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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I need help on this please!
Answer:
H, G, F, E
Step-by-step explanation:
If it isn't it's G, H, F, E
Hope this helps
help please asap!!!!only the correct answet please
Answer:
B
Step-by-step explanation:
WILL GIVE BRAINLIEST IF ANSWERED CORRECTLY!!!!!!
LMNP is rotated 90' clockwise around the origin.
8
7
6
5
4
M(3, 4) N(5, 4)
3
2
1
LO1)
2
P19,0)
3
4
5
6
7
8
9
What are the coordinates of N'?
O A. N'(4,-5)
O B. N'(-5, -4)
C. N'(-4,5)
D. N'(5,-4)
Answer:
B
Step-by-step explanation:
Answer:
im not sure but it may be B as if i cant see the photo
Step-by-step explanation:
tell me if i got it right or wrong :)
Write a fraction for each percent.
75% of 96
Answer:
72/96
Step-by-step explanation:
which graph shows the solution to the system of equations?y =-2x+1 and y =-3/2
Answer:
(1.25, -1.5)
Step-by-step explanation:
The system of equations:
y = -2x + 1
y = -3/2
So we know that the two lines meet at the point where y = -3/2 = -1.5
∴ -1.5 = - 2x + 1
2x = 1 + 1.5 = 2.5
x = 2.5 ÷ 2 = 1.25
So the solution to this system of equation (or where the two lines meet) is the point (1.25, -1.5)
PLS HURRY AND HELP
Darren had 3 apples represented by the variable (a) . He went to the store and bought 6 more apples to make a pie . Then his little brother Keith came into the kitchen and ate 2 of the apples. Write an expression to show how many Derran is left with.
Answer:
a + (6 -2)I'm not completely sure, but I hope this helps.
Alright fam, help me out here with these angles thanks!
Answer:
m∠3 = 127°
Step-by-step explanation:
From the given picture,
Two parallel lines have been given.
Angle 3 and another angle measuring 53° are located on a point of a straight line.
Therefore, both the angles will be supplementary.
m(∠3) + 53° = 180° [Property of supplementary angles]
m(∠3) = 180° - 53°
= 127°
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
Help this is the question pls help I need your help answer correctly
23 pts
Answer:
[tex]3/8* 16 \\3*2\\6[/tex]
Step-by-step explanation:
Thus the mileage of water for this vehicle is 6 miles per gallon.
Help! The screenshot is down below!!
Answer:
Step-by-step explanation:
A) Find the total minutes that Anna walked.To find the average number of minutes, divide the total minutes by total number of days
B) Average number of minutes =
[tex]\frac{15*9 + 30*5 + 40*7 + 45*3 + 50*6}{30}\\\\= \frac{135 + 150 + 280 + 135 + 300}{30}\\\\=\frac{1000}{30}\\\\= 33. 33[/tex]
Owen is going to an amusement park. The price of admission into the park is $40, and once he is inside the park, he will have to pay $2 for every ride he rides on. How much money would Owen have to pay in total if he goes on 7 rides? How much would he have to pay if he goes on rr rides? PLEASE
Answer:
He will pay $14 to go on 7 rides with admission he will pay a total of $54.
Step-by-step explanation:
Admission-40
One ride-2
40+(2x7)=54
[tex] {x}^{2} - 6x - 12[/tex]
How many solutions can be found for the system of linear equations represented on the
graph?
A) No solution
B) One solution
C) Two solutions
D) Infinitely many solutions
Answer:
No solution
Step-by-step explanation:
Use substitution
2x+1=2x-1
Subtract 2x on both sides
1= -1
No solution
short song i made what yall think of it?
Mason is laying tiles on his entryway. The tiles are each 2/9 feet long, and the entryway is 7 1/2 feet long. How many tiles will Mason need to buy in order to cover the length of the entryway? Explain.
Answer:
1 2/3
Step-by-step explanation:
7 1/2x2/9
The required number of tiles will be 34 covering the length of the entryway.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
We have been given that the tiles are each 2/9 feet long, and the entryway is 7 1/2 feet long.
We have to determine the number of tiles will he need to buy in order to cover the length of the entryway.
According to the given question, the required solution would be as:
So the number of tiles covering the length of the entryway will be
⇒ 7 1/2 ÷ (2/9)
⇒ 15/2 ÷ (2/9)
⇒ 15/2 / (2/9)
Reciprocal the term in the denominator
⇒ (15/2) x (9/2)
Apply the multiplication operation,
⇒ 135/4
Apply the division operation,
⇒ 34
Thus, the required number of tiles will be 34 covering the length of the entryway.
Learn more about Multiplication operations here:
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what do you call the 9 in the statement 30% of 9 is 3
Answer: You call the 9 a base.
Step-by-step explanation: 3 is the percentage or part of the whole or base.
Answer:
9 is the base of the statement.
