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

Given: ABC, MA=60,mC=45, AB=9Find: Perimeter Of ABC,Area Of ABC

Answers

Answer 1

Answer:

Perimeter of ΔABC: [tex]\frac{27}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] units

Area of ΔABC: [tex]\frac{81}{8}*\sqrt3 + \frac{243}{8}[/tex] units

Skills required: HS Geo, Special Triangles

Step-by-step explanation:

1) The best option is to break down this triangle. Let's draw an altitude from Point B down to Segment AC. The point from the altitude that intersects AC is Point D. BD is the height of our triangle, AC is the base.

2) Angle A is 60 degrees, and since Angle BDA is 90 degrees, Angle ABD is 30 degrees. We can use the 30-60-90 degree right triangle property for the triangle BDA.

This states that if the side opposite the 30 degree angle is [tex]x[/tex], the side opposite the 60 degree angle is [tex]x*\sqrt3[/tex], and the side opposite the 90 degree angle is [tex]2x[/tex].

AB is 9 units, and it is opposite the 90 degree angle. This means that [tex]2x=9, x = \frac{9}{2}[/tex] ==> This then means that AD, the segment opposite the 30 degree angle in this triangle is [tex]\frac{9}{2}[/tex] units. Segment BD (the height) is [tex]\frac{9}{2} * \sqrt3[/tex].

3) Angle C is 45 degrees, and Angle BDC is 90 degrees, which means that Angle CBD is 45 degrees. We can use the 45-45-90 degree right triangle property for the triangle BCD.

This states that if the side opposite the 45 degree angle is [tex]x[/tex], the other side opposite a 45 degree angle is also [tex]x[/tex], but the hypotenuse (side opposite the right (90 degree) angle) is [tex]\sqrt{2}*x[/tex].

BD is [tex]\frac{9}{2} * \sqrt3[/tex], which means DC is the same. BC, which is the hypotenuse is BD multiplied by square-root-2, which is [tex]\frac{9}{2} * \sqrt6[/tex].

4) Area is [tex]\frac{1}{2}*b*h[/tex], the base (b) is AC (which is [tex]\frac{9}{2}+\frac{9}{2}*\sqrt3[/tex]), the height is BD ([tex]\frac{9}{2}*\sqrt3[/tex]). When multiple you will get [tex]\frac{81}{4}*\sqrt3 + \frac{243}{4}[/tex], then this multiplied by 1/2 is

[tex]\frac{81}{8}*\sqrt3 + \frac{243}{8}[/tex] <--> this is the area!

5) Perimeter is just the sum of all side: 9 + [tex]\frac{9}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] = [tex]\frac{27}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] unit

Given: ABC, MA=60,mC=45, AB=9Find: Perimeter Of ABC,Area Of ABC
Given: ABC, MA=60,mC=45, AB=9Find: Perimeter Of ABC,Area Of ABC

Related Questions

Pls help I’m trying to solve for x

Answers

Answer: x = 28

Please give Brainliest if this helped you

Step-by-step explanation:

Guys, please help me faster will receive a Brainliest award if you answer my 2 of the math questions with the best given answers with the best step-by-step explanations, so here is an image for you to answer my 2 of the math questions as soon as possible. Well anyways, good luck on answering my 2 of the math questions and I will check the answers to see if it’s appropriate! :)

Answers

Answer:

Question 10.

Length of the side of the square = [tex]\sqrt{441} = 21[/tex]

By Pythagoras' Theorem,

Hypotenuse = [tex]\sqrt{21^{2} + 20^{2} }[/tex] (H > 0)

                     = 29 m

Ans: 29 m

Question 11.

By Pythagoras' Theorem,

Length of longer side of 42 km = 42- [tex]\sqrt{18^{2} - 15^{2} }[/tex] (L > 0)

                                                                     = 32.050 km (5 s.f.)

By Pythagoras' Theorem,

Length of the unknown side = [tex]\sqrt{32.050^{2} + 15^{2} }[/tex] (L > 0)

                                               = 35.4 km (3 s.f.)

Ans: 35 km

Can someone help me out here?​

Answers

Answer:

with what?

Step-by-step explanation:

HELLPPPPPP ASAP PLEASE

Answers

Answer:

the answer is A

Step-by-step explanation:

A company that teaches self-improvement seminars is holding one of its seminars in Middletown. The company pays a flat fee of $117 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $14 to purchase books and supplies. Each attendee will pay $15 for the seminar. Once a certain number of attendee register, the company will be breaking even. How many attendees will that take? What will be the company's total expenses and revenues?

Answers

Answers:

To reach the breakeven point, how many attendees will that take?     117  

What will be the company's total expenses and revenues?      $1755  for each  

=============================================================

Explanation:

x = number of attendees

C(x) = cost function for the company

C(x) = 14x+117

This is because the company pays $14 per person, so x of them accounts for 14x dollars. Then we add on the flat fee of $117 to get 14x+117 dollars overall.

In contrast, the revenue is

R(x) = 15x

because each attendee brings in $15 for the company

The breakeven point is when the cost and revenue are the same. This produces a profit of $0.

R(x) = C(x)

15x = 14x+117

15x-14x = 117

x = 117

If 117 people attend the seminar, then the company breaks even.

To check this, we'll compute the cost and revenue

C(x) = 14x+117

C(117) = 14*117+117

C(117) = 1755

R(x) = 15x

R(117) = 15*117

R(117) =  1755

The cost and revenue is $1755 for each. Because we get the same value, this confirms the correct x value.

Since 117 people is the breakeven point, the company should aim for an attendee count above this, so they can get a positive profit. At some point, there is a max capacity so x can't go up forever.

How many screeches are equal to 20 meows? 20 meows = 12 laughs 3 laughs = 2 purrs 40 purrs = 120 screeches

Answers

Answer:

24 screeches

Step-by-step explanation:

20M=12L=8P=24S

Olivia reads 72 pages in 40 minutes. How many pages can she read per minute?

Answers

Answer:

1.8 pages a minute

Step-by-step explanation:

Olivia can read 1.8 pages per minute.

solve for A and line AB

Answers

Answer:

a = 22

AB = 50

Step-by-step explanation:

[tex]a-5=17[/tex]

[tex]a=17+5[/tex]

[tex]a=22[/tex]

Line AB=2a+6

[tex]2(22)+6=44+6=50[/tex]

[tex]AB=50[/tex]

Hope this helps

A student earned a grade of 82% on a math test that had 20 problems. How many problems on this test did the student answer correctly? (round to the nearest whole number)

Answers

Answer:  16

Work Shown:

82% of 20 = 0.82*20 = 16.4 which rounds to 16

given a isotope with a 3 charge, a mass number of 28, and an atomic number of 13, what are:

Answers

Answer: The element described is aluminum.

Convert 1 = 4 to polar form.

Answers

Answer:The inverse tangent of 14 is θ=14.03624346° θ = 14.03624346 ° . This is the result of the conversion to polar coordinates in (r,θ) form.

Step-by-step explanation: i think this may help you

The blueprint for Moreno​'s living room has a scale of 2 inches equals 3 feet. The family wants to use a scale of 1 inch equals 2 feet. What is the width of the living room on the new​ blueprint? (The width is 12in)

Answers

Answer:

18 feet

Step-by-step explanation:

If 2 inches equals 3 feet, then 1 inch equals 1.5 feet. And if the width is 12 inches, you can multiply 1.5 by 12 to get the actual length of the living room. 18 feet!!! I hope this helps!!! :D

What’s the an and the a10

Answers

Answer:

an = -6 + n

a10 = -6+ 10 =4

Step-by-step explanation:

an should start at one behind the first number so it should be -6. Then we add  whatever the sequence is increasing by, which is 1 in this case, multiplied by n.

an = -6 + n

a10 = -6+ 10 =4

Each time Cali babysits, she gives 35% of
the money to her sister who comes and
helps out. Find the expression that
shows how much money Cali keeps each
time she babysits.
A. (0.35%
B. X-(0.35)
C. x/0.35
D. X-0.35

Answers

The answer is X-(.35)x

Please find the range of these numbers

Answers

Answer:

91 - 74 = 17

Step-by-step explanation:

The range is the difference between the highest and lowest values in a set of numbers.

Determine the range values for x

Answers

5x+2=47
5x=45
x=9
the final answer is 9

which ratio is equivalent to 4:10? Choose ALL the equivalent ratios from i-ready

Answers

Answer:

2:5 is the simplified form.

Step-by-step explanation:

4:10 => 4/10 => 2/5=> 2:5

Conclusion:

Therefore, the simplified form of 4:10 is 2:5.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

2:5 and 12:30

I hope this helps!

From: Aug1e

Which of the following is the contrapositive of the conditional below?

If 3 + 4 = 6, then 2 · 5 = 10.

If 2 · 5 = 10, then 3 + 4 = 6.
If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.
If 3 + 4 ≠ 6, then 2 · 5 ≠ 10.
If 3 + 4 ≠ 6, then 2 · 5 = 10.

Answers

Answer:

If 3 + 4 ≠ 6, then 2 · 5 = 10.

Step-by-step explanation:

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain." If p , then q .

how to see if matrix is one to one calculator

Answers

Answer:

look at the pivots (the leading 1's of the rows)

Step-by-step explanation:

Then, look at the pivots (the leading 1's of the rows). If we have a pivot in every column, then the nullspace of the matrix (and hence the kernel of T) is zero-dimensional. So, T is one-to-one if and only if the REF has pivot in every column.

I need help on this question
No links!

Answers

Answer:

>

Step-by-step explanation:

> means greater than and because 79 is greater than -5, the correct sign you would use will be >

79 > -5

>79 is greater than negative5

Katrina is solving the equation x minus 2 (x 3) = 4 (2 x 3) minus (x 4). Which equivalent equations might Katrina use? Check all that apply. X minus 2 x minus 6 = 8 x 12 minus x minus 4 x minus 2 x 6 = 8 x 12 minus x 4 x minus 2 x minus 6 = 8 x 12 minus x 4 x minus 2 x 3 = 8 x 3 minus x 4 Negative x minus 6 = 7 x 8 Negative x 6 = 7 x 16 Negative x minus 6 = 7 x 16 Negative x 3 = 7 x 7.

Answers

The value of x according to the equation is -7/4 and the equivalent equations that Katrina might use is x - 2x - 6 = 8x + 12 - x  - 4

Given the equation solved by Katrina expressed as;

x - 2 (x + 3) = 4 (2 x + 3) - (x + 4).

Expand using distributive law;

x - 2x - 6 = 4(2x) + 4(3) - x - 4

x - 2x - 6 = 8x + 12 - x  - 4

-x - 6 = 7x + 8

-x - 7x = 8 + 6

-8x = 14

x = 14/-8

x = -7/4

Hence the value of x according to the equation is -7/4 and the equivalent equations that Katrina might use is x - 2x - 6 = 8x + 12 - x  - 4

Learn more on expressions here: https://brainly.com/question/24734894

The value of x according to the equation is -7/4 and the equivalent equations that Katrina might use is x - 2x - 6 = 8x + 12 - x  - 4

Given the equation solved by Katrina expressed as;

x - 2 (x + 3) = 4 (2 x + 3) - (x + 4).

Expand using distributive law;

x - 2x - 6 = 4(2x) + 4(3) - x - 4

x - 2x - 6 = 8x + 12 - x  - 4

-x - 6 = 7x + 8

-x - 7x = 8 + 6

-8x = 14

x = 14/-8

x = -7/4

Hence the value of x according to the equation is -7/4 and the equivalent equations that Katrina might use is x - 2x - 6 = 8x + 12 - x  - 4

Learn more on expressions here: brainly.com/question/24734894

Tamir bought 2 1/2 pounds of fish at $5.50 per pound, and two bananas at the price shown

Answers

Answer:

8.50

Step-by-step


A. (4,1)
B.(-2,8)
C.(8,-2)
D.(-1,4)

Answers

Answer:

i think B is answer

Step-by-step explanation:

0.5x+9 = -3x+2

x = -2

y = -3x+2

y = -3(-2) +2

y = 6+2

y = 8

(x,y) = (-2,8)

B is the answer for sure fo sure

X-Y=5, 6X-6Y =?


I think it's 30, but i don't know , I tried to think of a way and I thought about taking the 6 as a common and multiplying it to X-Y, Like :6(X-Y), and since X-Y =5 it'll be 30?​

Answers

Answer:

Yes, it is 30

Step-by-step explanation:

And yes, you thought it through correctly.  6(X-Y) = 6*5

6(X-Y) = 30

Answer:

[tex]\displaystyle 6x - 6y = 30[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Terms/Coefficient

Factoring

Step-by-step explanation:

Step 1: Define

Identify.

x - y = 5

Step 2: Solve

Factor:                                                                                                               [tex]\displaystyle 6x - 6y = 6(x - y)[/tex]Substitute in expression:                                                                                 [tex]\displaystyle 6x - 6y = 6(5)[/tex][Order of Operations] Evaluate:                                                                      [tex]\displaystyle 6x - 6y = 30[/tex]

factor completely.
-3x^2+9x+30

Answers

Answer:

− 3 ( x − 5 ) ( x + 2 ) hope this helps

Step-by-step explanation:

Answer:

− 3 ( x − 5 ) ( x + 2

Step-by-step explanation:

Find the slope of the line passing through the points (8,-4) and (1,-9)

Answers

Answer:

Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values.

Answer: 0.71429

Step-by-step explanation:

Mrs. Rainer would like to buy 28
composition notebooks for her math class.
If they are on sale for $0.94 each, how
much will she spend, not including tax?

Answers

Answer:

$26.32

Step-by-step explanation:

0.94x28 = 26.32

(Meeting character limit)

What is this expression in simplest form?

Answers

Answer:

A. 1÷(X+1) (x-2)

some steps are directly

tag me in brainlist if you like it

How do I solve for x?

Answers

X + 36 = 16

16 - 36 = -20

X = -20

Here, the opposite angles of the triangle are equal. If 2 opp. angles in a triangle are equal, then the opposite sides will be equal as well.

So,

16 = x + 36

16 - 36 = x

-20 = x

______

Hope it helps ⚜

Find the area of each figure

Answers

30yd^2
Explanation-
B•h/2
10•6=60
60/2=30
:)
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