Consider the following vectors in component form
a = LeftAngleBracket 2, 10 RightAngleBracket. B = LeftAngleBracket negative 5, negative 12 RightAngleBracket. C = a minus b.
NEED HELP ASAP
What is the magnitude and direction angle of vector c?
|c| = 5, θ = 36.9°
|c| = 5, θ = 53.1°
|c| = 25, θ = 16.3°
|c| = 25, θ = 73.7°
Answers
Answer:
D
Step-by-step explanation:
The magnitude is 25 and the direction angle of vector c is 73.7°. Option D is correct.
Given, a=⟨2,10⟩, b=⟨-5,-14⟩, c=a-b
We need to find what is the magnitude and direction angle of vector c.
What is the magnitude and direction angle?Given a position vector v=⟨a,b⟩, the magnitude is found by |v|=√a²+b². The direction is equal to the angle formed with the x-axis, or with the y-axis, depending on the application. For a position vector, the direction is found by tanθ=(ba)⇒θ=[tex]tan^{-1}[/tex](ba).
Now, vector c=⟨7,24⟩|c|=[tex]\sqrt{7^{2} +24^{2} }[/tex]=25angle =tan(θ)=(168)⇒θ=[tex]tan^{-1}[/tex](168)= 73.7°.
Hence, the magnitude is 25 and the direction angle of vector c is 73.7°.
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Related Questions
A website that sells songs for downloading has two different price categories. Older songs are $0.99 and new releases are $1.29. Macy spent $15.36 downloading songs during the month. She downloaded a total of 9 songs. Write a system of equations that represents the situation where x is the number of songs Macy downloaded at $0.99 and y is the number of songs she downloaded at $1.29. You do not need to solve the equations.
Answers
Answer:
$0.99x plus $1.29y = 15.36
Step-by-step explanation:
Please help meh parents are yelling at me :(
Jasper is using the following data samples to make a claim about the house values in his neighborhood:
House Value
A $150,000
B $175,000
C $200,000
D $167,000
E $2,500,000
Based on the data, should Jasper use the mean or the median to make an inference about the house values in his neighborhood? (10 points)
Group of answer choices
He should use the mean because it is in the center of the data.
He should use the median because it is in the center of the data.
He should use the median because there is an outlier that affects the mean.
He should use the mean because there are no outliers that affect the mean.
Answers
Answer:
d:$167,00
Step-by-step explanation:
the lines are parallel, if one line has the slope of -1, what is the slope of the other line
Answers
Answer:
-1
Step-by-step explanation:
parallel lines always have the same slope
find the x- and y-intercepts of the line with equation 8x - 4y = -64
Answers
Answer:
x-intercept:8
y-intercept:16
Step-by-step explanation:
This is the equation of a straight line. When the line crosses the x-axis that is the x- intercept, the corresponding y-coordinate will be zero. Substituting y = 0 into the equation and solving for x gives the x-intercept.
8x-(4×0)=-64
-8x=-64
x=8 <= the x-intercept.
Similarly, when the line crosses the y-axis the corresponding x- coordinate will be zero. Let x = 0 and solve for y.
(8×0)-4y=-64
-4y=-64
y=16 <= the y-intercept .
Answer:
x = 1/2
y = -8
Step-by-step explanation:
Let's solve for x.
8x−4y=−64
Step 1: Add 4y to both sides.
8x−4y+4y=−64+4y
8x=4y−64
Step 2: Divide both sides by 8.
8x/8 = 4y−64 / 8
x= 1/2 y−8
What is the equation of this line?
y=3x−2
y=13x−2
y=2x−3
y=12x−3
Answers
Answer is A. y=3x−2 (i took the quiz on k12 and this was the correct answer so it may be different depending on your school)
Answer:
y = 2x - 3( Proof is down below!! )
I hope this helped!!
-GXLDIE <3
i need help with my math>
Answers
Answer:D
Step-by-step explanation: You can multiply the first equation by 2, and then add two equations together, find x, then plug in and find y and voila! its D
:D
Select the correct answer.
What is the greatest common factor of the numerator of 9x^3 - 3x^2 + 12x / 3x
A. 3x2
B. 12x
C. 3x
D. 9x3
Answers
Answer:
D is right
Step-by-step explanation:
Is it positive.,negative or no association
Answers
Answer:
positive
Step-by-step explanation:
it is going upwards. thats how you know
plz mark me brainliest, i need it to level up! just one more brainliest (itll help alot)
HAVE A GOOD DAY!!!
:D
what is the x and y intercept ??
Answers
Answer:
The x-interceptis1 and y-intercept is-4
Answer:
x intercept: 1
y intercept: -4
Step-by-step explanation:
If you look at where the line hits the x axis, it hits it at 1. And if you look at where the line hits the y axis it hits it at -4.
I will give brainliest!!!!
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 12 pieces and costs $8.
Let R represent the number of additional rolls that Sofia orders.
1) Which inequality describes this scenario?
Choose 1 answer:
A) 12 + 24R ≤ 100
B) 12 + 24R ≥ 100
C) 24 + 12R ≤ 100
D) 24 + 12R ≥ 100
2) What is the least amount of additional money Sofia can spend to get the sushi they need?
dollars
Answers
Answer:
The answer is given below <3
Step-by-step explanation:
The options are not given but I would list the inequalities needed to solve this problem.
As a result of increase in people to attend meeting, the number of sushi needed to be ordered is 100 pieces. Sofia has already ordered 24 pieces. If R is the number of additional rolls that Sofia orders.
The number of additional rolls that Sofia orders (R) must be greater than or equal to the difference between the number of Sushi needed to be ordered and the number of Sushi that has already being ordered. It is given by the inequality:
R ≥ 100 - 24
R ≥ 76
If each roll contains 12 pieces, the number of rolls needed (n) is given by:
n ≥ R/12
n ≥ 76/12
n ≥ 6.33
n ≥ 7
If each roll cost $8, the money needed to buy the sushi is given as:
Cost ≥ 8(7) ≥ $56
The morning Shift at the point grocery store is 6.5 hours long. If the cashiers make $10.25 Per hour, how much do they make each shift?
Answers
Answer:
$66.62
Step-by-step explanation:
10.25 x 6.5 = 66.625
6*10.25=61.5
10.25/2=5.125
61.5+5.125=66.625
round down for money -> 66.62
Brainliest to first!! Pls help!! :)
Answers
explanation:
can someone please help? what’s the measurement of x?
Answers
My explanation is because the angle is gives you is 62, and all of those are technically 90 degree angles that when all are added up they become 360 for the whole thing. 90-62=28, but you don’t need that angle. So my guess is that the angle with 62 degrees is going to be the same as the angles you are looking for.
Consider the number z = 5 – 5i StartRoot 3 EndRoot. What happens when z is raised to successively increasing powers?
Use the drop down menus to complete each sentence.
The modulus increases by a factor of
The argument increases by
Pi over 3.
Answers
The modulus increases by a factor of 10 and the argument increases by 5π/3.
What is the modulus of the complex number?The modulus of the complex number is the magnitude of the complex number. If z is the complex number such that z= p+qi
Then the modulus of the z will be =|z|= √p²+q²
We have,
z = 5 – 5i √3
So,
Now rewrite this given equation in the form of z = r(CosΘ + iSinΘ),
For this first calculate the modulus,
|Z| = √((5√3)² + 5²)
|Z| = √(25×3 + 25)
|Z| = √(100) = 10
And,
Argument, Θ = tan⁻¹ (b/a)
Θ = tan⁻¹ (5√3/5)
Θ = tan⁻¹ (√3)
Θ = 71
Therefore, the modulus increases by a factor of 10, and the argument increase by 5π/3.
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Answer:
Step-by-step explanation:
Solve the equations by substitution method: A) x+y=3, 2x+5y=12.
Answers
Answer:
x = 1, y = 2
Step-by-step explanation:
Original equations:
[tex]x+y=3\\2x+5y=12[/tex]
Substitute y and solve for x:
[tex]y=3-x\\2x+5y=12[/tex]
[tex]2x+5(3-x)=12[/tex]
[tex]2x+15-5x=12[/tex]
[tex]-3x=-3[/tex]
[tex]x=1[/tex]
Plug in x to solve for y:
[tex]1+y=3[/tex]
[tex]y=2[/tex]
x = 1, y = 2
Note: You can also substitute x and solve for y, then plug in y to solve for x. I did not do that here.
Answer:
x+y=3
x=3-y equation 1
2x+5y=12
2(3-y)+5y=12
6-2y+5y=12
6+3y=12
3y=12-6
y=6÷3
y=2 equation 2
again ,
putting value of equation 2 in equation 1
x=3-y
x=3-2
x=1
Donald can type 240 words in 6 minutes. How long will it take him to type a 1000-word essay if he types at the same rate?
Fill in the blanks with the correct values.
Answers
Donald can type 240 words in 6 minutes. How long will it take him to type a 1000-word essay if he types at the same rate?
This question can be solved by using proportions. The question has already given a proportion you need to fill in, which looks like this:
[tex]\displaystyle \frac{A}{B} =\frac{x}{1000}[/tex]
As you can see, the denominators are B and 1000, which represents the number of words. That means the number of words will go on the bottom, which leaves you with the number of minutes as the numerator.
Donald can type 240 words in 6 minutes. The number of words, 240, is the denominator, and the number of minutes, 6, is the numerator.
Substitute A and B with these values:
[tex]\displaystyle \frac{A}{B} =\frac{x}{1000} \rightarrow \frac{6}{240} =\frac{x}{1000}[/tex]
Now you need to cross multiply.
[tex]1000 \times 6=240 \times x[/tex]
Simplify:
[tex]6000=240x[/tex]
Lastly, you need to divide both sides by 240 to find the value of x alone. This is because 240 is being multiplied by x, and in order to leave x alone, you must do the opposite of it, which is dividing.
[tex]\displaystyle \frac{6000}{240} =\frac{240x}{240}[/tex]
[tex]\displaystyle x=25[/tex]
That means Donald can type 1000 words in 25 minutes. A is also equal to 6, and b is equal to 240.
__________________________________________________________
[tex]\displaystyle {\bf\frac{6}{240} =\frac{x}{1000}[/tex]
Solving this proportion indicates Donald could type his essay in 25 minutes.
__________________________________________________________
Visualizer
Write in point-slope form
(5,3) - 을
0
m-
(4,1) and (2-3)
Answers
For 0° ≤ x < 360°, what are the solutions to cos(StartFraction x Over 2 EndFraction) – sin(x) = 0?
Answers
Answer:
C
Step-by-step explanation:
Ed2021
The solutions of the given trigonometric equation are 60°, 180°, 300°.
What is a trigonometric equation?A trigonometric equation is an equation that consists of one or multiple trigonometric ratios of unknown angles.
The given trigonometric equation is:
cos (x/2) - sin (x) = 0
⇒ cos (x/2) - 2sin (x/2) cos (x/2) = 0
⇒ cos (x/2) [1 - 2sin (x/2)] = 0
Therefore, cos (x/2) = 0 = cos (90°) (x/2 can't be 270°)
⇒ x = 180°
Again, [1 - 2sin (x/2)] = 0
⇒ 2sin (x/2) = 1
⇒ sin (x/2) = 1/2
⇒ (x/2) = 30°, 150°
⇒ x = 60°, 300°
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eighteen more than five times a number x
Answers
Answer:
18 + 5x
Step-by-step explanation:
more than means adding
find the distance between PQ. P(3,4) and Q(6,8)
25
20
15
5
Answers
Marco bought 5 movies for $53. 10. Vance bought 3 movies for $31. 71. Who got the better deal?
Answers
Answer: Vance.
Step-by-step explanation: Vance got the better deal. this is because Marco bought 5 movies, and paid $53.10. Vance paid $31.71, and saved $2.50, because 53.10 rounds to 50, and 31.71 rounds to 30, and Vance added $1.71, and Marco added $3.10, making Vance get the better deal.
What is the relationship between the ratios?
4872and 69
Answers
Cuz if that is, here’s the Answer
48:72 is 8 times larger than 6:9
ASAPPP, can someone tell me the answer for this , i don’t want to flunk this assignment:/
Answers
Answer:
B
Step-by-step explanation:
X is about 4.5 times the amount given, so B. 337 1/2
Answer:
337.5 or 337½
Step-by-step explanation:
y∞x
y=kx(where k is the constant)
75=½k
cross multiplication
75×2=k
150=k
therefore the formula connecting x,k and y is y=150x
y=150×2¼
y=150×9/4
y=1350÷4
y=337.5or 337½
If f(x)=2x - 7 and g(x)=x^2-1, find f(g(-2)) =
Answers
Answer:
f(g(-2))=-122
Step-by-step explanation:
You need to put the f(x) ewuation into the g equation, and then solve.
8x-4+6x+15
I’ll give brainliest
if you answer!
Answers
Answer:
14X + 11
Step-by-step explanation:
Plz help!!!!!!!!! Due soon!
Answers
Answer:
520 Students
Step-by-step explanation:
If you multipy 650 by .8 you will get 520 and that is the percentage of students that is going.
Answer:
520 students will attend the field trip.
Step-by-step explanation:
The percentage of a number can be found by multiplying the percentage by the amount.
In this case, 650 times 80% is 520.
We can check our answer by dividing 520 by 650 and converting the decimal into a percentage.
If included in the table, which ordered pair, (-4,1) or (1,-4) would result in a relation that is no longer a function? Explain your answer.
(Pls hellp it's my last question)
Answers
Answer:(-4,1)
Step-by-step explanation:x values cannot be the same
Which statement about 3/5+7/10 is true?
A. The sum is a mixed number
B. The sum is a whole number
C. The least common denominator is 5
D. The least common denominator is 15
Answers
The true statement about 3/5+7/10 is (a) the sum is a mixed number
How to determine the true statement?The expression is given as:
3/5 + 7/10
Take the LCM and add both numbers
3/5 + 7/10 = (6 + 7)/10
Evaluate the sum
3/5 + 7/10 = 13/10
Simplify
3/5 + 7/10 = 1 3/10
The fraction 1 3/10 is a mixed number
Hence, the true statement about 3/5+7/10 is (a) the sum is a mixed number
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What is the equation of the line that passes through the point (6,-1) and has a slope of 1?
Answers
Answer:y
=
4
3
x
−
9
Explanation:
Given -
x
1
=
6
y
1
=
−
1
Slope
m
=
4
3
Given the slope and a point, the formula for the straight line equation is
(
y
−
y
1
)
=
m
(
x
−
x
1
)
y
−
(
−
1
)
=
4
3
(
x
−
6
)
y
+
1
=
4
3
x
−
6
.
4
3
y
+
1
=
4
3
x
−
8
y
=
4
3
x
−
8
−
1
y
=
4
3
x
−
9
What is the volume of the following sphere? Round your answer to nearest whole number. 10 cm
Answers
Answer:
4188.79 cm^3
Step-by-step explanation:
Use formula for volume of sphere from radius.