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.
Answers
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:
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
Work out the size of angle x and give reasons for your answer. Image attached.
Answers
Answer:
The answer of X would be 80°.
<FBD+100=180 (Co interior angle)
<FBD= 80
X= <FBD = 80° ( Being alternate angle)
7
Eddie had lunch at 10 minutes to 1 in the afternoon.
Fatimah had lunch at 11 45 on the same day.
Who had lunch later? How much later?
Answers
Answer: Eddie had lunch later than Fatimah.
Step-by-step explanation: Eddie had lunch at 10 minutes to one, which is 12:50. Fatimah had lunch at 11:45. So if you subtract 11:45 from 12:50, you find that Eddie had lunch 1:05 later than Fatimah.
Answer:
Eddie had lunch later.
He had lunch 1 hour 5 minutes later
Step-by-step explanation:
Eddie had lunch 10 min before 1
which means at 12 50.
Fatimah had lunch at 11 45 . Earlier than Eddie.
Eddie had lunch after her.
and How much later?
11 45 to 12 45 is 1 hour.
12 45 plus 5 minute is 12 50.
so it is 1 hour 5 minute
Charlie is helping refill ketchup bottles at his uncle's diner. He has a huge container with 2 gallons of ketchup, which he distributes evenly among 15 bottles. How much ketchup goes in each bottle? Write your answer as a proper fraction or mixed number.
Answers
Answer:
A = 2/15 gallons per bottle
Step-by-step explanation:
Given;
Total volume of ketchup V = 2 gallons
Number of bottles N = 15
The amount of ketchup per bottle A;
A = total volume of ketchup ÷ number of bottles
A = V/N
Substituting the values;
A = 2gallons ÷ 15bottles
A = 2/15 gallons per bottle
Answer:
2/15
Step-by-step explanation:
2 divided by 15 is the same or equal to 2/15
example: 2 divided by 15= 2/15
Factor completely. 7 +14 x + 7 x^2
Answers
Answer:
(7x+7 )(x+1 )
Step-by-step explanation:
7x²+14x+7
(7x+7 )(x+1 )
7x²+7x+7x+7
7x²+14x+7
Answer: 7(1+x)^2
Step-by-step explanation: I got it wrong because of that person at the top your welcome
Order these numbers from least to greatest.
1.4, 1.103, 1.1322, 1.13
Answers
Answer:
1.103,1.13,1.1322,1.4
Step-by-step explanation:
find the decimal places and u can figure out with they are greater than this decimal or less
Answer:
1.103, 1.13, 1.1322, 1.4
Step-by-step explanation:
hope that helped:D
Please help guys please
Answers
Answer: The answer is A
Step-by-step explanation:
85 percent of 2500cm
Answers
Answer:
2125
Step-by-step explanation:
of means multiply
85% * 2500
Change to decimal form
.85* 2500
2125
What is the following product?
Sqrt 30 • sqrt 10
2 sqrt 10
3 sqrt 10 4 Sqrt 10
10 sqrt 3
Answers
Answer:
10 sqrt 3.
Step-by-step explanation:
sqrt30 = sqrt10 * sqrt 3
so sqrt30 * sqrt10
= sqrt10 * sqrt10 * sqrt3
= 10 sqrt 3.
Answer:d
Step-by-step explanation:
the scale on a map is 1 : 15000 how many kilometers on the ground would be represented by 12 cm on the map?
Answers
Answer:
1.8 km
Step-by-step explanation:
The scale on the map is 1 : 15000.
This means that every 1 cm on the map is equal to 15000 cm on the ground.
12 cm on the map will therefore be:
12 * 15000 = 180000 cm
Let us convert to kilometres:
100000 cm = 1 km
180000 cm = 180000 / 100000 = 1.8 km
12 cm on the map will be 1.8 km on the ground.
2x + 12 = -2(4-2x)
X=10
X=-10
X=-5
X=5
Answers
Answer:
[tex] \boxed{x = 10} [/tex]
Step-by-step explanation:
[tex] = > 2x + 12 = - 2(4 - 2x) \\ \\ = > 2x + 12 = (( - 2) \times 4) - (( - 2) \times 2x) \\ \\ = > 2x + 12 = - 8 - ( - 4x) \\ \\ = > 2x + 12 = - 8 + 4x \\ \\ = > 2x - 4x + 12 = - 8 \\ \\ = > - 2x + 12 = - 8 \\ \\ = > - 2x = - 8 - 12 \\ \\ = > \cancel{-} 2x = \cancel{- }20 \\ \\ = > 2x = 20 \\ \\ = > x = \frac{20}{2} \\ \\ = > x = 10[/tex]
Question 3: Marla bought one necklace and two bracelets for $67.50. Use the following information to determine the amount she paid for each bracelet: The price of the necklace was $27. The bracelets were both the same price. Enter your numerical answer only in the box; do not include the dollar sign.
