On many cell phones with GPS, an approximate location can be given before the GPS signal is received. This is done by a process called triangulation, which works by using the distance from two known points. Suppose there are two cell phone towers within range of you, located 3000 feet apart along a straight highway that runs east to west, and you know you are north of the highway. Based on the signal delay, it can be determined you are 2050 feet from the first tower, and 1420 feet from the second. Determine the angle, \thetaθ, between your line of sight to the first tower and the highway to the nearest tenth of a degree. (A calculator is needed for this question)
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Explanation:
Refer to the diagram below.
If we focus on triangle ACD, then we can use the pythagorean theorem to say
d^2 + m^2 = 2050^2
d^2 = 2050^2 - m^2
Now if we focus on triangle DCB, we can also use the pythagorean theorem to say
d^2 + n^2 = 1420^2
2050^2 - m^2 + n^2 = 1420^2 ...... replace d^2 with 2050^2 - m^2
n^2 - m^2 = 1420^2 - 2050^2
n^2 - m^2 = -2,186,100
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In the diagram, I set up m and n such that m+n = 3000. This solves to n = 3000-m
We can then say
n^2 - m^2 = -2,186,100
(3000-m)^2 - m^2 = -2,186,100
m^2 - 6000m + 9,000,000 - m^2 = -2,186,100
-6000m + 9,000,000 = -2,186,100
-6000m = -2,186,100 - 9,000,000
-6000m = -11,186,100
m = (-11,186,100)/(-6000)
m = 1864.35
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We now have enough to find angle theta, which is the angle between segments AC and AD (the line of sight to the first tower and the highway lines respectively)
We'll focus entirely on triangle ACD
cos(angle) = adjacent/hypotenuse
cos(A) = AD/AC
cos(theta) = m/2050
cos(theta) = 1864.35/2050
cos(theta) = 0.90943902439024 which is approximate
theta = arccos(0.90943902439024)
theta = 24.572056388088
theta = 24.6 degrees
Make sure your calculator is in degree mode. One way to check is that cos(60) should evaluate to 0.5
Complete the statement. Round to the nearest hundredth if necessary.
7 gal = c
PLZZZZZZZ
PLS HELP ME ITS DUE AT 4
Explain why these two equations are different
5(x+4)=60 and 5x+4=60
Step-by-step explanation:
When you use the distributive property, you multiply everything inside the parentheses by the number outside of the parentheses. When you distribute, the equation becomes 5x+20=60 vs 5x+4= 60. Hope this helps!
Write an expression to match, and then evaluate.
1/8 the sum of 23 and 17
Write the expression on your paper.
PLZ HELP I HAVE NO CLUE WHAT TO DO
Answer:
142 cm^2
Step-by-step explanation:
2(L*H)+2(L*W)+2(W*H)=SA
7*3=21
21*2=42
7*5=35
35*2=70
5*3=15*2=30
30+70+42=142
What is the solution to this system of equations using elimination. -7x -8y =9 and -4x + 9y = -22
Answer:
x = 1
y = -2
Step-by-step explanation:
We have the system of equations:
-7*x - 8*y = 9
-4*x + 9*y = -22
To solve this type of system, we need to start by isolating one of the variables in one of the equations.
I will isolate the variable x in the first equation to get:
-7*x - 8*y = 9
-7*x = 9 + 8*y
x = (9 + 8*y)/(-7)
x = -(9 + 8*y)/7
Now we can replace this in the other equation to get:
-4*(-(9 + 8*y)/7) + 9*y = -22
And now we can solve this for y, we will get:
(4/7)*(9 + 8*y) + 9*y = -22
(4/7)*9 + y*(9 + 8*(4/7)) = -22
y*(63/7 + 32/7) = -22 - (36/7)
y*(95/7) = -(22*7/7) - (36/7)
y = (7/95)*(-(22*7/7) - (36/7)) = (-22*7 - 36)/95 = -2
y = - 2
Now we can replace this in the equation x = (9 + 8*y)/(-7) to find the value of x:
x = (9 +8*(-2))/(-7) = 1
Then the solution for the system is the pair (1, -2)
That means:
x = 1
y = -2
PLease help
WILL GIVE BRAINLIEST
Answer:
41.472 m²
8.449m²
Step-by-step explanation:
c) scale facot is 7.2/5 = 1.44
the square scale factor is 1.44^2 = 2.0736
times 20 by this to get the area
2.0737x 20 = 41.472 m²
d) 2.8/6 = SF = 0.467
0.2178 x 38.8 = 8.449m²
"twice as old as y decreased by 10
Answer:
2y = 2(-10) = -20
Step-by-step explanation:
Chris can type 150 words in 4 minutes. How many words can he type in 1 minute?
