Work out the length QR.
Give your answer correct to 3 significant figures.
Total marks: 5
Answers
Answer:
The length of QR is 29.9 cm
Step-by-step explanation:
Let us revise the sine and cosine rules
In triangle ABC:
[tex]\frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}[/tex] ⇒ sine rule
(AC)² = (AB)² + (BC)² - 2(AB)(BC)cos(∠B) ⇒ cosine rule
Let us use these rules to solve the question
In Δ PQS
∵ [tex]\frac{PS}{sin(Q)}=\frac{QS}{sin(P)}[/tex]
∵ PS = 11.7 cm
∵ m∠P = 95°, m∠Q = 28°
→ Substitute them in the rule above
∴ [tex]\frac{11.7}{sin(28)}=\frac{QS}{sin(95)}[/tex]
→ By using cross multiplication
∴ QS × sin(28) = 11.7 × sin(95)
→ Divide both sides by sin(28) to find QS
∴ QS = 24.82680292 cm
Now let us use the cosine rule to find QR
In Δ QSR
∵ (QR)² = (QS)² + (RS)² - 2(QS)(RS)cos(∠QSR)
∵ RS = 10.2 cm
∵ m∠QSR = 110°
→ Substitute these values in the rule above
∴ (QR)² = (24.82680292)² + (10.2)² - 2(24.82680292)(10.2)cos(110)
∴ (QR)² = 893.631984
→ Take √ for both sides
∴ QR = 29.89367799
→ Round it to 3 significant figures
∴ QR = 29.9 cm
Related Questions
Nancy made 20 ounces of a snack mix that was 1/5 peanuts, 30% raisins, and 5 ounces of chocolate chips. the rest was granola how many ounces of granola were in Nancy's snack mix?
Answers
Answer:
5
Step-by-step explanation:
First of all, we have a lot of different forms of part/whole's. We have a fraction, a percentage, and a number. How do we make this work???
Let's convert our percent and fraction to ounces, because that is what the question is talking about.
1/5 of 20
1/5=x/20
20=5x
/5 /5
4=x
Now lets convert our percent into ounces.
30% of 20
30/100=x/20
30(20)=100x
600=100x
/100 /100
6=x
Now we have our ounces, we now need to find what is the granola. To do that, we need to add the number of everything else, and then subtract that by the total ounces.
4+6+5=15
20-15=5
The answer would be 5 ounces of granola!
100 POINTS!!!
If you have a line parallel to the line given by the equation
what would be the slope of the parallel line?
EXPLAIN
Answers
Answer:
The first choice
Step-by-step explanation:
The slope of a line parallel to the original line is the same. Also, a slope does not have x after it.
if p is q and q is r which statement must be true
A.S is p
B.R is p
C. p is s
D. P is R
Answers
Answer: D
Step-by-step explanation:
Answer:p is r
Step-by-step explanation:
Can someone help me with this please 1/4(5x+16/3)-2/4(3/4x+1/2)=-5.
Answers
Hope this help
X/4+7=3
Test answer!!
Answers
Answer:
-16
Step-by-step explanation:
you have to first subtract 7 from 3 to get -4. then multiply 4 with -4 to get -16.
Answer:
[tex] \frac{x}{4} + 7 = 3 \\ or \: \frac{x}{4} = 3 - 7 \\ or \: \frac{x}{4} = - 4 \\ or \: x = - 4 \times 4 \\ or \: x = - 16 \\ \\ therefore \: the \: value \: of \: x \: is \: - 16.[/tex]
Find the sum of the measures of the interior
angles of a convex 70-gon.
Answers
Therefore, for this question,
n=70
the sum of interior angles=180*(70-2)=180*68=12240 degree
Pls mark me as the Brainliest as I really need it!
1. Karen has a square cartolina whose sides measure 60
cm each. She cuts the cartolina into two equal rectangles.
Find the perimeter of one piece of rectangle.
2. A rectangle has a length of 30 cm and a width smaller
by 5 cm. What is its perimeter?
Answers
If Karen cut her square cardboard into two equal rectangles, the perimeter of those rectangles is 180cm. On the other hand, if the rectangle is 25 cm wide, the perimeter would be 110 cm.
What is the perimeter of a geometric figure?
The perimeter of a geometric figure is the measure of the length of all its sides. In this case, if Karen has a square of cardboard with a side of 60cm, it can be inferred that she would have two rectangles with a height of 30cm and a base of 60cm, so the perimeter would be:
30cm + 60cm + 30cm + 60cm = 180cmOn the other hand, if the rectangle has a base of 30cm and a height of 25cm, the perimeter would be:
25cm + 30cm + 25cm + 30cm = 110cmLearn more about perimeter in: https://brainly.com/question/6465134
What happens if the red lines are NOT parallel. Which angle types are still congruent?(please help)
Answers
Answer:
If they are not parallel they will cross.
