Mathematics High School

The diagram shows triangle ABC. Calculate the length of AC

Answers

Answer 1

Given:

In triangle ABC, AB=8.2 cm, C=13.5 cm and angle A= 81 degrees.

To find:

The length of AC.

Solution:

According to the Law of Sines:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

Using Law of Sines, we get

[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c}[/tex]

[tex]\dfrac{\sin (81^\circ)}{13.50}=\dfrac{\sin C}{8.2}[/tex]

[tex]\dfrac{\sin (81^\circ)\times 8.2}{13.50}=\sin C[/tex]

[tex]\sin^{-1}\dfrac{\sin (81^\circ)\times 8.2}{13.50}= C[/tex]

[tex]C\approx 36.86^\circ[/tex]

Using angle sum property, we get

[tex]\angle A+\angle B+\angle C=180^\circ[/tex]

[tex]81^\circ+\angle B+36.86^\circ=180^\circ[/tex]

[tex] \angle B =180^\circ-81^\circ-36.86^\circ [/tex]

[tex] \angle B =62.14^\circ [/tex]

Now,

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]

[tex]\dfrac{\sin (81^\circ)}{13.50}=\dfrac{\sin (62.14^\circ)}{b}[/tex]

[tex]b=\dfrac{13.50\times \sin (62.14^\circ)}{\sin (81^\circ)}[/tex]

[tex]b\approx 12.08[/tex]

Therefore, the length of AC is 12.08 cm.

Related Questions

What is the sum of the geometric sequence 1, -6, 36, ... If there are 6 terms? (1 point)

Answers

Answer:

-6665

Step-by-step explanation:

The given GP is :

1, -6, 36, ...

Number of terms = 6

The sum of n terms of a GP is given by :

[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]

Here,

a = 1, n = 6, r = 36/-6 = -6

So,

[tex]S_6=\dfrac{1((-6)^6-1)}{(-6)-1}\\\\=-6665[/tex]

So, the sum of th GP is -6665.

Which function is linear

A. F(x) = |3x| + 4
B. F(x) = 1/3x + 4
C. F(x) = 3x - 4
D. F(x) = |3x| - 4

Answers

D is the answer you got to do

Answer:

D. F(x) = |3x| - 4

Step-by-step explanation:

PLEASE HELP ME!!!
Greg said that he wrote a fraction greater than 3/12, is less than 75/100, and has 6 as a denominator. What is his fraction?

Answers

Given:

A fraction is greater than [tex]\dfrac{3}{12}[/tex], is less than [tex]\dfrac{75}{100}[/tex].

The fraction has 6 as a denominator.

To find:

The fraction value.

Solution:

Let x be the required fraction.

According to the given information, we get

[tex]\dfrac{3}{12}<x<\dfrac{75}{100}[/tex]

[tex]\dfrac{1}{4}<x<\dfrac{3}{4}[/tex]

We know that, [tex]\dfrac{1}{4}<\dfrac{2}{4}<\dfrac{3}{4}[/tex]. So,

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

[tex]x=\dfrac{1}{2}[/tex]

We need 6 as the denominator.

Multiply the numerator and denominator by 3.

[tex]x=\dfrac{1\times 3}{2\times 3}[/tex]

[tex]x=\dfrac{3}{6}[/tex]

Therefore, the required fraction is [tex]\dfrac{3}{6}[/tex].

The fraction that Greg wrote is 3/6.

What is a fraction?

A fraction is a quantity that is not a whole number. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/2.

What fraction did Greg write?

The first step is to express 3/12 and 75/100 in its simplest form.

3/12 = 1/4

75/100 = 3/4

The second step is to determine the difference between the fractions

3/4 - 1/4

[tex]\frac{3 - 1}{4}[/tex] = [tex]\frac{2}{4} = \frac{1}{2}[/tex]

The third step is to multiply by 3

3/6

To learn more about subtraction of fractions, please check: https://brainly.com/question/915789

You can open the picture and help me and ty if you are

Answers

Answer:

-35/8=t

Step-by-step explanation:

-7/4=2/5t

simplify by dividing each side by 2/5

-35/8=t

find the sales tax for A cd if the cd cost $14.29 and the sales tax is 7.25%

Answers

Answer:

the sales tax is 1.036 if you solve in this equation 7.25/100*14.29

!Please Help !
Find the volume of this cylinder

Answers

Answer:

volume of cylinder= pie × radius square× height

= 22/7×4×20

=1760/7

=251.42cm

Answer:

using 3 for pi it's V = 960cm^3

Step-by-step explanation:

R is the radius, which as stated, is half the diameter.

r = 8cm / 2 = 4cm

H is the height, which is shown to be 20cm

h = 20cm

V = pi*r^2*h

V = pi*(4cm)^2*20cm

substituting 3 for pi as requested.

