If the acute angle made by lines /and mis 24° and AABC is reflected across line /
followed by a reflection across line m, find the angle through which AABC is rotated.
B
m
Answers
The angle through which ΔABC is rotated is; Option A: 48°
How to Interpret Transformation Reflection?Reflection is an example of transformation in which a given image is flipped over a reference line which changes the orientation of the figure, but preserves its length and shape. Thus, a rotational transformation is formed by two reflections.
In the given question, image ABCD is reflected over lines I, then m at an angle of 24° to each other. Since rotation is twice the acute angle with respect to the center of rotation, therefore ABCD rotates through an angle of 24 * 2 = 48°
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Related Questions
what is the difference between 15
Answers
Answer:
its an odd number
Step-by-step explanation:
PLEASE HURRY!!!!!!!!
Mr. Jackson has decided to open a new health club in his town. To decide whether he will have enough members to be successful, he hires a researcher to conduct a survey. What is the population from which the researcher should choose a sample?
A. People who exercise regularly.
B. Members of other health clubs in the town.
C. Trainers at other health clubs.
D. His friends and family.
Answers
Answer:
I would say b since this would tell him how many people are wiling to join a health club
Hope This Helps!!!
Emil is running a lemonade stand. He sells half of his lemonade in the morning, a quarter of what was left at lunchtime, and a third of what was left in the afternoon. When he closes for the day, he has 4 liters of lemonade left. How many liters of lemonade did he start the day with?
Answers
Answer:
16 Liters of the correct answer.
Emil started his lemonade stand with 12 litres of Lemonade.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-Emil is running a lemonade stand. He sells half of his lemonade in the morning, a quarter of what was left at lunchtime, and a third of what was left in the afternoon.
When he closes for the day, he has 4 litres of lemonade left. Let the total lemonade he started with is x litres. Now we will form an expression from the given data to calculate the value of x.
x - (x/2) -(1/4)(x/2) - ( 1/4)(x/2)(1/3) = 4
x - ( x/2) - (x/8) - ( x/24) = 4
[ 24x -12x -3x - x][24] = 4
8x = 96
x = 12 liters
Therefore Emil started his lemonade stand with 12 liters of Lemonade.
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Find the value of x.
10
135-
Answers
Step-by-step explanation:
[tex] \frac{x}{12} = \frac{x + 4}{5 + 12} \\ [/tex]
[tex] \frac{x}{12} = \frac{x + 4}{17} \\ [/tex]
Now cross multiply...
[tex]12(x + 4) = 17x[/tex]
[tex]12x + 48 = 17x[/tex]
[tex]12x - 17x = - 48[/tex]
[tex] - 5x = - 48[/tex]
Now divide both term by same number
[tex] \frac{ - 5x}{ - 5} = \frac{ - 48}{ - 5} \\ [/tex]
[tex]x = 9.6[/tex]
You are standing 22 feet from a tall building that has a glass elevator on the exterior wall facing you.
You watch the elevator as it ascends to the top of the building. The height h (in feet) of the elevator
above the ground can be modeled by / = 22 tan e, where © is the angle of elevation. Graph the
function. Describe what happens to © as h increases.
Answers
a. Find the graph in the attachment
b. As h increases, e tends to 90°
a. How to graph the function?
Since you are standing 22 feet from a tall building that has a glass elevator on the exterior wall facing you. You watch the elevator as it ascends to the top of the building.
The height h (in feet) of the elevator above the ground can be modeled by h = 22tane.
To plot the graph, we see that the function is the tangent function.
