Answer:
Velocity of plane is 100 mi/hr along northeast direction
Step-by-step explanation:
From the question it is given that Initial velocity of plane is 150 mi/hr along east north direction and wind is blowing at 50 mi/hr along southwest direction
since the velocity of wind and plane is exactly opposite
⇒ relative velocity of plane with respect to wind is given by
[tex]v_r_e_l = v_p - v_w[/tex] where [tex]v_p[/tex] is the velocity of plane = 150mi/hr and [tex]v_w[/tex] = velocity of wind = 50 mi/hr
Therefore, [tex]v_r_e_l = v_p - v_w[/tex] = [tex]v_r_e_l = 150 - 50 = 100 mi/hr[/tex] alond northwest direction
Therefore, velocity of plane is 100 mi/hr along northeast direction
By working with the velocity vectors, we will find that the direction of motion of the plane is 28.7 south of east.
Working with the velocity vectors:
First, we need to define our coordinate axis, I will define the x-axis as the east and the y-axis as the north.
We know that the plane travels at 150 mi/hr at 100° east of north, notice that if we measure from the positive x-axis, this is equivalent to an angle of -10°.
Then the x-component of the velocity is: 150mi/hr*cos(-10°) = 147.7 mi/hrThe y-component of the velocity is: 150mi/hr*sin(-10°) = -26 mi/hr.
So the vector is:
V = < 147.7 mi/hr, -26 mi/hr >
Now we know that the wind blowing at 50mi/hr at southwest, exactly southwest would be at an angle of 225°, so the components of the vector are:
x-component: 50mi/hr*cos(225°) = -35.4 mi/hry-component: 50mi/hr*sin(225°) = -35.4 mi/hr.So the vector is:
W = < -35.4 mi/hr, -35.4 mi/hr>
The sum of the vectors gives the total velocity of the plane in the wind, we will get:
V + W = < 147.7 mi/hr -35.4 mi/hr , -26 mi/hr -35.4 mi/hr >
V + W = <112.3 mi/hr, -61.4 mi/hr>
The direction of a vector <x, y> is given by:
θ = Atan(y/x)
Then in this case the direction of the plane is:
θ = Atan(-61.4 mi/hr/112.3 mi/hr) = -28.7°
So the direction of the plane is 28.7° south of east.
If you want to learn more about vectors, you can read:
https://brainly.com/question/17108011
ABCDE~GHJDF Complete statement
Answer:
FE
Step-by-step explanation:
i hope you help this answer
For the two similar figures, the expression can be written as:
[tex]\dfrac{GH}{AB} = \dfrac{JD}{CD}[/tex]
What is the similarity?In geometry, similarity refers to the property of two figures that have the same shape but possibly different sizes. Two figures are considered similar if their corresponding angles are congruent and their corresponding sides are proportional.
For example, two triangles are similar if they have the same shape but can be different in size. This means that the corresponding angles of the two triangles are equal and the corresponding sides are in proportion.
The symbol used to denote similarity is "~". For example, if triangle ABC is similar to triangle DEF, we write it as:
ABCDE~GHJDF are similar. So the ratios of the sides of the figure can be written as,
[tex]\dfrac{GH}{AB} = \dfrac{JD}{CD}[/tex]
To know more about similarity follow
https://brainly.com/question/30068992
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Since starting a new recycling plan, Aaron's office recycles 7 kilograms of paper each week,
How many weeks will it take Aaron's office to recycle a total of 28 kilograms of paper?
Answer: 4 weeks
Step-by-step explanation: 28 divided by 7 is 4.
HELO URGENT WILL GIVE BRAINLIEST IF CORRECT
Sry the app makes the photo so bad quality but anyways can someone please help me
Answer:
B also the full name of vertically angles is called the vertically opposite angle theorem or voat
Juan bought fruit from the grocery store. The variables below define his purchase. Juan’s bananas cost half as much as apples. Which equations can be used to model his purchase? Select each correct equation. *
Answer:
[tex]B = \frac{1}{2}A[/tex]
[tex]A = 2B[/tex]
Step-by-step explanation:
Given
Represent apple with A and Banana with B
Required
Determine the relationship between A and B
From the question, we understand that:
B costs half as much as A
This can be represented as:
[tex]B = \frac{1}{2} * A[/tex]
[tex]B = \frac{1}{2}A[/tex]
Multiply both sides by 2
[tex]2*B = \frac{1}{2}A*2[/tex]
[tex]2B = A[/tex]
[tex]A = 2B[/tex]
help help help help help
Answer:
Step-by-step explanation:
1) (-6 , 2) ; (3 , -5)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{-5-2}{3-[-6]}\\\\= \frac{-5-2}{3+6}\\\\= \frac{-7}{9}\\[/tex]
m = -7/9 ; (-6 , 2)
y - y₁ = m(x -x₁)
y - 2 = (-7/9)(x - [-6])
[tex]y - 2 = \frac{-7}{9}(x + 6)\\\\y -2 = \frac{-7}{9}x + \frac{-7}{9}*6\\\\y - 2 = \frac{-7}{9}x - \frac{7*2}{3}\\\\ y = \frac{-7}{9}x - \frac{14}{3} + 2\\\\y = \frac{-7}{9}x -\frac{14}{3} + \frac{2*3}{1*3}\\\\y = \frac{-7}{9}x - \frac{14}{3} + \frac{6}{3}\\\\y = \frac{-7}{9}x - \frac{8}{3}[/tex]
2) (3 , -4) ; m= 3
[tex]y - y_{1} = m(x - x_{1}[/tex])
y - [-4] = 3(x - 3)
y + 4 = 3x - 3*3
y + 4 = 3x - 9
y = 3x - 9 - 4
Ans: y = 3x - 13
3) m = 2 ; y-intercept (b) = 3/2
y = mx + b
Ans: y = 2x + (3/2)
4) (-1, 3 ) ; (2 , 0)
Slope = [tex]\frac{0 - 3}{2-[-1]}[/tex]
[tex]= \frac{-3}{2+1}\\\\= \frac{-3}{3}\\\\= 1[/tex]
m = 1; ( -1 , 3)
y - 3 = 1(x -[-1])
y - 3 = 1(x + 1)
y - 3 = x + 1
y = x + 1 + 3
Ans: y = x + 4
5)(2, 1) ;m = -3
y - 1 = (-3)(x - 2)
y - 1 = -3x + 6
y = -3x + 6 +1
Ans: y = -3x + 7
Step-by-step explanation:
1) (-6 , 2) ; (3 , -5)
Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}
x
2
−x
1
y
2
−y
1
\begin{gathered}= \frac{-5-2}{3-[-6]}\\\\= \frac{-5-2}{3+6}\\\\= \frac{-7}{9}\\\end{gathered}
=
3−[−6]
−5−2
=
3+6
−5−2
=
9
−7
m = -7/9 ; (-6 , 2)
y - y₁ = m(x -x₁)
y - 2 = (-7/9)(x - [-6])
Which is a better state?
Ny or Florida
(Doing this for a statistic question)
Answer:
I would personally say Florida. When looking at things such as race, NYC has many races, and New York has very different neighborhoods and lifestyles.
In Florida, most people are more laid back, and there are not that many differences in race and other aspects.
Find x & y so that quadrilateral is a parallelogram. (Look at image)
Answer:
x = - 6 y = 13
Step-by-step explanation:
we know when the diagonals bisect it divides into two equal parts so
-4x - 2 = -3x + 4
-4x + 3x = 4 + 2
- x = 6
x = - 6
Now
2y + 8 = 3y - 5
3y - 2y = 8 + 5
y = 13
Hope it will help :)❤
Can someone help me I have two more other questions they are 15 points each I just posted them right now! Thanks so much I will give brainliest
Answer:
80˚
Step-by-step explanation:
Since the angles are equal, we can make this equation:
2x + 65 = 8x + 5
60 = 6x
x = 10
so if we put x = 10 in 8x + 5 we get
8x + 5
8(10) + 5
80 + 5
85
The movie starts at 3:15 p.m. and ends at 5:08 p.m. How long is the movie?
Answer:
1 hour and 53 minutes
Step-by-step explanation:
Your welcome
please answer the question below
Answer: 220
Step-by-step explanation:
Will already has 148 he bought 8 packages that contains 9 in each so 8 x 9 = 72 then add 148 to 72 and you will have your total which is 220.
Kevin wants to buy a new pair of jeans if the jeans were originally $40 but are on sale with 25% discount
how much will Kevin have to pay for the jeans?
Answer: Kevin will have to pay $30 for the jeans.
Answer:
He will have to pay 30$
Step-by-step explanation:
Please answer the question :)
Answer:
the lenght of the shortest side is 12
Step-by-step explanation:
So first add them all up becuase perimeter
3x+3x+5x-4+5x-4
You’ll get 16x-8
16x-8=56
16x=64
x=4
So then plug it in
3x=3*4=12
5x-4=5*4-4=16
so 12 is the shortest side
1) Diego drank x ounces of juice. Lin drank 1/4 less than that
2) Lin ran x miles. Diego ran 3/4 more than that
3) Diego bought x pounds of almonds Lin bought 1/4 of that
(Drag and drop plz help)
Answer:
Follows are the solution to this question.
Step-by-step explanation:
Please find the solution file for the question in the attachment.
The perimeter of a polygon is 96 ft.
Write and solve an equation to find “m”.