Answers
Answer:
Each bracelet costs 20.25
Step-by-step explanation:
Here's what was given in the equation:
Total Price: $67.50
Price of necklace: $27
We can subtract the $27 from the $67.50 to get $40.5
Since we know that both bracelets are the same price we can divide the $40.5 by 2 to get two of the exact same prices. The result is $20.25 for each bracelet.
Hope this helps
Answer:
20.25
Step-by-step explanation:
Took test got it right.
model -5 + (-6) on the number line
Answers
Answer:
-5+(-6 )= -11 so you would pinpoint -11 on the number line
Step-by-step explanation:
The ratio x:y is 3:1
Which of the following statements is correct?
1)x is 3/4 of y
2) y is 1/3 of x
3) x is 1/3 of y
4) y is 1/4 of x
Answers
y is ⅓ of x
step by step explanation.ratio of x to y is 3:1
x=¾
y=¼
¼÷¾=⅓
that means y is ⅓ of x
to confirm the answer.when you take¾×⅓=¼.
Answer:
Its B
Step-by-step explanation:
30% of consumers prefer to purchase elecktronicks online you randomly select 8 consumers find the probability that the number of consumers who prefer to purchase electronics online is a exactly 5 be more than 5 &c at most 5
Answers
Answer:
see below
Step-by-step explanation:
Take the number of people surveyed and multiply by 30 %
8 * 30%
Change to decimal form
8 * .3
2.4
About 2.4 will purchase online
Yoooooo help me out pls
-ayyyyy
Answers
Answer:
probably a. metres
Step-by-step explanation:
hectometres are huge and the other two are super small so thats my guess lol
Answer:
Step-by-step explanation:
A square meters-
Millimeters are super small
And the other ones are to huge
Dats easy
Write each polynomial in standard form. What is the name of the polynomial based on its degree and number of terms?
a. 3 + 5x − 4x2
b. 8x + x + 5 + x3
Answers
Answer:
Step-by-step explanation:
(a) 3 + 5x − 4x^2 should be written as −4x2 + 5x + 3. This is a QUADRATIC function.
(b) 8x + x + 5 + x^3 should be re-written first as 9x + 5 + x^3 and then as
x^3 + 9x + 5. This is a CUBING function.
Angle sum theorem
25°
30°
Answers
Answer:
x = 125°
y = 180-125 = 55°
Step-by-step explanation:
The angles should sum to 180 in a triangle.
Since the other two are 25 and 30, for the third one, 180-25-30 = 125 is left, which is x.
Now y and x are supplementary angles, which means that x+y is also 180°.
So y = 180-x = 55°
Answer:
y = 55°
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
y is an exterior angle of the triangle, thus
y = 25° + 30° = 55°
Solve for x in the diagram below.
200
(3x + 10°
Answers
Answer:
x = 20°
Step-by-step explanation:
4x + 10 = 90
4x = 80
x = 20
Answer:
[tex] \boxed{x\degree = 20\degree} [/tex]
Step-by-step explanation:
Two Angles are Complementary when they add up to 90° (a Right Angle).
[tex] = > x\degree + (3x + 10)\degree = 90\degree \\ \\ = > x\degree + 3x\degree + 10\degree = 90\degree \\ \\ = > 4x\degree + 10\degree = 90\degree \\ \\ = > 4x\degree = 90\degree - 10\degree \\ \\ = > 4x\degree = 80\degree \\ \\ = > x\degree = \frac{80}{4} \degree \\ \\ = > x\degree = 20\degree [/tex]
Which equation can you use to calculate the
missing credit score?
*-780
1.07
28
x - 28
780=
1.07
28 =
x-1.07
780
Answers
Answer:
1.07=x-780/28
Step-by-step explanation:
Miss credit score: 810
Answer:
810
Step-by-step explanation:
Jun-seo notices that there are 13 right-handed players on his baseball team and 2 left-handed players. What is the ratio of right-handed players to left-handed players?
Answers
Answer:
The ratio of right handed to left handed players is 13 to 2
Step-by-step explanation:
Here in this question, we are asked to give the ratio of right handed to left handed players.
To give this ratio, we shall need to know the numbers of right handed players and left handed players.
From the question, we can see that there are 13 right handed and 2 left handed players.
Thus, the ratio of right handed to left handed players is 13:2
The cost of a hall rental for a wedding is $500. Each meal at the wedding will cost an additional $45.50
a) Write an algebraic expression equation for the total cost of the wedding.
b) Calculate how many people attended the wedding if the wedding cost totalled $3912.50.
Answers
Answer:
a) 45.50p + 500
b) 45.50p + 500 = 3912.50
p = 70
Step-by-step explanation:
p = number of people
$45.50 for a meal for each person, so:
45.50p
The constant is $500, so let's add that to the expression:
45.50p + 500
This month the local power company charges $9.12 per kilowatt-hour for electricity. Write an equation that represents the total amount a customer will pay for their usage.
Answers
Answer:
9.12 x time x kilowatt
Step-by-step explanation:
we can describe 12×-8 as an expression . it can also be written as 4(3×-2) 4 and 3×-2 are both...of 12×-8
Answers
Answer:
factor
Step-by-step explanation:
I NEED HELP! WILL BE GIVING BRAINLIEST TO THE CORRECT ANSWER + 30 POINTS!!!!
Answers
Answer:
l = 20 cm
w = 12 cm
Step-by-step explanation:
P = 64 = 2w + 2l
2w = 4 + l
64 = 4 + l + 2l
64 - 4 = 3l
3l = 60
l = 20 cm
2w = 20 + 4
2w = 24
w = 12 cm
For a polynomial function y = f(x), where f(1/3)=0, one of the factor would be
Answers
Answer:
(x-1/3) is one of the factors
Step-by-step explanation:
Using the reverse of the zero product property
(x-a) = 0 where a is one of the roots
x-1/3 = 0
(x-1/3) is one of the factors
Answer:
x-1/3) is the answer
Step-by-step explanation:
zero product property
PLEASE HELP!!Write an algebraic expression to represent the following verbal expression.
eight more than the product of a number and 100
Select one:
O a. 100x + 8
O b. 100x - 8
O c. 100 + 8x
O d. 8 - 100x
Answers
Answer:
work is pictured and shown
An expression to represent the given verbal expression is,
⇒ 100x + 8
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The verbal expression is,
''Eight more than the product of a number and 100.''
Let an number = x
So, We can formulate;
⇒ Eight more than the product of a number and 100.
⇒ 8 + x × 100
⇒ 8 + 100x
Learn more about the mathematical expression visit:
brainly.com/question/1859113
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Brian & Paul share a lottery win of £7800 in the ratio 1 : 4. Brian then shares his part between himself, his wife & their son in the ratio 1 : 6 : 3. How much more does his wife get over their son?
Answers
Answer:
The wife gets £468 over the son
Step-by-step explanation:
Firstly, we shall calculate the total amount Brian made from from what he and Paul won.
The ratio is 1:4, meaning for every 2 part Brain takes, Paul takes 4
Paul’s share is thus 1/5 * 7800 = 7800/5 = £1560
Now we have another ratio for sharing the amount Brain has at home.
The total ratio here is 1+6+3 = 10
The share of the wife will be 6/10 * 1560 = 6 * 156 = 936
The son share is half of this which is 936/2 = 468
The difference between their shares is £936-£468 = £468
Help please! look at the attachment
Answers
Answer:
B
Step-by-step explanation:
What is the value of x?
0
va units
1v3 units
2/3 units
3/2 units
Answers
Answer:
Step-by-step
In ordinary arithmetic, the expression has no meaning, as there is no number which, when multiplied by 0, gives a (assuming a ≠ 0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 00 is also undefined; when it is the form of a limit, it is an indeterminate form. explanation:
In the diagram, AB is parallel to DE. Also, DE is drawn such that the length of DE is half of the length of AB. If sin A = 0.5, then what is sin E?
A) 2
B) 1
C) 0.5
D) 0.25
E) 0.1
Answers
Answer:
C
Step-by-step explanation:
PLATO
So, sin E=0.5. Therefore, option C is the correct answer.
Given that, AB║DE and sinA= 0.5.
We need to find the value of sin E.
How to find the value of sin?The value of sinθ must always be between −1 and 1. So the domain of f(x) = sinθ contains all the real numbers, but the range is −1 ≤ sin x ≤ 1. We can also see that the function repeats itself every 360°.
Now, sinA = 0.5
⇒∠A=30°
∠A=∠E=30° (∵∠A and ∠E are alternate angles)
Therefore, option C is the correct answer.
To learn more about trigonometry visit:
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