The tangent function has the value -∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°
Since e is our angle of elevation and e ≥ 0, that is 0 ≤ e ≤ 90°. So, we choose the range of values for which tane ≥ 0. So, 0 ≤ tane ≤ +∞
So, we plot h = 22tane for 0 ≤ e ≤ 90°
Find the graph in the attachment
b. What happens to e as h increases?From the graph, we seet that at high h or as h increases, e tends to 90°
So, as h increases, e tends to 90°
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. A housing down payment is money that a
prospective buyer provides up front when
purchasing a home and is usually a per-
cent of the purchase price of the home. A
lender typically requires private mortgage
insurance (PMI) when the buyer's down
payment is less than 20% of the purchase
price. To secure a mortgage, buyers also
need to have additional cash on hand
for closing costs and prepaid property
tax. Suppose a buyer wants to purchase
a $375,000 house and must have $7,200
on hand for closing costs and property
tax. Which of the following inequalities
represents the total funds (f) the buyer
must have on hand to secure the mortgage
without having to pay PMI?
A) f≤0.2(375,000) + 7,200
B) f≥0.2(375,000) +7,200
C) f≤0.2(375,000 +7,200)
D) f≥0.2(375,000 +7,200)
Answers
Answer:
B) f≥0.2(375,000) +7,200
Step-by-step explanation:
≥ means 'at least'
4 Quick algebra 1 question for 50 points!
Only answer if you know the answer, tysm!
Define the domain and range of each function: (in the pictures)
Answers
[tex]f(x )= - 2x[/tex]
Domain: ( - ∞ , ∞ ) or ] -∞ , ∞ [Range: ( - ∞ , ∞ ) or ] -∞ , ∞ [B)[tex]g(x) = \frac{1}{2} x {}^{2} + 5[/tex]
Domain: ( - ∞ , ∞ ) or ] -∞ , ∞ [Range: [ 5 , ∞ [ or [ 5 , ∞ )C)Domain: ( - ∞ , ∞ ) or ] -∞ , ∞ [Range: ( - ∞ , ∞ ) or ] -∞ , ∞ [D)Domain: ( - ∞ , ∞ ) or ] -∞ , ∞ [Range: ( - ∞ , - 3 ] or ] - ∞ , - 3 ]#1
y=-2xDomain
(-oo,oo)Range
(-oo,oo)#2
y=0.5x²+5Domain
(-oo,oo)Range
[5,oo)#3
Its graphed
Domain=Range=(-oo,oo)
#4
Domain
(-oo,oo)Range
[-3,-oo) or (-oo,-3]
5 Quick algebra 1 questions for 50 points!
Only answer if you know all 5, Tysm! :)
Answers
answers
6. y = -1/2x + 8
7. y = 15
8. y = -3/4x + 1
9. y = 6x + 3
10. y = 1/3x - 4
steps
equation of the line that is perpendicular means the number next to the x should be a negative reciprocal
number next to the x is the slope
6. y=2x+5
y = mx + b
m = 2
b = -5
negative reciprocal would be
-1/2x
m = -1/2
(2, 7) means x = 2 y = 7
substitute
7 = -1/2(2) + b
7 = -1 + b
b = 8
answer is y = -1/2x + 8
7.
y = 5; (11, 15)
b = 5
m would be 0 because there is no slope
15 = 0*11 + b
b = 15
y = 15
8.
line goes through
(0,-2) and (3,2)
get slope
y2-y1/x2-x1
2-(-2) / 3 - 0
4/3
y = 4/3x
point slope form
y - y1 = m (x-x1)
y - -2 = 4/3 (x - 0)
y+2 = 4/3x
y = 4/3x - 2
negative reciprocal slope would be for perpendicular
-3/4x
(12, 10)
y = mx + b
10 = 3/4(12) + b
10 = 9 + b
1 = b
b = 1
y = -3/4x + 1
9.
y = -1/6x + 1; (− 2, — 9)
negative reciprocal slope would be for perpendicular
+6x
(− 2, — 9)
y = mx + b
get b
-9 = 6(-2) + b
-9 = -12 + b
b = 3
y = 6x + 3
10.
6x+2y=14; (12, 0)
2y= -6x+14
y= -3x+7
negative reciprocal slope would be for perpendicular
1/3x
y = mx + b
get b
0 = 1/3(12) + b
0 = 4 + b
b = -4
y = 1/3x - 4
Wonder waves aquarium just opened a new tropics wing, with a large main tank and a small observation tank. there are 75 fish in the large tank, 25 of which are angelfish. there are 25 fish in the small tank, 5 of which are angelfish. do the tanks have the same ratio of angelfish to total fish?
