Triangle P Q R is shown. Angle R P Q is 99 degrees and angle P Q R is 31 degrees. The length of Q R is 11. Determine the measures of all unknown angles and side lengths of ΔPQR. Round side lengths to the nearest hundredth.

Triangle P Q R Is Shown. Angle R P Q Is 99 Degrees And Angle P Q R Is 31 Degrees. The Length Of Q R Is

Answers

Answer 1

Answer:

[tex]\angle PRQ = 50^\circ[/tex]

PR = 5.74 units and

PQ = 8.53 units

Step-by-step explanation:

We are given the following details:

[tex]\angle RPQ =99^\circ[/tex]

[tex]\angle PQR =31^\circ\\\text{Side QR} = 11\ units[/tex]

To find:

[tex]\angle PRQ =?\\Side\ PR = ?\\Side\ PQ = ?[/tex]

We know that the sum of all the angles of a triangle is equal to [tex]180^\circ[/tex]

i.e.

[tex]\angle PQR +\angle PRQ +\angle RPQ =180^\circ\\\Rightarrow 31^\circ +\angle PRQ +99^\circ =180^\circ\\\Rightarrow \angle PRQ = 180-130\\\Rightarrow \angle PRQ = 50^\circ[/tex]

To find the sides, we can use Sine rule:

As per Sine rule:

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

Where a, b and c are the sides opposite to [tex]\angle A,\angle B,\angle C[/tex] respectively.

Using Sine rule in given triangle:

[tex]\dfrac{11}{sin 99} =\dfrac{b}{sin 31} =\dfrac{c}{sin 50}\\\\\text{Solving }\dfrac{11}{sin 99} =\dfrac{b}{sin 31} \\\Rightarrow b = \dfrac{11}{sin 99} \times sin31\\\Rightarrow b =5.74\ units\\\\\text{Now, Solving }\dfrac{11}{sin 99} =\dfrac{c}{sin 50} \\\Rightarrow c = \dfrac{11}{sin 99} \times sin50\\\Rightarrow c =8.53\ units[/tex]

So, sides are

PR = 5.74 units and

PQ = 8.53 units

Answer 2

Answer:

Answer:

PR = 5.74 units and

PQ = 8.53 units

Step-by-step explanation:

We are given the following details:

To find:

We know that the sum of all the angles of a triangle is equal to

i.e.

To find the sides, we can use Sine rule:

As per Sine rule:

Where a, b and c are the sides opposite to  respectively.

Using Sine rule in given triangle:

So, sides are

PR = 5.74 units and

PQ = 8.53 units

Step-by-step explanation:


Related Questions

Lucky's Market purchased a new freezer for the store.
When the freezer door stays open, the temperature
inside rises. The table shows how much the
temperature rises every 15 minutes. Find the unit rate.
temperature (°F) =10
number of minutes =15
°F per minute

Answers

Answer:

1/3 degreees/min

Step-by-step explanation:

In 15 min, temp. rises by 10 degrees

This means that 10 degrees / 15 min = 2 deg / 3 min

1/3 degree/min

The unit rate of change in °F per minute is 0.667°F/ min .

What is an Equation ?

An equation is a statement formed when variables are equated by a constant or another variable by an equal sign.

It is given that

The rate of increase of temperature with increasing time is given

The unit rate of change in °F per minute has to be determined .

In 15 minutes , the temperature changes by  10°F

The rate of unit change is 10 / 15 = 0.667

20/30 = 0.667

40/60 = 0.667

Therefore the unit rate of change in °F per minute is 0.667°F/ min .

To know more about Equation

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2(x+1)+3x=37 *what is x??​

Answers

2(x+1)+3x=37

simplifythe left side:

2x +2 +3x = 37

Combine like terms:

5x +2 = 37

Subtract 2 from both sides:

5x = 35

Divide both sides by 5:

x = 7

Answer:

x=7

Step-by-step explanation:

2(x+1)+3x=37

Distribute

2x+2 +3x = 37

Combine like terms

5x+2 = 37

Subtract 2 from each side

5x+2-2=37-2

5x = 35

Divide by 5

5x/5 = 35/5

x=7

Look at the graph What is slope of the line

Answers

Where is the graph, I see no graph at all we can’t answer without a picture sorry

Answer:

You didn't insert the/a file

Step-by-step explanation:

Please help! Correct answer only!

