The diagram shows three points P, Q and R on horizontal ground.
PQ = 50 m, PR = 100 m and angie PQR = 140°.
Calculate angle PRO.
Answers
Answer:
m<PQR = 18.7°
Step-by-step explanation:
Apply the Law of Sines,
[tex] \frac{Sin A}{a} = \frac{Sin B}{b} [/tex]
Where,
Sin A = Sin 140
a = 100 m
Sin B = Sin R (<PRQ)
b = 50 m
Substitute
[tex] \frac{Sin 140}{100} = \frac{Sin R}{50} [/tex]
Cross multiply
[tex] 100*Sin(R) = 50*Sin(140) [/tex]
Divide both sides by 100
[tex] Sin(R) = \frac{50*Sin(140)}{100} [/tex]
[tex] Sin(R) = 0.32139 [/tex]
[tex] R = Sin^{-1}(0.32139) [/tex]
R ≈ 18.7° (nearest tenth)
m<PQR = 18.7°
The angle PRO is 1.7 degrees.
Given that,
The diagram shows three points P, Q, and R on horizontal ground.
PQ = 50 m, PR = 100 m and angle PQR = 140°.
We have to determine,
The angle PRO.
According to the question,
The value of angle PRO is determined by using the sin rule-following all the steps given below.
[tex]\rm \dfrac{sina}{a} = \dfrac{sinb}{b}[/tex]
Where, Sin A = Sin 140 , a = 100 m , Sin B = Sin R (<PRQ) , b = 50 m
Substitute all the values in the formula,
[tex]\rm \dfrac{sin140}{100} = \dfrac{sinR}{50}\\\\ \dfrac{0.64}{100} = \dfrac{sinR}{50}\\\\0.0064 = \dfrac{sinR}{50}\\\\0.0064 \times 50 = sinR\\\\0.321 = sinR\\\\R = sin{-1}(0.321)\\\\R = 18.7 \ degree[/tex]
Hence, The angle PRO is 1.7 degrees.
For more details refer to the link given below.
https://brainly.com/question/12895249
Related Questions
solutions of the quadratic $x^2 + 7x - 18 = 0.$
Answers
(x^2+7x-18) can be factored into (x+9)(x-2). Set each part equal to zero and solve for x.
x+9=0 => x=-9
x-2=0 => x=2
I’m guessing the dollar signs aren’t supposed to be there.
The solution of the quadratic equation x² + 7x - 18 = 0 will be 2 and negative 9.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The quadratic equation is given below.
x² + 7x - 18 = 0
Factorize the quadratic equation, then we have
x² + 7x - 18 = 0
x² + 9x - 2x - 18 = 0
x(x + 9) - 2(x - 9) = 0
(x + 9)(x - 2) = 0
x = 2, -9
The arrangement of the quadratic condition x² + 7x - 18 = 0 will be 2 and negative 9.
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Which expression is equivalent to 3/5x +3
2/5x + 1/5x
4/5x - 1/5x + 3
2/5x + 3 3/5x -1
1 + 3/5x + 2
1 +x/5 + 2
1 + 2/5x +3
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If f(x) = 4x − 1 and g(x) = −3x + 2 (a) Find ℎ(x) = f(x) + g(x)
Answers
Answer:
x+1
Step-by-step explanation:
4x - 1 + (-3x) + 2 = x + 1
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x
+
10
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When would the following conditional be false?
If you study for the test, then your grade will be higher than a 75.
You study for the test, and your grade is an 80.
You study for the test, and your grade is a 70.
You do not study for the test, and your grade is an 80.
You do not study for the test, and your grade is a 70.
Answers
According to the conditional statement, the false option is:
You study for the test, and your grade is a 70.The statement is:
"If you study for the test, then your grade will be higher than a 75."It says nothing about not studying for the test, hence the third and fourth options are ignored.
If you study, you are ensured a grade higher than 75, hence, the false option is:
You study for the test, and your grade is a 70.You can learn more about conditional statements at https://brainly.com/question/11073037
All I need is the answer Please and thank you
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Should be 40ft. If not, I dearly apologize.
Answer:
40ft tall
Step-by-step explanation:
Hope this helps :)
Of the 16 new students in a swim class, 6 said they knew how to do the butterfly stroke. Write a ratio that is equivalent to 6/16.
Need answer ASAP. I will provide brainliest in this Q.
Answers
EXPLANATION: 6/16 = 3/8
what is the cosine rule
Answers
Answer:
The sum of the squares of the lengths of the other sides minus twice the product of the other two sides multiplied by the cosine of angle contained between them equals the square of the length of any side of a given triangle.
Step-by-step explanation:
hope it helps
Select the correct answer.
If you divide -16 into 5 equal parts, how much is each part equal to?
A.
-4
B.
-3.2
C.
+2.4
D.
+5
Answers
Answer:
B) -3.2
Step-by-step explanation:
-16/5 = -15/5 - 1/5 = -3 - 0.2 = -3.2
If a die is thrown, the probability of getting even number is
a)1/2 b)1/6 c)1/3 d) 2/3
Answers
Answer:
A 1/2
Step-by-step explanation:
Its a half chance since theres 6 sides so 1/2:)
Answer:
[tex]b) \frac{1}{2} [/tex]
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Doubt clarification - use comment section.
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Given info:- In ∆ABC, right-angled at c in which AB = 10in, BC = 26 in and we have to find out the measure of AC = ?
Explanation:
In right angled ∆OCB, AC ⟂ CB,
AB² = AC²+CB²
[By Pythagoras theorem]
(10)² = AC²+(26)²
10*10 = AC²+(26*26)
100 = AC²+676
AC² = 676-100
AC² = 576
AC = √(576)
AC = 24 in.
Hence, the measure of right-agled in which AC is 24 in.
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Answer:
yes
option B
you're correct
If 333 + 555 = 999 And 123 + 456 = 488 And 505 + 213 = 809 Then 344 + 732 = ???
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Answer:
1076
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
lol, uhm, this is a little bit of a strange question ngl, but I guess it's testing you on measurements and units, right?
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A large bowl and a small bowl both contain gems. of the gems in each bowl are red. All the gems from the two bowls are now put into a third bowl. What fraction of the gems in the third bowl will be red?
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Elsa drove 715 miles in 13 hours, At the same rate, how long would it take her to drive 275 miles?
Answers
Answer:
Driving 275 miles would take Elsa 5 hrs.
Step-by-step explanation:
Write and solve an equation of ratios:
715 mi 13 hrs
------------- = --------------
275 mi x
This leads to: 715x = 13(275), or x = 5 (hrs)
Driving 275 miles would take Elsa 5 hrs.
PLEASE, LAST POINTS! ( GIVING BRAINLIEST) TO GET BRAINLIEST ANSWER 6 and 8 PLEASE. LAST 10 POINTS!
Answers
Answer:
6; 6⁒2
10; 10⁒2
0; 3(0)+3
1; 3(1)+3
2; 3(2)+3
3; 3(3)+3
4; 3(4)+3
Step-by-step explanation:
each line is in order.
Answer:
6. inputs: 2, 6, 10
8. inputs: 0, 1, 2, 3, 4
Step-by-step explanation:
Use your knowledge of arithmetic facts.
6.x = 2, 2÷2 = 1
x = 6, 6÷2 = 3
x = 10, 10÷2 = 5
__
8.x = 0, 3×0 +3 = 3
x = 1, 3×1 +3 = 6
x = 2, 3×2 +3 = 9
x = 3, 3×3 +3 = 12
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x varies directly with y. If x is 108 when y is 180, find x when y is 150.
