Answer:
[tex]90^{\circ}[/tex]. In other words, these two vectors are perpendicular (orthogonal) to one another.
Step-by-step explanation:
Let [tex]\|a\|[/tex] and [tex]\|b\|[/tex] denote the magnitudes of vector [tex]a[/tex] and vector [tex]b[/tex]. The dot product between these two vectors is represented as [tex]a^{T}\, b[/tex]. Let [tex]\theta[/tex] denote the angle between the two vectors. The cosine of this angle would be equal to:
[tex]\begin{aligned}\cos(\theta) &= \frac{a^{T}\, b}{\|a\| \|b\|}\end{aligned}[/tex].
The dot product between vector [tex]a = \langle 1,\, 2\rangle[/tex] and [tex]b = \langle 1,\, -1/2\rangle[/tex] is:
[tex]\begin{aligned}a^{T}\, b &= {\begin{bmatrix}1 \\ 2\end{bmatrix}}^{T}\, \begin{bmatrix}1 \\ -1/2\end{bmatrix} \\ &= 1 \times 1 + 2 \times \left(-\frac{1}{2}\right) \\ &= 0\end{aligned}[/tex].
The magnitudes of the two vectors are:
[tex]\begin{aligned}\| a \| &= \sqrt{1^{2} + 2^{2}} \\ &= 5\end{aligned}[/tex].
[tex]\begin{aligned}\| b \| &= \sqrt{1^{2} + \left(-\frac{1}{2}\right)^{2}} \\ &= \frac{1}{2}\, \sqrt{5}\end{aligned}[/tex].
Therefore:
[tex]\begin{aligned}\cos(\theta) &= \frac{a^{T}\, b}{\|a\| \|b\|} \\ &= \frac{0}{5 \times (\sqrt{5} / 2)} \\ &= 0\end{aligned}[/tex].
Among all angles between [tex]0^{\circ}[/tex] and [tex]180^{\circ}[/tex], the only angle with a cosine of [tex]0[/tex] is [tex]90^{\circ}[/tex]. Therefore, the angle between vector [tex]a[/tex] and vector [tex]b[/tex] must be [tex]90^{\circ}\![/tex]. Hence, these two vectors are perpendicular to one another.
What is the volume of this object?
PLSSS HELP RIGHT ANSWER BRAN;EST
Answer:
23 cubic units
Step-by-step explanation:
1st layer: 8 units
2nd layer: 7 units
3rd layer: 5 units
4th layer: 3 units
8+7+5+3 = 23
See the attachments below
Hope this helps :)
In how many ways can you spell the word FOOT in the grid below? You can start on any letter F, then on each step you can step one letter in any direction (up, down, left, right, or diagonal).
There are six ways in which the word FOOT may be spelt starting at any letter.
What is combination?The term combianntion offers a plausible way to carry out a selection as long as we do not give preference to the order in which the selection is made. In this case, we are told that we can start from any letter therefore order is not important.
There are four letters in FOOT and one letter is repeated twice therefore;
4C2 = 4!/(4-2)! 2!
4C2 = 4 * 3 * 2!/2! * 2 * 1
4C2 = 12/2
4C2 = 6
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Can somebody please help me
Answer: C
Step-by-step explanation:
This is just a straight definition - for a normal distribution, the percent within 2 standard deviations of the mean is about 95.44%.
Write the word sentence as an inequality.
1. A number x divided by 3 is at most 5
An inequality that represents this word sentence is ____ .
[tex]\boxed{ \dfrac{x}{3} \leq 5}[/tex]
Explanation:A number {x} {divided by} {3} is {at most} {5}.
↧ ↧ ↧ ↧ ↧
x ÷ 3 ≤ 5
[tex]\text{Inequality formed} \rightarrow \boxed{ \dfrac{x}{3} \leq 5}[/tex]
Answer:
[tex]\sf \dfrac{x}{3}\leq 5[/tex]
Step-by-step explanation:
x divided by 3 = x/3
at most 5 means "equal or less than 5" = ≤ 5
Final solution
[tex]\sf \dfrac{x}{3}\leq 5[/tex]
------------------------------------------------------------------------------------------------
Extra information
Alternative ways of writing the inequality:
x ÷ 3 ≤ 5
[tex]\sf \dfrac13x\leq 5[/tex]
If AC= 8x-14 and EC = 2x + 11, solve for x.
Step-by-step explanation:
AC= 8x-14
AC+14=8x
x=(AC+14)÷8
EC=2x+11
EC-11=2x
x=(EC-11)÷2
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Step-by-step explanation:
Over the interval [0,2pi), what are the solutions to cos(2x) = cos(x)? check all that apply
[tex] \cos(2x) = \cos(x) [/tex]
Solution (1)
[tex]2x = x + 2k\pi[/tex]
[tex]2x - x = 2k\pi[/tex]
[tex]x = 2k\pi[/tex]
for k=0 / for k=1 / for k=-1
x=0 / x=2π / x=-2π
acc / acc / rej
solution (2)
[tex]2x = - x + 2k\pi[/tex]
[tex]2x + x = 2k\pi[/tex]
[tex]3x = 2k\pi[/tex]
[tex]x = \frac{2k\pi}{3} [/tex]
for k=0 / for k=1 / for k=-1
x=0 / x=2π/3 / x=-2π/3
acc / acc / rej
Note that i'm trying values of K which make the answer belong to our interval;
So our solution which i will represent as a set is;
S € {0,2π/3,2π}
Write an equation for the graph in terms for x
Y=
Which of the following polynomials has solutions that are not real numbers?