You can play a game with a wheel whose rim is divided into equal sections marked with the numbers from 1 to 10. If you play, the attendant will spin the wheel and a ball will land in a random section. If the number the ball lands on is odd, you win $25. If the number the ball lands on is even, you win nothing. If you play the game, what is the expected payoff?

$___

Answers

Answer:

$12.5

Step-by-step explanation:

Since there is a 50% chance of landing on an odd number, the expected payoff is 0.5*25=12.5. Hope this helps!

if f(x)=x+3 g(x)=2x+6 find (f+g)(x)

Answers

Answer:

3x + 9

Step-by-step explanation:

For value of (f+g)(x) add two functions up

x + 3 + 2x + 6 = 3x + 9

A healthy human body is approximately 18% carbon by weight. Determine how many pounds of carbon a body weighing 200 lbs contains. How many kilograms would that be? Use 0.454 kg equals 1 lb in your conversion. A. 440 lb. Of carbon; 16 kg of carbon b. 36 lb. Of carbon; 79 kg of carbon c. 36 lb. Of carbon; 16 kg of carbon d. 440 lb. Of carbon; 79 kg of carbon

Answers

Answer:

c. 36 lb. Of carbon; 16 kg of carbon

Step-by-step explanation:

An healthy body is approximately 18% carbon by weight. To determine how many pounds of carbon a body weighing 200Ibs contain can be gotten below.

A healthy person has approximately 18% carbon by weight. Therefore, the number of pounds of carbon for a person weighing 200 Ibs is

pounds of carbon = 18/100 × 200

pounds of carbon = 36 Ibs

According to the question the weight should be in kg.Therefore, we have to convert using the conversion rate you highlighted.

1 Ib = 0.454 kg

36 Ibs = ? kg

cross multiply

weight of carbon in kg = 0.454 × 36

weight of carbon in kg = 16.344 kg

weight of carbon in kg ≈ 16 kg

PLEASE HELP!!!!!! PLEASE

Answers

Answer:

C

Step-by-step explanation:

A<B<D do not make sense

I need this for my notes so i can know what to do. What is the length of AC? And Length of AB?

Answers

Answer:

AC 5

AB = 3

Step-by-step explanation:

AC = distance between the points

C-A = 3 - -2 = 3+2 = 5

The distance is 5

AB = distance between the points

B-A = 1 - -2 = 1+2 = 3

The distance is 3

Answer:

AC = 5

AB = 3

Step-by-step explanation:

AC:

3 - X = -2

3 - 5 = -2

AB:

1 - X = -2

1 - 3 = -2

True or false: the set of whole numbers is equal to the set of natural numbers

Answers

Answer:

False

Step-by-step explanation:

This statement is false.

The set of whole numbers include the set of Natural numbers "N" = {1, 2, 3, 4, 5, 6, ...}, the set of the negatives of the natural numbers: {-1, -2, -3, -4,...}, and the zero: {0}

We see then that the set of Natural numbers is a subset of the set of whole numbers Z = {... -4,-3,-2,-1, 0,1, 2, 3, 4, 5, ...}

Answer:

false

brainliest to me!

Step-by-step explanation:

0 is a whole number but not a natural number so its false!

What is the solution to this system of linear equations? x + y = 4 x − y = 6 (4, 6) (6, 4) (5, −1) (−1, 5)

Answers

Answer:

x= 4 y = -1

(5,-1)

Step-by-step explanation:

x + y = 4 x − y = 6

Add the two equations together to eliminate y

x + y = 4

x − y = 6

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

2x = 10

Divide by 2

2x/2 = 10/2

x = 5

Now find y

x+y = 4

5+y = 4

Subtract 5 from each side

5+y-4 = 4-5

y = -1

Answer

5,-1

Step-by-step explanation:

edg 2020

what is the answer to 18−(2x+1) = ???

