Two forest rangers are standing on a road that runs east-west. One sights a forest fire in the direction 31° east of
north. The other sights the same fire 57° west of north.
Find the distance from each ranger to the forest fire and
the shortest distance from the fire to the road.
Answers
Answer: The forest ranger closest to the fire is at a distance of 9.92 miles (nearest hundredth).
Draw a horizontal line AB of length 15 miles to represent the positions of the two forest rangers.
Point A is to the left and point B is to the right.
Complete triangle ABC so that m∠A = 41° and m∠B = 56°.
The point C represents the location of the fire.
Let x = length of BC. It is the shortest distance from the forest ranger B to the fire because BC is opposite the smaller angle of 41°.
Because the sum of angles in a triangle is 180°,
m∠C = 180° - (41° + 56°) = 83°.
From the Law of Sines,
x/sin(41) = 15/sin(83)
x = 15*[sin(41)/sin(83)] = 9.915 mi
Step-by-step explanation:
Draw a horizontal line AB of length 15 miles to represent the positions of the two forest rangers.
Point A is to the left and point B is to the right.
Complete triangle ABC so that m∠A = 41° and m∠B = 56°.
The point C represents the location of the fire.
Let x = length of BC. It is the shortest distance from the forest ranger B to the fire because BC is opposite the smaller angle of 41°.
Because the sum of angles in a triangle is 180°,
m∠C = 180° - (41° + 56°) = 83°.
From the Law of Sines,
x/sin(41) = 15/sin(83)
x = 15*[sin(41)/sin(83)] = 9.915 mi
Related Questions
A right rectangular prism has a length of 9, a width of 4, and a height of 5. How many unit cubes can fit in the prism?
Answers
Answer:
The answer is 54 cubes.
Step-by-step explanation:
PLEASE HELP!!!!!
find the area of the polygon.
Answers
Answer:
2 cm is were youll find the polygon at. it shouldnt be hard to see the area of were the polygon is
Answer:
208 cm²
Step-by-step explanation:
14 cm × 16 cm = 224 cm²
14 cm - 6 cm = 8 cm
8 cm × 2 cm = 16 cm²
224 cm² - 16 cm² = 208 cm²
Do all circles have all right angles?
Yes or no
Answers
Answer:
They do
Step-by-step explanation:
Both have 4 90 degree (right) angles.
A triangle has 3 sides and 3 angles. The angles of a triangle always add up to 180 degrees.The “angle” of a circle is 360 degrees – all the way around.
Hope this helps (Sometimes i think circles don't have any angles at all)
A telecommunications company in a small town had 450 phone subscribers before they introduced a plan for newly joining members. The company recorded an approximate 50% increase each month in the number of new phone subscribers, where they had one new subscriber at the start of the plan. The number of phone subscribers x months after the plan was launched is modeled by the function below.
Answers
Answer:
450 x (1 + 0.5) ^ X = Phone subscribers
Step-by-step explanation:
Since a telecommunications company in a small town had 450 phone subscribers before they introduced a plan for newly joining members, and the company recorded an approximate 50% increase each month in the number of new phone subscribers, where they had one new subscriber at the start of the plan, to determine the number of phone subscribers x months after the plan was launched, the following function must be considered and solved:
450 x (1 + 0.5) ^ X = Phone subscribers
So, for example, in 3 months, the number of subscribers would be the following:
450 x (1 + 0.5) ^ 3 = 1,518.75
Thus, in 3 months, the company would have 1,518 subscribers.
find the value of given expression
[tex] \sqrt{8100} [/tex]
Answers
Answer:
90 is the answers for the question
The diagonals in a kite __________.
a) bisect each other
b) are perpendicular
c) are congruent
⇒
Answers
Type the expression that results from the following series of steps:
Start with y, add 7, multiply by 3, then subtract 6.
Answers
Answer:
3y-4
Step-by-step explanation:
y+7×3-3
(y×3)+7-3
3y-4
Find the length of side x.
Give your answer to 1 decimal place.
105°
18 cm
15 cm
Х
Answers
Freddie invests £6600 in an account that pays 3 % compound interest per annum for the two years, then 1 % . Work out how much money Freddie will have in his account in 8 years.
Answers
Using compound interest, it is found that Freddie will have £7433 in his account in 8 years.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.For the first two years, the parameters are given as follows:
P = 6600, r = 0.03, n = 1, t = 2.
Hence the amount is:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(2) = 6600\left(1 + 0.03)^{2}[/tex]
A(2) = 7002.
For the final 6 years, the parameters are:
P = 7002, r = 0.01, n = 1, t = 6.
Hence the amount after 8 years is:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(6) = 7002\left(1 + 0.01)^{6}[/tex]
A(6) = 7433.
Freddie will have £7433 in his account in 8 years.
More can be learned about compound interest at https://brainly.com/question/25781328
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Write the equation for each circle with the given radius and center.
5. radius: 2, center: (4, -3)
6. radius: 7, center: (-1, 10)
Answers
Answer:
Step-by-step explanation:
Equation of a circle is
[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex] where (h,k) is the center and r is radius
#5 Radius 2, Center (4,-3)
[tex](x-4)^{2} +(y+3)^{2} =4[/tex]
#6 Radius 7, Center (-1,10)
[tex](x+1)^{2} +(y-10)^{2} =49[/tex]
find the length of x
urgent pls help.
Answers
Answer:
Step-by-step explanation:
the triangles are congruent and the factor is 1/2
x=8/2=4
Edgar and his older sisters, Diana and Katy, are going to visit their grandmother. Edgar is too young to drive, so Diana and Katy each drive the same amount of time to complete the 5-hour trip. How long does each of Edgar's sisters drive?
Answers
Answer:
2.3 hours or 2 hours and 30 minutes thinkkk
Someone please please help
Answers
Answer:
The amount of apples is the Xs and The cost is the Ys
Step-by-step explanation:
Help 10 points picture included
Answers
Combine like terms to simplify the following expression:
12x + 4y - 3x + 2 - 8y2 + 3^2
Answers
Answer:
−8y^2+9x+4y+11
Step-by-step explanation:
=12x+4y+−3x+2+−8y^2+9
Combine Like Terms:
=12x+4y+−3x+2+−8y^2+9
=(−8y^2)+(12x+−3x)+(4y)+(2+9)
=−8y^2+9x+4y+11
Good luck <3
Answer:
-8y^2+9x+4y+8
Step-by-step explanation:
^ refers to squared in my answer
Please help me solve these exponents
Answers
A basketball player recorded her points for 11 consecutive games. Her points are listed below.
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
A basketball player recorded her points for 11 consecutive games. Her points are listed below.
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
A basketball player recorded her points for 11 consecutive games. Her points are listed below.
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
A basketball player recorded her points for 11 consecutive games. Her points are listed below.
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
A basketball player recorded her points for 11 consecutive games. Her points are listed below.
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
A basketball player recorded her points for 11 consecutive games. Her points are listed below.
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
A basketball player recorded her points for 11 consecutive games. Her points are listed below.
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
A basketball player recorded her points for 11 consecutive games. Her points are listed below.
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
A basketball player recorded her points for 11 consecutive games. Her points are listed below.
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
A basketball player recorded her points for 11 consecutive games. Her points are listed below.
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
A basketball player recorded her points for 11 consecutive games. Her points are listed below.
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
Answers
Answer:
23
Step-by-step explanation:
The number of points that she would need to score in her 12th game in order to decrease the interquartile range by 1 point is; 23
What is the Interquartile range?An interquartile range is one of the measure of variability that measures the spread of middle 50% of the data.
The formula to calculate interquartile range is:
IQR = Q₃ - Q₁
where;
Q₃ is third quartile
Q₁ is first quartile
The given points when arranged in increasing order gives us:
13, 15, 17, 18, 20, 20, 21, 22, 24, 25,27
Q₁ is the (n + 1)/4 terms = 3rd term.
Thus; Q₁ = 17
Q₃ is 3(n + 1)/4 term = 9th term.
Thus; Q₃ = 24
Then; IQR = 24 - 17
IQR = 7
The desired interquartile range should decrease by 1 point. Thus;
Desired IQR = 7 - 1 = 6.
To find the score of the 12th game, let us try 23 points as the score of the 12th game:
Thus;
Q₁ = 17.5
Q₃ = 23.5
IQR = 23.5 - 17.5
IQR = 6
Thus, required number of points is 23.
Read more about Interquartile Range at; https://brainly.com/question/3859769
What is the Pythagorean Theorem
Answers
Answer:
see below
Step-by-step explanation:
The Pythagorean theorem is for right triangles. It uses the two legs and the hypotenuse
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
Answer:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
Step-by-step explanation:
If (x²- 4) = (x + 2) = x - 2, which polynomial should fill in the blank below?