Answers
Answer:
No, the ratio is not the same.
Step-by-step explanation:
75 total (large tank) / 25 total (small tank) = 3
25 angelfish (large tank) / 5 angelfish (small tank) = 5
The ratio of angelfish to total fish is not the same. When we scale up from the small tank to large tank in terms of total fish, we have a factor of 3. However, when we scale up from the small tank to large tank in terms of angelfish, we have a factor of 5. For the ratio to be the same, these factors would need to be identical.
an elevator has a maximum load restriction of 2.5 tons. is it safe for two tile layers weighing 175 ib and 240 ib plus 80 boxes of tile weighing 50 ib each
Answers
Using proportions, it is found that the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each lb has 0,0005 tons. Hence the total weight in tons that we want to put in the elevator is:
T = (175 + 240 + 80 x 50) x 0.0005 = 2.2075 tons.
Hence, the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.
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In order to compute the area of a particular circle, Juan first measures the length of its diameter. The actual diameter is 20 cm, but Juan's measurement has an error of up to $20\%$. What is the largest possible percent error, in percent, in Juan's computed area of the circle
Answers
The largest possible error in the area of the circle is of 44%.
What is the area of a circle?The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
With a diameter of 20 cm = radius of 10 cm, the area in cm² is given by:
[tex]A = \pi \times 10^2 = 100\pi[/tex]
With the error, with a diameter of 20 x 1.2 = 24 cm = radius of 12 cm, the area in cm² is given by:
[tex]A = \pi \times 12^2 = 144\pi[/tex]
The error is given by:
[tex]E = 144\pi - 100\pi = 44\pi[/tex]
The percent error is the error divided by the initial amount, multiplied by 100%, hence:
[tex]P = \frac{44\pi}{100\pi} \times 100\% = 44\%[/tex]
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CAN SOMEONE HELP PLEASE
a = 3, b = 5, and c = 7. What is m&B° to the nearest tenth?
Answers
Answer: 38.2 degrees
Step-by-step explanation:
[tex]b^2 = a^2 + c^2 - 2ac \cos B\\\\5^2 = 3^2 + 7^2 - 2(3)(7) \cos B\\\\25 = 58-42 \cos B\\\\-42 \cos B=-33\\\\\cos B=\frac{33}{42}\\\\B \approx 38.2^{\circ}[/tex]
d
an and David are marking exam papers. Each set takes Dan 35 minutes and David 1 hour. Express the times Dan and David take as a ratio.
Give your answer in its simplest form.
Answers
Answer:5
Step-by-step explanation:
Everyday Math
574. The population of the United States on July 4,2010 was almost 310,000,000. Write the number in scientific notation.
Answers
Answer:
If the population of the United States on July 4,2010 was almost 310000000 then, the number in scientific notation is [tex]$3.1 \times 10^{8}$[/tex].
Step-by-step explanation:
- Given
Population of the United States on July 4,2010 was almost 310000000 .
- To write the number in scientific notation.
- Firstly, move the decimal point so that the first factor is greater than or equal to 1 but less than 10 .
- Then, count the number of decimal places, n, that the decimal point was moved.
- Then, write the number as a product with a power of 10.
- Finally, check the scientific notation.
Step 1 of 2
Moving the decimal point-
Move the decimal after 3 . so that 3.10000000 is between 1 and 10 .
Now, we know the decimal point was moved 8 places to the left.
Step 2 of 2
Writing the number as a product with a power of 10 -
Since, 310000000 is greater than 1 so the power of 10 will have the exponent 8 .
Therefore, the number becomes-
[tex]$$31000000=3.1 \times 10^{8}$$[/tex]
Now, checking the scientific notation-
[tex]$$\begin{gathered}3.1 \times 10^{8}=3.1 \times 100000000 \\=310000000\end{gathered}$$[/tex]
Which of the following lines will have a negative slope? Select all that apply
Answers
Answer:
1, 5
Step-by-step explanation:
-16/4=-4
10/5=2
1/2=1/2
-1/-3=1/3
-1/4/1/2=-1/2
The negative ones are your answer.
Identifying Transformations On a coordinate plane, triangle A has points (3, 3), (6, 3), (6, 9). Triangle A prime has points (negative 2, negative 1), (negative 2, negative 2), (negative 3, negative 2). Determine all the transformations needed to transform the pre-image, A, to the image, A'. Select all that apply. dilation by a scale factor of 1/2 dilation by a scale factor of 1/3 reflection over the x-axis translation to the left 4 units translation down 3 units
Answers
Triangle A was dilated by a scale factor of 1/3 and reflected over the x axis to form triangle A'
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
Triangle A was dilated by a scale factor of 1/3 and reflected over the x axis to form triangle A'
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Answer:
b d e
Step-by-step explanation:
For the following exercises, find the x- and y-intercepts of the graphs of each function.
26. f(x) = 4| x − 3 | + 4
Answers
For the function f(x) = 4|x - 3| + 4, we have that:
The function has no x-intercepts.The y-intercept is of y = 16.What is the x-intercept of a function?The x-intercept of a function is the value of x when y = f(x) = 0, hence:
0 = 4|x - 3| + 4
4|x - 4| = -4
|x - 4| = -1
The absolute value cannot be negative, hence the function has no x-intercepts.
What is the y-intercept of a function?The x-intercept of a function is the value of y = f(x) when x = 0, hence:
f(0) = 4|0 - 3| + 4 = 12 + 4 = 16.
The y-intercept is of y = 16.
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Rectangular prism B is the image of rectangular prism A after dilation by a scale factor of \frac{1}{2} 2 1 . If the volume of rectangular prism B is 8 m^3 3 , find the volume of rectangular prism A, the preimage.
Answers
The quantities which are squares or multiple of linear things twice grow by square of scale factor. The volume of rectangular prism A = 64 m³
How does dilation affect length, area, and volume of an object?Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.
So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:
L = k × M
where 'k' will be called as scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.
So, area of first figure = k² × area of second figure
Similarly, Volume of first figure = k³ × volume of second figure.
It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.
Given that the Rectangular prism B is the image of rectangular prism A after dilation by a scale factor of 1/2.
Scale factor = (Length of rectangular prism B)/(Length of rectangular prism A)
1/2 = (Length of rectangular prism B)/(Length of rectangular prism A)
Now, the volume of the rectangular prism can be written as,
(Scale factor)³ = (Volume of rectangular prism B)/(Volume of rectangular prism A)
(1/2)³ = 8 m³ /(Volume of rectangular prism A)
The volume of rectangular prism A = 64 m³
Hence, The volume of rectangular prism A = 64 m³
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50 POINTS HELP NOW
Find the logarithm base 10 of each number:
10
Answers
The logarithm base 10 of the number 10 is 1
How to solve logarithm ?We have to find logarithm base 10 of number 10.
Therefore, using logarithm rule
logₐ a = 1
Hence,
log₁₀ 10 = 1
Therefore, logarithm base 10 of the number 10 is 1
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Answer:
1
Step-by-step explanation:
Select the graph that correctly displays this system of equations and point of intersection.
Answers
The solution of the equations will be the point of intersection of the two lines
Equation of a lineA line is the shortest distance between two points. The equation of a line in standard form is given as Ax + By = C
According to the question, we are to pot the following lines.
4y +3x = 0
4y - x = 16
The solution of the equations will be the point of intersection of the two lines as attached.
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What type of triangle is shown below?
31°
28.5
19.2
109°
40%
991
Answers
Answer:
could u send a photo please
The main floor of Kinsey's home is 1,425 square feet. The upper level is 875 square feet with one unfinished bedroom that measures 150 square feet. The finished basement is 1,425 square feet with 7.5-foot ceilings. Kinsey's MLS listing includes below-grade square footage in livable area. What's the reportable square footage for Kinsey's home
Answers
The reportable square footage for Kinsey's home = 2150square feet.
