Find the solutions for a triangle with a = 16, c =12, and B = 63º.

a. A = 71.6°; C = 52.89; b =12.0

C. A = 68.6° C = 45.40; b=12.0

b. A = 71.6°; C = 45.40; b =15.0

d. A = 68.6°; C = 52.89; b=15.0

Answers

Answer 1

Answer:

b. A = 71.6°; C = 45.40°; b =15.0

Step-by-step explanation:

The missing values can be found with the help of the Law of Cosine and properties of triangles:

Side b (Law of Cosine)

[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a \cdot c \cdot \cos B}[/tex]

[tex]b = \sqrt{16^{2}+12^{2}-2\cdot (16)\cdot (12) \cdot \cos 63^{\circ}}[/tex]

[tex]b \approx 15.022[/tex]

Angle A (Law of Cosine)

[tex]\cos A = -\frac{a^{2} - b^{2}-c^{2}}{2\cdot b \cdot c}[/tex]

[tex]\cos A = - \frac{16^{2}-15.022^{2}-12^{2}}{2\cdot (15.022)\cdot (12)}[/tex]

[tex]\cos A = 0.315[/tex]

[tex]A= \cos^{-1} 0.315[/tex]

[tex]A \approx 71.639^{\circ}[/tex]

Angle C (Sum of internal angles in triangles)

[tex]C = 180^{\circ} - 63^{\circ} - 71.639^{\circ}[/tex]

[tex]C = 45.361^{\circ}[/tex]

Hence, the right answer is B.


Related Questions

Solve for x. Describe the steps taken to find the solution.
3( 4x - 3) + 8 = 2x + 10x -1

Answers

Answer:

see below

Step-by-step explanation:

3( 4x - 3) + 8 = 2x + 10x -1

Distribute

12x - 9 +8 = 2x+10x -1

Combine like terms

12x - 1 = 12x - 1

Subtract 12x from each side

12x - 1 -12x = 12x - 1-12x

-1 = -1

This is true for all values of x

x = all real numbers

Answer:

All real numbers are solutions.

Step-by-step explanation:

3 ( 4x - 3 ) +8 = 2x + 10x - 1       Example 1:

12x - 9 + 8 = 12x  - 1                    3 ((4*1) -3) + 8 = (2*1) + (10*1) - 1

        - 12x = -12x                           3 ((4) - 3) + 8 = (2) + (10) - 1

      -9 + 8 = -1                                 ( 12 - 9 ) + 8 = 12 - 1

             -1 = -1                                            3 + 8 = 12 - 1

Example 2                                                       11 = 11

3 ((4*6) - 3) + 8 = (2*6) + (10*6) - 1

3 ((24) - 3) + 8 = (12) + (60) - 1

       72 - 9 + 8 = 72 - 1

              72 - 1 = 72 - 1

                    71 = 71

Karen has a coupon for $1.52 off any
candy related item. She decides to buy
a package of 9 chocolate bars that
normally costs $10.25. If Karen uses
her coupon, what will the price per
chocolate bar be?

Enter​

Answers

Answer:

$8.73 per package of candy bars

Step-by-step explanation:

10.25 - 1.52=

a pool is in the shape of a rectangular prism holds 1800 cubic feet of water. the pool is 6 feet deep and 10 feet wide. what is the length of the pool in yards

Answers

Answer:

Step-by-step explanation:

length = 1800 / 6/10 = 30 ft long = 10 yard

answer with work pls !!

Answers

19.3 x 9.5 = 183.35 with the correct answer

Dr. Barber needs to pay her employees $15.00 an hour. If she has five
technicians and they each worked 25 hours, how much money in total will Dr.
Barber pay all of the technicians?​

Answers

Answer:

$1,875

Step-by-step explanation:

$15.00 per hour (multiply by hours)

per technician (multiply by technicians)

so: 15x25=375 then 375x5=1,875

Answer:

$1875

Step-by-step explanation:

First, let's find how many hours the technicians worked

She has 5 technicians, and the each worked 25 hours

We can multiply 5 and 25 to find the total number of hours

5*25=125

Now we know that the technicians worked 125 hours altogether. Now, we need to find how much money that is.

They worked 125 hours, and they are paid $15 per hour

We can multiply 125 and 15 to find the cost

125*15=1875

So, Dr. Barber will pay the technicians $1875 in total

please help asap, will mark brainlest. Thanks

Answers

Answer:

2.

4x^2 + 4 - 5x + x - 2x^2 + 8

= (4x^2 - 2x^2) + (x - 5x) + (4 + 8)

= 2x^2 - 4x + 12

=> D is correct

3.

2x^2 + 6x - 7x + 8 - 3x^2 + 1

= (2x^2 - 3x^2) + (6x - 7x) + (1 + 8)

= -x^2 - x + 9

=> C is correct

4.

B is correct (4 and 3)

Hope this helps!

:)

HURRY PLEASE!! WILL MARK THE BRAINLIEST

Which of the following are factors of the
polynomial?

Answers

Answer:

All of the above

Step-by-step explanation:

In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Since, they all have a degree of 1 they are all polynomials.

PLS HELP THIS IS A LOT OF PIONTS SO BE FAST

Answers

Answer:

see below

Step-by-step explanation:

distance = rate * time

meters Edgar ran= e*t

meters Mathieu ran = m*t

Difference in meters per second is the difference in rates= m-e

Number of seconds = time = t

Answer:

this took like forever but there u go

Step-by-step explanation:

distance = rate * time

meters Edgar ran= e*t

meters Mathieu ran = m*t

Difference in meters per second is the difference in rates= m-e

Number of seconds = time = t

325,310,289,288,285,285,285,280,273. the mean of the set is 290 pounds what is the mean absolute deviation of the data set,to the nearest whole number

Answers

Answer:

276

Step-by-step explanation:

That’s all i need to know. Thanks!

Answers

Answer:

c = 5

Step-by-step explanation:

a^2 + b^2 = c^2

3^2 + 4^2 = c^2

9 + 16 = 25

c^2 = 25

sqrt of 25 = 5

c= 5

Answer:

c=5

Step-by-step explanation:

Please help me find MAD for this

Answers

Answer:

I know I'm 10 days late on this, but the answer is 1.5

Step-by-step explanation:

1. Add 3+7+4+2:

[tex]3+7+4+2=16[/tex]

2. Divide it by 4 because we have 4 numbers being added:

[tex]\frac{16}{4} =4[/tex]

3. Subtract 4 from all numbers:

[tex]4-3=1, 7-4=3, 4-4=0,4-2=2[/tex]

4. Add the differences:

[tex]1+3+0+2=6[/tex]

5. Divide again by 4:

[tex]\frac{6}{4} =1.5[/tex]

Please send help I really need your help

Answers

Answer:

#4: 4 hits

Step-by-step explanation:

At first, you are given the ratio 1/37 which you can scale to 148 by dividing and multiplying both by. So you divide 148/37 to reach 4 and then multiply 4 by 1 to find out that about four hits will prbably be made.

Answer:

the answer for number four is four and number five is 39

I am not sure about number 5 plz check                                                             somebody.

Step-by-step explanation:

In the diagram shown, 4 24, and 22 = 23. The sum of the measures of the four
angles is 120°. The measure of 22 is 10° less than the measure of 4. What is the
combined measure of angles 1, 2 and 3?
A. 85°
B. 95°
C. 105
D. 115°

Answers

The correct answer is B

Math question down below

Answers

Answer:

c.

Step-by-step explanation:

10.98/2=5.49

16.19/3=5.40

21.15/4=5.29

26.85/5=5.37

What is the value of x?
A.2
B.3
C.6
D.7

Answers

Answer:

A

Step-by-step explanation:

Given 2 secants from a point outside the circle.

Then the product of the external part and the entire secant of one secant is equal to the product of the external part and the entire secant of the other secant, that is

(x + 1)(x + 1 + 11) = (x + 4)(x + 4 + 1)

(x + 1)(x + 12) = (x + 4)(x + 5) ← expand both sides

x² + 13x + 12 = x² + 9x + 20 ← subtract x² + 9x from both sides

4x + 12 = 20 ( subtract 12 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2 → A

The table shows the cost in dollars, y, for renting a pair of snow skis or renting a snowboard for x days. Which function shows the combined cost in dollars, y, for renting two pairs of snow skis and two snowboards for x days? y = 45x + 60 y = 90x + 120 y = 25x + 25 y = 20x + 35

Answers

Answer: this is the right answer y = 90x + 120

Step-by-step explanation:

Suppose f(x) = x2. What is the graph of g(x)= 1/3f(x)

Answers

Answer:

Step-by-step explanation:

The graph of f(x) = x^2 is a parabola opening up and with vertex at (0, 0).

The graph of (1/3)f(x) is also a parabola that opens up and has vertex at (0, 0), but this new graph has been vertically compressed by a factor of 3.

The graph of g(x) = 1/3 f(x) is parabola. (as shown in the following image.)

What is the graph of a function?

"The graph of a function f is the set of all points in the plane of the form (x,  f(x))."

For given example,

f(x) = x²

The graph of a function f(x) would be a parabola with vertex at origin (0, 0).

And g(x) = 1/3 f(x)

⇒ g(x) = 1/3 (x²)

We know, the greater the quadratic coefficient, the narrower the parabola and the lesser the quadratic coefficient, the wider the parabola.

Since for a parabola g(x) the quadratic coefficient is 1/3.

This means the parabola g(x) is wider than the parabola f(x)

So, the graph of g(x) is the graph of f(x) scaled by 1/3 units.

The graph of g(x) is parabola (as shown in following figure)

Learn more about the graph of the function here:

https://brainly.com/question/27757761

#SPJ2

The three friends drove to a park that had batting cages and pitching machines that tossed the balls to the batter automatically. Rameck took his place, ready to bat. "Keep your hands together," George shouted from the other side of the fence. "Bend your knees a little," Sampson offered. "I've watched the Yankees for years," Rameck said, ignoring both of them. "Baseball is easy!” The machine pitched the first ball. Rameck swung with a powerful twist. He missed. The second ball erupted from the machine. Rameck swung again. He missed it by a mile. A third ball came. He swung and missed that one, too. The balls kept coming. Rameck kept swinging. And missing. —We Beat the Street, Sampson Davis et al, Using the drop-down menus, identify the correct sequence of events. First: Second: Third:

Answers

Answer:

first B,second A, third C on edg

Step-by-step explanation:

Answer:

answer is D

Step-by-step explanation:

What is the area of a rhombus if one diagonal is 6 centimeters and the other diagonal is 8 centimeters?

Answers

Answer:

24 cm²

Step-by-step explanation:

The area (A) is calculated as

A = [tex]\frac{1}{2}[/tex] product of the diagonals, that is

A = 0.5 × 6 × 8 = 24 cm²

Find the Surface Area of the Square Pyramid

Step 1:

Step 2:

Step 3:

Step 4: *

(20 Points)

Answers

Step-by-step explanation:

Step 1:   Set up the formula for the surface area of a regular pyramid.

SA = [tex]\frac{p*h}{2} + B[/tex]

where :

SA equals the total surface area of the pyramid,  p equals the perimeter of the base,   h equals the slant height of the pyramidB equals the area of the base.

Step 2:  Plug the perimeter of the base into the formula

you can calculate the perimeter by multiplying the length of one edge by the number of edges.

Step 3: plug the value of the slant height into the formula (it is not the perpendicular height)

Step 4: find the area of the base (depend on the shape of the base)

Hope it will find you well.

If p stands for "this meal is delicious

Answers

Answer:

I don't understand.......

DVD players are going out of fashion in the modern era. If 400,000 DVD players were sold this year and sales are declining at a rate of 31% per year, how many will be sold 3 years from now?

130,000
131,404
128,000
399,876

Answers

Answer:

c

Step-by-step explanation:

Answer:

399,876

Step-by-step explanation:

So, 400,000 DVD sales with a 31% decline means in the first year following, there will be a decline of 124,000 DVDs sold. So we need to take 400,000-124,000 which equals a starting point for your two is 276,000 dvds. Then, add 123,876, which gives you 399,876.

Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
(4n^2 + -5n + -1) (3n^2)

Answers

Answer:

[tex]12n^4-15n^3-3n^2[/tex]

Step-by-step explanation:

The first step is to distribute the [tex]3n^2[/tex] to [tex](4n^2-5n-1)[/tex], like so:

[tex](4n^2-5n-1)[/tex][tex](3n^2)[/tex]

[tex]12n^4-15n^3-3n^2[/tex]

What number should be added to x^2−24x in order to complete the square?


-144


-24


12


144

Answers

Answer:

x^2 - 24x + 144

Step-by-step explanation:

24/2(1)= 24/2= 12

(12)^2= 144

Megan has a bag containing 5 pink marbles, 3 orange marbles, 6 green marbles, and 2 yellow marbles.

Megan started to develop a probability model. Here is the sample space.
S = {P, P, P, P, P, O, O, O, G, G, G, G, G, G, Y, Y}

Part A
put in order where it would go on the table 2/16, 3/16, 5/16, 6/16
Help Megan complete the model by assigning probabilities to the four listed events. Drag each fraction to the correct probability.

Part B
Suppose Megan drew a marble 80 times. Estimate how many times she should expect to draw an orange marble. Megan would draw an orange marble ____
times.

Answers

Step-by-step explanation:

To find the probability

Total marbles = 5 + 3 + 6 + 2 = 16

P pink = 5/ 16

P orange = 3/16

P green = 6/ 16 = 3/8

P yellow = 2/16 = 1/8

Part B when we divide 80 by 16 = 5

So she drew every marble 5 times

So 3 x 5 = 15

She drew the orange marble 15 times

What is the solution to Negative 1 minus 7? A number line going from negative 10 to positive 10. –8 –6 6 8

Answers

Answer:

-8

Step-by-step explanation:

plug it into a calculator. its taking 7 away from an already negative number.