Answers
Answer:
X=90
Step-by-step explanation:
k=3/5
X=3/5×150
X=90
X cube+6x-16=0
find all solutions by factoring.
answers
(-2,8)
(-8,2)
(2,8)
(-8,-2)
Answers
Answer:
(b) {-8, 2}
Step-by-step explanation:
The given equation
x³ +6x -16 = 0
cannot be factored in integers. It has one irrational real root near x=1.759, and two complex roots.
__
Perhaps you want to factor ...
x² +6x -16 = 0
(x +8)(x -2) = 0
This has solutions x = -8 and x = 2 that make the factors be zero.
_____
Additional comment
"Cubed" refers to an exponent of 3.
Answer:
Option b] (2,-8)
Step-by-step explanation:
⇒ x³ + 6x - 16 = 0
♦ the value of one root is irrational and other two are complex roots.
⇒ x² + 6x - 16 = 0
⇒ (x + 8)(x - 2) = 0
⇒ x = 2 , -8
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9y + 2 = 58; {4,5,6}
Please show your work.
A, Y=4
B, Y=5
C, Y=6
Answers
Answer:
6
Step-by-step explanation:
Replace y with each of your answers and then solve from thwre.
Grayson is flying a kite, holding his hands a distance of 2.75 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 26
∘
∘
. If the string from the kite to his hand is 145 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answers
The position of the kite with the point directly beneath the kite at the same
level with the hand and the hand for a right triangle.
The height of the kite above the is approximately 66.314 feet.Reasons:
The height of his hands above the ground, h = 2.75 feet
Angle of elevation of the string (above the horizontal), θ = 26°
Length of the string, l = 145 feet
Required:
The height of the kite above the ground.
Solution:
The height of the kite above the ground is given by trigonometric ratios as follows;
[tex]\displaystyle Height \ of \ kite, \, k_h = \mathbf{h + l \times sin(\theta)}[/tex]
Therefore;
[tex]\displaystyle Height \ of \ kite, \, k_h = 2.75 + 145 \times sin(26^{\circ}) \approx \mathbf{66.314}[/tex]
The height of the kite above the, [tex]k_h[/tex] ≈ 66.314 feet
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Determine which postulate or theorem can be used to prove that ASEA = A PEN E O A. ASA OB. SSS O C. AAS O D. SAS
Answers
Answer:
asa is the correct answer
The postulate or theorem can be used to prove that triangles are congruent is ASA rule.
What are congruent triangles?Two triangles are said to be congruent when they have congruent corresponding parts.
Given is a figure having two triangles, we need to find the rule, that can prove that both the triangles are congruent,
∠ S ≅ ∠ P [given]
∠ SEA ≅ ∠ PEN [vertically opposite angles]
SE ≅ EP [given]
∴ Δ SEA ≅ Δ PEN by ASA rule
ASA rule :-
If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.
Hence, the postulate or theorem can be used to prove that triangles are congruent is ASA rule.
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can someone help with this
Answers
[tex]R.H.S\\\\=(a+b)(a^3-a^2b-ab^2+b^3)\\\\=a^4-a^3b-a^2b^2+ab^3 + ba^3-a^2b^2-ab^3+b^4\\\\=a^4+b^4-2a^2b^2\\\\\neq a^4 +b^4\\\\\\\text{Hence, }(a+b)(a^3-a^2b-ab^2+b^3) =a^4+b^4 ~ \text{is not true.}[/tex]
30 points! "A triangle with the side lengths of these numbers can not exist: 9, 3, and __?"
Answers
Answer:
A triangle with the side lengths of these numbers can not exist: 9,3 and 6
Step-by-step explanation:
hope it helps
Step-by-step explanation:
Let the third side be x
We know that
Sum of two sides of a triangle must be greater than the third side
So,
9 + 3 > x
12 > x (1)
Also, difference of two side of triangle must be smaller than the third side
9 - 3 < x
6 < x (2)
From 1 and 2 we concluded
6 < x < 12
The length of third side would lie between 7 to 11
Given that a/b=3/5 and b/c=4/5
Find a:b:c giving your answer in its simplest form
Answers
Answer:
12 : 20 : 25
Step-by-step explanation:
Express the ratios in terms of a
[tex]\frac{a}{b}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )
3b = 5a ( divide both sides by 3 )
b = [tex]\frac{5}{3}[/tex] a
[tex]\frac{b}{c}[/tex] = [tex]\frac{4}{5}[/tex] ( cross- multiply )
4c = 5b ( divide both sides by 4 )
c = [tex]\frac{5}{4}[/tex] b = [tex]\frac{5}{4}[/tex] × [tex]\frac{5}{3}[/tex] a = [tex]\frac{25}{12}[/tex] a
Then
a : b : c
= a : [tex]\frac{5}{3}[/tex] a : [tex]\frac{25}{12}[/tex] a ( multiply each part by 12 to clear the fractions )
= 12a : 20a : 25a ( divide each part by a )
= 12 : 20 : 25
Are the ratios 12:6 and 2:1 equivalent?
Answers
Answer:
no
Step-by-step explanation:
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Answer:
Yes!
Step-by-step explanation:
Here, ratios can be rewritten by fractions.
12:6 is [tex]\frac{12}{6}[/tex] which equals to 2,
2:1 is also [tex]\frac{2}{1}[/tex] which is 2.
To get 12 from 2, you multiply by 6.
Multiply the same thing to the denominator(1), and you get 6. So:
12:6 = 2:1
If f(x)=3x+2 and g(x)=x2−x, find the value. f(x)+1
Answers
Answer:
F(x) +1 = 3x+3
Step-by-step explanation:
F(x)+1= 3x+3
Place the fraction 1/2 on the number line.
Answers
Answer:
in the middle
Step-by-step explanation:
I did this before
Amy is solving the equation using the steps shown.
Which could be the correct next step in solving the equation?
Subtract 2 from both sides of the equation to yield (x 2 – 16) = 0.
Subtract 2 from both sides of the equation to yield (, x , 2, – 16) = 0.
Multiply (x 2 – 16)(x + 2) on the left side of the equation to yield x 3 + 2x 2 – 16x – 32 = 0.
Multiply (, x , 2, – 16)(, x, + 2) on the left side of the equation to yield , x, , 3, + 2, x, , 2, – 16, x, – 32 = 0.
Factor (x 2 – 16) on the left side of the equation to yield (x + 4)(x – 4)(x + 2) = 0.
Factor (, x , 2, – 16) on the left side of the equation to yield (, x, + 4)(, x, – 4)(, x, + 2) = 0.
Add 16 to both sides of the equation to yield x 2(x + 2) = 0.
Add 16 to both sides of the equation to yield , x , 2, (, x, + 2) = 0.
Answers
The correct next step Amy could take is to factor (x^2 - 16) on the left side of the equation to yield (x + 4)(x – 4)(x + 2) = 0.
The equation is given as:
[tex]\mathbf{(x^2 - 16)(x + 2) = 0}[/tex]
The possible next steps are:
1. Expand the equation as follows
[tex]\mathbf{x^3+2x^2-16x-32 = 0}[/tex]
2. Express x^2 -16 as a difference of two squares as follows
[tex]\mathbf{(x + 4)(x- 4)(x + 2) = 0}[/tex]
However, the correct step in this case is to factor x^2 - 16 as a difference of two squares to give [tex]\mathbf{(x + 4)(x- 4)(x + 2) = 0}[/tex]
This is so, because the question says Amy is trying to solve for variable x.
This step will ensure that she gets the possible values of x, unlike expanding the whole equation .
Hence, the correct next step is [tex]\mathbf{(x + 4)(x- 4)(x + 2) = 0}[/tex]
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PLZ HELP ME
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Answer:
the domain is -11,10 but i didnt know if you wanted that or not
Step-by-step explanation:
