Please help! 30 points!
Use the Law of Cosines to solve the problem.
A ship travels due west for 83 miles. It then travels in a northwest direction for 111 miles and ends up 165 miles from its original position. To the nearest tenth of a degree, how many degrees north of west did it turn when it changed direction? Show your work.
Answer: [tex]64.2^{\circ}[/tex]
Step-by-step explanation:
According to the cosine rule
[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
Here, [tex]a=83, b=111, c=165,\ C=180^{\circ}-\theta[/tex]
Putting values
[tex]\Rightarrow \cos (180^{\circ}-\theta)=\dfrac{83^2+111^2-165^2}{2\times 83\times 111}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{6889+12321-27225}{18426}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{-8015}{18426}=-0.4349\\\\\Rightarrow 180^{\circ}-\theta=\cos^{-1}(-0.4349)=115.77^{\circ}\\\Rightarrow \theta=64.23\approx 64.2^{\circ}[/tex]
So, the ship turns by [tex]64.2^{\circ}[/tex] north of west
The ship turned an at angle of 64.2 degrees north of west
Represent the angle, the ship turned due north of west with theta.
From the figure, we have the following equation
[tex]\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}[/tex]
So, we have:
[tex]\cos(A) = \frac{83^2 + 111^2 - 165^2}{2 * 83 *111}[/tex]
Evaluate the expression on the right-hand side
[tex]\cos(A) = -0.4350[/tex]
Take the arc cos of both sides
[tex]A = \cos^{-1}(0.4350)[/tex]
[tex]A =115.8^o[/tex]
The value of theta is then calculated as:
[tex]\theta = 180 -A[/tex]
This gives
[tex]\theta = 180 -115.8^o[/tex]
[tex]\theta = 64.2^o[/tex]
Hence, the ship turned an at angle of 64.2 degrees north of west
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besties besties please help im desparate
What in the flipping Jeapordy is this, but anyway:
1) Simran needs a 65% to score an 80 test average
2) The length is 13 centimeters
3) Jake purchased 4 gadgets
4) 100 candles would need to be sold
5) You bought 3 drinks
Answer:
Step-by-step explanation:
miss girl you need homework plugs sorry queen have a good day
Line d has a slope of 3/2. Line e has a slope of -2/3. Are line d and line e parallel or
perpendicular?
Answer:
We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect
13 (a) Write 2016 as the product of prime factors.
Answer: 2^5*3^2*7*1
Step-by-step explanation:
Five percent of canned goods get bumps or dents in the cans during manufacturing. Let X = the number of cans that are inspected before one with a bump or dent is found.
What is the mean and standard deviation of X?
Mean =
Standard deviation =
Answer:
Mean = 20
Standard deviation = 19.494
Step-by-step explanation:
I got it right.
Help will give b if correct
Answer:
0.28
Step-by-step explanation:
28 divided by 100=0.28
Answer:0.28m
Step-by-step explanation:
A square has a perimeter of 76 cm. Each side measures x + 3.
What is the value of x, in centimeters?
The value of given x is 16
Given that:
Perimeter of square = 76 cm
Side of square = (x + 3)
Find:
The value of x
Computation:
Perimeter of square = 4[Side]
76 = 4[x + 3]
76 = 4x + 12
4x = 76 - 12
4x = 64
x = 64 / 4
x = 16
The value of x = 16
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help me pls AAAAAAAA
Answer:
10/3 liters
Step-by-step explanation:
Divide (4/3) by 2, then multiply by 5
Answer:
10/3 liters
Step-by-step explanation:
Your welcome, hope this helps you
Joe runs an M&M's factory and is reviewing the bagging machines. They drop M&M's into bags on a conveyor belt, with 39 M&M's going into each bag. Write an equation for the number of bags 'B' that can be filled from a supply of M&M's 'T'. Write your equation in the form of B=_____________.
The equation for the number of bags 'B' that can be filled from a supply of M&M's 'T' will be T / 39.
How to explain the equationThe formula to determine how many bags 'B' can be filled with M&M's from a stockpile of 'T', where each bag contains 39 candies, is:
B = T/39
This computation takes the sum of all M&M's in 'T' and divides it by the quantity of candies present in each sack (39), producing the amount of bags 'B' that can be filled.
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factorise p-q-x(q-p)
Answer:
(1 + x)(p - q)
Step-by-step explanation:
Given
p - q - x(q - p) ← distribute parenthesis by - x
= p - q - qx + px ← rearrange terms in p and terms in q
= p + px - q - qx ( factor first/second terms and third/fourth terms )
= p(1 + x) - q(1 + x) ← factor out (1 + x) from each term
= (1 + x)(p - q)
A die is rolled 3. What is the probability of getting a 1 on the first roll, a 2 on the second roll, and a 3 on the third roll
Answer:
The probability of getting 1,2 and 3 after rolling once , second and thrice is
1/6
Step-by-step explanation:
These are all independent events.
The sample space = [1,2,3,4,5,6]
A die has 6 sides
1. If this die is thrown once, the probability of getting a 1 is = 1/6
2. If we roll the dice a second time, the probability of getting a 2 is independent from the first time it was rolled, so the sample space remains the same. The probability is also 1/6
3. If we rolled a 3rd time the probability remains 1/6 also
The speed of boat in still water is 15km/hr if needs 4 more his to travel 63 km against the current of a river than it needs to travel down the river determine the system of equation
Answer:
[tex]\frac{63}{15 - c} - \frac{63}{15 + c} = 4[/tex]
Step-by-step explanation:
The systems of equations are
Let us assume the rate of the current be c
Now actual speed against the current is (15 - c)
And, the actual speed with the current is (15 + c)
Here we applied the time formula i.e. distance by speed
Also the upstream time - downstream time = 4
Now the equations are
[tex]\frac{63}{15 - c} - \frac{63}{15 + c} = 4[/tex]
I need help ASAP please
Answer:
It's actually B
Step-by-step explanation:
The measures of the sides are x , x , and x√2 . In a 45°−45°−90° triangle, the length of the hypotenuse is √2 times the length of a leg. To see why this is so, note that by the Converse of the Pythagorean Theorem , these values make the triangle a right triangle.
So x = 4 in this example and the side measures would be 4, 4, and 4√2 which is B
The table shows the running speeds of 10 randomly selected ostriches. Speed (mlles per hour) 35 40 37 33 36 34 32 36 41 36 Based on the data, select the most reasonable prediction about the speed of ostriches.
A. The typical ostrich runs at speeds greater than 40 miles per hour
B. The top speed of an ostrich is 40 miles per hour.
C. The typical ostrich runs at a speed of about 30 miles per hour
D. The typical ostrich runs at a speed of about 36 miles per hour.
Answer:
D;the tropical ostrich runs at a speed of about 36 miles per hour
Answer: It is D, The typical ostrich runs at a speed of about 36 miles per hour.
Step-by-step explanation:
I took the quiz on A p e x^^
Using the dimensions shown, you could create a rectangular prism. Caculate the surface area for the rectangular prism. A 30m2 b 56m2 c 60m2 d 112m2
Answer:
550ft²
Step-by-step explanation:
Since we are not given the dimension of the rectangular prism. Let us assume;
Length of the rectangular base L = 10ft
Width of the rectangular base W = 15ft
height of the prism H = 5ft
Total surface area of the prism = 2(LW + WH + LH)
Substitute the given values
Total surface area of the prism = 2{10*15 + 15*5 + 10*5}
Total surface area of the prism = 2(150+75+50)
Total surface area of the prism = 2(275)
Total surface area of the prism = 550ft²
Here are the score that Jenna has received on her seven quizzes 16 11 20 16 12 17 18 what is the lower quadrille
Answer:
12
Step-by-step explanation:
lower quartile is the median of 11, 12, and 16
What is the diameter of the Orange below ? HINT : D = 2r
Answer:
umm don't know.....
Step-by-step explanation:
......
6ya +7y{a
Find the sum
O 13y^2
O O 13ay
O 13y/2a
0 13ya
Problem PLS HELP MY GRADES GOING DOWN
Answer:
$248
Step-by-step explanation:
given:
4 deposits
$62
solve:
4 × $62= $248
Answer:
$248
Step-by-step explanation:
You can answer it two ways:
1) add 62 + 62 + 62 + 62 = 248
2) multiply 4 * 62 = 248
Answer: $248
14 cm
12 cm
22 cm
Find the area of the trapezoid. and show Work
A. 108 cm
B. 432 cm
C. 60 cm
D. 216 cm
Answer:
D. 216 cm
Step-by-step explanation:
1. I assume 14 is a 22 is b and 12 is h
2. Trapezoid Area Formula
[tex]A = \frac{1}{2}(a+b)h[/tex]
3. Plug in numbers
[tex]A = \frac{1}{2}(14+22)12[/tex]
[tex]216 = \frac{1}{2}(14+22)12[/tex]
please hurry if answer is correct i will give brainlyyyyest thx
In this task, you will calculate the area of a complicated shape by splitting it into simpler shapes. Cut out shape C. Shape C is not a regular shape, so you cannot directly apply a formula to find its area. Split shape C into simpler shapes whose areas you can find by applying formulas. List the simple shapes into which you divided shape C, and measure their sides. Write all the measurements in inches.
Answer:
i could only get part one done
Step-by-step explanation:
Perimeter is a measurement of the distance around a shape and area gives us an idea. Understanding how much space you have and learning how to fit shapes ... If the shape is a polygon, then you can add up all the lengths of the sides to find the perimeter. ... You can write “in2” for square inches and “ft2” for square feet
Jehle and Liam a bowl serving 0.5÷200 Jehle says the question will be Less than 0.5 Liam says the quotient would be more than 0.5 which student is correct
Answer:
Jehle is correct.
Step-by-step explanation:
Given - Jehle and Liam a both solving 0.5÷200.
Jehle says the quotient will be Less than 0.5.
Liam says the quotient would be more than 0.5
To find - Which student is correct ?
Proof -
Given expression is 0.5 ÷ 200
It is equivalent to
[tex]\frac{0.5}{200} = \frac{5}{2000} = \frac{1}{400}[/tex] = 0.0025 < 0.5
∴ we get
The expression is Less than 0.5
So, Jehle is correct.
Nikea went running three days in a row. She ran 3 1/2 miles on Monday. She ran the same distance on Tuesday as she did on Wednesday. She ran a total of 7 1/4 miles on all three days. Which of these equations can be used to find the numbers of miles, x, that Nikea ran on Tuesday and Wednesday? Select all that apply.
A. 2x=7 1/4−3 1/2
B. 2x +3 1/2 = 7 1/4
C. 3 1/2 + x + x = 7 1/4
D. 3 1/2 + x = 7 1/4
E. 7 1/4 + 3 1/2 =2x
Answer; A B and C are the correct answers also please do not follow the other links answer
Step-by-step explanation:
How many fewer throws travelled more than 6 3/4 meters than travelled 6 3/4 meters or less
Answer:
this is not a complete question cause u did not give full numbers
Step-by-step explanation:
not trying to steal points can u finish the question
A window shaped like a parallelogram has an area of 73 2 3 square feet. The height of the window is 8 2 3 feet. How long is the base of the window?
Answer:
8 1/2 feet
Step-by-step explanation:
Here is the complete question
A window shaped like a parallelogram has an area of 73 2/3 square feet. The height of the window is 8 2/3 feet. How long is the base of the window?
A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length
Area = base x height
73 2/3 = 8 2/3 x base
divide 73 2/3 by 8 2/3
221/3 x 3/26 = 8 1/2 feet
What is the value of x?
Answer:
I have no idea. But I just want to let you know to not put this many points, because people are going to take them without answering the question. And I don't know the answer because there are multiple x's.
Answer:
x = 8
Step-by-step explanation:
Remark
I agree with the other responder. You need only pay 20 points to get our attention. (20 will give us 10).
The length from the intersect point to the circle times the entire length of the secant is equal to any other secant divided up the same way.
Put simpler
Equation
(x + 2)(x + 2 + 2x- 8) = (x + 1)(x + 1 + 2x - 5)
Combine like terms
Solution
(x + 2)(3x - 6) = (x + 1)(3x - 4) Remove the brackets on both sides.
3x^2 + 6x - 6x - 12 = 3x^2 + 3x - 4x - 4 Combine the like terms
3x^2 - 12 = 3x^2 - x - 4 Subtract 3x^2 from both sides
- 12 = - x - 4 Add 4 to both sides
-12 +4 = - x
- 8 = - x Multiply both sides by -1
x = 8
Carlos is helping his grandfather paint the patio in their backyard. What is the area of the patio?
Geomotry 10th grade easy 25 points
Answer: 1=60°
Step-by-step explanation:
First, let's take our given angle of 30°
30° is in a right triangle, so the angles must be 90°, 60°, and 30°
Now the angle that is 45° makes angle 1 congruent to angle 60°
Meaning angle 1 is 60°
Answer:
m < 1 = 60
Step-by-step explanation:
Since the transversal is perpendicular to m,
it implies that the triangle formed by the perpendicular transversal, the slant transversal and the line m is a right angle triangle.
We use vertically opposite angles property to bring m<1 in to the right triangle.
We now use the sum of interior angles property to obtain,
m < 1 + 30 + 90 = 180
This implies that,
m < 1 + 120 + 180
We group like terms to obtain,
m < 1 = 180 - 120
This means that,
m < 1 = 60
We could have also used corresponding angles property, then
m < 1 + 30 = 90
m < 1 = 90 - 30
m < 1 = 60
factorise fully :
4(x - y)^2 - 9(x + y)^2
Answer:
- ( 5x + y ) ( x + 5y )
or
-5x^2 - 5y^2 - 26xy
Answer:
Step-by-step explanation:
4(x^2-2xy+y^2)-9(x^2+2xy+y^2)
4x^2-8xy+4y^2-9x^2-18xy-9y^2
-5x^2-26xy-5y^2
-5x^2-xy-25xy-5y^2
-x(5x+y)-5y(5x+y)
(-x-5y)(5x+y) or you can also remove the negative one to get
-(x+5y)(5x+y)
If your credit card is stolen and the thief runs up a total debt of $1,000, but you notify the issuer of the card as soon as you discover it is missing, what is the maximum amount that you must pay according to Federal law?
Answer:
50 dollars
Step-by-step explanation:
college website