The angle types that are still congruent are the angles that are the same size.
Step-by-step explanation:
Parallel lines never cross but non parallel lines cross.
Could I please have BRAINLIEST?Answer:
vertical ?
Step-by-step explanation:
sorry if wrong :')
. Paul plans to have a rectangular garden adjacent to his garage. He will use 36 feet of fence to
enclose three sides of the garden. The area of the garden, in square feet, can be modeled by
w) - W(36 - 2w), where w is the width in feet,
(a) On the set of axes below, sketch the graph of f(w)
Answers
The area of the garden is the product of its width and its length
How to plot the graph of f(w)?The given parameters are:
Perimeter = 36 feet
f(w) = w(36 - 2w)
The second expression above represents a function whose input is w; i.e. function w or f(w)
Next, we plot the graph of f(w) using a graphing calculator
See attachment for the graph of f(w)
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https://brainly.com/question/24487155
At the end of a snow storm, Elijah saw there was a lot of snow on his front lawn. The temperature increased and the snow began to melt at a steady rate. There was a depth of 18 inches of snow on the lawn when the storm ended and then it started melting at a rate of 1.5 inches per hour. Write an equation for S, in terms of t, representing the depth of snow on Elijah's lawn, in inches, t hours after the snow stopped falling.
Answers
Answer:
S = 18 - 1.5t
Step-by-step explanation:
The initial value is 18 inches
The rate of change is -1.5 inches per hour
t is the number of hours
S = 18 - 1.5t
How do you factor m^2+6m-7
Answers
Answer:
Your answer is: (m-1) (m+7)
Step-by-step explanation:
Hope this helped : )
can iget some help on this pls
Answers
Answer:
-2 1/3
Step-by-step explanation:
i hope this helps you!
This figure has two intersecting lines and a ray. What is the value of x?
108°
72°
19°
37°
Answers
Answer: The answer is 37
Step-by-step explanation:
If you subtract 71 from 108 the answer is 37
Since the angles of (x + 71)º is opposite to the same vertex to the angle of 108º, it is found that x = 37º.
The ray generated two angles, xº and 71º.Adding these angles, there is an angle of (x + 71)º, which is opposite to the same vertex to the angle of 108º, meaning that they have the same measure.
Applying the equality:
[tex]x + 71 = 108[/tex]
[tex]x = 108 - 71[/tex]
[tex]x = 37[/tex]
Thus, x = 37º.
A similar problem is given at https://brainly.com/question/16742265
Joni climbed 230 feet up a hill and then rappelled down 300 feet into a valley.
Write an addition expression to represent the situation
Answers
Answer:
230-300= -70
All you have to do is subtract :)
solve for x. 3x+9=15x-5. show work
Answers
Sol:
3x-15x=-5-9
or,-12x=-14
or,x=14/12
or,x=1.667
so, x=1.667
Answer:
[tex]3x+9=15x-5[/tex]
[tex]3x+9-9=15x-5-9[/tex]
[tex]3x=15x-14[/tex]
[tex]3x-15x=15x-14-15x[/tex]
[tex]-12x=-14[/tex]
[tex]\frac{-12x}{-12}=\frac{-14}{-12}[/tex]
[tex]x=\frac{7}{6}[/tex]
or
[tex]x=1.1666[/tex]
What is (184730248764874252034*9748242241036484916485)\(9489258234569786578024628435672046*72386438952467922592641964870)+(892187341935496495*2873937610)+(903781)?
Answers
i cant tell if thats a real question or not but ahhhhh thats a big number
Who ever is reading this:
I love u.
U matter.
The world needs u
hang in there ik it may be bad but u deserve the world <3
ur beautiful for who u r, not wht u look like. no matter ur shape, size, color, gender.. anything
don't give up bby i need u to live.
i wish i could take everyones problems so yall wouldn't have to have em but i cant so just know ily and if anyone needs to talk u can talk to me
Pls pass this on. Everyone deserves to know this. ♥️♥️
just copy and paste its not hard pls this could save someones life
Answer:
it 40 super easy
Step-by-step explanation:
х
у
-11
-3
-1
-3
0
9
un lwin
13
21
Which function best represents the relationship shown in the graph? 8.51
А
1
y -x + 1
B
y = 4x - 1
C y = x + 4
Dy = 4x + 1
Answers
Given that ∠2 ≅ ∠6.
Which theorem proves that line d is parallel to line e.
Alternate interior angle theorem
Converse of the alternate interior angle theorem
Alternate Exterior angle theorem
Converse of the alternate exterior angle theorem
Answers
Answer:
Converse of the alternate exterior angle theorem
Step-by-step explanation:
just took the test ;)
The theorem that proves that lines d and e are parallel to each other, given that <2 is congruent to <6 is: D. Converse of the alternate exterior angle theorem
When a transversal cuts across two parallel lines, there are special angles formed having relationship with each other.