Answers

Answer & Step-by-step explanation:

18 - (2x + 1)

Distribute the negative sign (-) to 2x + 1.

18 - 2x - 1

Put -2x in the beginning of the expression and combine like terms.

-2x + 17

So, the answer to 18 - (2x + 1) is -2x + 17.

Add the polynomials.
(4x + 11) + (12x + 2)
a
16x + 13
b
12x + 9
С
25x + 16
d. 19x + 13

Answers

Answer:

[tex](4x + 11) + (12x + 2) =(4x + 12x) + (2 + 11) = 16x + 13[/tex]

Step-by-step explanation:

Answer = a. 16x+13

What is 6 divided by 2

Answers

Answer: 3
To check:
2 * 3 = 6

Answer:

3

Step-by-step explanation:3x2=6

An oil company fills 1/10
of a tank in 1/5, hour. At this rate, which expression can be used to determine how long it will take for the tank to fill completely?
10
10 hours
01
. 5 hours
10
.
1
10
hour
5
5-10 hours

Answers

Answer:

So if the company fills in 1/10 of a tank in 1/5 hour. We should multiply by 10

so that means that the tank will be 100% full because 10/10 = 100%

That also means we need to multiply it by 1/5. 1/5*10 = 10/5.

Therefore we get 2 hours.

Thanks for the question. I am working my way up to brainliest and and Master Answerer

Step-by-step explanation:

A function is defined by f (x) = 5 (2 minus x). What is f(–1)? –5 5 15

Answers

Answer: 15

Step-by-step explanation: 2 minus negative 1 is the same as 2+1. 2 plus 1 is 3 and 5 times 3 is 15. Therefore, 15 is your answer.

Answer:

15

Step-by-step explanation:

took the test on EDGE

how can you find dictance between points and cordinte plances

Answers

Answer:

Distance = [tex]\sqrt{(x^{2}-x,)^{2} +(y^{2} -y,)^{2}[/tex]

The price of a train ticket consists of an initial fee plus a constant fee per stop. The table compares the number of stops and the price of a ticket (in dollars). What is the initial fee?

Answers

Answer:

Initial Fee is $2.

Step-by-step explanation:

What is the slope of the line that passes through the points (4,7) and (5,3)?

Answers

in mx+b form i think it would be y= -4+23
where your slope is negative four

I will be showing you the graphing method.

To find the slope of the line using the graphing method,

we start by plotting our two points.

We will call (4,7) point A and (5,3) point B.

Now daw a line that contains these points.

Now remember that the slope or m is equal to the rise/run.

So to get from point A to point B, we rise -4 units

and run 1 unit so our slope is -4/1 or -4.

A lock requires a 3 number combination using the numbers 0 through 9, none of which may be repeated. How many outcomes are possible?

48

720

12010




Answers

Answer:

720

Step-by-step explanation:

The lock requires that repetition is not allowed.

The possibles numbers are 0 - 9, that is, 10 digits.

The first number in the combination can be picked from the 10 digits.

This means that there are 10 possible choices.

The second number in the combination can now only be picked from 9 digits.

This means that there are 9 possible choices.

The third number in the combination can now only be picked from 8 digits.

This means that there are 8 possible choices.

Therefore, the number of possible outcomes in the combination is:

10 * 9 * 8 = 720 outcomes

Someone who knows what they doing

Answers

Answer: 25.12 and 12.56

Step-by-step explanation:

in the formula, you will notice that you are trying to identify the base(b) and calculate the volume(V). and they are written at the top of the page, 12.56 cm^2 and 25.12cm^3. so the missing things are 25.12 and 12.56.

please help urgent ❤️❤️❤️❤️

Answers

Answer:

B,Friday

Step-by-step explanation:

4 to 9 is 5 hours,the total hours for the week is 32.5 hours

For questions 1 - 2, complete the given table of values. Then sketch a graph that shows two complete cycles. 1. Y=- cosx 2. Y = sin x+1

Answers

Answer:

See attachment.

Step-by-step explanation:

See attachments.

An employee at a factory is paid $9.25 per hour plus an $8.00 bonus for every 20 transformers assembled. Last week an employee worked 36 hours and assembled 380 transformers. How much money did the factory employee actually earn per hour last week rounded to the nearest cent?

Answers

Answer:

2664

Step-by-step explanation:

9.25×36+(380÷20)×8

C. Courtney got a remote control car for her birthday. It is a metallic
purple with chrome wheels that are 1 1/2 inches in diameter. She said to
her friend, Dylan, “My remote control car goes faster than my mom's
car on the freeway.” “No way,” said Dylan. Courtney said, “I will prove it to
you.” Courtney measured off a distance of 115 inches. Dylan said, “Okay, I
will time how long it takes your car to travel that distance. I have a stopwatch
feature on my watch.” Courtney raced her remote control car over the
115-inch distance. Dylan said, “Wow, that only took 3.21 seconds. That seems
really fast.” “See, I told you,” said Courtney. “But really how fast is it going?”
answered Dylan. Determine the speed of Courtney's remote control car and
compare its speed to that of a regular car traveling on the freeway. Explain
how you found your solution. Why might the manufacturer get away with
advertising that the remote control car Travels Faster Than Life?


please help!!!!

Answers

Answer: No. the remote control car traveled 2 miles per hour whereas a car typically travels between 30 miles per hour and 60 miles per hour.

Step-by-step explanation:

[tex]\dfrac{115\ inches}{3.21\ seconds}\times \dfrac{1\ foot}{12\ inches}\times \dfrac{1\ mile}{5280\ feet}\times \dfrac{60\ seconds}{1\ minute}\times \dfrac{60\ minutes}{1\ hour}\\ \\\\=\dfrac{414,000\ miles}{203,385.6\ hours}\\\\\\=\dfrac{2.0\ miles}{1\ hour}[/tex]

Speed of Courtney's remote control car is: 2 mph

Courtney's remote control car is slower than an average freeway car  since averagely the speed of a car on the freeway is usually 60 mph.

Given that:

Distance covered by Courtney's car = 115 inches

Time taken to cover that distance = 3.21 seconds

Converting inches to miles and seconds to hours:

[tex]1 inch \approx 0.0000158 miles\\115 inches = 115 \times 0.000158 miles\\=\approx 0.00182 miles\\\\3.21 seconds = \dfrac{1}{3600} \times 3.21 \: hours\\= 0.00089 \: hours\\[/tex]

Thus speed of Courtney's car can be calculated as

[tex]Speed = \dfrac{distance}{time}\\\\= \dfrac{0.00182}{0.00089} mph\\\\= 2.089 mph \approx 2 mph[/tex]

Thus Speed of Courtney's car is approx 2 miles per hour whereas the average speed of a car on a freeway is about 60 miles per hour.

Learn more here:

https://brainly.com/question/11583742

1. Find the measure of

Answers

Answer:

39 degrees

Step-by-step explanation:

It is shown that there is a 90 degree angle one part is given so 90-51=39 degrees.

Answer:

b = 39°

Step-by-step explanation:

The box means that it is a right angle and a right angle means it is 90 degrees.

90 degrees - 51 degrees = 39 degrees

b = 39°

Answer ASAP, please!!!! Will mark brainliest!!! 25 points!!!!!
A vendor pays a rock band 13 of the total profit from T-shirts and sweatshirts sold at every concert. The vendor paid the rock band $726 after the last concert. If the profit from T-shirts sales was $1,632, what was the profit from sweatshirt sales?

Answers

1/3 of the profits is $1632 * 1/3 which would equal, $544

so 726- 544= $182 sweatshirt sales

but we're looking for 1/3 of sweatshirt sales, so

3 * 182 = $546 and that's your answer

Answer:

"ill get back to you on that lol"

Step-by-step explanation:

Susan Marciano invested part of her 28,000 bonus in a fund that paid a 10% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each investment if her overall net profit was 2,410

Answers

Answer:

amount invested in funds that earned 10% is $25,000, while the amount invested in stock that suffered 3% loss $3,000.

