A running race follows a triangular course. The first leg of the race is in a straight line, covering 4.4km. Runners turn an angle of 79 deg for the second leg, and then turn again 77 deg to head back to the start line to finish the race. What is the length of the entire race, to the nearest tenth of a kilometer?
Answers
Answer:
The length of the entire race is 9,5km
Step-by-step explanation:
Required
Determine the length of the race.
To aid my explanation, I have added an attachment which shows the triangular course.
From the attachment, we have:
A as the starting point and the following measurement;
[tex]\angle B = 11^{\circ[/tex]
[tex]\angle C = 13^{\circ} + 79^{\circ} = 92^{\circ[/tex]
[tex]\angle A + \angle B + \angle C = 180^{\circ}[/tex]
[tex]\angle A = 180^{\circ} - (\angle B + \angle C )[/tex]
[tex]\angle A = 180^{\circ} - (11^{\circ}+92^{\circ})[/tex]
[tex]\angle A = 77^{\circ}[/tex]
[tex]\angle B = 11^{\circ[/tex]
[tex]\angle C = 92^{\circ[/tex]
[tex]c = 4.4km[/tex]
Apply sine rule
[tex]\frac{a}{sin\ A} = \frac{b}{sin\ B} = \frac{c}{sin\ C}[/tex]
[tex]\frac{a}{sin\ 77^{\circ}} = \frac{b}{sin\ 11^{\circ}} = \frac{4.4}{sin\ 92^{\circ}}[/tex]
[tex]\frac{a}{sin\ 77^{\circ}} = \frac{b}{sin\ 11^{\circ}} = \frac{4.4}{0.9994}[/tex]
[tex]\frac{a}{sin\ 77^{\circ}} = \frac{b}{sin\ 11^{\circ}} = 4.403[/tex]
Split to solve for a and b
[tex]\frac{a}{sin\ 77^{\circ}} =4.403[/tex]
[tex]\frac{b}{sin\ 11^{\circ}} = 4.403[/tex]
Make a the subject
[tex]\frac{a}{sin\ 77^{\circ}} =4.403[/tex]
[tex]a = 4.403 * sin(77^{\circ})[/tex]
[tex]a = 4.403 * 0.9744[/tex]
[tex]a = 4.3km[/tex]
Make b the subject
[tex]\frac{b}{sin\ 11^{\circ}} = 4.403[/tex]
[tex]b = 4.403 * sin(11^{\circ})[/tex]
[tex]b = 4.403 * 0.1908[/tex]
[tex]b = 0.8km[/tex]
The length of the race is:
[tex]Length = a + b + c[/tex]
[tex]Length = 4.3km + 0.8km + 4.4km[/tex]
[tex]Length = 9.5km[/tex]
Related Questions
in a 5th grade class, 9/10nof the students like going to the movies. Of those students 4/5 like popcorn. Of the students that like popcorn, 2/3 of them also like candy. what fraction of the students class like popcorn at the movies? What faction lf the students in class like popcorn and candy at the movies?
Answers
Answer:
48%
Step-by-step explanation:
9/10 of the students like going to the movies.
4/5 of 9/10 is 72/100 or 72%.
2/3 of 72 is 48.
So, 48% of the students like popcorn, candy, and going to the movies.
School A has graduated 1,700 students and graduates
50 students every year. School B has graduated 600
students, but graduates 150 every year. How many years (Y)
will it be before School B has as many graduates as School A?
Answers
Answer:
the answer is 11 years
Step-by-step explanation:
if school A is graduated 50/years,
the graduated in 11 years is 550
added of graduated 1,700 in 550 is 2,250
if school B is graduated 150/years,
the graduated in 11 years is 1650
added of graduated 600 in 1650 is 2,250
so School A and B is to be equal in 11 years
Hi please I need answer.I will make brainliest who can answer this.Thank youuu
Answers
9514 1404 393
Answer:
(0, 0) 2, 4, 5
(-1, -1) 1, 2, 4, 5
(2, -1) 1, 2, 4, 5
(-2, 2) 2, 4
Step-by-step explanation:
The graph shows the solution sets of the inequalities. Each inequality is graphed in a different color to aid identification of the solution areas.
The purple area, x + 3y ≥ 6, does not contain any of the given points.
The inequalities satisfied by the given points are listed above.
Ten people put 63 boxes on a red truck and 38 boxes on a blue track About how many boxes did they load in all
Answers
Answer:
63+38=101
Step-by-step explanation:
Juanita borrowed $600 to purchase a new computer. She was charged 7% interest for two years. She used the simple interest formula to find the interest.
I = 600(7)(2)
What error did Juanita make and how will her error affect the interest she calculates? Explain
{_____________________________
whoever does best get brainliest
Answers
Answer:
The correct formula should be I= 600(0.07)(2). Juanita made a very common error, she didn't put the percentage of interest in decimal form; or she didn't put the percent sign on it so we know to put it in decimal form. Her error will make a big difference; with using her calculations the answer would be $8,400. With the correct formula the answer is $84.
Hope this help! :)
Given :-
Juanita borrowed $600 .Rate of Interest = 7% .Time = 2yrs .To find :-
Error made by her.Answer :-
As we know that the formula for Simple interest is ,
SI = P*R*T / 100Substitute ,
I $600* 7 * 2 / 100 I = $ 84 .So here she did not write 7 % as 7/100 instead she wrote 7 .
I don't know I need help.
Which of the following numbers can be expressed as repeating decimals?
3 over 7, 2 over 5, 3 over 4, 2 over 9
2 over 9 and 3 over 4
3 over 7 and 2 over 5
2 over 5 and 3 over 4
3 over 7 and 2 over 9
Answers
Answer:
2/9 = 0.2 repeating
3/7 = 0.428571 repeating
Step-by-step explanation:
Yep here we go again:
The x-axis represents the number of hours before or afternoon, and the y-axis represents the temperature in degrees Celsius.
At 9 a.m., it was below freezing. In what quadrant would this point be plotted? Use Roman Numerals in your answer: Either I, II, III, or IV
At 11 a.m., it was 10 degrees Celsius. In what quadrant would this point be plotted?
Here is the image T ^ T ( I will also give brainliest!)
Answers
Answer:
9 am it will be IV quadrant
11 it will be I quadrant
hope it helps u
If at 9 a.m. the temperature was below freezing, which means below 0 degrees Celsius, then the point would be plotted in the third quadrant (III).
What is coordinate plane?The coordinate plane has four quadrants, which are numbered using Roman numerals I, II, III, and IV, and they are separated by the x-axis and y-axis.
In this case, the temperature was below freezing at 9 a.m., which means it was less than 0 degrees Celsius.
The point would be plotted in the third quadrant (III), where the x-value is negative and the y-value is negative, because the x-axis represents the time in hours before noon and the temperature is negative.
At 11 a.m., however, the temperature was 10 degrees Celsius, which is a positive value.
Thus, the point would be plotted in the first quadrant (I), where both the x-value and the y-value are positive, because the x-axis represents the time in hours before noon and the temperature is positive.
For more details regarding coordinate plane, visit:
https://brainly.com/question/13611766
#SPJ2
Kirk is getting a raise of 5% due to inflation. His normal salary is $56,000 per year. Which of the following calculations gives Kirk's new salary, in dollars? A. 56,000 +5 B. 56,000 + 56,000(0.05) C. 56,000 + 56,000(0.50) D. 56,000 + 56,000(5) E. 56,000(.05)
Answers
Answer:
The answer is B. 56,000 + 56,000(0.05) because 5% or expressed in decimals 0.05 multiplied by the quantity 56,000 gives us 5% of Kirk's normal salary and added to his normal salary will give us his new salary.
(His new salary is 58,800 and 5% of his normal salary is 2,800)
A loaf of bread costs 3.00 dollars today. The same size loaf cost 20 cents in 1955. what percentage of todays price did someone in 1955 pay for bread?
Answers
Answer:
About 6.7%
Step-by-step explanation:
Can someone help me with this math question plz i will appreciate it. So this is the question: some of the methods you can use to add or subtract are?.
Answers
Answer:
add: jump strategy, adding up to ten, do the tens last, compensation method, double when the numbers are the same, count from a number upwards
Subtract: take away, minus decrease, leave, how many are left over, difference between, half/halve
Step-by-step explanation:
¿entre las fracciones 33/96 y 34/96 podrían encontrarse más números fraccionarios? ¿ cuántos?
Answers
Susan Marciano invested part of her $27,000 bonus in a fund that paid a 12% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each investment if her overall net profit was $1,590.
Answers
The Value that you insert into a function is know as the?
Answers
Answer:
Step-by-step explanation:
Most commonly, that value would be the "independent variable."
We evaluate the function at that particular value of the independent variable.
Maggie wants to make a special card for Valentine’s Day. She starts with a
square piece of red paper with a side length of 12 cm. She then pastes two white
semi-circles, each with radius 3 cm, and a white triangle onto the square sheet of
red paper, as shown below. Determine the total amount of area available in the white region for Maggie’s special valentine greeting.
Answers
Answer:
I don't know
Step-by-step explanation:
I tried to search it up to get it correct but all it showed me was useless websites that didn't give me the answer
Trapezoid ABCD has an area of 57. BC = 7 and AD = 12. What is the height of the trapezoid?
Answers
Answer:
Step-by-step explanation:
57x2/(12+7)=6
Fay has a lemonade stand.
She spends £42 on ingredients.
She sells each glass of lemonade for £1.20.
If she sells 50 glasses of lemonade, what is her total profit?
Answers
Step-by-step explanation:
1.50 x 30 = 45
to find total profit - 45-42= 3
Answer:
she made a profit of 18$
50*1.2=60-42=18
Step-by-step explanation:
Please help ten points
Answers
B=55 degrees
C=25 degrees
10/27=a/135
what is the answer for this equation?
Answers
Answer:
So we have this equation:
10/27 = a/135
What we can do is multiply both sides by 27 and 135:
10*135 = a * 27
1350 = 27a
a = 1350/27. = 50.
Solve: -3k(1-6k)=6k+21
Answers
Answer: Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Exact Form:
k
=
3
+
√
177
12
,
3
−
√
177
12
Decimal Form:
k
=
1.35867789
…
,
−
0.85867789
…
Step-by-step explanation
35 points!!! Help!! Make sure u answer all!!!
Answers
Answer:
Expression for Perimeter: 6x + 6
x = 12 cm
Verify A = 360:
2(12) x (12+3) = 360
24 x 15 = 360
360 = 360
Step-by-step explanation:
1.N% of 40 is 10. Solve for N. Just put the number.
2.Mia finished 60% of her homework in 45 minutes. how many minutes will it take her to complete all of her homework? Remember her total homework is 100%
Answers
Step-by-step explanation:
N% of 40=10N/100×40=10
N=10×100/40=25
2.
60%of homework=45min
1%of homework=45/60=3/4min
100%of homework =3/4 ×100=75 min
BCDE is a rhombus. Find the missing measures.
BC = 28 and BD = 32
CD =
FD =
EF =
EC =
Answers
Answer: CD=28
FD= 16
Step-by-step explanation:
Are these two triangles congruent? *
Answers
Answer:
not congruent because none of the angles match
Answer:
Not Congruent
Step-by-step explanation:
No.
Two corresponding sides measure 8 and 4.
The other two corresponding sides measure 7 and 3.5.
In order to be congruent, each pair of corresponding sides has to be congruent.
Fill in the blanks to write the fraction 3/4 as in different ways
Answers
Answer:
1.3/4 × 2/2 = 6/8
2.3/4 × 3/3 = 9/12
3.3/4 × 4/4 = 12 /16
4. 3/4 × 5/5 = 15/20
PLS HELP ASAP I MEAN ASAP PLS
Answers
Answer:
(B). - 3 ≤ x < 1
Step-by-step explanation:
[tex]\frac{\sqrt{x+3} }{\sqrt{1-x} }[/tex]
Given expression is defined for
1). x + 3 ≥ 0 ⇒ x ≥ - 3
and
2). 1 - x > 0 ⇒ x < 1
- 3 ≤ x < 1
Plz help me with this question
Answers
Answer:
C
Step-by-step explanation:
Remark
There are probably a couple of ways that you could do this. I'm going to pick the most obvious way.
Givens.
KN = 2.5
NO = 10
LM = 3
MP = x
Equation
NO/KN = PM / LM
Solution
10 / 2.5 = x / 3 Cross multiply
2.5x = 10 * 3 Combine
2.5x = 30 Divide by 2.5
x = 30/2.5
x = 12
That looks like it should be the answer, and it almost is, but you are asked for LP.
LP = LM + MP
LP = 3 + 12
LP = 15
The answer is 15
Can any one help me on this question ?
Answers
Answer:
70°
Step-by-step explanation:
2x +x + 80° + 70° = 360° { being sum of angles of quadrilateral }
3x + 150° = 360°
3x = 360° - 150°
3x = 210°
x = 70°
Hope it will help :)
Answer:
70
Step-by-step explanation:
Since sum of all angles in a quadrilateral is 360°
angle P+ angle Q + angle R + angle S= 360°
80+70+x+2x=360
3x= 360-150
3x = 210
x = 210/3
x= 70
Salesman Scott received $2,792.79 for selling a property. If the gross commission was 6.5 % of the sale price, the listing salesman received 12% of the gross commission and Scott received 45% of the balance, how much did the property sell for?
Answers
Answer: The property sold for $5,870.41.
Step-by-step explanation:
Let x be the selling price of the property.
Then, gross commission = 6.5% of x = 0.065x
listing salesman received = 12% of ( 0.065x) = 0.12 (0.065x) = 0.0078 x
Balance = x - ( 0.065x) - (0.0078 x)
= (1+0.065-0.0078)x
= 1.0572x
Scott received = 45% of (1.0572x)
=0.45 (1.0572x)
= 0.47574x
Now, [tex]0.47574x=2,792.79[/tex]
[tex]\Rightarrow\ x=\dfrac{2792.79}{0.47574}\\\\\Rightarrow\ x=5870.41[/tex]
Hence, the property sold for $5,870.41.
Use the Distributive Property to simplify the expression. 8(s−1) =
Answers
Answer:
the answer would be 8s -8
Step-by-step explanation:
I learned this a long time ago
Answer:
anong grade Yan tol??g7 g7 g8 g9 g10 g11 g12?
find a ⋅ b
a = 7i - 4j, b = 4i + 3j
Answers
Answer:
28i^2 + 5ij - 12j^2
Step-by-step explanation:
(7i-4j)(4i+3j)
7i times 4i is 28i^2
7i times 3j is 21ij
-4j times 4i is -16ij
-4j times 3j is -12j^2
In equation it looks like this:
28i^2+21ij-16ij-12j^2
Simplify 21ij and -16ij
21ij-16ij is 5ij
So the answer is:
28i^2 + 5ij - 12j^2
Hope this helps!
Answer:
The answer is 16
Step-by-step explanation: