Given: △ABC, m∠A=60°
m∠C=45°, AB = 9
Find: Perimeter of △ABC
Area of △ABC
ABC is scalene

Answers

Answer 1

Answer:

Perimeter = 32.3

Area = 95.24

Step-by-step explanation:

Given:

△ABC, m∠A=60°

m∠C=45°, AB = 9

To find:

Perimeter of △ABC

Area of △ABC

Solution:

Using angle sum property in a triangle:

m∠A + m∠B + m∠C = 180°

m∠B = 180° - 45° - 60° = 75°

As per Sine Rule:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]

Where  

[tex]a[/tex] is the side opposite to [tex]\angle A[/tex]

[tex]b[/tex] is the side opposite to [tex]\angle B[/tex]

[tex]c[/tex] is the side opposite to [tex]\angle C[/tex]

[tex]\dfrac{BC}{sin60^\circ} = \dfrac{AC}{sin 75^\circ} = \dfrac{AB}{sin 45^\circ} \\\Rightarrow \dfrac{BC}{\frac{\sqrt3}{2}} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow BC = 12.73\times 0.87 \\\Rightarrow BC = 11.08[/tex]

[tex]\Rightarrow \dfrac{AC}{0.96} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow AC = 12.73\times 0.96 \\\Rightarrow AC = 12.22[/tex]

Perimeter of △ABC = AB + BC + AC = 9 + 11.08 + 12.22 = 32.3

Area of a triangle is given as:

[tex]\dfrac{1}2\times ab sin(angle\ between\ a\ and\ b)[/tex]

[tex]\Rightarrow \dfrac{1}{2}\times AB\times AC\times sinA\\\Rightarrow 9\times 12.22\times sin 60\\\Rightarrow \bold{95.24}[/tex]


Related Questions

Need help will mark Brainliest

Answers

Answer:

40

Step-by-step explanation:

You know that angle m<SRT is 40, because it's a supplementary angle with 140. 180 - 140 = 40.

Next, you also know that the interior angles of a triangle add up to 180, so you would now make an equation adding all three angles and setting them equal to 180.

40 + 3x + 4 + 8x + 4 = 180

You would now add like terms.

11x + 48 = 180

You would now subtract 48 from both sides.

11x = 132

You would now divide both sides by 11.

x = 12

You would now plug x into m<RST, 3x + 4.

3(12) + 4 = m<RST

36 + 4 = m<RST

40 = m<RST

How to change a fraction to a decimal

Answers

So what is the question

Answer:

just divide the numerator by the denominator

Step-by-step explanation:

an example is ⅔ as a decimal is about .666 or .7

V = 4 + at, solve for A

Answers

Answer:

a=v-4

Step-by-step explanation:

A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 35 minutes.

Answers

Answer:

Step-by-step explanation:

From the given information:

[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]

Given that the solution is pumped at a slower rate of 4gal/min

Then:

[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]

[tex]R_{out}= \dfrac{2A}{50+t}[/tex]

The differential equation can be expressed as:

[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]

Integrating the linear differential equation; we have::

[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]

[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]

multiplying above integrating factor fields; we have:

[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]

[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]

[tex](50 + t)^2 A = (50 + t)^3+c[/tex]

A = (50 + t) + c(50 + t)²

Using the given conditions:

A(0) = 20

⇒ 20 = 50 + c (50)⁻²

-30 = c(50) ⁻²

c = -30 × 2500

c =  -75000

A = (50+t) - 75000(50 + t)⁻²

The no. of pounds of salt in the tank after 35 minutes is:

A(35) = (50 + 35) - 75000(50 + 35)⁻²

A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]

A(35) =69.6193 pounds

A(35) [tex]\simeq[/tex] 70 pounds

Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.

Find the slope of the line passing through the points (-4,7) and (2,-8)

Answers

Answer:

[tex]m=\frac{-5}{2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Point (-4, 7)

Point (2, -8)

Step 2: Find slope m

Substitute:                    [tex]m=\frac{-8-7}{2+4}[/tex]Subtract/Add:               [tex]m=\frac{-15}{6}[/tex]Simplify:                        [tex]m=\frac{-5}{2}[/tex]

which is the right andwer?????????? please help me

Answers

Answer:

The first one

ABC is similar to XYZ. The lengths of two sides of each triangle are given in the figure. Find the length of side x.

Answers

Answer:

x=7/3

Step-by-step explanation:

AB/XY=BC/YZ

The length of {x} is equivalent to 7/3 units.

What is scale factor? How it is used in Dilating sides?

Scale factor tells us by how much one quantity is greater than the other. It is denoted by K. Mathematically -

K = a/b.

Rewriting, we get -

a = Kb

If a side length [a] of any 2 - D figure is dilated by a scale factor of [k], then the length of new side will be [Ka].

Given is that ABC is similar to XYZ.

Since, the two triangles are similar, than their corresponding sides will be proportional to each other. This means that the ratio of corresponding sides will be equal. Mathematically -

BC/YZ = AB/XY = AC/YZ = K [scale factor]

We can write -

8/(2[tex]\frac{2}{3}[/tex]) = 7/x

8/(8/3) = 7/x

8 x 3/8 = 7/x

3 = 7/x

x = 7/3

Therefore, the length of {x} is equivalent to 7/3 units.

To solve more questions on dilation, visit the link below-

brainly.com/question/13439872

#SPJ2

What number group is 45/5 in

Answers

Answer:

Its in rational

Step-by-step explanation:

Answer:

45/5 is a rational number

Step-by-step explanation:

45/5 is equal to 9.

9 is a rational number.

5x-3(x-2)-x

Helppppp I just need you to simplify and show your work plz =)

Answers

The answer would be: x+6

5x-3(x-2)-x

5x-3x + 6-x

x+6

Answer:

x+6

Step-by-step explanation:

5x-3(x-2)-x

5x-3x+6-x

x+6

Find the value of X.

Answers

Answer:

x = 6

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

32+4 is 36

90-36 is 54

9 times 6 is 54

54+4 is 58

58+32 is 90

pls mark me brainliest :)

son
Undaunted co
American re
Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form?

Answers

Answer:

Slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Let's take two points on the line graphed for a function.

Slope of this linear function = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

Between two points chosen,

Rise = Vertical distance on y-axis (Increase or decrease) from one point to the second

Run = Horizontal distance on x-axis from one point to second

Let the points on the graph are (-8, 0) and (0, 4).

Rise = 4

Run = 8

Therefore, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex] = [tex]\frac{4}{8}[/tex]

Slope = [tex]\frac{1}{2}[/tex]

Given (3x + 2) : (x - 2) = 7:5, what is the
value of x?​

Answers

Answer:

(3x+2)/(x-2)=7/5

5(3x+2)=7(x-2)

15x+10=7x-14

15x-7x=-14-10

8x=-24

X=-24/8

X=-3

PLEASE HELP ME SIMPLIFY THIS PLEASE SHOW WORK TO! THANK YOU 5.3x - 9 + 7.6x

Answers

Answer:

12.9x - 9

your welcome

The legs of a right triangle measure 8 inches and 12 inches. What is the area
of the triangle?
A. 192 sq. inches
B. 24 sq. inches
C. 48 sq. inches
D. 96 sq. inches

Answers

Answer:48 sq. Inches

Step-by-step explanation:

Answer in Slope form

Answers

Answer:

y=1/4x+3

Step-by-step explanation:

Can you Explain how to do this plz

Answers

it is -18 because -18 divided by 6 is -3. then -5+-3 is -8

Instead of having a cake, Ruben wants to make ice cream sundaes at his next birthday party.
He thinks each person will eat 2 cups of ice cream, and there will be 24 people at his party.
How many 1-gallon tubs of ice cream should he buy?
tubs

Answers

Answer:

he should buy 3 gallons

Step-by-step explanation:

There are 16 cups in a gallon, and if each person will eat 2 cups, and there are 24 ppl, multiply 24 by 2 to get the number of cups.

24 x 2 = 48.

Then, divide that by 16 (the number of cups in a gallon) to t how many gallons.

48 ÷ 16 = 3

so, he needs 3 gallons

hope this helped!  

please help im stuck​

Answers

Answer:

NOT a relation and NOT a function

The first one it’s not rational or a function I believe

A password contains eight ​digits. How many different passwords can be​ formed?

