The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 31 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:
Answers
The equation that can be used to find the height of the tree is as follows:
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
The height of the tree is 35.6 m
How to use sine rule to find height of the tree?Th equation that can be used to find the height of the tree uses the principle of sine rule.
Therefore,
[tex]\frac{h}{sin 29} =\frac{40}{sin(180-4-29)}[/tex]
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
Therefore,
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
cross multiply
h sin 147 = 40 sin 29°
h = 40 sin 29° / sin 147
h = 19.3923848099 / 0.54463903501
h = 35.6015636045
h = 35.6 m
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Related Questions
Can you prove these similar triangle step by step?
Answers
Answer:
If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. the remaining sets of angles will be congruent and the remaining corresponding sides will be in proportion.
hopes this helps
Step-by-step explanation:
These are 2 questions please help me
Answers
Answer:
Step-by-step explanation:23
6 students equally shared 1/2 of a pan of brownies what fraction of a whole pan a brownies did each student eat?
A. 12
B. 3
C. 1 /12
D. 1/3
Answers
Answer:
The answer would be D
Step-by-step explanation:
The local news is conducting a poll of the residents' opinions regarding a new traffic law that is being proposed. At the end of a news segment, viewers had the opportunity to dial in or use social media to choose whether they agree or disagree with the law. A large sample size was represented, and this poll was repeated again one week later with similar results. When working with this data, what best applies?
Answers
Options :
a. The surveys are biased because people chose to respond or not.
b. Because of the large sample size, the results are most accurate of all members of the community.
c. The same sampling methods were used for both polls, demonstrating reliability.
Answer:
a. The surveys are biased because people chose to respond or not
Step-by-step explanation:
When surveys incorporates a large number of people of a whole population, coupled with the fact that subjects of the survey or research are not compelled to make a choice or air their opinion. In the scenario above, opinion about the new policy is to be expressed by a large audience whereby there is a high tendency that some will no interest in the news nor its content. Leaving only those audience who are more interested and likely the most affected by the policy to respond. This way there will be no distinction between those who disagree and those who fail to respond. It would be more advisable to employ a sample audience who are interested and woykd give a verdict on the policy.
1. (a) Find the remainder when 5x2 – 3x + 6 is divided by 2x-1
Answers
Answer:
The answer is 5/2X - 1/4. The remainder is 23/4.
A movie theater has a seating capacity of 289. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2106, How many children, students, and adults attended?
Answers
Answer:
Number of children in theater = 94
Number of students = 46
Number of adults in theater= 47
Step-by-step explanation:
Total seating capacity in the theater = 187
Let us assume the number of students in the theater = m
and assume the number of children in the theater = 2k
So, the number of adults in theater = Half of number of children = 2k/2 = k
⇒ Number of ( Adults + Children + students) = 187
⇒ k + 2k + m = 187, or 3k + m = 187
Step-by-step explanation:
Find the GCE.
10rs, 35rst
Answers
expression equivalent to 3(7x + 9)
Answers
Answer:
21x + 27
Step-by-step explanation:
3(7x + 9)
21x+27is your answer
Find the slope of the line passing through the points (-2,3) a
and
(-9,6).
Answers
===================================================
Apply the slope formula
m = (y2-y1)/(x2-x1)
m = (6-3)/(-9-(-2))
m = (6-3)/(-9+2)
m = 3/(-7)
m = -3/7
This means each time you go down 3 units, you go to the right 7 units.
Slope = rise/run = -3/7
rise = -3 and run = 7
The independent variable is represented by the symbol(s)
1. Y
2. xy
3. Both A and B
4. X
5. None of the above
Answers
Answer:
4
Step-by-step explanation:
because variable is independent
HELP ASAP PLS!!!
Marsha recorded the time it took six children of different ages to run one lap around the track. Using the line of best fit, what is closest to the length of time it should take Marsha's 8 year old son to run one lap? Write the equation that represents the situation in slope-intercept form.
Answers
Answer:
176 seconds
Step-by-step explanation:
By using regression line calculator,
Equation of the line of best fit will be,
T = -12.55x + 276.52
Here , T = time taken to cover one lap
x = Age
If the age of Marsha's son is 8 years then expected time taken by her son to cover one lap will be,
T = -12.55(8) + 276.52
T = -100.4 + 276.52
T = 176.12 seconds
Therefore, approximate time taken by Marta's son will be 176 seconds.
ROBERT bought 2 packages of cookies for $6.00. How much would 3 packages of cookies cost?
Answers
Answer:
9.00$
Step-by-step explanation:
6 divided by 2 = 3 so each pakage cost 3$ so it would be 9.00$
what is 4½ pls anwser
Answers
Answer:
9/2
Step-by-step explanation:
Answer:
4.5 or 9/2
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answers
Answer:
Step-by-step explanation:
The change in y over the change in x between points is the slope. 53-29 over 3-2 is the slope. 24/1 is 24. You need the equation in y=mc+b form. b is the y intercept. (0, -19) is the point from the table containing the y int.. b=-19. Plug 24 and -19 into mc+b. To get y=24x-19
Perform the operation.