The main floor of Kinsey's home is 1,425 square feet.
The upper level is 875 square feet with one unfinished bedroom that measures 150 square feet.
The finished basement is 1,425 square feet with 7.5-foot ceilings.
That means the square footage of the upper floor plus the main floor (minus the unfinished laundry area).
Kinsey should report square feet (1425+875- 150)
= 2150square feet.
Hence, The reportable square footage for Kinsey's home = 2150square feet.
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Having some trouble here need some help not really good at this
Answers
Answer:
none of these are correct
Step-by-step explanation:
Which equation has infinite solutions?
3(x – 1) = x + 2(x + 1) + 1
x – 4(x + 1) = –3(x + 1) + 1
2x + 3 = 2 x plus 3 equals StartFraction one-half EndFraction left-parenthesis 4 x plus 2 right-parenthesis plus 2.(4x + 2) + 2
StartFraction one-third EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals 3 left-parenthesis x plus 1 right-parenthesis minus x minus 2.(6x – 3) = 3(x + 1) – x – 2
Answers
The equation that has an infinite number of solutions is [tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]
How to determine the equation?An equation that has an infinite number of solutions would be in the form
a = a
This means that both sides of the equation would be the same
Start by simplifying the options
3(x – 1) = x + 2(x + 1) + 1
3x - 3 = x + 3x + 2 + 1
3x - 3 = 4x + 3
Evaluate
x = 6 ----- one solution
x – 4(x + 1) = –3(x + 1) + 1
x - 4x - 4 = -3x - 3 + 1
-3x - 4 = -3x - 2
-4 = -2 ---- no solution
[tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]
2x + 3 = 2x + 1 + 2
2x + 3 = 2x + 3
Subtract 2x
3 = 3 ---- infinite solution
Hence, the equation that has an infinite number of solutions is [tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]
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Complete question
Which equation has infinite solutions?
3(x – 1) = x + 2(x + 1) + 1
x – 4(x + 1) = –3(x + 1) + 1
[tex]2x + 3 = \frac{1}{2}(4x + 2) + 2[/tex]
[tex]\frac 13(6x - 3) = 3(x + 1) - x - 2[/tex]
Consider the equality xy k. Write the following inverse proportion: y is inversely proportional to x. When y = 12, x=5.
Answers
Answer:
[tex]y=\dfrac {60} {x}[/tex] or [tex]xy=60[/tex] (depending on your teacher's format preference)
Step-by-step explanation:
Proportionality backgroundProportionality is sometimes called "variation". (ex. " 'y' varies inversely as 'x' ")
There are two main types of proportionality/variation:
DirectInverse.Every proportionality, regardless of whether it is direct or inverse, will have a constant of proportionality (I'm going to call it "k").
Below are several different examples of both types of proportionality, and how they might be stated in words:
[tex]y=kx[/tex] y is directly proportional to x[tex]y=kx^2[/tex] y is directly proportional to x squared[tex]y=kx^3[/tex] y is directly proportional to x cubed[tex]y=k\sqrt{x}}[/tex] y is directly proportional to the square root of x[tex]y=\dfrac {k} {x}[/tex] y is inversely proportional to x[tex]y=\dfrac {k} {x^2}[/tex] y is inversely proportional to x squaredFrom these examples, we see that two things:
things that are directly proportional -- the thing is multiplied to the constant of proportionality "k"things that are inversely proportional -- the thing is divided from the constant of proportionality "k".Looking at our questionIn our question, y is inversely proportional to x, so the equation we're looking at is the following [tex]y=\dfrac {k} {x}[/tex].
It isn't yet clear what the constant of proportionality "k" is for this situation, but we are given enough information to solve for it: "When y=12, x=5."
We can substitute this known relationship pair, and find the "k" that relates this pair of numbers:
Solving for k, and finding the general equationGeneral Inverse variation equation...
[tex]y=\dfrac {k} {x}[/tex]
Substituting known values...
[tex](12)=\dfrac {k} {(5)}[/tex]
Multiplying both sides by 5...
[tex](12)*5= \left ( \dfrac {k} {5} \right ) *5[/tex]
Simplifying/arithmetic...
[tex]60=k[/tex]
So, for our situation, k=60. So the inverse proportionality relationship equation for this situation is [tex]y=\dfrac {60} {x}[/tex].
The way your question is phrased, they may prefer the form: [tex]xy=60[/tex]
Find the value of z.
Answers
Answer:
z = 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the altitude- on- hypotenuse theorem
(leg of large Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)
z² = 8 × (8 + 1) = 8 × 9 = 72 ( take square root of both sides )
z = [tex]\sqrt{72}[/tex] = [tex]\sqrt{36(2)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex] = 6[tex]\sqrt{2}[/tex]
Answer:
[tex]z = 6 \sqrt{2} [/tex]
Step-by-step explanation:
The solution is in the image
A pianist plans to play 4 pieces at a recital from her repertoire of 20 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible
Answers
There are 1,16,280 different recital programs possible.
Given: A pianist plans to play 4 pieces at a recital from her repertoire of 20 pieces and is carefully considering which song to play first, second, etc.
It means the repetition of pieces is not allowed.
When repetition is not allowed, then the number of ways to arrange n things where r things taken together is given by:-
[tex]^{n} P_{r} =\frac{n!}{(n-r)!}[/tex]
Now, the number of different recital programs are:-
[tex]^{20} P_{4} =\frac{20!}{(20-4)!}=\frac{20*19*18*17*16!}{16!}=116280[/tex]
Hence, there are 1,16,280 different recital programs possible.
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1011 base 2 -1001 base 2
Answers
Answer:0
Step-by-step explanation:
Question 4 of 5
Use the drawing tools to form the correct answer on the number line.
Graph the solution set to this inequality.
-4(1 + 3) ≤ -21
Drawing Tools
Select
Point
Open Point
Ray
>
Click on a tool to begin drawing.
A+++
-10
-8
-6
-4
-2
0
Delete
2
4
Undo
6
20.
8
Reset
10
?
os
Answers
The solution set of -4(x + 3) ≤ -21 is x ≥ 2.25
How to graph the solution set?The inequality is given as:
-4(x + 3) ≤ -21
Divide both sides by -4
x + 3 ≥ 5.25
Subtract 3 from both sides
x ≥ 2.25
This means that the solution set of -4(x + 3) ≤ -21 is x ≥ 2.25
See attachment for the number line
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an airplane flies in the path shown by the vector line UV on the graph below. what is the magnitude and direction of line UV? (1 unit represents 1 mile)
Answers
The magnitude and direction of line UV is 19.7° South of West for 8.1 miles
How to find the magnitude of the vector line UV?The magnitude of the vector line UV is given by the length of the line UV,
d = √[(x₂ - x₁)² + (y₂ - y₁)²] where
(x₁, y₁) = (2, 3) and (x₂, y₂) = (-2, -4)Substituting the values of the variables intot he equation, we have
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(-2 - 2)² + (-4 - 3)²]
d = √[(-4)² + (-7)²]
d = √[4² + 7²]
d = √[16 + 49]
d = √65
d = 8.06 miles
d ≅ 8.1 miles
So, the magnitude of vector line UV is 8.1 miles
How to find the direction of the vector line UV
The direction of the vector line UV is given by Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)] where
(x₁, y₁) = (2, 3) and (x₂, y₂) = (-2, -4)Substituting the values of the variables into the equation, we have
Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)]
Ф = tan⁻¹[(-4 - 3)/(-2 - 2)]
Ф = tan⁻¹[(-7)/(-4)]
Ф = tan⁻¹[7/4]
Ф = tan⁻¹[1.75]
Ф = 60.26°
Ф ≅ 60.3°
Its bearing from the north-south line is α = 90° - Ф
= 90° - 60.3°
= 19.7°
So, its direction is 19.7° South of West
So, the magnitude and direction of line UV is 19.7° South of West for 8.1 miles
Learn more about vectors here:
https://brainly.com/question/26700114
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