Answer:
The angle between the two vectors is 84.813°.
Step-by-step explanation:
Statement is incomplete. Complete form is presented below:
Let be (6,-3, 1) and (8, 9, -11) vector with same origin. Find the angle between the two vectors.
Let [tex]\vec u = \langle 6, -3, 1 \rangle[/tex] and [tex]\vec v = \langle 8,9,-11 \rangle[/tex], the angle between the two vectors is determined from definition of dot product:
[tex]\theta = \cos^{-1} \left(\frac{\vec u \,\bullet \,\vec v}{\|\vec u\|\cdot \|\vec v\|} \right)[/tex] (1)
Where:
[tex]\vec u[/tex], [tex]\vec v[/tex] - Vectors.
[tex]\|\vec u\|[/tex], [tex]\|\vec v\|[/tex] - Norms of each vector.
Note: The norm of a vector in rectangular form can be determined by either the Pythagorean Theorem or definition of Dot Product.
If we know that [tex]\vec u = \langle 6,-3,1 \rangle[/tex] and [tex]\vec v = \langle 8, 9,-11 \rangle[/tex], then the angle between the two vectors is:
[tex]\theta = \cos^{-1}\left[\frac{(6)\cdot (8) + (-3)\cdot (9) + (1)\cdot (-11)}{\sqrt{6^{2}+(-3)^{2}+1^{2}}\cdot \sqrt{8^{2}+9^{2}+(-11)^{2}}} \right][/tex]
[tex]\theta \approx 84.813^{\circ}[/tex]
The angle between the two vectors is 84.813°.
Please help me on this question I really need help. :,)
Answer:
a. (7, 27) Polly was incorrect.
b. (3, 1) Polly was correct.
Step-by-step explanation:
a.
y = 4x - 1
2x - y = -13
We can solve this by substitution. Our first equation gives us y. Plug that into our second equation for each instance of y.
2x - y = -13
2x - (4x - 1) = -13
First distribute the negative sign across the parentheses.
2x - 4x + 1 = -13
Combine like terms.
-2x + 1 = -13
-2x = -14
Divide both sides by -2.
x = 7
Now that we know x, plug its value into one of our original equations.
y = 4x - 1
y = 4(7) - 1
Solve.
y = 28 - 1
y = 27
Our solution is (7, 27).
Let's check our answer by plugging both values into one of our original equations.
2x - y = -13
2(7) - 27 = -13
Solve.
14 - 27 = -13
-13 = -13
Your solution is correct.
Polly's solution was (-2, -9), which is incorrect.
b.
3x + 6y = 15
-2x + 3y = -3
Let's solve this by elimination. To solve by elimination means to eliminate a variable from the equation.
We have 3x & -2x and 6y & 3y. Notice that 6 and 3 can be simplified easily. To eliminate y, we want to multiply each factor of the second equation by -2.
-2x + 3y = -3
-2(-2x + 3y = -3)
4x - 6y = 6
Write the equations together.
3x + 6y = 15
4x - 6y = 6
Now we can see that the y variable will cancel out.
Apply the elimination method.
3x + 6y = 15
4x - 6y = 6
________
7x = 21
Divide both sides by 7.
x = 3
Now that we know x, plug its value into one of our original equations.
3x + 6y = 15
3(3) + 6y = 15
Solve.
9 + 6y = 15
6y = 15 - 9
6y = 6
y = 1
Our solution is (3, 1).
Let's check our answer by plugging both values into one of our original equations.
-2x + 3y = -3
-2(3) + 3(1) = -3
Solve.
-6 + 3 = -3
-3 = -3
Your solution is correct.
Polly's solution was (3, 1), so she was correct.
Hope this helps!
The value of y varies directly with x. When y = 75, x = ½ . What is the value of y when x is 2 ¼ ? A. 168.75 C. 66.67 B. 16.67 D. 337.5
Answer:
Step-by-step explanation:
The value of y varies directly with x. When y = 75, x = ½ . What is the value of y when x is 2 ¼ ? A. 168.75 C. 66.67 B. 16.67 D. 337.5
y ∝x
y = kx
k = y/x
Which is a solution to the equation
79 - 2 - 472
g.
96
Answer:
[tex]-395[/tex]
Step-by-step explanation:
[tex]79-2= 77-472 = -395[/tex]
Please I really need help
Answer:
19/4 =12
Step-by-step explanation:
The 19/4 is a fraction, 19 being the top (numerator)
and 4 being the bottom (denominator)
which number is equivalent to
6^2×6^3
A. 150
B. 623
C. 327
D. 252
Answer:
150
Step-by-step explanation:
A rectangular garden has an area of 84 square feet and a length of 7 feet. What is the width of the garden?
Answer:
12 ft
Step-by-step explanation:
Given data
Area= 84 ft^2
Length= 7ft
The expression for the area is
Area= L*W
substitute
84=7*W
W= 84/7
W= 12ft
Hence the width is 12 ft
Answer:12ft
Step-by-step explanation:
cual es la fraccion equivalente de 105/275
Answer:
21/55
Step-by-step explanation:
dividamos por 5
= 21/55
Given that x = 5.7 m and θ = 43°, work out BC rounded to 3 SF
Answer:
BC ≈ 4.17
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos43° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{5.7}[/tex] ( multiply both sides by 5.7 )
5.7 × cos43° = BC , then
BC ≈ 4.17 ( to 3 sf )
Graph each function. State the domain and range.
Answer:
Just put it in Geogebra classic. It's an app that helps very much with functions!
HELP!! Choose the fraction pair that is equivalent.
A) 4/5 and 8/20
B) 3/4 and 4/3
C) 3/12 and 1/3
D) 8/24 and 1/3
Can someone plz help !!!
Answer:
3
Step-by-step explanation:
5 + 4 = 9
12 - 9 = 3
In order to find the missing length you will need to add up the given lengths then subtract that from the total perimeter.
PLEASE HELP!!!!!!!!!!!!!!!!!!!!
Answer:
g(x) = -x²
Step-by-step explanation:
By looking at the graph and equation of the blue quadratic line, you know the y-intercept is 4. When you look at the red one you can see the y-intercept is 0 so then the equation should be g(x) = -x²
Answer:
Answer B
Step-by-step explanation:
If both the function have the same shape, it means that the function f(x) is just shifted downwards to obtain function g(x).
The function f(x) is given as,
[tex]f(x) = 4 - x^{2}[/tex]
Shifting the curve downwards by 4 unites, the function g(x) is obtained,
[tex]g(x) = f(x) - 4\\g(x) = 4 -x^{2} - 4\\g(x) = -x^{2}[/tex]
I think option B is the correct choice.
Answer ASAP! Best Answer Will Be Awarded!
Answer:
B
Step-by-step explanation:
4x-8y=16
add 8y to both sides, so you get
8y+16=4x
then subtract 16 from both sides
8y=4x-16
divide by 8 on both sides
y=1/2x-2
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
ft²
The figure contains a triangle. One side is 3.8 feet. A second side is 4. 3 feet. The angle between the given sides is 53 degrees.
Step-by-step explanation:
i forgot sorry
Answer:
6.52 i took the test
Step-by-step explanation:
Which piecewise function is shown on the graph?
Answer:
Option A
Step-by-step explanation:
Just substitute each value of x in the graph to find the correct function.
When be graph the functions given, we find that option A is correct.
What is meant by to graph a function?To graph a function, you have to select x-values and plug them into the equation. Once you plug those values into the equation, you will get a y-value. Your x-values and your y-values make up your coordinates for a single point. Keep plugging in x-values to get coordinates to plot more points on the graph, and then you will see your graphed function once the dots are connected.
Using the graph,
For x < = -2, y = 5.
For -2 < x < 1, the function is a polynomial.
We have two options, either [tex]y = x^{2} -5\ or\ y = x^{2} +5[/tex]
The polynomial must have the point (0,-5) on it.
For [tex]y = x^{2} -5[/tex] , when x = 0, y = -5.
Hence, it is the correct option.
For x >= 1,
Using graph, we see that when y = 0, x lies between 3 and 4.
For equation, [tex]y = 2^{(x-2)} - 2\\[/tex], when y = 0, x = 3, so it is not correct.
For equation, [tex]y = 2^{(x-2)} - 3\\[/tex], when y = 0, x = 3.584, hence it is correct.
Learn more about graphing a function here
https://brainly.com/question/27757761
#SPJ2
find the slope
y= 1/3x + 18
Answer:
1/3
Step-by-step explanation:
y = mx + b
m is the slope and b is your y-intercept.
Answer:
m = 1/3
Step-by-step explanation:
hiii please help i’ll give brainliest:)
Answer:
Geographic Features of Ancient Greece
Step-by-step explanation:
Greece has all these attributes on the list
Answer:
Geographic Features of Ancient Greece
Step-by-step explanation:
plzzzzzzzzzzzzzzzzzzzzzzzz give brain alist
Can you guys help me find the area of this shape. I've literally tried everything and got it wrong.
Answer:
110 square centimeters.
Step-by-step explanation:
The area for a trapezoid can be figured out with the equation (a + b)h/2.
(9 * 5) + (9 + 4)10/2 {Work inside the parentheses first.}
45 + (13)10/2 {Divide 10 by 2 to get 5.}
45 + 13(5) {Multiply 13 by 5 to get 65.}
45 + 65 {Add 45 & 65 to get 110.}
110 square centimeters.
The area of the figure is 110 square centimeters.
What data does the x-axis show?
25 points ***!!
Answer:
time in weeks
Step-by-step explanation:
The area of a trapezoid is 60 square feet. If the bases of the trapezoid are 8 feet and 12 feet, what is the height?
O 6 ft
O 4A
O 3 ft
O 15 ft
Answer:
6
Step-by-step explanation:
60 = 12+8 divided 2 times height
60 = 20/2 x H
60 = 10 x H
60/10 = h
6 = H
Giving brainlist to whoever answers
Answer:
420
Step-by-step explanation:
volume = length x width x height
12 x 5 x 7 = 420
3x + 7 = 9x + 3
No solution one solution or infinite
Answer:
One solution.
Step-by-step explanation:
X=2/3 or x=2.6666
Answer:
x=2/3
Step-by-step explanation:
3x + 7 = 9x + 3
Collect like terms (subtract 3x from both sides and subtract 3 f4=rom both sides)
The resulting equation will look like this:
4=6x
=6x=4
Divide be 6 on both sides:
x=4/6
Simplify:
x=2/3 :-)
Find the circumference and area of each circle. PLEASE HELP!
Answer:
There are so many!
For circumference use = 2 pi r
For area use = pi r²
I have told only formula, else you may lack practice. try to solve yourself
A regular polygon has
Answer:
a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
Step-by-step explanation:
Answer:
A regular polygon has 5 sides
The height of a box is 30 inches.
What is the height of the box in feet?
Answer:
2.5 feet
Step-by-step explanation:
Answer:
2.5 feet
Step-by-step explanation:
[tex] \frac{30}{12} = 2.5[/tex]
6. The roots of the equation 2x2 + 4 = 9x are
a. Real, rational, and equal
b. Real, irrational, and unequal
Real, rational, and unequal
d. Imaginary
Answer:
c. Real, rational and unequal
(-18, -17)
(18,-17)
(18 , 17)
(-18 , 17)
Answer:
(-18, -17) in 3rd Quadrant
(18, -17) in 4th Quadrant
(18, 17) in 1st Quadrant
(-18, 17) in 2nd Quadrant
-TheUnknownScientist
PLEASSE HELP!!! find the midpoint
Answer:
Option B --> (8, -5)
Step-by-step explanation:
To find the midpoint, we use the equation-
[tex]\frac{x1 + x2}{2} , \frac{y1 + y2}{2}[/tex]
The coordinates given were (8, -2) (8, -8)
x1= 8,
x2 = 8
y1 = -2
y2= -8
Substituting these values in the equation:-
[tex]\frac{8+ 8}{2} , \frac{-2 + -8}{2}[/tex]
[tex]\frac{16}{2} , \frac{-10}{2}[/tex]
Coordinates of midpoint will be ---> (8, -5)
please help me do it I only have 3 min
Answer:
1 A. 1080°
1 B. 142°, 74°,74°, 125°, 125°
Step-by-step explanation:
1A.
The sum of the measure of the interior angle of a convex octagon is given as
S = (n-2)180°................. Equation 1
Where n = 8 sides
S = (8-2)180°
S = 6×180°
S = 1080°
1B.
The sum of the angle of a convex pentagon is given as
S = (5-2)180°
S = 3×180°
S = 540°
From the diagram,
2x+142+2x+(3x+14)+(3x+14) = 540
10x+170 = 540
10x = 540-170
10x = 370
x = 37°
Hence,
∠H = ∠K = 2(37) = 74°,
∠M = ∠L= (3×37)+14 = 111+14 = 125°
help appreciated :)
thank you
Answer:
-
He spent 1 hour in total
-
1 hour
There's two Xs on the graph indicating that he had two 1/2 hour hikes, so you just add that up. And that's 1 hour woo