The vectors u = ❬6, –9❭ and v = ❬–24, 36❭ are parallel to each other because the cosine of the angle θ is equal to -1. (Right choice: A)
How to determine the relationship between two vectors
By linear algebra we can use the definition of dot product to determine the relationship between two vectors, whose cases are described below:
Two vectors are orthogonal if and only if cos θ = 0.Two vectors are parallel if and only if cos θ = 1 or cos θ = -1.And the expression for the cosine of the angle between the two vectors is:
[tex]\cos \theta = \frac{\vec u \,\bullet\,\vec v}{\|\vec u\|\cdot \|\vec v\|}[/tex] (1)
Where [tex]\|\vec u\|[/tex] and [tex]\|\vec v\|[/tex] are the norms of the two vectors, which are determined by Pythagorean theorem.
Now we proceed to calculate the angle between the two vectors:
[tex]\cos \theta = \frac{(6)\cdot (-24)+(-9)\cdot (36)}{(3\sqrt{13})\cdot (12\sqrt{13})}[/tex]
cos θ = -1
Thus, the vectors u = ❬6, –9❭ and v = ❬–24, 36❭ are parallel to each other because the cosine of the angle θ is equal to -1. (Right choice: A)
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What is 85% of 21?
I need to know for school because we're doing this project.
Answer:
85% of 21 is 17.85.
Researchers used two footballs of the same size to examine the effect of helium on kicking distance. One football was filled with air, and the other was filled with helium. Eleven people participated in the study. Each person kicked the football filled with air and the football filled with helium, and the kicking distances, in yards, were recorded. The football that was kicked first was determined by the flip of a fair coin, and the people did not know which football was filled with air and which was filled with helium. What type of study was conducted by the researchers and, of the following, which is the appropriate t-interval for inference?.
For the study conducted by the researchers,
The type of study that was conducted is a matched-pairs designThe appropriate t-interval for inference is a t-interval for a mean differenceHow to determine the type of study?From the question, we have the following highlights:
One football was filled with air (the control group)The other was filled with helium (the experimental group)When a study used a control group and an experimental group, then such study is a matched-pairs design.
How to determine the appropriate t-interval for inference?The appropriate t-interval for inference for a matched-pairs design is the t-interval for a mean difference
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What’s 1+7+6+8+10-12+5+22-4-12+16
Answer:
The answer to your question is 47
Step-by-step explanation:
You just add and subtract the question the your answer will be 47. Brainly patrol, stop deleting me.
The answer is 72
Step-by-step explanation:
1+7=8
8+6=14
14+8=22
22+10=32
32+12=44
44+5=49
49+22=70
70-4=66
66-12=56
56+16=72
Find the range: 40, 90, 36, 68, 90, 11, 88, 54
Answer:
79
Step-by-step explanation:
90-11=79
Answer:
79
Step-by-step explanation:
To find the range, subtract the biggest number and the smallest number. In this case, it would be 90-11 which is 79.
The following graph shows the feasible region for which system of inequalities?
The feasible region which is shown is the graph of is of the solution of inequalities y<4,x>=0,x<4 and y>=1. which is option C.
What is inequality?An inequality is like an equation but is expressed in greater than ,less than, greater than or equal to, less than or equal to signs. It is equated to find the range of variables.
How to graph inequality?The given graph has three lines showing different inequality.
One which is parallel to x axis and present at y=4 is doted and because the region from this line is towards origin so the sign between y and 4 is of < sign and we don't use equal to sign as it is doted. The inequality will be y<4
Other line is also parallel to x axis at y=1 but it is not doted and the region shaded is away from the line and origin so we use > than sign and equal to sign. The inequality will be y>-1.
The solution lies in first quadrant so x>=0.
One line is parallel to y-axis at x=4 and because the solution is towards origin so we will use <=0 sign as it is not dotted also.
Hence the inequalities are y<4,x>=0<x<4, y>1.
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If I had a grade of 81 in a mathematics class and earned a 90 on a TEST grade, what would be the grade then be?
Answer:
It depends how much percent the test is worth on your grade, and how much test grades you have. It would definitely raise to at least an 83 though.
Let's check
Mark before=81Mark after=90Total
81+90171Grade
171/285.5find the length of the missing side.
1) 52 cm
2) 42cm
3) 25 cm
4) 48 cm
Answer:
52 cm
Step-by-step explanation:
Use the pythagorean theorem to solve for missing sides in a right triangle.
