NO LINKS!!! Draw and solve each triangle.

1. a= 3, b= 4, C= 40°
2. a= 3, c= 2, B=110°
3. a= 12, b= 13, , c= 5
4. a= 5, b= 8, c = 9​

Answers

Answer 1
Answers:a = 3, b = 4, c = 2.5720;  A = 48.5702, B = 91.4298, C = 40a = 3, b = 4.1357, c = 2;  A = 42.9719, B = 110, C = 27.0281a = 12, b = 13, c = 5;  A = 67.3801, B = 90, C = 22.6199a = 5, b = 8, c = 9;  A = 33.5573, B = 62.1819, C = 84.2608

The missing values are highlighted in bold, which are approximate to four decimal places (with the exception of B = 90 in problem 3).

Lowercase letters a,b,c are side lengths; Uppercase letters A,B,C are angles opposite the sides mentioned.

The drawings are shown below.

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

Explanation:

Problem 1

Use the Law of Cosines to solve for side c

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 3^2 + 4^2 - 2*3*4*cos(40)

c^2 = 6.61493337

c = sqrt(6.61493337)

c = 2.57195128

c = 2.5720

Now apply the Law of Sines to find angle A

sin(A)/a = sin(C)/c

sin(A)/3 = sin(40)/2.57195128

sin(A) = 3*sin(40)/2.57195128

sin(A) = 0.74976647

A = arcsin(0.74976647)

A = 48.57015285

A = 48.5702

Once we know two angles of a triangle, we can then subtract their sum from 180 to get the third missing angle.

A+B+C = 180

B = 180 - (A+C)

B = 180 - (48.57015285+40)

B = 91.42984715

B = 91.4298

-----------------------------------

Problem 2

Like with the previous problem, we can use the Law of Cosines to solve for the missing side.

b^2 = a^2 + c^2 - 2*a*c*cos(B)

b^2 = 3^2 + 2^2 - 2*3*2*cos(110)

b^2 = 17.10424172

b = sqrt(17.10424172)

b = 4.13572747

b = 4.1357

Now use the Law of Sines to find angle A

sin(A)/a = sin(B)/b

sin(A)/3 = sin(110)/4.13572747

sin(A) = 3*sin(110)/4.13572747

sin(A) = 0.68164014

A = arcsin(0.68164014)

A = 42.9719427

A = 42.9719

Then we can wrap things up like so

A+B+C = 180

C = 180 - (A+B)

C = 180 - (42.9719427+110)

C = 27.0280573

C = 27.0281

-----------------------------------

Problem 3

Use the Law of Cosines to find angle A.

a^2 = b^2 + c^2 - 2*b*c*cos(A)

12^2 = 13^2 + 5^2 - 2*13*5*cos(A)

144 = 194 - 130*cos(A)

-130*cos(A) = 144 - 194

-130*cos(A) = -50

cos(A) = (-50)/(- 130)

cos(A) = 0.38461538

A = arccos(0.38461538)

A = 67.38013505

A = 67.3801

We could use the Law of Cosines to find angle B, but I'll use the Law of Sines instead.

sin(A)/a = sin(B)/b

sin(B) = b*sin(A)/a

sin(B) = 13*sin(67.38013505)/12

sin(B) = 0.99999999998574

sin(B) = 1

B = arcsin(1)

B = 90

It turns out we have a 5-12-13 right triangle (though usually c is the longest side instead of b).

Now we could use the Law of Cosines to find angle C, but the steps shown below are much quicker in my opinion that don't involve any trig functions.

A+B+C = 180

C = 180 - (A+B)

C = 180 - (67.38013505 + 90)

C = 22.61986495

C = 22.6199

-----------------------------------

Problem 4

The steps will basically be identical to problem 3, but with different numbers of course.

First we need the Law of Cosines to find angle A.

a^2 = b^2 + c^2 - 2*b*c*cos(A)

5^2 = 8^2 + 9^2 - 2*8*9*cos(A)

25 = 145 - 144*cos(A)

-144*cos(A) = 25 - 145

-144*cos(A) = -120

cos(A) = (-120)/(-144)

cos(A) = 0.83333333

A = arccos(0.83333333)

A = 33.55730976

A = 33.5573

Now use the Law of Sines to find angle B.

sin(A)/a = sin(B)/b

sin(B) = b*sin(A)/a

sin(B) = 8*sin(33.55730976)/5

sin(B) = 0.88443328

B = arcsin(0.88443328)

B = 62.18186103

B = 62.1819

Lastly,

A+B+C = 180

C = 180 - (A+B)

C = 180 - (33.55730976 + 62.18186103)

C = 84.26082921

C = 84.2608

-----------------------------------

Side notes:

The phrasing "solve the triangle" means to find all three sides and all three angles.Each answer is approximate with the exception of B = 90 in problem 3.Intermediate calculations were done to eight decimal places. The final answers are to four decimal places. In the first two problems, we can prove only one triangle is possible due to the SAS triangle congruence theorem.For the last two problems, only one triangle is possible because of the SSS triangle congruence theorem.I used GeoGebra to make each triangle shown below.
NO LINKS!!! Draw And Solve Each Triangle.1. A= 3, B= 4, C= 402. A= 3, C= 2, B=1103. A= 12, B= 13, , C=

Related Questions

A basket is filled with white eggs and brown eggs. Half of the white eggs are cracked.
An egg is randomly selected from the basket. What is the probability that it is a cracked, white egg?
Write your answer as a fraction.

Answers

1/2 would be the fraction, because half the eggs are white
1/2 because half of them are broken and half of them is not broken

What is the solution to the system of equations below?
3x + 4y = 2
2x – 4y = 8
A. (2,-2)
B. (6,5)
C. (4,4)
D. (2, -1)

Answers

Answer:

D. (2, -1)

Step-by-step explanation:


What is the LEADING COEFFICIENT of the polynomial: 2x^2y - 7x^2y^3 + 6xy^2

Answers

Answer:

-7

Step-by-step explanation:

Leading coefficient:  the number written in front of the variable with the largest degree.

If a term has two or more variables, its degree is the sum of the exponents of its variables

For  [tex]2x^2y - 7x^2y^3 + 6xy^2[/tex]

The degree of the first term of the polynomial is 3 (2 + 1 = 3)The second term of the polynomial is of degree 5 (2 + 3 = 5)The third term of the polynomial is of degree 3 (1 + 2 = 3)

Therefore, the leading coefficient is -7 since the greatest sum of the exponents is of the second term.

[tex]\mathbb{FINAL\;ANSWER:}[/tex]

[tex]\huge\boxed{\sf{The\;coefficient\;is\;-7}}[/tex]

[tex]\mathbb{SOLUTION\;WITH\;STEPS:}[/tex]

Hi! Hope you are having a nice day!

The leading coefficient of the given polynomial is -7.

Why? Because the leading coefficient is the number written before the variable with the largest exponent.

In this case, it's -7, because it's written next to a term that's cubed, and that's the largest exponent in the polynomial.

Also, if a term has two variables (or more) then we add the exponents in that term in order to get the degree of the term.

In this case, it's 5.

Hope you could understand everything.

#CarryOnLearning

What is the value of X?

Answers

Solution:

Note that:

3x + 50 = 6x - 10 (Vertically opposite angles)

Simplify the equation to find x.

Add 10 both sides.

3x + 50 = 6x - 10=> 3x + 50 + 10 = 6x - 10 + 10=> 3x + 60 = 6x

Subtract 3x both sides.

3x + 60 = 6x=> 3x - 3x + 60 = 6x - 3x=> 60 = 3x

Divide 3 both sides.

60 = 3x=> 60/3 = 3x/3=> x = 20

Answer:

x = 20

Step-by-step explanation:

opposite angles = equal angles

we solve with a proportion

3x + 50 = 6x - 10

50 + 10 = 6x - 3x

60 = 3x

x = 60 : 3

x = 20

here a subtraction problem that has been solved incorrectly what is the right way 74-25=59​

Answers

Step-by-step explanation:

74-25 is not equal to 59 the correct answer is 74-25=49

Mario bought tickets to the amusement park. They were originally 45$ each. However, they were on sale for 30$. What percentage discount did Mario recieve?

Answers

He received a discount of %66.7

HELP anyone mr brainly or any smart math people and do it fast asap !

Answers

Answer:

m∠R = 60°

explanation:

Its a isosceles triangle, thus m∠R = m∠Ptotal interior angles of triangle sum up to 180°

Let the angle be x,

x + x + 60° = 180°

2x = 180° - 60°

2x = 120°

x = 60°

Answer:

Step-by-step explanation:

Sum of interior angles in a triangle = 180degree

PQ=QR so triangle PQR is an isosceles triangle

The two base angles of an isosceles triangle are equal

So <R = <P

m<R + m<P + 60degree = 180degree

m<R = (180-60)/2 = 60degree

The probability of an event is 84%. Describe the likelihood of the event.

Answers

Answer:

Please read below.

Step-by-step explanation:

P(event)= favorable outcomes / total outcomes

0.84 * 100 = 84

100 - 84 = 16

84 favorable outcomes

16 unfavorable outcomes

100 total outcomes

Therefore there is a 84% chance of it happening.

Therefore there is a 16% chance of it not happening.

P(event) = 84/100

8.4 out of 10

Describe it how ever you want. 8.4 out of 10 is a pretty good bet to me. I would put my money on it. There isn't a lot of context to the question. But, I hope this helps!

It means 840 times out of 1000 times, an event is likely to happen or in other words, there is an 84% chance of happening an event.

What is probability?

Probability is to measure the occurrence of an event.

It is given that

probability of an event = 84% or 0.84

This means, P(E) = 0.84

Number of favorable outcomes/ Total outcomes =84

Let us say Total outcomes are 1000

So favorable outcomes = 1000*0.84

Favorable outcomes = 840

Therefore, It means 840 times out of 1000 times, an event is likely to happen or in other words, there is an 84% chance of happening an event.

To get more about probability visit:

https://brainly.com/question/24756209

look at the attachment

Answers

Answer:

3

Step-by-step explanation:

1(8)+2(16)+3(24)+4(32) ÷ 8+16+24+32

8+32+72+128÷ 8+16+24+32 = 240÷80 = 3

Solve the system of equations. Enter your answer as an ordered pair (x, y). 4x+y=−1 −5x−2y=−4

Answers

Answer:

Step-by-step explanation:

4x + y = - 1 -------------(I)

-5x - 2y = -4 -----------(II)

Multiply the equation (I) by 2 and then add the equations.

(I)*2        8x + 2y = -2

(II)          -5x - 2y = -4  {Now add and y will be eliminated}

             3x         = -6

                       x = -6/3

x = -2

Substitute x = -2 in equation (I)

4*(-2) + y = -1

-8     + y = -1

          y  = - 1 + 8

           y = 7

Answer:

(-2, 7)

Step-by-step explanation:

4x + y = -1

-5x - 2y = -4

---------------------------------------

2(4x + y = -1) = 8x + 2y = -2

---------------------------------------

8x + 2y = -2

-5x - 2y = -4

3x = -6

÷3   ÷3

x = -2

-----------------------------------------

4(-2) + y = -1

-8 + y = -1

+8          +8

y = 7

I hope this helps!

In 1949, the inflation rate in the United States was -2%If a car cost $1500 at the beginning of the year, what did it cost at the end of the year

Answers

Based on the inflation rate in the United States in 1949, the cost of the car at the end of the year would be $1,470.

What is the cost of the car at year's end?

The cost can be found by the formula:

= Cost x (1 + inflation rate)

The inflation rate is negative so solving gives:

= 1,500 x (1 - 2%)

= $1,470

Find out more on inflation at https://brainly.com/question/777738.

What is the equation of the line in point slope form

Answers

Answer:

y=x-40

Step-by-step explanation:

If f(x)= 3x^2- 4 and g(x) = 2x-6, what is g(f(2))?
-16
0-2
O 8
10

Answers

Answer:

10

Step-by-step explanation:

g(f(x)) = g(3x² - 4) = 2(3x² - 4) - 6

so

g(f(2) = 2(3*2² - 4) - 6 = 2*8 - 6 = 16 - 6 = 10

sfiso is having a party and needs the following
36 bottles of coke
60 cup cakes
what is the ratio of the number of bottles of coke sfiso buys

Answers

The ratio of the number of bottles of coke sfiso buys to cupcakes is 3 :5.

What are ratios?

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within another value. The sign used to represent ratios are :.

Ratio of coke bottles to cupcakes = 36 : 60

= 3 : 5

To learn more about ratios, please check: https://brainly.com/question/25927869

A bag of chips has 212 servings in it. How many servings of chips are in 8 bags

Answers

Answer:

8

Step-by-step explanation:

I simplified the fraction into a decimal (2.5) then proceeded to multiply it by 8 to compensate for each bag of chips.





The table to show how the number of cookies (c) depends on the number of plates (p). Find the values of x and y. List the answer
in the order of x,y



A) 45, 54

B) 54, 63

C) 63, 72

D) 72, 81

Answers

Answer:

B

Step-by-step explanation:

because 4 plates multiplied by 9 equals 56 and 5x9=45. Therefore you need to multiply both 6 and 7 by 9 to get your answer. I hope I'm right. :)

A bag contains six red balls and six blue balls. If three balls are selected at random what is the probability of getting three red balls?

Answers

1/2 x 1/2 x 1/2 = 1/8

Please helpp me?!!!! I will fail my Calc class!!

Answers

Step-by-step explanation:

Using that fact that,

[tex] \cos(u) = \frac{x}{r} [/tex]

and

[tex] {r}^{2} = {x}^{2} + {y}^{2} [/tex]

We need to find sin which that formua is

[tex] \sin(u) = \frac{y}{r} [/tex]

We know what r and x is so we need to find y.

[tex] {8}^{2} = { - 3}^{2} + {y}^{2} [/tex]

[tex]64 = 9 + {y}^{2} [/tex]

[tex]55 = {y}^{2} [/tex]

[tex] \sqrt{55} = y[/tex]

Sin is positve on the interval pi/2 to pi. so we get

[tex] \sin(u) = \frac{ \sqrt{55} }{8} [/tex]

b.

[tex] \tan(u) = \frac{y}{x} [/tex]

so

[tex] \tan(u) = - \frac{ \sqrt{55} }{3} [/tex]

c.

[tex] \sec(u) = \frac{r}{ x} [/tex]

[tex] \sec(u) = - \frac{8}{3} [/tex]

d.

[tex] \sin(2u) = 2 \sin(u) \cos(u) [/tex]

[tex]2 ( \frac{ \sqrt{55} }{8} )( - \frac{3}{8} ) = \frac{ - 6 \sqrt{55} }{64} = \frac{ - 3 \sqrt{55} }{32} [/tex]

e.

[tex] \cos {}^{} (2u) = \cos {}^{2} (u) - \sin {}^{2} (u) [/tex]

[tex]( \frac{ - 3}{8} ) {}^{2} - ( \frac{ \sqrt{55} }{8} ) {}^{2} = \frac{ - 46}{64} = - \frac{23}{32} [/tex]

Opposite of -4 degrees celsis​

Answers

Answer : 4 Degrees Celsis​

Explanation : Use The Absolute Value

I  -4  I = 4

◊ YusuCr ◊

Answer: 4 degrees Celsius

Hope this helps!

Select the correct answer.

What is the measure of the indicated central angle ?

A.
None of the above
B.
54°
C.
27°
D.
96°
E.
48°

Answers

Answer:

C. 27

Step-by-step explanation:

Arc length = fraction of the circle * circumference

Arc length = fraction of the circle * 2 * pi *r

3/4 pi  = fraction of the circle * 2 * pi *5

3/4 pi  = fraction of the circle *10 pi

Divide each side by 10pi

3/4 pi

-------- = fraction of a circle

10 pi

3/40 = fraction of a circle

A circle is 360 degrees

3/40 = x/360

Multiply by 360

3/40 *360 = x

27 = x

What is the value of 5n-3 when n=5?

Answers

Answer:

22

Step-by-step explanation:

We are given the expression:—

[tex]\displaystyle \large{5n-3}[/tex]

When n = 5, substitute/change n to 5:—

[tex]\displaystyle \large{5(5)-3}[/tex]

Evaluate:—

[tex]\displaystyle \large{25-3=\boxed{22}}[/tex]

__________________________________________________________

Summary

  Substitution

Changing or replacing from a term to another terms/expression is called substitution.

Examples:—

If we are given the expression [tex]\displaystyle \large{2y-1}[/tex] and we want to find the value when y = 4, simply replace y-term to 4.

[tex]\displaystyle \large{2(4)-1=8-1=\boxed{7}}[/tex]

__________________________________________________________

If you have any doubts regarding my answer/explanation, do not hesitate to ask in comment!

Maria earned $60 from babysitting. She donated $6. How much money does Maria donate for every dollar that she earns?

Answers

Maria donates 10 cents from every dollar she earns

Jace and jake are brothers and are having a spring party. They will be inviting a lot of friends. There will be a total of 14 people at the party. They will have pizza and soda pop and watch a movie. The soda pop comes in 6 packs and costs $2. 98 per pack. Pizza costs $6.75 each is cut into a slices. The movie costs $4.25 to rent. Each small table can seat 4 people. How many 6 packs of soda do jace and jake need to buy if each person has one pop?

Answers

Answer:

3 packs of sodas would need to be bought.

Step-by-step explanation:

6  x 2 = 12 which isn't enough

6 x 3 = 18 which is more than enough

At a toy factory, three out of every
12 dolls are made with curly hair,
What percent of the dolls are
made with curly hair?

Answers

Answer:

25%

Step-by-step explanation:

25% of the dolls are made with curly hair.

Answer:

4%

Step-by-step explanation:

12 / 3= 4

The diameter of
a circle is
12 yards.
What is the circumference? d= 12yd
use 3.14 for π

Answers

Answer:

37.68 yards

Step-by-step explanation:

Circumference = π x diameter

So if you pull in the numbers to the formula...

circumference = 12 x 3.14

37.68 = 12 x 3.14

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

A right rectangular prism has a length of 15 millimeters, a width of 3 millimeters, and a height of 4 millimeters.