Answer:
37.5
Step-by-step explanation:
37.5 wpm
Answer:
37.5 words per minute!
Step-by-step explanation:
Chris can type 150 words, dividing the amount of words by the minutes can give us the rate per minute.
150/4= 37.5 words per minutes
You just found the rate of which Chris types per minute!
Los ángulos a y b son complementarios sabiendo q a es =60 grados indique cuanto mide el ángulo b
Find the value of x. Then find the measure of each labeled angle.
Answer:
x = 111
Step-by-step explanation:
x + x - 42 = 180 {Lines are parallel. So, they are supplementary}
2x - 42 = 180
Add 42 to both sides
2x - 42 + 42 = 180 + 42
2x = 222 {Divide both sides by 2}
x = 222/2
x = 111
2. Jeremy drinks 2 pints of milk every 3 days. How much milk would
Jeremy drink in 60 days? *
Answer: 40
Step-by-step explanation: 60/3= 20 20x3= 60 20x2=40
. Which combinations hold the same amount of liquid as a 14-cup jug? A. 2-quart bottles and 4-pint bottles B. 3-quart bottles and 2-cups C. 1-quart bottle and 6-pint bottles and 2-cups D. 1-quart bottle and 10-cups E. 2-quart bottles and 2-pint bottles and 2-cups
Answer:
B, D, and E
Step-by-step explanation:
8 oz = 1 cup
1 qt = 32 oz
1 pint = 16 oz
14 cups = 8 x 14 = 112 oz
A) 64 + 64 = 128 no
B) 96 + 16 = 112 yes
C) 32 + 96 + 16 = 144 no
D) 32 + 80 = 112 yes
E) 64 + 32 + 16 = 112 yes
10 / 16 = n / 19
round to the nearest 100th if needed
Answer:
exact form is 95/8 decimal form 11.875 and mixed number form n= 11 7/8
M_ABD = 90°. Find m2ABC.
A
(3x – 3)
(x-7)°
B
D
Answer:
positive and negative or c1
2/3•x-9=12 solve for x?
Answer:
31.5
Step-by-step explanation:
Ok.
2/3x - 9 = 12
2/3x = 21
x = 21*(3/2)
x = 63/2 = 31.5
Answer:
[tex]x=\frac{63}{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} \times x-9=12[/tex]
Add 9 to both sides:
[tex]\frac{2}{3}x-9+9=12+9\\\frac{2}{3}x=21[/tex]
Multiply both sides by 3/2:
[tex](\frac{3}{2} )\times(\frac{2}{3}x)=(\frac{3}{2} )*(21)\\x=\frac{63}{2}[/tex]
x = 63/2 is your answer.
IM AWARDING POINTS AND BRAINLIEST ITS DUE ASAP
The expression (3x^7)^4 is equivalent to cx^n. What is the value of c?
Answer:
the answer would be c=81x^28-n I hope it helps!
Answer:
c=81x^28-n
Step-by-step explanation:
[tex]c=81x^{28-n}[/tex]
In the following picture ABCD ~ AEFG.
Which equation can be used to find the value of x?
A function is a mathematical rule that.....
A. Has one or more exponential expressions
B. Can be graphed as a straight line
C. Sends every input to only one output
D. Sends every output to only one input
Answer:
B
Step-by-step explanation:
A function can be graphed as a straight line, as long as it isn't vertical.
A jar contains 4 red marbles, 8 blue marbles, and 2 green fond the probabillity of picking a red marbles, replacing the item, and then picking a blue marble?