20²+48²= missing side
20²+48²=2704
Take the square root of 2704 to get the missing side.
[tex] \sqrt{2704 } = 52[/tex]
Answer :
52 cm⠀
Explanation :
This is Right Angled Triangle.⠀
Solution :
We'll solve this using the Pythagorean Theorem.
where,
AB (20 cm) is the perpendicularBC (48 cm) is the Base.AC is the Hypotenuse.⠀
We know that,
[tex]{\longrightarrow \bf \qquad (AC) {}^{2} = (AB) {}^{2} +( BC) {}^{2} } \\ \\ [/tex]
Now, we will substitute the given values in the formula :
[tex]{\longrightarrow \sf \qquad (AC) {}^{2} = (20) {}^{2} +( 48) {}^{2} } \\ \\ [/tex]
We know that, (20)² = 400 and (48)² = 2304. So,
[tex]{\longrightarrow \sf \qquad (AC) {}^{2} = 400 + 2304 } \\ \\ [/tex]
Now, adding 400 and 2304 we get :
[tex]{\longrightarrow \sf \qquad (AC) {}^{2} = 2704 } \\ \\ [/tex]
Now, we'll take the square root of both sides to remove the square from AC :
[tex]{\longrightarrow \sf \qquad \sqrt{ (AC) {}^{2}} = \sqrt{2704} } \\ \\ [/tex]
When we take the square root of (AC)² , it becomes AC,
[tex]{\longrightarrow \sf \qquad AC = \sqrt{2704} } \\ \\ [/tex]
We know that, square root of 2704 is 52 .
[tex]{\longrightarrow \sf{\pmb{ \qquad AC = 52 }}} \\ \\ [/tex]
So,
The measure of the missing side (AC) is 52 cm .What is the volume of this cube?
Answer: 1 inc^3
Step-by-step explanation:
V = A^3
Where a = side
V = 1 ^3
V = 1 inch^3
Or in meteres it is 1.6387064e-5
Step-by-step explanation:
HOPE THIS HELPS IF NOT SORRYYYY !!!!!
To buy an article marked Rs. 20,000, we get a discount of 15% and have to pay the value added tax (VAT) at the rate of 13%. How much value added tax amount we have to pay to buy that article ?
Answer:
Based on the given conditions, formulate:: 13%×20000×(1−15%)
Calculate the sum or difference: 0.13×20000×0.85
Calculate the product or quotient: 2210
Given that k // I, identify the congruent angles in the
triangles.
212
v
m
22
v
23
A mixed economy is dependent only on the choices of individuals and businesses a combination of individual choice and government protection where people produce and trade traditional goods completely based on government decisions
Answer:
In general, a mixed economy is "a combination of individual choice and government protection," although the balance tends to lean more towards individual choice.
Answer:
a combination of individual choice and government protection
Step-by-step explanation:
Is the following shape a rectangle? How do you know?
Answer:
B.Yes,the adjacent sides are perpendicular,and the opposite sides are parallel
Answer:
B. Yes, the opposite sides are perpedicular, and the opposite sides are parallel
Step-by-step explanation:
This is because for a rectangle to be a rectangle, it has to have four sides whose opposite sides are equal (so parallel) and adjacent sides meets at 90° (so perpendicular), both of which this shape is shown to be.
Hope this helps. If you have any further questions, let me know!
- profparis
The circumference of a circle is 8 3.14cm. What is the DIAMETER of the circle?
A) 2 cm
B) 4 cm
96 cm
D) 8 cm
E) 16 cm
Circumference = pi x diameter
Given circumference: 8pi
Diameter = 8
Correct answer: D) 8 cm
Hope this helps!
What is the volume of a cone in cubic inches with a radius of 2 inches and a height of 3 inches use 3.14 for pie round your answers to the nearest hundredth
radius r = 2 in
height h = 3 in
slant height s = 3.60555128 in
volume V = 12.5663706 in3
lateral surface area L = 22.6543468 in2
base surface area B = 12.5663706 in2
total surface area A = 35.2207174 in2
In Terms of Pi π
volume V = 4 π in3
lateral surface area L = 7.21110255 π in2
base surface area B = 4 π in2
total surface area A = 11.2111026 π in2
At the buffet luncheon guests could choose one meat, one side and one salad. If there were 3 different meats, 7 sides and 4 salads, how many possible combinations would there be?
Answer:
i believe that its 84
Step-by-step explanation:
dr. orchid has 9 paintings she wants to hang side by side on her wall. (a) in how many ways can she arrange all 9 paintings? show your work. (b) if she only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display? show your work.
She can arrange the 9 paintings in 362,880 different ways, and she can select 126 different combinations of 4.
In how many ways can she display the 9 paintings?For the first position, she has 9 options.For the second position, she has 8 options (one is already taken).
And so on for the rest of the positions.
The total number of different combinations is equal to the product between the numbers of options:
C = 9*8*7*6*5*4*3*2*1 = 9! = 362,880
b) This will be given by the combinations of 4 out of 9, or:
C(9, 4), where:
[tex]C(9, 4) = \frac{9!}{(9 - 4)!*4!} = \frac{9*8*7*6}{4*3*2*1} = 126[/tex]
She can select 126 different combinations of 4 paintings.
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Find the perimeter of each figure.
6 cm
2 cm
2 cm
6 cm
Answer:
Assuming that you are listing the length of each side of the figure, we can add the values together. The perimeter is 16 cm.
Step-by-step explanation:
6+2+2+6=16 cm
hard question help!!!!
Answer:
A
Step-by-step explanation:
You can do 22/4 and that will give you 5.5. Since A gives the multiply chart for 5.5 to 4, the answer is A
In the following expression, 6 and -6 are like terms.
6- 6 + 8a
a) True
b) False
Answer:
no there not
Step-by-step explanation:
6 and 6 are like terms because they have no negative sign but -6 and -6 are like terms because they have a negative sign
Fill in the table using this function rule
y=5+4x
please help like u don’t know how many times I’ve posted this :,)
Plug in the values of x and solve for y:-
y=5+4x
y=5+4(4)
y=5+16
y=21
________________________________
y=5+4x
y=5+5(5)
y=5+20
y=25
_________________________________
y=5+4x
y=5+4(8)
y=5+32
y=37
___________________________________
y=5+4x
y=5+4(10)
y=5+40
y=45
__________________________________
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
Answer:
see explanation
Step-by-step explanation:
substitute the values of x from the table into the rule and evaluate for y
x = 4 → y = 5 + 4(4) = 5 + 16 = 21
x = 5 → y = 5 + 4(5) = 5 + 20 = 25
x = 8 → y = 5 + 4(8) = 5 + 32 = 37
x = 10 → y = 5 + 4(10) = 5 + 40 = 45
then
x y
--------
4 21
5 27
8 37
10 45
Which phrase best describes the translation from the graph y = 2(x - 15)2 + 3 to the graph of y = 2(x - 11)2 + 3?
4 units to the left
4 units to the right
8 units to the left
8 units to the right
What change has been caused?
y=2(x-15)²+3y=2(x-15+4)²+3y=2(x-11)²+3Change in x (+4)
Means
translation is 4units leftOption A
Answer:
translate 4 to the left
Step-by-step explanation:
ED 2022
Philippe went to the farmer's market and spent $2.35 on apples, $1.85 on bananas, and $3.10 on blueberries. How much did Phillipe spend in total? (3 points) a $7.30 b $7.55 c $8.30 d $8.55
Answer:
a. $7.30
Step-by-step explanation:
2.35 + 1.85 + 3.10 = 7.30
Find the area of the composite figure.
A: 96.75 units2
B: 112.5 units2
C: 139.5 units2
D: 192
The area of the composite figure from the image attached is 112.5 units²
What is the area of a composite figure?The area of a composite figure refers to the sum total of all the areas of the shapes in that composite figure. This can be done by first identifying the shapes in that composite figure, then finding each area, followed by the addition of all the areas to determine the area of the composite figure.
From the given figure; we can break it down into:
A parallelogramA rectangleA triangleThe area of a parallelogram = b × h
where;
b & h refers to the length of the two opposite diagonal lines.The area of a parallelogram = 9 × 6
The area of a parallelogram = 54 units²
The area of a rectangle = Length × breadth
The area of a rectangle = (9 × 3) units²
The area of a rectangle = 27 units²
The area of the triangle [tex]\mathbf{=\dfrac{1}{2}\times b \times h}[/tex]
where;
Base = b Height = hThe area of the triangle [tex]\mathbf{=\dfrac{1}{2}\times b \times h}[/tex]
The area of the triangle [tex]\mathbf{=\dfrac{1}{2}\times 9 \times 7}[/tex]
The area of the triangle [tex]\mathbf{= 31.5 units^2}[/tex]
Therefore, the area of the composite figure is:
= 54 + 27 + 31.5
= 112.5 units²
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PLEASE HELP !! #24 & #26
Answer:
Step-by-step explanation:
Sum of exterior angles of any Polygon = 360°
23. x + 65 + 106 + 78 = 360
x + 249 = 360
{To find the value of x, subtract 249 from both sides}
x = 360 - 249
x = 111°
_________________________________________
24. x + x + 59 + 48 + 50 + 39 + 58 = 360
2x + 254 = 360
2x = 360 - 254
2x = 106
x = 106 ÷ 2
x = 53°
____________________________________________
25. 2x + 3x + 44 +85 + 71 = 360
5x + 200 = 360
5x = 360 - 200
5x = 160
x = 160 ÷ 5
x = 32°
_______________________________________________
26. x+ 2x + 77 + 40 + 45 = 360
3x + 162 = 360
3x = 360 - 162
3x = 198
x = 198 ÷ 3
x = 66°
can someone help me ?
Answer:
Make 2 rectangles and find perimeter and then divide by 2.
Step-by-step explanation:
Hope that helps.
There are 31 passengers split between 3 cars in the Metrolink. How many passengers per car?
Answer:
10 passengers in every car
One left he choose the car which he want
explanation:
MAY IT HELP U
Answer:
Since the answer is a decimal we have to state that two cars had 11 passangers while one car had 10 passangers.
Step-by-step explanation:
Step 1: Determine the unit rate
Passangers per car
Passangers / car
(31 passangers) / (3 cars)
10.333 passangers / car
Answer: Since the answer is a decimal we have to state that two cars had 11 passangers while one car had 10 passangers.
At noon, there are 700 juniors and 1,100 seniors at a college fair. After 12:00 p.m., 20 juniors arrive every 15 minutes and 45 seniors leave every 15 minutes.
What is the ratio of juniors to seniors at 2:00 p.m. in fraction form?
The ratio of juniors to seniors at 2:00 p.m. in fractional form is 43 / 37
What is ratio?Ratio is a term that is used to compare two or more numbers.
Therefore,
At 12 pm(noon) there are 700 juniors and 1100 seniors at the college fair. After 12:00 pm 20 juniors arrive every 15 minutes and 45 seniors leave every 15 minutes. Therefore,
The Junior population at 2:00 pm is as follows;
12 pm to 2pm is 120 minutesThen, 120 / 15 = 8
20 × 8 = 160 students
The junior student increased by 120 by 2pm.
The Senior population at 2:00 pm is as follows;
45 × 8 = 360 students
360 senior student left by 2 pm.
Therefore,
Junior student by 2pm = 700 + 160 = 860 students
Senior student by 2 pm = 110 - 360 = 740 students
The ratio of juniors to seniors at 2:00 p.m. in fraction form is 860 / 740 = 43 / 37
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Hello people ~
Sketch the graph for y=cot ^-1 (cot x)
Answer:
[tex]\sf y=cot^{-1}(cot(x))[/tex]
[tex]\sf \implies cot(y)=cot(x)[/tex]
[tex]\sf \implies \dfrac{1}{tan(y)}=\dfrac{1}{tan(x)}[/tex]
[tex]\sf \implies tan(x)=tan(y)[/tex]
[tex]\sf \implies y=x[/tex]
[tex]\sf \implies y=x\pm\pi n[/tex]
Drag each tile to the correct box. Not all tiles will be used.
The table represents the balance of Sylvia's loan, y, over a period of 24 months, x. She used technology to create the scatter plot shown and
determined the best fit equation to model the data, y=-382.05x +
25,077.40. Determine how long it will take to reach the given balances
Using the given linear function, it is found that:
The balance will be of approximately $17,000 in month 21.The balance will be of approximately $0 in month 66.What is the function for the balance?The balance after x months is modeled by:
y = -382.05x + 25077.4.
Hence, it will be of approximately $17,000 at x for which y = 17000, hence:
17000 = -382.05x + 25077.4
x = (25077.4 - 17000)/382.05
x = 21.
We apply the same logic to find when it will be of approximately 0.
0 = -382.05x + 25077.4
x = (25077.4 - 0)/382.05
x = 66.
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What is the result of subtracting 4x + 3xy + 2y
from 5x + 3xy + 6y ?
1. x² + 47
x + 4y
8. -X- 4y
-x
C. -X – 4y
-
D. x² + 4y