Answers

Now lets assume you use a stronger password with a mix of lowercase and uppercase characters, such as "blUeFisH", then the character set is 52. In this case, there are 52^8 possible combinations of 8 character passwords. So, to break an 8 character password, it will take (1.7*10^-6 * 52^8) seconds / 2, or 1.44 years.

QUESTION 16 Which of the numbers below are related in the same way as 3259 and 2? A. 5789 and 29 B. 3174 and 6 C. 2749 and 4 D. 9047 and 12

Answers

Answer:

Option (B)

Step-by-step explanation:

Relation between two numbers 3259 and 2,

3259 → 3 × 2 + 5 - 9 = 2

Now we will check the relation in the given options,

Option (A).

5789 → 5 × 7 + 8 - 9 = 34

Option (B).

3174 → 3 × 1 + 7 - 4 = 6

Option (C).

2749 → 2 × 7 + 4 - 9 = 9

Option (D).

9047 → 9 × 0 + 4 - 7 = -3

Therefore, Option (B) shows the same relation.

A cake recipe called for using 6 ¼ cups of sugar before baking and another 5 ¾ cups after baking. What is the total amount of sugar needed in the recipe?

Answers

Answer:12 cups of sugar are needed in the recipe

Step-by-step explanation:

6 ¼ + 5 ¾ =11 4/4=12

The total amount of sugar needed for the cake recipe is 12 cups.

Given that, A cake recipe called for using 6¼ cups of sugar before baking and another 5¾ cups after baking.

What is addition of two fractions?

To add fractions there are three simple steps:

Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator.

Step 3: Simplify the fraction (if possible)

Now, the total amount of sugar needed

6¼ + 5¾

= 25/4 + 23/4

= (25+23)/4

= 48/4

= 12

Hence, the total amount of sugar needed for the cake recipe is 12 cups.

To learn more about the addition of fractions visit:

https://brainly.com/question/17544795.

#SPJ2

Someone please help answer completely !

Answers

Answer:

the answer is  [tex]T=\frac{VP}{8}[/tex]

Step-by-step explanation:

V=[tex]\frac{8T}{P}[/tex]

you need to make T the subject of the formula:

step1: multiply P for both sides.

V=[tex]\frac{8T}{P}[/tex]

VP=8T

step2: divide by 8 for both sides.

T=[tex]\frac{VP}{8}[/tex]

the answer is  [tex]T=\frac{VP}{8}[/tex]

What is 31.99 divided by 5.99 in long division? Explain & I will mark as brainliest

Answers

Answer:

Its 5.3405  I think:>

Step-by-step explanation:

Estimate the area of the inregular shape. Explain your method and show your work.
Please help 100 points and brainliest

Answers

27.5

Im not sure what my method was called but if u still need help comment and I will look it up for u

Answer:

30

Step-by-step explanation:

Since we are estimating. We know that it is about 5 units on top and about 6 units on the side. Therefore, you would multiply them

5*6=30

That is why the area of this irregular shape is 30 units.

Which is the graph of y=3/4x-3

Answers

Answer:

need the graph, but go to desmos for answer to graphing questions

Step-by-step explanation:

HELP PLEASE!! NUMBER 6!!

You will get the brainiest if you can tell me how you did it, so I can finish doing them myself lol. If It comes back right, I will give it you instantly. Thank you very much.

Answers

Answer:

hey it's not clear....

300/12.500000000000000000​

Answers

Answer: 24

Step-by-step explanation: Hope this helps.

Write a different expression that has the same quotient as -3/8 and 3/8.

Answers

Answer:

x = -3/8

Step-by-step explanation:

What is the answer I’m dumb

Answers

Answer:

9units

Step-by-step explanation:

2
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CHAPTER 22
Statistics and Central Tendencies
results are shown in the table below.
Number of visits
Number of people
1
6
2 3
119
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7.
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(a) Find the median number of visits per person.
(b) Calculate the mean number of visits per person.
[ Jan., paper 1, No. 21
ling between two cities, 3/8 of the passengers ar
Fifty people visiting a museum were asked how many times they had visited the museum​

Answers

Answer:

p

Step-by-step explanation:

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