For two lines to be parallel, such relationship must exist. That is what a converse theorem seeks to prove.
We are told that <2 is congruent to <6.Both angles are exterior angles that also lie opposite each other along the transversal. That makes them alternate exterior angles.<2 will be congruent to <6 if lines d and le are parallel to each other.Therefore, the theorem that proves that lines d and e are parallel to each other, given that <2 is congruent to <6 is: D. Converse of the alternate exterior angle theorem
Learn more here:
https://brainly.com/question/10565830
C
5 mi
12 mi
What is the length of the hypotenuse?
C =
miles
Answers
144+25=169
Square root of 169 is the answer
C= 13 mi
A pre-paid cell phone plan has a flat rate of $15 with an additional cost of $0.15 per
minute. At most, how many minutes can Chelsea purchase if she has $35?
Write an inequality for this statement, write out 3 values that would make the inequality true
Answers
Answer:
anything less than 133 would be true
Step-by-step explanation:
35 ≥ 0.15m + 15
solve for m
subtract 15 from both sides
20 ≥ 0.15m
divide both sides by 0.15
133.33 ≥ m
m cannot be more than 133 minutes
pls help answer don't understand
Answers
Answer:
1.1
Step-by-step explanation:
square root of 1.19- 1.09087...- rounded to 1.1
Answer:
it is 1.1
you should use calculator
Step-by-step explanation:
:)
What did you include in your response? check all that apply. an intercept can be found by letting d = 0 in the equation and solving for q, or by letting q = 0 in the equation and solving for d. the bank could be filled with 54 quarters and no dimes. the bank could be filled with no quarters and 135 dimes.
Answers
Answer:
if this is on edge just choose all of them
4. If the area of a rectangle is 6 m2, then the dimensions must be 2 meters by 3 meters. oh
Answers
Answer:
False.
Step-by-step explanation:
The formula that is used to find the area of a rectangle is given by :
A = l×b
Where,
l is length and b is breadth
If area of a rectangle is 6m², it means we need to find the factors of 6. The factors of 6 are 2 and 3. If we multiply 2 and 3, we get 6.
Other possibility can be 1 m by 6 m because if we muliply 1 m and 6 m, we get 6m².
It means there are more than one possibiliy about the length and breadth of the rectangle.
Hence, the given statement is not true.
a toy manufacturer estimates that 16% of its products are defective. if it produces 550 toys in one day, how many will be defective?
Answers
Answer:
88 toys
Step-by-step explanation:
If 16 percent of them are defective we want to multiply 550 by .16. This gets you 88.
I am in 8th grade and i need help on Pre Algebra could you help me?
Answers
Answer:
Sure, what do you need help on?
What is the midpoint of the segment below?
Answers
Answer:
A. (0,2)
Step-by-step explanation:
Yara have two rectangular gardens in her backyard the smaller garden is 1/2 foot long and 2/3 foot wide the larger Garden is 4 feet long and 5 feet wide what is the area of the small garden in square feet what is the area of the large garden in square feet
Answers
Given that :
Area of a rectangle is : A = l×b
For smaller garden,
Length, l = [tex]\dfrac{1}{2}\ \text{foot}[/tex]
Width, [tex]b=\dfrac{2}{3}\ \text{foot}[/tex]
Area of a smaller garden is :
[tex]A=\dfrac{1}{2}\times \dfrac{2}{3}\\\\A=0.34\ \text{foot}^2[/tex]
For larger garden,
length, l' = 4 feet
Width, b' = 5 feet
Area of a larger garden is :
[tex]A'=l'\times b'\\\\A'=4\times 5\\\\A'=20\ \text{feet}^2[/tex]
So, the area of a smaller garden is 0.34 sq ft and that of a larger garden is 20 sq ft.
A family paid $21,600 as a down payment for a home. If this represents 12% of the price of the home find the price of the home.
Answers
21, 600 = 12 /100 x X.
21,600 x 100/12 = X
180,000 = X
The big Xs are X, and the small xs are times.
Hope this helps.
Use the algebra tiles to model x - 2.
Then choose the answer that describes the correct
tiles.
O one blue x tile and two orange + tiles
o
one orange x tile and two blue – tiles
O one blue x tile and two blue – tiles
one orange x tile and two orange + tiles
Answers
Answer:
The answer is B.
Step-by-step explanation:
took the assignment :P
It is B. I took the test
and the guy above me is also correct.
Have a nice day!! :D
Write the decimal 0.597 as a fraction.
Answers
Answer:
0/6
Step-by-step explanation:
Hope this helps I'm just typing rn bc it says it needs to be longer