(9x2 + 6x – 7) + (-9x - 5)
PLS HELP ASAP PLS
Answers
Answer:
21
Step-by-step explanation:
(9x2 + 6x – 7) + (-9x - 5) = 21
Answer:
The answer is 21
Step-by-step explanation:
I searched it up.
six times the sum of a number and 8 equals 2
Answers
Answer:
24
Step-by-step explanation:
6*8x:2
48x:2
x:48/2
x:24
what is the value of c?
Answers
Answer: C= 26
Step-by-step explanation:
24^2+10^2=26^2
Joe and his friend are going hiking they bring with them a container that holds 1/2 of gallons of water if they share the water equally will fraction of a gallon would each friend get?
A. 1/3
B. 3/2
C. 1/4
D. 1/6
Answers
C. 1/4
I hope this helps!
HELP ME!!!!!!!!!!!!!!
Answers
Answer:
i wanna say it would be 1,735-3%y
help pls will give brainiest
Answers
Answer:
A= (3,3)
B= (4,1)
C= ( 1,0)
Step-by-step explanation:
Answer:
Step-by-step explanation:
A 2, -1
B 1, -3
C 4, -4
Hope this helps!
Thanks for Brainliest!
On Monday morning, Mr. Descartes asked his Algebra II students whether they had gone to the carnival in town over the weekend.
"I did," said Kristen. "I went on the Teacups ride twice, the rollercoaster twice, and the Spinning Vortex once. I had a lot of fun for only $20."
"I went on those rides, too!" exclaimed Jorge. "Just once each on the Teacups and rollercoaster, but three times on the Spinning Vortex, all for $25."
"I did five Teacup rides," said Lakesha. "And two rollercoaster rides, and one Spinning Vortex. I spent $29."
Marc listed off the same rides. "Three Teacups for me, plus two rollercoasters, plus two rides on the Spinning Vortex, all for – "
"You don't need to say," interrupted Mr. Descartes. "I know how much you spent."
How much are the rides? How much did Marc spend
Answers
Answer:
Cost of one Teacup = $3
Cost of one Roller coaster = $4
Cost of one Spinning Vortex = $6
Marc spent = 3x + 2y + 2z = $29
Step-by-step explanation:
Let
Cost of one Teacup = x
Cost of one Roller coaster = y
Cost of one Spinning Vortex = z
In Kristen case -
2x + 2y + z = $20
In Jorge case -
x + y + 3z = $25
In Lakesha case -
5x + 2y + z = $29
In Marc case -
3x + 2y + 2z = ?
Now, we have
2x + 2y + z = $20 ......(1)
x + y + 3z = $25 ........(2)
5x + 2y + z = $29 .........(3)
Now,
Subtract equation (1) from equation (3), we get
5x + 2y + z - ( 2x + 2y + z ) = $29 - 20
⇒5x + 2y + z - 2x - 2y - z = $9
⇒3x = $9
⇒x = $3
Now,
Multiply be 2 in equation (2) , we get
2x + 2y + 6z = $50 ........(4)
Now,
Subtract equation (1) from equation (4), we get
2x + 2y + 6z - ( 2x + 2y + z ) = $50 - 20
⇒2x + 2y + 6z - 2x - 2y - z = $30
⇒5z = $30
⇒z = $6
Now,
Put the values of x and z in equation (2) , we get
$3 + y + 3($6) = $25
⇒$3 + y + $18 = $25
⇒y + $21 = $25
⇒y = $25 - 21
⇒y = $4
∴ we get
Cost of one Teacup = x = $3
Cost of one Roller coaster = y = $4
Cost of one Spinning Vortex = z = $6
Marc spent = 3x + 2y + 2z = 3($3) + 2($4) + 2($6) = $9 + $8 + $12 = $29
What is the volume of the prism?
Answers
Answer:
Step-by-step explanation:
For the past three years, Nigel has grown 1 1/5 inches each year. How many total inches has he grown in the past three years?
Answers
Answer: 3.6? I believe is the right answer.
:D
Step-by-step explanation: 1 1/5 times 3 is how I got 3.6
Answer:
3 3/5
Step-by-step explanation:
Nigel would have grown 3 3/5 inches in the past 3 years
( 6/5 x 3/1 )
( =18/5 )
and then you would be simplifying 18/5
and that's how you would get your answer 3 3/5
.......Can I please be marked Brainliest
please thank you:)
Find an equation of a line with slope -4 and y-intercept 9. y =
Answers
Answer:
Y= -4X+9
Step-by-step explanation:
solve the equation by the help of the standard equation Y = MX + C
where M is the slope and C is the Y intercept
Please help this is due today!
Do not answer this with one answer ,blank, or a ridiculous answer.... this is serious please.