(x + 2)x____= x² - 4
O x² – 4
OX-2
O x + 2
O x²-2
Answers
Answer:
x-2
Step-by-step explanation:
(x+2)× ___=(x+2)(x-2)
___=(x+2)(x-2)/(x+2)
___=x-2
The polynomial which should be filled in the blank is (x - 2).
What are Polynomials?Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.
Given that,
x² - 4 = (x + 2) (x - 2).
We have to find the blank space.
By commutative property, the other side is also equal.
That is,
(x + 2) (x - 2) = x² - 4
Hence the correct option is (x - 2).
Learn more about polynomials here :
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What does 602.93+9.5%=
Answers
find the value lamda...
Answers
A circular garden has a diameter of 10 yards. What is the area of
the garden? Use 3.14 for iz
HELPPP?? ASAPP???
Answers
Answer:
Step-by-step explanation:
you do 10/2 for the radius, so that will be 5. then you do 3.14*5*5= 78.5
A recipe for banana bread calls for 4 bananas for every 8 cups of sugar. What is the ratio of bananas to cups of sugar
Answers
Answer:
1:2 is the ratio
Step-by-step explanation:
The graphs of linear functions f and g are shown on the grid below.
Which function is best represented by the graph of g?
Answers
Answer: g(x)=3f(x)
Step-by-step explanation:
So we know it isnt a translation. Which eliminates the first 2 answer choices. So its between the last 2. If it were 1/3 the grap would have been steeper.
I hope this helps!
Question 13 (1 point)
(07.05 MC)
What is the solution to the equation 4x + 2(x - 2) = 4x + x - 12? (1 point)
O 1) -8
2) -1
3) 1
04) 8
Answers
Answer:
-8
Step-by-step explanation:
4x+2(x-2)=4x+x-12
4x+2x-4=5x-12
6x+2x-4=5x-12
x-4=-12
x=-8
I think of a number I double it and subract two I get nine
Answers
Answer:
5.5
Step-by-step explanation:
Let [tex]x[/tex] be equal to the number.
1) Convert the clues into an equation
If you double it ([tex]2x[/tex]) and subtract two ([tex]-2[/tex]), you get 9 ([tex]=9[/tex]).
[tex]2x-2=9[/tex]
2) Solve the equation
[tex]2x-2=9[/tex]
Add 2 to both sides
[tex]2x-2+2=9+2\\2x=11[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{11}{2} \\x=5.5[/tex]
Therefore, the number is 5.5.
I hope this helps!
ramon has 6.75 kg coffee. he wants 0.25 kg bags. how many bags does he need?
Answers
Answer:
Ramon would need 27 bags
Step-by-step explanation:
This is because if you divide 6.75 by 0.25 you would get 27
Ramon needs 27 bags of 0.25 kg each for his 6.75 kg coffee.
To determine the number of 0.25 kg bags Ramon needs for his 6.75 kg coffee, we divide the total weight of the coffee by the weight of each bag.
Total weight of coffee = 6.75 kg
Weight of each bag = 0.25 kg
Number of bags = Total weight of coffee / Weight of each bag
Number of bags = 6.75 kg / 0.25 kg
Calculating this division, we find:
Number of bags = 27
Therefore, Ramon needs 27 bags of 0.25 kg each for his 6.75 kg coffee.
To know more about bags click here :
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Pls help I don’t understand
Answers
Hi there, it wont let me leave this page without posting a answer and I don't have an answer. I dont know why it wont let me.. So I thought instead of just posting a blank answer I would give you an explination for my actions. I am not doing this on purpose or for points im just trying to help others.. If you want you can reply back to my comment and I will give you 10 coins. Since I did just take 5 of yours, and it seems only fair. Again my apoligizes.
Mary is buying a case of water. She spends $7.99 for a case of 24 bottles. What is the unit rate? (Cost for 1 bottle) *
Answers
Answer:
so I'm not 100% sure but in these types of questions you are supposed to divide
so you have a pack of 24 bottles for 7.99
so you would do 7.99÷24 = 0.33
then to check it you can multiply
0.33× 24 bottles and it gives you 7.93 which is super close to 7.99 anyway I hope this helps ...
The line L1, is y= 5x+1
The line L2, is 2y-10 +3=0
Show how these 2 lines are parallel
Answers
Answer:
Step-by-step explanation:
L₁: y = 5x + 1
Slope of L₁ = 5
L₂: Did you mean 2y - 10x +3 = 0 ?
2y = 10x - 3
y = 5x - 1.5
Slope of L₂ = 5
L₁ and L₂ have the same slope, so the lines are parallel.