When a triangle is inscribed in a semicircle where a diameter of the circle is a side of the​ triangle, the triangle formed is always a right triangle. If an isosceles triangle​ (two equal​ sides) is inscribed in a semicircle with a radius of 9 ​inches, find the length of the two legs of the triangle.

Answers

Answer 1

Answer:

Step-by-step explanation:

diameter = 18 inches

each leg = 18/√2 = 9√2 ≅ 12.7 inches

Answer 2

The length of the two legs of the isosceles triangle is 9√2.

What is a triangle?

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

When a triangle is inscribed in a semicircle with one side being the diameter of the circle, a right triangle is always created.

Also, the radius of semicircle is 9 inches,

Since, the isosceles triangle inscribed in the semicircle.

Sides of an isosceles triangle are equal, therefore the corresponding angle will also equal.

The sum of all three angles of a triangle is 180°

x+x+90 = 180

2x = 90

x=45

radius of circle is 9 inches, therefore diameter of circle = 18 inches

Apply sin rule,

18/sin90 = x/sin45

18/1 = x/1/√2

x= 9√2

The length of the side of the isosceles triangle is 9√2.

To know more about Triangle on:

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When A Triangle Is Inscribed In A Semicircle Where A Diameter Of The Circle Is A Side Of The Triangle,

Related Questions

Which of these would be the opposite of a progressive tax?

Answers

c

A regressive tax is the opposite of a progressive tax because you pay a higher tax rate as your income decreases.

Answer:

b

Step-by-step explanation:

A salesman with an annual base salary of $35,000 gets a 5% commission on the first $600,000
in sales, a 7% commission on the next $300,000, and 8% on sales above $900,000. What would
be his total compensation for the year if he sold $1 million of product?

Answers

Answer:

11%

I think im sorry if im wrong

Step-by-step explanation:

Which of the following is an example of a conditional statement?

Answers

Answer:

The correct answer is A, If I practice football, then I will improve.

In 2003, 520,000 acres of farmland in a region were devoted to growing nuts. By 2012 ,the number of acres used to grow nuts had increased 820,000.Find the average rate of change in the number of acres in a region used to grow nuts from 2003 to 2012.

Answers

Answer:

Average rate of change = 33,333.33acre per year

Step-by-step explanation:

Given:

Farm land in 2003 = 520,000 acre

Farm land in 2012 = 820,000 acre

Find:

Average rate of change

Computation;

Number of year = 2012 - 2003

Number of year = 9 year

Average rate of change = [Farm land in 2012 - Farm land in 2003] / Number of year

Average rate of change = [820,000 - 520,000] / 9

Average rate of change = [300,000] / 9

Average rate of change = 33,333.33acre per year

Pleaseee helpppp!!! 20 points

Answers

Answer:

The correct option is (A).

Step-by-step explanation:

The given expression is :

[tex]\dfrac{14x^4y^6}{7x^8y^2}[/tex]

The numerator contains 14x⁴y⁶ and the denominator is 7x⁸y².

We can write it as :

[tex]\dfrac{14x^4y^6}{7x^8y^2}=\dfrac{7\times 2\times x^4\times y^2\times y^4}{7x^4\times x^4\times y^2}[/tex]

Canceling the common terms,

[tex]=\dfrac{2y^4}{x^4}[/tex]

So, the correct option is (A).

A spinner has an equal chance of landing on each of its six numbered regions. After spinning it, what are the chances it lands in region 2 or 4?​

Answers

Answer:

33 1/3% or 1/3

Step-by-step explanation:

Possible outcomes = 6

Favourable outcomes = 2

2/6 = 1/3 = 33 1/3%

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Find the probability of choosing a letter other than the letter E from a bag that contains the fifteen letters of the name DANIEL BERNOULLI. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answers

Answer:

The probability of getting a letter which is not E is 13/15.

Step-by-step explanation:

DANIEL BERNOULLI

The total number of elements in sample space = 15

The probability of getting letter E is

= 2/15

The probability of getting a letter which is not E is

[tex]1 - \frac{2}{15}\\\\\frac{13}{15}[/tex]

Luisa is planning a bridal shower for her best friend. At the party, she wants to serve 3 beverages, 3 appetizers, and 3 desserts, but she does not have time to cook. She can choose from 15 bottled drinks, 10 frozen appetizers, and 13 prepared desserts at the supermarket. How many different ways can Luisa pick the food and drinks to serve at the bridal shower

Answers

Answer:

Luisa can pick the food and drinks to serve at the bridal shower in 15,615,600 different ways.

Step-by-step explanation:

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

Also

The order in which the food and drinks are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Beverages:

3 from a set of 15. So

[tex]B = C_{15,3} = \frac{15!}{3!12!} = 455[/tex]

Appetizers:

3 from a set of 10. So

[tex]A = C_{10,3} = \frac{10!}{3!7!} = 120[/tex]

Desserts:

3 from a set of 13. So

[tex]D = C_{13,3} = \frac{13!}{3!10!} = 286[/tex]

How many different ways can Luisa pick the food and drinks to serve at the bridal shower?

By the fundamental counting principle, as beverages, appetizers and desserts are independent:

[tex]T = B*A*D = 455*120*286 = 15,615,600[/tex]

Luisa can pick the food and drinks to serve at the bridal shower in 15,615,600 different ways.

What is 17.445 - 6.76 rounded to the nearest tenth

Answers

Answer:

10.7

Step-by-step explanation:

17.445 - 6.76= 10.685

10.685 is 10.7 when rounded to the nearest tenth!

Use the zero product property to find the solutions to the equation x2 – x – 6 = 0.

Answers

Answer:

x=3 and x=-2 is the root of given eq

Answer:

Use the zero product property to find the solutions to the equation x2 – x – 6 = 0.?

x = –2 or x = 3 is the answer

Step-by-step explanation:

I can’t figure it out!! Please help!

Answers

I think the answer is 20

Solve for x.
4
15
6
X
x = [?]
Enter the number in decimal form

Answers

Answer:

66

Step-by-step explanation:

x / 6 + 4 = 15

To find x ;

Subtrac4 from both sides

x / 6 + 4 - 4 = 15 - 4

x / 6 = 11

Multiply both sides by 6

x / 6 * 6 = 11 * 6

x = 66

Value of x = 66

describe an experiment to determine convection currents in water​

Answers

Answer:

When you boil water heat transfer takes place and the heat gets transferred to the water from the stove ( could be considered conduction or radiation), and when the heat is transferred to the water the cold water sinks whereas the hot water rises this rapid movement of convection is called convection currents.

Hope I helped :)

the volume of a cone with a radius of 6 and slant height of 10

Answers

Answer:

21.161

Step-by-step explanation:

use Pythagoras theorem ti find your slant height

then you use your formula which

[tex]1 \3\pi {r }^{2} h[/tex]

What is the area of the triangle

Answers

Answer:

45.1 km^2

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

formula of area of the triangle mean 1/2 of bh

so the answer is 45.1

Step-by-step explanation:

[tex]base \: = 11km \\ height = 8.5km \\ area = let(x) \\ so \\ x = \frac{1}{2}bh \\ \: = \frac{1}{2} \times 11 \times 8.5 \\ \ = {1}{2} \times 90.2km \\ = 40.5km[/tex]

thank me later!!

please help me please!!!!​

Answers

Answer:

A) angle ACD

B) angle CBA

C) angle ACB

D) angle EBD and angle DBA

E) MDB and CDA

F)DBA

Step-by-step explanation:

Insta: lankey.t

When setting the temperature of a refrigerator, is -1 or -5 the coldest!

Answers

Answer:

-5 is the answer

Step-by-step explanation:

Answer:

-5 corresponds to the coldest temperature here.

Step-by-step explanation:

-5 is to the left of -1 on a number line and is therefore smaller than -1.

What term number will have 400 square in it?

Answers

Answer:

400^2 = 160 000

Step-by-step explanation:

The square of a number means the product of a number by itself, while the perfect square ... For example, the number 9 is a perfect square because it can be expressed as a product of ... A square football pitch has a perimeter of 400 meters.

A field currently holds 20 tulips. The number of tulips will grow by 70% each year. The field can only sustain 300 plants. Use th logistic growth model to predict the population in the next 3 years,​

Answers

Answer: [tex]98.26[/tex]

Step-by-step explanation:

Given

Current population of tulips is 20

Each year it grows 70%

Field can sustain 300 tulips

After 1 year population becomes

[tex]\Rightarrow 20(1+70\%)\\\Rightarrow 20(1.7)\\\Rightarrow 34[/tex]

after 2 years it is

[tex]\Rightarrow 34(1+0.7)\\\Rightarrow 34\times 1.7\\\Rightarrow 57.8[/tex]

After 3 years

[tex]\Rightarrow 57.8(1+0.7)\\\Rightarrow 98.26[/tex]

after n years, the tulips becomes

[tex]\Rightarrow 20(1.7)^n[/tex]

PLEASE HELP ME!!!!
Find the expected value of the winnings
from a game that has the following
payout probability distribution:
6 8
10
Payout ($) 0 4
Probability 0.5 0.2 0.15 0.1 0.05
Expected Value = [?]
Round to the nearest hundredth.

Answers

Answer:

3.00

Step-by-step explanation:

Given that :

Payout(X) : ___ 0 ___ 4 ___ 6 ____ 8 _____ 10

Probability (p(x) 0.5 _ 0.2 __0.15 __0.1 ___ 0.05

Expected value :E(X) = ΣX* p(x)

E(X) = (0*0.5) + (4*0.2) + (6*0.15) + (8*0.1) + (10*0.05)

E(X) = 3

Expected value = 3.00

Solve each equation.
a) 2x = 7
b) 4x = 3
c) 6x = 3
d) 7x = 13
HOW DO YOU SOLVE THESE I NEED THE ANSWER FOR THE QUESTION HELPPPP PLEASEEEE!!!!!!

Answers

Step-by-step explanation:

hey :) if you need help download algebrator. I use it ALL the time pls download it and try it out. it'll give you explanations

Answer:

a) x = 7/2

b) x = 4/3

c) x = 1/2

d) x = 13/7

Step-by-step explanation:

(this is the same process for every one of them. I did C for you)

Let's solve your equation step-by-step.

6x=3

Step 1: Divide both sides by 6.

6x/6 = 3/6

x=1/2

PLEASE HELP FAST I NEED HELP WITH THIS!

Answers

Answer:

Step-by-step explanation:

13. Find the total number of coinsss

8+4+3+1

=16

First pick:

1/16

Second pick:

1/15

So I guess your chances are 1/16+1/15 ?

=31/240

hopefully

14.

add the sockss

3+4+3

= 10

First pick

1/10

Second Pick

1/9

Add them:

19/90

Forgive me if this is wrong

:,)

NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at math.

A student divided f(x) = 3x^3 + 8x^2+ 5x - 4 by x+ 2 and found the remainder was r= -6.Based on the remainder theorem, what can be concluded about f(x)?

A: The function f(x) = 3x^3 + 5x- 4 has a zero at -6.

B: The point (-2,-6) lies on the graph of f(x).

C: The y-intercept of the graph of f(x) is -6.

D: The function f(x) = 3x^3 + 8x^2 + 5x - 4 has a zero at -2.​

Answers

Answer:

b

Step-by-step explanation:

Need help
Even
Odd
Neither

Answers

Answer:

Odd function

Step-by-step explanation:

....

Match each pair of equations with the property that justifies why they are equivalent.

Not all properties will be used.

Answers

9514 1404 393

Answer:

subtractionmultiplicationcombine like terms

Step-by-step explanation:

The properties of equality say the value of the variable does not change if the same function is performed on both sides of the equal sign.

a) 4x +7 = 19   ⇒   4x = 12

The value -7 was added to both sides. Equivalently, 7 was subtracted from both sides. The Subtraction Property of Equality was used.

__

b) 2x/3 = 8   ⇒   2x = 24

Both sides were multiplied by 3. The Multiplication Property of Equality was used.

__

c) 5x -6 +2x = 22   ⇒   7x -6 = 22

Terms 5x and 2x were combined and written as 7x. We call this Combine Like Terms.

y adjusted for wind chill (in degrees Fahrenheit, give
formula:
y=-26 + 1.3x
Estimate the actual temperature if the temperature
Fahrenheit.

Answers

Answer:

The actual temperature is: -6.92

Step-by-step explanation:

Given

[tex]y = -26 + 1.3x[/tex]

Required

Find x when [tex]y = -35[/tex]

Substitute [tex]y = -35[/tex] in [tex]y = -26 + 1.3x[/tex]

[tex]-35 = -26 + 1.3x[/tex]

Collect like terms

[tex]1.3x = 26 - 35[/tex]

[tex]1.3x = -9[/tex]

Solve for x

[tex]x =-9/1.3[/tex]

[tex]x =-6.92[/tex]

Noah is carrying a bag that weighs 2.5 pounds. What is the weight of the bag equal to?
A. 30 oz.
B. 40 oz.
C. 50 oz.
D. 60 oz.

Answers

Answer:

B. 40 oz.

Step-by-step explanation:

B. 40 oz. (1 pound = 16 ounces)

Determine whether ABC and DEF are similar. If so, write the similarity ratio and a similarity statement.

Answers

Answer:

Step-by-step explanation:

DEF is similar to CBA

because angle

angle C = angle D

angle B = angle E

angle A = angle F

The ratio is

10.8/5.4 = 9/4.5 = 6.4/3.2 = 2

Which of the following is not a property of zero?

Answers

Answer:

D is not correct

Step-by-step explanation:

"If you add zero to a number, the answer will be that same number" is incorrect

Answer: Option

2 (or B)

Step-by-step explanation:

You can't divide by 0.

can someone PLEASE help me solve this equation ? due soon

Answers

[tex]\sf{Given : 3tanx + 7 = \dfrac{2}{(1 - sinx)(1 + sinx)}}[/tex]

We know that : (a - b)(a + b) = a² - b²

[tex]\implies \sf{3tanx + 7 = \dfrac{2}{1 - sin^2x}}[/tex]

We know that : 1 - sin²x = cos²x

[tex]\implies \sf{3tanx + 7 = \dfrac{2}{cos^2x}}[/tex]

[tex]\sf{\bigstar \ \ We \ know \ that : \boxed{\sf{\dfrac{1}{cos^2x} = sec^2x}}}[/tex]

[tex]\implies \sf{3tanx + 7 = 2sec^2x}[/tex]

We know that : sec²x = 1 + tan²x

[tex]\implies \sf{3tanx + 7 =2(1 + tan^2x)}[/tex]

[tex]\implies \sf{2 + 2tan^2x - 3 tanx - 7 = 0}[/tex]

[tex]\implies \sf{2tan^2x - 3 tanx - 5 = 0}[/tex]

[tex]\implies \sf{2tan^2x - 5tanx + 2tanx - 5 = 0}[/tex]

[tex]\implies \sf{2tanx(tanx + 1) - 5(tanx + 1) = 0}[/tex]

[tex]\implies \sf{(tanx + 1)(2tanx - 5) = 0}[/tex]

[tex]\implies \sf{tanx = -1 \ (or) \ tanx = \dfrac{5}{2} }[/tex]

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