V = 3*(4cm)^2*20cm - 3 * (16cm^2) * 20cm = 48cm^2 * 20cm = 960cm^3

Samantha went to a concession stand and bought three pretzels and four sodas and paid a total of $11.25 for them. Raza went to the same stand and bought five pretzels and two sodas and paid a total of $8.25.
(a) Could pretzels have cost \$1.75 each and sodas $1.50 each ? How can you evaluate based on the information given ?
(b) Letting x equal the unit cost of a pretzel and letting y equal the unit cost of a soda, write a system of equations that models the information given .
(c) Solve the system of equations using the elimination method or a matrix,
(d) Leah went to the same concession stand and bought two sodas, how many pretzels would she need to buy so that she spent the same amount on both

Answers

Answer:

No, because their respective prices are $0.75 and $2.25

Step-by-step explanation:

Let's assume that the price of each pretzel is x and the price of each soda is y

3x + 4y = 11.25_____ equation 1

5x + 2y = 8.25_____ equation 2

Multiply equation 2 by the figure 2 so as to have both equation sharing the same coefficient of y

10x + 4y = 16.5____ equation 1

3x + 4y = 11.25____ equation 2

Now subtract equation 2 from 1

7x = 5.25

X = 5.25/7

X = 0.75

Now substitute x = 0.75 in equation 1

10x + 4y = 16.5

10(0.75) + 4y = 16.5

7.5 + 4y = 16.5

4y = 16.5 - 7.5

4y = 9

Y = 2.25

Therefore,the cost of each pretzel is $0.75 while that of soda is $2.25

Find value of x
I need it fastttttt

Answers

Answer:

x=1

Step-by-step explanation:

you have to put x on one side. send -10 to the other side. Add 10 on both sides to delete 10.

7x-10+10=3x-6+10

now it leaves you with 7x=3x+4

Now you have to send 3x to the other side because you are solving for x. subtract both sides by 3x to delete 3x on the other side.

7x-3x=3x-3x+4

how it leaves you with 4x=4

now you divide both sides by 4

4/4x=4/4

Hence, x=1

Answer:

standard form: 4x - 4 = 0

factorisation: 4(x - 1) = 0

solutions: x = 4/4 = 1

therefore, x is 1

What is the area of this parallelogram?

A. 60 cm²

B. 66 cm²

C. 72 cm²

D. 132 cm²

PLS HELP I'LL GIVE BRAINLIST!!

Answers

Answer:

132, (D)

Step-by-step explanation:

area = base * height

= (5 + 6) * 12 = 11 * 12 = 132

Answer:

The answer is D, 132 cm^2! Brainleist pls!

Three integers x, y and z satisfy 34x+5ly=6z. If y and z are primes, find the
value of x, of y and of z

Answers

x= -3/2y+3/17z
y=-2/3x+2/17z
z=-17/3x+17/2y

how many times larger is 4.5 times 10^6 than 4.5 times 10^4

Answers

Answer:

100 Times larger.

Step-by-step explanation:

4500000/45000=100

Which are true statements when comparing the data in the box plots? Select three choices.
The data for elementary school are more consistent than those for middle school.
More of the data for middle school lie closer to the median than the data for elementary school.
About 50% of elementary school students watch between 4 and 7 hours of television each week.
About one-half of middle school students watch less than 2 hours of television each week.
On average, middle school students watch less television than elementary school students each week.

Answers

Answer:

A,C,E

Step-by-step explanation:

Answer:

A- The data for elementary school are more consistent than those for middle school.

C- About 50% of elementary school students watch between 4 and 7 hours of television each week.

E- On average, middle school students watch less television than elementary school students each week.

Step-by-step explanation:

Edge 2021 December 8th

What is the answer to 2x^4 x x^3=

Answers

Use this. It’s really good

Ten out of every 32 people
surveyed play Among Us.
What percent of people
surveyed play Among Us?
Please help

Answers

10 divided by 32 is 32.25
multiply 32.25 by 100
then u get 32%

Answer:

31.25%

Step-by-step explanation:

Man its the search engine

Great brushwork btw

11. What number is 30% of 12? What are you going to solve?
a. rate
b. percentage
c. base
d. decimal

Answers

Answer:

3.6 D. decimal

Step-by-step explanation:

write 2 paragraphs using function notation

Answers

Answer:

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Step-by-step explanation:

TJ averages being the imposter 2 times every 5 games of Among Us. How many games does he have to play to be the imposter ones?

Answers

Answer:

Step-by-step explanation:

If the expression 9x + (4 – 3x) + 7is simplified completely, how many terms will the expression contain?

Answers

Answer: 2 terms

Step-by-step explanation:

There are two terms because

One is __x the other is the constant

9x + 4 - 3x + 7

6x + 4 - 7

6x - 3 has two terms

If the given mathemtical expression is simplified completely, the expression would contain 2 terms.

How to simplify the expression?

Given this expression: 9x + (4 – 3x) + 7

Remove the brackets : 9x + 4 - 3x + 7

Add similar terms: 6x + 11

To learn more about mathematical expressions, please check: https://brainly.com/question/11980704

Brandy is watching a baseball game. So far, 8 out of 10 batters
have gotten a hit. What is the experimental probability that the
next batter will get a hit?

Answers

Answer:

8/10 aka 4/5 chance

Step-by-step explanation:

if 8/10 batters have hit the ball that means that the chance that the next ball is hit is 8/10, reduced its 4/5 chance or 80%

Help me please What is angle

Answers

Answer:

2 = 25 degrees

Step-by-step explanation:

A right angle is 90 degrees... So, 90-65 helps you find the missing angle.

90-65=25

Angle 2=25

What is the solution to the system of equations shown below?

Answers

Answer:

Need to see the solution

Step-by-step explanation:

Answer:

what

Step-by-step explanation:

which where is the equation

Select all equations that have graphs with the same y-intercept. y = 3x - 8 y = 3x - 9 y = 3x + 8 y = 5x - 8 y = 2x - 8 y = ⅓x - 8

Answers

The y intercept is the one without the x with it so all the -8 ones are the same intercept

Can someone help me pls

Answers

Answer:

12.3 foot i think

Step-by-step explanation:

P.S. there will be no shadow of the boy if he is standing next to the statue because the shadow of the statue will cover him

just for fun

In WXY, w=130 inches, x=270 inches and y =190 inches. Find the area of WXY to the nearest square inch

Answers

Answer:

11304

Step-by-step explanation:

Delta math

Can i get help plz this question rlly hard

Answers

Answer:

1890

Step-by-step explanation:

Answer:

I believe your answer is 1512

Step-by-step explanation:

4.2 x 2 = 8.4 this is the area, each inch is equal to 15 feet, there are 180 inches in 15 feet. so 8.4 x 180 = 1512.

PLS PLS HELP ME I HAVE 5 MINS
I WILL GIVE YOU BRAINLY!!!

Answers

4/6 = 12/18

8/10 = 16/20

2/5 = 4/10

1/4 = 4/16

Can I get brainiest please.

100 points help ASAP!!!!

Answers

Answer:

True

False

True

Step-by-step explanation:

its not even 100 points

Answer: This is 9 points. True,False, False,True is the answer by the way.

Step-by-step explanation:

In a bookcase, there are
fiction books for every 7 nonfiction books. There are 44 books in the bookcase. How many nonfiction books are in the bookcase?

Answers

Answer:

20 Books

Step-by-step explanation:

Which of the following is the coefficient in the algebraic expression 2x+4?
А. у
B. 2
C. 4
D.

Answers

Answer:

B. 2

Step-by-step explanation:

The number next to the variable is the coefficient. So, it is 2

Answer:

Step-by-step explanation:

2 is the coefficient and x is the variable.

help me with these 3 and i’ll love you forever and give you brainliest:)

Answers

Answer:

18. 5

19. 1

20. B) (0,-11)

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