Step-by-step explanation:

Let x be the amount invested in funds that earned 10%.

Then the amount invested in stock that suffered 3% loss is 28,000 - x.

The profit from investment in funds is 10%x

The loss from investment in stock is 3%(28,000 - x).

The net profit is 10%x - 3%(28,000 - x).

As the net profit given in the problem is $2410, we have:

10%x - 3%(28,000 - x) = 2410

Solving for x, we have:

10x - 3(28,000 - x) = 241000 (multiply both sides by 100)

10x - 84000 + 3x = 241000

13x = 241000+84000

13x = 325000

x = 325000/13

x = 25,000

So

the amount invested in funds that earned 10% is $25,000.

the amount invested in stock that suffered 3% loss is 28,000 - x = 28000 - 25000 = $3,000.

A basket has at most 150 applies in it. Then the number of apples in the basket if the number of apples satisfy the following conditions If counted in pairs, one remains; If counted in threes, two remains; If counted in fourss, three remains; If counted in fives, four remains; If counted in sixes, five remains; If counted in sevens, nothing remains; (A) 116 (B) 117 (C) 118 (D) 119

Answers

Answer:

Number of apple = 119

Step-by-step explanation:

Given

[tex]Max_{Apple} = 150[/tex]

Required

Find the actual number of apples;

When counted in any numbers, the number being counted is the divisor;

Take for instance, when counted in pairs, the divisor is 2

When counted in threes,  the divisor is 3

and so on...

So; from the question, we understand that; when the apple is counted in 2s,3s,4s,5s, and 6s; what's left is always one less than the divisor

This means that the number of apple must satisfy the following conditions

Less than 1501 less than the Common Multiple of 2,3,..,6Divisible by 7

The common multiple of 2,3,..6 are 60, 120 ,180,240.....

Recall that, these multiples must satisfy the three conditions above;

1. Less than 150: Only 60 and 120 satisfy condition.

At this point, we'll discard other numbers (180,240,300.....)

2. 1 less than the Common Multiple of 2,3,..,6:

1 less than 60: 60 - 1 = 59

1 less than 120: 120 - 1 = 119

3. Divisible by 7

At this point, we'll divide 59 and 119 by 7 to see if they satisfy this condition;

[tex]\frac{59}{7} = 8.42857142857[/tex]

[tex]\frac{119}{7}=17[/tex]

The results of these division shows that 59 is not divisible by 7;

Hence, the actual number of apple is 119

Number of apple = 119

Triangle A B F is shown. Line B F is extended through point G. Line F A is extended through point C. A line is drawn from point A to point D. A line is drawn from point F to point E. Which represents an exterior angle of triangle ABF? ∠BAD ∠AFE ∠CAD ∠CAB

Answers

Answer:

(D) [tex]\angle CAB[/tex].

Step-by-step explanation:

The diagram is attached below:

Theorem: An exterior angle of a triangle is equal to the sum of the opposite interior angles.

The exterior angle is the angle formed by the third side and a straight line which forms a supplementary angle with the third interior angle.

In the diagram:

[tex]\angle ABF$ and \angle AFB[/tex] are opposite interior angles.

The third angle is [tex]\angle BAF[/tex]

The angle which forms a supplementary angle with [tex]\angle BAF[/tex] is [tex]\angle CAB[/tex].

Therefore, the exterior angle of triangle ABF is  [tex]\angle CAB[/tex].

Answer:

D

Step-by-step explanation:

Just took the test and got it right


Help me ASAP please.

If two lines intersect and one angle measures 25°, what are the measures of the other angles?


25
75
155
125

Answers

Answer:

155 and 25

Step-by-step explanation:

Answer: 155

Step-by-step explanation:

Two Lines that intersect form TWO angles. The sum of the Two Angles is always 180 degrees.

180-25 = 155

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