Answer:
8/49
Step-by-step explanation:
Given data
Sample space
4 red marbles
8 blue marbles
2 green
Sample size
4+8+2 = 14
Pr(picking a red)
Pr(red)= 4/14= 2/7
With replacement
Pr(picking a blue)
Pr(blue)= 8/14= 4/7
Hence the probability of picking a red marble, replacing the item, and then picking a blue marble
= 2/7*4/7
= 8/49
A STADIUM HAS 15,600 SEATS. IT HAS 60 ROWS OF SEATS ALTOGETHER. THE 35 ROWS AT THE BACK HAVE 300 SEATS EACH. THE REST OF THE ROWS AT THE FRONT HAVE THE SAME NUMBER OF EACH SEATS EACH. HOW MANY SEATS ARE THERE IN EACH OF THE ROWS AT THE FRONT
Answer: The number of seats in each of the rows at the front =204
Step-by-step explanation:
Let x = The number of seats in each of the rows at the front.
Given: Total seats = 15,600
Total rows = 60
Rows in back = 35
Rows in front = 60-35=25
Total seats in front = 25x
Each row in the back has 300 seats.
Total seats in the back =300 x35=10500
Seats in front = 15600-10500=5100
i.e. [tex]25x=5100\Rightarrow x=\dfrac{5100}{25}=204[/tex]
Hence, the number of seats in each of the rows at the front =204
Triangle Sum Practice - Digital
Find the value of x, and then use that value to determine each angle measure of the triangle.
4. JKLM is a parallelogram. Find JM.
J
к
8x + 4
4x + 20
M
L
Answer:
36
Step-by-step explanation:
8x + 4 = 4x + 20
8x - 4x = 20 - 4
4x = 16 divide both sides by 4
x = 4 and JM = 8x + 4 replace x with 4
8×4 + 4 = 36
Answer:
36
Step-by-step explanation:
8x + 4 = 4x + 20 ( being opposite sides of parallelogram)
8x - 4x = 20 - 4
4x = 16
x = 16 / 4
x = 4
JM = 8x + 4
=8 * 4 + 4
= 32 + 4
= 36
Hope it will help :)
In a bag, there are 15 tickets bearing the numbers 1 to 15. One ticket is drawn at
random from the bag. Find the probability that the ticket drawn bears a number
multiple of 3.
Answer:
1 in 5
Step-by-step explanation:
Multiples of 3 from 1 to 15:
3, 6, 9, 12, 15
Find the lowest multiple of 3.
Formula for probability:
Probability number is drawn/total
3/15
Convert it to simplest form.
1/5
I am not so sure about this, but I have seen people do this, hope I'm not wrong.
100%
The distance between Boomtown and Dayville on a map is 13.0 cm. The scale of the map is 10 cm = 25 km
Approximately how far apart are Boomtown and Dayville?
Answer:
32.5
Step-by-step explanation:
We can set this problem up as a proportion:
[tex]\frac{10}{25} = \frac{13}{x}[/tex] In doing this, we find the exact distance from Boomtown to Dayville. Another way to do it is by dividing 25 by 10, to get 2.5, then multiplying 2.5 by 13 to get 32.5
Using the picture above, find the value ofr. Round to the nearest tenth plssssi need helpppppp
Answer:
11.4
Step-by-step explanation:
Since this triangle is a right triangle, we can solve using SOHCAHTOA.
Our angle is 25 degrees and the given hypotenuse length is 27. So, the best trigonometry equation to use would be sine, since it includes the hypotenuse and the opposite side, which is the r length that we are looking for.
Through SOHCAHTOA, sin 25° = [tex]\frac{opp}{hyp}[/tex]
sin 25° = [tex]\frac{r}{27}[/tex]
r = 27 (sin 25°)
Using a calculator, 27 (sin 25°) ≈ 11.4
Which axis did the point (-7, -6) reflect over if it ended up at (7, -6)? *
X-axis
Y-axis
Answer:
x axis
Step-by-step explanation:
it will be higher than the first point but not move left or right so by visualising it would be reflected by the x-axis
3 out of 12 candies are orange. In a bag of 100, about how many candies are orange?
Answer:
88 is the answer
Step-by-step explanation:
How?
Like this...
3 out of 12 candies are orange, then how many candies are orange?
100 - 12 = 88If you are not sure .. you can also verify your answer by this
12 + 88 = 100It means that your answer which is coming 88 is absolutely correct!Help me, witch are the true!!!?
Answer:
A is the answer hope this helps
Help me answer this. thx
Step-by-step explanation: