The correct answer is |w| = 5.5; θ = 156.1°. The given magnitudes and direction angles of vectors u and v, and their subtraction to obtain vector w, the correct values are |w| = 5.5 and θ = 156.1°.
Given that |u| = 4 at an angle of 210°, and |v| = 9 at an angle of 315°, and w = u - v, we need to find the magnitude and direction angle of w.
|u| = 4 at an angle of 210°:
Let the terminal side of vector u make an angle of θ1 with the positive x-axis.
So, tanθ1 = (sinθ1)/(cosθ1) = (-4√3)/(-4) = √3
Therefore, θ1 = tan⁻¹(√3) + 180° = 210°
|v| = 9 at an angle of 315°:
Let the terminal side of vector v make an angle of θ2 with the positive x-axis.
So, tanθ2 = (sinθ2)/(cosθ2) = (-9)/(-9) = 1
Therefore, θ2 = tan⁻¹(1) + 315° = 225°
Now, w = u - v:
|w| = |u| * |v| * cos(θ1 - θ2)
|w| = 4.9 * cos(210° - 225°)
|w| = 5.5
Also, θ = 180° + (θ1 - θ2) + tan⁻¹(9√3/4)
θ = 156.1°
Hence, |w| = 5.5; θ = 156.1° is the correct option.
In conclusion, based on the proper values for the vector w's magnitude and direction angle are |w| = 5.5 and = 156.1°. These values are given for the vectors u and v.
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Given the function below, what is the g(-8)?
g(x)=2x+1
someone solve please
In ΔTUV, t = 410 cm, ∠U=27° and ∠V=78°. Find the length of v, to the nearest 10th of a centimeter.=
Answer: 415.2
Step-by-step explanation:
help please
4 − ( −12) + ( −7) =
............................................9
The width A rectangle is 3 cm less then its length. The perimeter of the rectangle is 30 CM. Find The length and width of the rectangle
w = l - 3
w = 9 - 3
w = 6
//
l = 9
w = 6
//
p = 2(9) + 2(6)
p = 30
The diagram shows two right-angled triangles. PQR and QST are straight lines. It is given that sin x = [tex]\frac{15}{17}[/tex] . Find the value of cos y.
Step-by-step explanation:
[tex] \sin(x) = \frac{15}{17} = \frac{23 + c}{34} \\ 34 \times 15 = 17(23 + c) \\ 510 = 391 + 17c \\ 17c = 119 \\ c = 7[/tex]
[tex] \sin (y) = \frac{7}{25} \\ y = 16.26 \\ \cos(16.26) = \frac{ \alpha }{25} \\ 0.96 = \frac{ \alpha }{25} \\ \alpha = 24 [/tex]
[tex] \cos(y) = \frac{24}{25} [/tex]
Solve the equation.
5x = 3x²+1
5+ 13
a
5-√13
c.
-5+ √13
5- V13
X=
or
or
12
12
6
6
b.
-5+ √13
5-√3
d.
S+~13
5- 13
Of
12
or
12
6
6
Which of the following correctly describes the product below?
A.
irrational
B.
rational
C.
a combination of both rational and irrational
D.
neither rational nor irrational
Answer:
C is the answer your looking for
Convert the following quadratic equation to vertex form. 2) 3x2 - 12x - 5
Answer:
3(x - 2)² - 17
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Using the method of completing the square.
Given
3x² - 12x - 5 ← factor out 3 from the first 2 terms
= 3(x² - 4x) - 5
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² - 4x
= 3(x² + 2(- 2)x + 4 - 4 ) - 5
= 3(x - 2)² - 12 - 5
= 3(x - 2)² - 17 ← in vertex form
The slope is 2.92, which shows a positive relationship because it is a positive number. The
longer a person’s hair, the more it will cost to get the hair highlighted. This makes sense, as
more product is required to highlight more hair.
Each letter in the word "TEXTBOOK" is written on an identical tile and placed in a bag. What is the probability of
drawing a vowel on the first try?
Answer:
37.5% or 3/8
Step-by-step explanation:
There are 8 total letters, and only 3 vowels, which can be the fraction 3/8. 3/8 as a percent is 37.5%. Hope this helps!
Answer:
Capital letters and Rotations marks
Given the following parallelogram: Solve for x.
7x + 70
16x - 20
Answer:
x=10
Step-by-step explanation:
7x+70=16x-20
70=9x-20
9x=90
x=10
James has 838 feet of rope. There are 17 teams of hikers. If James gives an equal amount of rope to each team, how much rope will each team receive?
Answer:
838 ÷ 17 = 49.29 feet each
Step-by-step explanation:
divide the total rope by number of hikers equals amount of rope each hiker will receive.
Consider the polynomial function h(x) = x^6 - 3x^5 - 17x^3
What is the end behavior of the graph of h?
Choose 1 answer:
PLEASE HELP
Answer: As x -> positive infinity, h(x) -> positive infinity, and as x -> negative infinity, h(x) -> positive infinity
Step-by-step explanation:
Khan Academy!! Hope this helps :)
Mr. Alvarez makes a walkway of 3 cement slabs.He uses 14 cubic feet of cement to make the walkway.Each square slab has a volume of 4 cubic feet
Answer:
I suppose that you want to see how we can find the volume of each individual slab with the given information, the procedure is as follows.
The walkway has 3 cement slabs,
He uses a total amount of 14 cubic feet to make the complete walkway.
This means that the 3 cement slabs together have a total volume of 14 ft^3
To find the volume of each slab, we need to find the quotient between the total volume and the total number of slabs, then we get:
Volume of each slab = (14 ft^3)/3 = 4 ft^3
This means that each cement slab has a volume of 4 ft^3.
Answer:
6 ft^3
Step-by-step explanation:
PLZZ HELP ME IM DOING A TEST RNNNN.
Answer:
5(x)+5(y)=10
10(x)+2(y)=12
Step-by-step explanation:
i just got done with that same thing
I need help with a/d
Answer:
yeah whats the question asking >:(
What is the area of the triangle?
6 square inches
18 square inches
12 square inches
30 square inches
Answer:
answer is 6.
Step-by-step explanation:
the base as 4 in. times the height as 3in. divided by 2= 6in.
I need help with math if you don't know the answer get out of the question and don't answer it and give the wrong answer or some link or even say "I don't know" or anything like that it's not fair to me cause it a waste of my points I will report your if you do that :) have a nice day and stay safe
Answer:
1.5 or 1 1/2 pounds of candy
Step-by-step explanation:
First, divide 2 into 4 equal pieces. You do this because of the denominator in 3/4.
2 divided by 4= 0.5
Then 0.5 times 3 because of the numerator in 3/4.
0.5 times 3= 1.5
You can convert this into the fraction 1 1/2 or you can leave it a 1.5
Hope this helps!
[tex]4x\leq 12[/tex]
Divide each term by
4
and simplify.
Inequality Form:
r ≤ 3
Interval Notation:
( − ∞ , 3 ]
please help me with this
Answer: B
Step-by-step explanation:
What is the value of 6(2b-4) when b=5?
Answer:
126
Step-by-step explanation:
Step-by-step explanation:
When b = 5 Then
6( 2b - 4)
= 6 ( 2 *5 - 4)
= 6 ( 10 - 4)
= 6 * 6
= 36
Hope it will help :)
Sari wrote the equivalent ratios below to convert cups to fluid ounces. How many fluid oz. Are in 9 cups.
Answer:
the number of fluids ounces in 9 cups is 72 fluid ounces
Step-by-step explanation:
The computation of the number of fluids ounces in 9 cups is shown below:
As we know that
In 1 cup = 8 fluid ounces
So for 9 cup it is
= 9 × 8
= 72 fluid ounces
hence, the number of fluids ounces in 9 cups is 72 fluid ounces
Find the discriminant of x2-6x -10 = 0, and determine the number of real solutions of the equation.
Answer:
76
2 real solutions
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0
Discriminant: b² - 4ac
Positive - 2 solutions Equal to 0 - 1 solution Negative - No solutions/ImaginaryStep-by-step explanation:
Step 1: Define
x² - 6x - 10 = 0
Step 2: Identify Variables
Compare quadratic.
x² - 6x - 10 = 0 ↔ ax² + bx + c = 0
a = 1, b = -6, c = -10
Step 3: Find Discriminant
Substitute in variables [Discriminant]: (-6)² - 4(1)(-10)[Discriminant] Evaluate exponents: 36 - 4(1)(-10)[Discriminant] Multiply: 36 + 40[Discriminant] Add: 76This tells us that our quadratic has 2 real solutions.
Which of the following are properties of the circumcenter of a triangle? Check
all that apply.
A. The circumcenter is at the intersection of the perpendicular
bisectors of the triangle's sides.
B. The circumcenter of an obtuse triangle is always outside it.
M C. The circumcenter is equidistant from each vertex of the triangle.
D. The circumcenter is equidistant from each side of the triangle.
Answer: A. The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides.
C. The circumcenter is equidistant fromeach vertex of the triangle.
D. The circumcenter is equidistant from each side of the triangle.
Step-by-step explanation:
The properties of the circumcenter of a triangle from the options given include:
• The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides.
• The circumcenter is equidistant fromeach vertex of the triangle.
• The circumcenter is equidistant from each side of the triangle.
Option B is wrong as the circumcenter of an obtuse triangle is not always outside it. For the circumcenter, there is intersection of all the three lines and it's not important that they should always be outside.
These two figures are the image and pre-image of a
dilation.
Find the value of x.
4 m
6 m
4 m
6 m
8 m
9 m
6 m
Answer:
4m i think it sounds about right
Answer: the answer is 9m or D
Step-by-step explanation:
A rectangular lettuce patch, 560 square feet in area, is to be fenced off against rabbits. Find the least amount of fencing required if one side of the land is already protected by a barn. What are the dimensions?
The dimensions for the least amount of fencing is 16.7 ft by 33.5 ft
Let x represent the length of the fence and y represent the width of the fence.
Since the area is 560 square feet, hence:
Area = length * width
560 = xy
y = 560/x
One side of the land is already protected by a barn, hence:
Perimeter (P) = x + x + y = 2x + y
P = 2x + y
P = 2x + 560/x
For least amount of fencing, dP/dx = 0, hence:
dP/dx = 2 - 560/x²
0 = 2 - 560/x²
560/x² = 2
2x² = 560
x = 16.7
y = 560/16.7 = 33.5 ft
The dimensions for the least amount of fencing is 16.7 ft by 33.5 ft
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Rodrigo practiced playing the guitar 15 1/3 hours over the past 3 weeks.
He practiced for 5 1/4 hours during the first week and 5 2/3 hours during the second week.
How much time did Rodrigo spend practicing during the third week? Use the numbers and symbols to select the equation that represents the problem. Then solve the equation. Symbols may be used more than once or not at all.
15 1/3, 5 1/4, 5 2/3, x, =, and +.
The equation that represents the problem is
a. 15 1/3 = x - 5 1/4 - 5 2/3
b. x = 15 1/3 + 5 1/4 + 5 2/3
c. x + 15 1/3 = 5 1/4 + 5 2/3
d. 15 1/3 = 5 1/4 + 5 2/3 + x
Answer: d. 15 1/3 = 5 1/4 + 5 2/3 + x
Step-by-step explanation:
15 1/3 (total) = 5 1/4 (first week) +5 2/3 (second week) +x (third week)
When you add the amount of time Rodrigo practiced each week, you get the total amount of time he practiced
what's [2+(2x3)]x5.
17.
Is the relation a function? Why or why not?
{(–8, –4), (–2, 0), (1, 3), (–2, 6)}
A. Yes; only one range value exists for each domain value.
B. No; the relation passes the vertical line test.
C. No; two range values exist for domain value –2.
D. Yes; two range values exist for domain value –2.
Answer:
C. No; two range values exist for domain value –2.
Step-by-step explanation:
The relation is not a function.
The -2 in the domain repeats
Since
x
=
−
2
produces
y
=
0
and
y
=
6
, the relation
(
−
8
,
−
4
)
,
(
−
2
,
0
)
,
(
1
,
3
)
,
(
−
2
,
6
)
is not a function.
The relation is not a function.