Answer:

-8 correct me if im wrong

Step-by-step explanation:

PLEASE ASAP
graph
-1

Answers

Answer:

on a graph paper draw the coordinate plane and locate -1 and draw a horizontal line

Step-by-step explanation:

please help:)))))))))))))

Answers

Answer: The area is 103.5

Step-by-step explanation: The question becomes very simple once you know how to split this object into objects that you most likely know how to solve the area of. In truth, if you split the shapes in triangles and rectangles, you would find 4 rectangles and a triangles. Once you have solved the area of all of them, you would just have to add. How I solved it goes like this. I added 22.5 as the triangle, 35 as a rectangle, 2 as another rectangle, 18 as another rectangle, and 26 as the final rectangle.(take note that these numbers are the areas of the split shapes) If you added correctly, you would get 103.5

WIll give brainliest help!!!

Answers

Answer:

d

Step-by-step explanation:

Answer:

C. 35

Step-by-step explanation:

7/40=x/200

200/40 x 7=35

A spinner with 4 colors is spun for a total of 50 trials. Yellow was selected 10 times. What is the experimental probability of the spinner landing on yellow?
A. 2/25
B. 1/5
C. 1/4
D. 2/5

Answers

Answer:

b. 1/5

Step-by-step explanation:

10/50 = 1/5

Other Questions
A chemist needs 2.00 liters of hydrochloric acid. How many pints is this? Find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6.A) y equals 1 divided by 24 x squaredB) y2 = 6xC) y2 = 24xD) y equals 1 divided by 6 x squared From the moment the first car started how many hours will it take the second car to catch up to the first Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Why should extra precautions against sun exposure be taken when boating? Water cancels out most sunscreens. UV rays are blocked over land, but not over water. The heat of the water increases potential skin damage. The water reflects UV rays, adding to exposure. Clasifica las siguientes oraciones en yuxtapuestas, coordinadas osubordinadas (7 puntos)Sal de casa; tom el autobs; me dirig a la oficina.Tom el autobs, pero no me dirig a la oficina.Hay una foto en la cual esa modelo se ve muy bien.El reloj que me regalaron, se ve muy bien.Jams estudiaba de noche ni estudiaba de da ni estudiaba de tarde.Ir si me invitan.No salga usted a la calle; llueve torrencialmente. 20 is what percent of 60 Tom, Dan and Phil work indifferent teams at Springfield Automotive. Tom's team ensures that all the raw materials, machinery, tools and other production equipment are available for the employees around the clock. Any procurement needs have to be addressed to Tom, who also takes part in high-level decisions regarding the number of units to produced, exported and so on. Dan works as part of a team of eight members who concentrate the day-to-day productions; they also ensure that the quality checks are done and inspect each other's work. Phil is the operations manager, who works for 5 hours in the production department and then spends the rest of his time assisting management as an internal consultant on manufacturing issues. His input is crucial in improving the production process. Dan's contribution is toward the __________. Which was NOT one of the factors that encouraged Americans to go to war in World War I? a The sinking of the Lusitania b The women's suffrage movement c Propaganda to support Britain and criticize Germany d The Zimmermann telegram The value of a car with an initial purchase price of $18,250 depreciates by11% per year. 19Which gas is the most abundant greenhouse gas?A.ozoneB.chlorofluorocarbonC.carbon dioxideOD.methaneE.water vaporResetNext The given system of eqqations models the coins in a jar containing n nickels, d dimes, and a quarters. Which statement ismodeled by one of the equations in the system?q- dun0 250+ 0 100+ 0.05n-6.05+0+-36The number of nickels is equal to the total number of dimes and quartersThe total value of the coins in the jar is $36There is a total of 36 coins in the jarThere is an equal number of nickels, dimes, and quarters A circle with circumference 8 has an arc with a 288 central angle what is the length of the arc The humanpopulation growthcurve looks likea -curvepopulation.Please help!!! I'm in quite in a bit of a pickle... so, please? and I never forget to mark brainiest If you spun the spinner 1 time, what is the probability it would land on a white piece? What is a herbivore? please help! Which of the following sentences is in passive voice?A. A house was built at the end of the roadB. The spider built a complicated webC. I just finished building my airplane model when the phone rangD. I am building a new house for my dog The table gives the mass of liquids with a volume of 5 cm3. A 2-column table with 4 rows. Column 1 is labeled liquid with entries water, glycerin, milk, olive oil. Column 2 is labeled Mass (grams) with entries 5, 6.3, 5.15, 4.9. Density is the ratio of mass to volume. Density = mass volume What is the density of milk? Use the drop-down menu to complete the statement. The density of milk is StartFraction grams Over centimeters cubed EndFraction. 1What did the North give the South in the Compromise of 1850?