Answer:
m = 12
Step-by-step explanation:
Total perimeter = 3m + 3m + m + m = 96
so, 8m = 96
then m = 12
B
113°
72°
А
с
D
Write a list of steps that are needed to find the measure of ZB.
Step-by-step explanation:
the exterior angle is equal to the sum of the interior angles on the opposite side.
As in angle BCD = angle BAC + angle ABC
113 = 72+angle ABC
angle ABC = 41
Answer:
180-113 to find the linear angle.
add that result with 72.
once found the sum, use 180 to subtract the sum to get angle B.
Given: f(x) = 1/x+5 and g(x) = x - 2.
What are the restrictiorts of the domain of f(g(x))?
0 x4 -5
O X-3
OX= 2
There are no restrictions.
Answer:
The restriction of the domain of f(g(x)) is that x cannot be 3.
Step-by-step explanation:
The first step to solve this question is finding the function, replacing the values. So
[tex]f(x) = \frac{1}{x+5}[/tex]
[tex]g(x) = x - 2[/tex]
[tex]f(g(x)) = f(x - 2) = \frac{1}{x - 2 + 5} = \frac{1}{x - 3}[/tex]
The function is a fraction, which means that the restriction is that the denominator cannot be zero. So
[tex]x - 3 \neq 0[/tex]
[tex]x \neq 3[/tex]
The restriction of the domain of f(g(x)) is that x cannot be 3.
A. 3(x+2)=18 B. 3x+6=18
Answer:
B
Step-by-step explanation:
3x6 is 18 so therefore its B
Plsss help ASAP the semester is about to end and I have to finish so many assignments
Answer:
f(15,055) is the number of pages in a book with 15,055 words.
Step-by-step explanation:
f(w) = length of book (in pages).
w = number of words
Thus, from the options given, the only true statement about the function is that:
f(15,055) = number of pages of a book that has 15,055 words.
"f(15,055)" is the length of a book consisting of 15,055 words. It does not imply that there are 15,055 pages.
(x-2)(x+8)=0 Solve for x
please help :) worth 10 points
Answer:
a. (0,3)
b. (-4,-3)
c. (-2,0)
d. (-1 1/3, 1)
e. (4,9)
f. (-3 1/3, -2)
Step-by-step explanation:
Evaluate −4(14)6x for x=13. Enter your answer as a fraction in simplest form in the box.
Write an equation for the following table.
Answer:
y= 38x
Step-by-step explanation:
It is going up by 38 each time. There is no b value (y=mx + b), because if you times 6 by 38, you get 228. You don't need to add any remainders.
is social media company conducted research on the number of our high school students are on social media and the hours of leaf they receive based on the scatterplot in the image what is the best prediction of the number of hours a high school school student sleeps when he spends 1 hour and social media
Answer:
8.5 hours
Step-by-step explanation:
Draw a line of best fit to predict
write an expression that is equivalent to 1/3x+3/4+2/3x-1/4-1/3-2/3x
Answer: 1/3x + 1/6
Step-by-step explanation:
The expression that is equivalent to 1/3x+3/4+2/3x-1/4-1/3-2/3x would be:
= 1/3x + 2/3x - 2/3x + 3/4 - 1/4 - 1/3
= 1/3x + 3/4 - 1/4 - 1/3
= 1/3x + 1/2 - 1/3
= 1/3x + 3/6 - 2/6
= 1/3x + 1/6
Answer:
1/3x + 2/4
Step-by-step explanation:
(1/3x + 2/3x = 3/3x/ 1 - 2/3 = 1/3) (3/4 - 1/4 = 2/4
Circle the fraction equal to 0.1%
91 points need help now . Emanuel put 12 marbles on one pan
of a scale. On the other pan, he put
4 marbles, then he added 8 more
marbles to that side. Each of the-
marbles weighs 1 ound. Is the scale
balanced? Explain.
Answer: I believe the scale is balanced.
Step-by-step explanation: I stated that because since the other side of the scale contained 12 marbles that were 1 pound each that would be 12 pounds and then since 4+8=12 12 pounds of marbles were also put on the other side.
2. The ratio of boys to girls in Spanish class is 2:4. If there are 24 total students in class, how many boys and
girls are there?
Boys
Girls
Answer:
there are 8 boys and 16 girls
hope this helped :-)
Step-by-step explanation:
24:4=6
6+2=8
8+8=16
8:2=4
8+8+4+4=24
4+4=8
What is the expression of 82 and 95
Answer: 88.5
Step-by-step explanation:
Step 1: Address the formula, input parameters & values.
Input parameters & values:
The given numbers are 82 & 95
Step 2: Find the sum of the given two numbers.
sum = 82 + 95 = 177
Step 3: Divide the sum by 2 to get the average.
average = 177/2
= 88.5
Can the sides of a triangle have lengths 1, 5, and 5?
Yes or no?
Answer:
Yes it can have the lengths 1, 5 and 5