Step-by-step explanation:
Since 30% is the rate which shows a percent symbol. 9 is the base which is the basis of the statement. Then 3 is the percentage you got from the 30% of 9.
Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. The diagram is not drawn to scale.
Answer:
x = 7[tex]\sqrt{2}[/tex] and y = 7
Step-by-step explanation:
Since this is 45 45 90 triangle, each leg is the same length so y = 7 too and x is always [tex]a\sqrt{2}[/tex] so x = 7[tex]\sqrt{2}[/tex]
The values of [tex]x[/tex] and [tex]y[/tex] are required.
The required values are
[tex]x=9.9\ \text{units}[/tex]
[tex]y=7\ \text{units}[/tex]
The given triangle is a right angled triangle.
Two given angles are [tex]90^{\circ}[/tex] and [tex]45^{\circ}[/tex]
The sum of the angles is [tex]180^{\circ}[/tex]
The missing angle is
[tex]180-(90+45)=45^{\circ}[/tex]
Since, the two angles are equal the side opposite the angles will also be equal.
So,
[tex]y=7[/tex]
Applying the Pythagoras theorem.
[tex]7^2+7^2=x^2\\\Rightarrow x=\sqrt{7^2+7^2}\\\Rightarrow x\approx 9.9[/tex]
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18 entre 12 (división) Porfa respondan, mi ama me pega con la chancla si no lo hago,, es lo único que me faltam
Answer:
Step-by-step explanation:
18 dividido por 12 es 1.5 , esto se puede probar haciendo division larga o multiplicando 1.5 por 12
1.5 * 12 = 18
Espero que te haya ayudado la respuesta y que ahores el chancletazo.
Fidel has a rare coin worth $550. Each decade, the coin's value increases by %10
Which kind of function best models the relationship between time and the coin's value?
Answer: Exponential
Step-by-step explanation: I did it in khan
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)
Determine the value of x in each figure.
HELPPPPP PLEASEEEEE
Answer:
15°
Step-by-step explanation:
120° and 8x are vertically opposite angles, which are always equal.
=> 8x = 120°
=> x = 120/8
=> x = 15°
Use the Distributive Property to write an expression equivalent to 4(5x + 11)
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{If you’re doing the DISTRIBUTIVE PROPERTY... all you have to}\\\large\text{MULTIPLY 4 within your PARENTHESES.}[/tex]
[tex]\large\text{}[/tex][tex]\large\text{4(5x) + 4(11)}[/tex]
[tex]\large\text{4(5x) = 20x}[/tex]
[tex]\large\text{4(11) = 44}[/tex]
[tex]\large\text{\bf = 20x + 44 }[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \huge \bf 20x + 44}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:}[/tex]
[tex]\large\text{Your GUIDE}\downarrow[/tex]
[tex]\textsf{Distributive formula}[/tex]
[tex]\textsf{a(b + c)}[/tex]
[tex]\textsf{a(b) + a(c)}[/tex]
[tex]\textsf{= ab + ac}[/tex]
(10*2)*3=( )* ( ) * ( )
=
=
Answer:
c= 10 d=2 e=10 f=2 g= 10 h= 6 k=1
Step-by-step explanation:
I am not sure about the g, h and k though.
but cube root means the number thrice.
I hope it helps.
A bouncy ball is dropped such that the height of its first bounce is 7 feet and each successive bounce is 67% of the previous bounce's height. What would be the height of the 8th bounce of the ball? Round to the nearest tenth (if necessary).
Answer:
4.79
Hope this helps! :D
Answer: 0.2
Step-by-step explanation:
30 divided by 12 pls hurry
Answer:
2.5 is the correct answer.
Step-by-step explanation:
Hope this helped Mark BRAINLEST!!!
Please Help Me Answer:
-6n - 5 = 31
Answer:
n = - 6
Step-by-step explanation:
Given
- 6n - 5 = 31 ( add 5 to both sides )
- 6n = 36 ( divide both sides by - 6 )
n = - 6
Answer:
n= -6
Step-by-step explanation:
-6n=31+5
-6n=36
n=36÷-6
n= -6
Find the discriminant. (Must Show Work)
-9m^2+m-7=0
Answer:
-251
Step-by-step explanation:
the discriminant .b^2-4ac
=1-4×(-9)×(-7)
=1-252=-251
What is the equation of a line with a slope of 2 and a y intercept of -5?
Answer:
y=2x-5
Step-by-step explanation:
The slope is how you move so you could also call it m
The y intercept is where you begin so you could call it b
So every time you need to find the equation or which one is like the slope just remember m=move b= begin
y=mx+b
If it takes Joan 10 weeks to make 2 dollhouses, how long will it take her to make 15 dollhouses?
10 points
A. 75 weeks
B. 3 weeks
C. 30 weeks
D. 150 weeks
Answer:
D 150 thats easy multiply or add