What is the surface area of the prism?

Answers

Answer:

The answer is 234

Step-by-step explanation:

Hope it helps

Please help worth 50points!!
Correct answers only please

Answers

Answer:

a for the fist c  for 2 d for 3 and idontknow

4

Step-by-step explanation:

Answers:Choice DChoice CChoice CChoice DChoice B

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

Explanations:

Problem 1

v = 9i - 4j means we move 9 units to the right and 4 units down.

Another way to write this is v = <9, -4>

----------------------

Problem 2

R = (-19, 6)

S = (-35, 13)

Subtract x coordinates:  xS - xR = -35 - (-19) = -16

Subtract y coordinates: yS - yR = 13 - 6 = 7

Those results form the vector v = -16i + 7j

This vector indicates we move 16 units left and 7 units up when going from point R(-19,6) to point S(-35,13).

----------------------

Problem 3

t = -5i + 12j

||t|| = sqrt( (-5)^2 + (12)^2 )

||t|| = 13

theta = arctan(12/(-5))

theta = -67.38

Add on 180 to get to the proper quadrant Q2

-67.38 + 180 = 112.62

Therefore,

[tex]t = 13\bigg\langle \cos(112.62^{\circ}), \ \sin(112.62^{\circ})\bigg\rangle[/tex]

----------------------

Problem 4

The x, y components are the coefficients of the linear form.

This allows us to go immediately from <-39,16> to -39i + 16j

----------------------

Problem 5

P = (-5,11)

Q = (-16,4)

Subtract x coords: xQ - xP = -16 - (-5) = -11

Subtract y coords: yQ - yP = 4 - 11 = -7

The component form of vector t is <-11, -7> and this vector is in Q3.

r = sqrt(a^2 + b^2)

r = sqrt( (-11)^2 + (-7)^2 )

r = 13.038 is the approximate length of the vector.

theta = arctan(b/a)

theta = arctan(-7/(-11))

theta = 32.471

Add on 180 so we get to Q3

32.471+180 = 212.471

Therefore, we have

[tex]x = r\cos(\theta) = 13.038\cos(212.471^{\circ})\\\\y = r\sin(\theta) = 13.038\sin(212.471^{\circ})\\\\t = xi + yj\\\\t = 13.038\cos(212.471^{\circ})*i + 13.038\sin(212.471^{\circ})*j\\\\[/tex]

in which you could write into this slightly more compact form

[tex]t = 13.038\bigg\langle\cos(212.471^{\circ}),\sin(212.471^{\circ})\bigg\rangle\\\\[/tex]

For more info, check out polar to cartesian conversion formulas.

solve the system y= 4x + 1 and 3x+2y =13

Answers

Given :

[tex]{\qquad \sf \dashrightarrow y= 4x + 1 \: –––– \sf \: (i)}[/tex]

[tex]{\qquad \sf \dashrightarrow 3x + 2y = 13 \: –––– \sf \: (ii)}[/tex]

Now, Substituing the value of y in equation (ii) :

[tex]{\qquad \sf \dashrightarrow \: 3x + 2y = 13 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: 3x + 2(4x + 1) = 13 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: 3x + 8x + 2 = 13 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: 11x + 2 = 13 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: 11x = 13 - 2 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: 11x = 11 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: x = \dfrac{11}{11} }[/tex]

[tex]{\qquad \sf \dashrightarrow \bf \: x = 1 }[/tex]

Now, substituting the value of x in equation (i) :

[tex]{\qquad \sf \dashrightarrow y= 4x + 1}[/tex]

[tex]{\qquad \sf \dashrightarrow y= 4(1) + 1}[/tex]

[tex]{\qquad \sf \dashrightarrow y= 4 + 1}[/tex]

[tex]{\qquad \bf \dashrightarrow y= 5}[/tex]

Given u = (2, -8) and v = (8, -2), what is u times v?

Answers

Answer:

[tex]u\cdot v=32[/tex]

Step-by-step explanation:

Assuming [tex]u[/tex] and [tex]v[/tex] are vectors, their dot product is [tex]u\cdot v[/tex] where [tex]u_1v_1 + u_2v_2[/tex]:

[tex]u\cdot v=u_1v_1+u_2v_2=(2)(8)+(-8)(-2)=16+16=32[/tex]

Therefore, [tex]u\cdot v=32[/tex]

what is photography ...........​

Answers

Answer:

Photography is when you take photo's with style or just take photo's.

Step-by-step explanation:

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