Answers
Answer:
perdita is correct
Step-by-step explanation:
perdita is correct because A isoceles triangle has two of the same. The triangle will just be very very thin
What is the x- value of the midpoint between A (-8,-6) and B (0, 6)?
Answers
Answer:
Step-by-step explanation:
Take average of the x-coordinates of A and B.
(-8+0)/2 = -4
x-coordinate of midpoint = -4
The required x value of the midpoint between A(-8, -6) and B (0, 6) is -4.
Given that,
To determine the x value for the midpoint between A (-8,-6) and B (0, 6).
Coordinate, is represented as the values on the x-axis and y-axis of the graph. Where x coordinate of the graph is called an abscissa and y coordinate of the graph is called ordinate.
The midpoint is that point of the line which has an equal distance from both ends of the line.
the x value of the midpoint between A(-8, -6) and B (0, 6) is given by,
x = ( x1 + x 2) / 2
x = ( - 8 + 0 ) / 2
x = - 8 / 2
x = - 4
Thus, the required x value of the midpoint between A(-8, -6) and B (0, 6) is - 4.
Learn more about coordinate here:
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i) Coordinates of point P
a) (1,1) b) (1,2) c) (2,1) d) (1,0)
ii) Coordinates of point Q
a) (0,-3) b) (-3,0) c) (-3,-3) d) (0,3)
iii) Coordinates of point T
a) (-4,-2) b) (-2,-4) c) (4,-2) d) (-2,4)
iv) (Ordinate of T) – (Abscissa of R)
a) -4 b) 4 c) 0 d) -2
v) (Abscissa of Q) – (Ordinate of S)
a) -4 b) 4 c) 2 d) -2
Answers
Given:
Five points P, Q, R, S ,T on a coordinate plane.
To find:
The coordinates of (i) P, (ii) Q, (iii) T, (iv) (Ordinate of T) – (Abscissa of R) and (v) (Abscissa of Q) – (Ordinate of S).
Solution:
From the given graph it is clear that the coordinates of given points are
P = (1,1)
Q = (-3,0)
R = (-2,-3)
S = (2,1)
T = (4,-2)
(i)
Coordinates of point P are (1,1).
Therefore, the correct option is (a).
(ii)
Coordinates of point Q are (-3,0).
Therefore, the correct option is (b).
(iii)
Coordinates of point T are (4,-2).
Therefore, the correct option is (c).
(iv)
Ordinate is y-coordinate and abscissa is x-coordinate.
Ordinate of T = -2
Abscissa of R = -2
(Ordinate of T) – (Abscissa of R) = -2 - (-2)
= -2 + 2
= 0
Therefore, the correct option is (c).
(v)
Abscissa of Q = -3
Ordinate of S = 1
(Abscissa of Q) – (Ordinate of S) = -3 - 1
= -4
Therefore, the correct option is (a).
Joseph invested $6,700 in an account paying an interest rate of 5.2% compounded quarterly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $13,950?
Answers
Answer:
Step-by-step explanation:
A=P(1+r/c)^(ct), where a is final value, P is the initial value or principle, r is the interest rate, and c is the number of compounding periods in a year.
ln(A/P)/ln(1+r/c)=ct so
t =(ln(A/P)/(cln(1+r/c)), given A=13950, P=6700, r=0.052, c=4
t=(ln(13950/6700))/(4ln(1.013))
t=14 years
Answer:
14
Step-by-step explanation:
PLEASE HELP QUICK IF I DONT GET HELP I WILL FAIL, IVE GOTTEN NO HELP PLEASE!! I HAVE 10 MINS. The function that represents the amount of caffeine, in milligrams,
remaining in a body after drinking the two Mountain Dew sodas is given
by f(t) = 110(0.8855)^t where t is time in hours. How much caffeine is left in
a person’s body 10 hours after drinking two Mountain Dew sodas?
Answers
Answer:
Step-by-step explanation:
f(10) = 110×0.8855¹⁰
You can do the math.
Answer:
32.6045597492
Step-by-step explanation:
110(.8855)^10
Chris received $50,000 from his grandparents as a graduation gift. So, he has decided to invest the money
to pay his living cost at a college, which is $3,000 a year. There are two options: a bond that pays 12% and
a CD that pays 5%. How much should he invest in the bond? [Please round your answer to 2 decimal places.]
Answers
Answer: $7142.86
Step-by-step explanation:
Let the amount to be invested in the bond be represented by y.
Based on this, the amount to be invested in the CD will be: = 50000 - y.
From the information given, yearly interest on bond is 12%, this will be:
= 12% × y = 0.12 × y = 0.12y
Also, interest on CD will be:
= 5% × (50000 - y)
= 0.05(50000 - y)
Then, the equation to get the amount to be invested in bond will be:
0.12y + 0.05(50000 - y) = 3000
0.12y + 2500 - 0.05y = 3000
0.12y - 0.05y = 3000 - 2500
0.07y = 500
y = 500/0.07
y = 7142.8571
y = 7142.86
The amount to be invested in bond will be $7142.86