measures five eighths foot of ribbon for a costume. She needs seven pieces of ribbon with that same length. What is the total length of ribbon Teresa needs to make all the costumes?

Answers

Answer:

[tex]Total\ Length = \frac{35}{8}\ ft[/tex]

Step-by-step explanation:

Given

[tex]Length = \frac{5}{8}\ ft[/tex]

[tex]Number = 7[/tex]

Required

Determine the total length

Since, he ribbons are of the same lengths.

The total length is calculated as:

[tex]Total\ Length = Length * Number[/tex]

[tex]Total\ Length = \frac{5}{8}\ ft * 7[/tex]

[tex]Total\ Length = \frac{5 * 7}{8}\ ft[/tex]

[tex]Total\ Length = \frac{35}{8}\ ft[/tex]

c

Step-by-step explanation:

Teresa measures five eighths foot of ribbon for a costume. She needs seven pieces of ribbon with that same length. What is the total length of ribbon Teresa needs to make all the costumes? (2 points)

a

one and four eighths feet

b

two and three fifths feet

c

four and three eighths feet

d

five and two fifths feet

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