A
x2 - 6x +3
B
x2 + 4x +3
-*? - 9x - 10
x? + 2x +3
Answer:
Option 4 is correct.
Step-by-step explanation:
To find: Polynomial whose solution are not real numbers.
Given Polynomials are Quadratic Polynomial.
So, we can check if solution of quadratic polynomial by find & checking value of discriminant.
Standard form of Quadratic polynomial is given by
ax² + bx + c
then Discriminant, D = b² - 4ac
If, D > 0 ⇒ Solutions are distinct real numbers
if, D = 0 ⇒ Solutions are equal real numbers
if, D < 0 ⇒ Solutions are not real numbers (They are complex conjugates)
Option A:
By comparing with standard form
a = 1 , b = -6 , c = 3
D = (-6)² - 4 × 1 × 3 = 36 - 12 = 24 > 0
Thus, Solutions are Real numbers.
Option B:
By comparing with standard form
a = 1 , b = 4 , c = 3
D = (4)² - 4 × 1 × 3 = 16 - 12 = 4 > 0
Thus, Solutions are Real numbers.
Option C:
By comparing with standard form
a = -1 , b = -9 , c =-10
D = (-9)² - 4 × (-1) × (-10) = 81 - 40 = 41 > 0
Thus, Solutions are Real numbers.
Option D:
By comparing with standard form
a = 1 , b = 2 , c = 3
D = (2)² - 4 × 1 × 3 = 4 - 12 = -8 < 0
Thus, Solutions are not Real numbers.
Therefore, Option 4 is correct.
Step-by-step explanation:
What are the possible transformations that could have been used to create the red figure from the blue figure ABCD?
Answer:
I believe you are correct in saying the option you are clicked on, B.
Step-by-step explanation:
it would make the most sense
The perimeter of the triangle at the right is 22.6 in. What is the value of n?
A. 3.5
B. 4.6
C. 7.8
D. 9.4
Answer:
A. 3.5
Step-by-step explanation:
The perimeter is just the sum of all of the side lengths. The sides of this triangle are n inches, (n + 5.2) inches, and (2n + 3.4) inches.
So, your equation is n + n + 5.2 + 2n + 3.4 = 22.6 inches.
You can combine like terms (adding together all of the n's and all of the numbers) to simplify your equation to 4n + 8.6 = 22.6 inches.
Subtract 8.6 from both sides of the equation to get 4n = 14, and divide both sides by 4 to get n = 3.5.
Hope this helps! :)
Consider an experiment of tossing an unbiased coin three times. What is the probability of obtaining four heads?
Answer:
0.0625
Step-by-step explanation:
the probability of getting 4 heads in a row is 0.5^4
answer is 0.0625 or 1/16
Which expression is equivalent to the following complex fraction?
Answer:I think it might be D but i'm not 100% sure
Find the greatest possible number of consecutive zeros at the end of the product of three positive integers if the sum of these three integers equals 939.
Answer:
I think its 5 consecutive zeros.
Step-by-step explanation:
This would be a guess but I think you would need two numbers in the hundreds that also have 2 parts of which have a product of a number ending in 0, like 4 and 5.
So my guess would be
400 * 500 * 39
= 7800000
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
6-3/4x+1/3=1/2x+5
2
3
6
12
Answer:
12 because it is a common factor of the denominators
Answer:
178
Step-by-step explanation:
Give an example of a well-stated research question that involves estimating a characteristic about the population of part-time students at your college.
Improve the following research question so that it is a well stated research question. Research Question: Do students work a lot of hours?
Answer:
1) what is the number of male part time students between the ages 15 - 19 years?
2) do students work more than 4 hours a day?
Elise drinks 2 cups of water per hour on Friday. At a certain time, she has already had 4 cups of water. On Friday, Jacob drinks 3 cups of water per hour, and at the same time of day, he has only had 2 cups of water for the day.
Write a system of equations that can be used to determine when Elise and Jacob will have drank an equal amount of water after drinking water for the same number of hours after 10:00 am.
How many hours will it take for Elise and Jacob to drink an equal amount of water?
By finding and solving a system of equations, we will see that after 2 hours they will drink the same amount of water.
How to write and solve the system of equations?For Elise, the number of cups consumed after the 10:00 am is:
y = 2*x + 4
Where x is the number of hours after 10:00 am.
For Jacob, the number is:
J = 3*x + 2
Then the system of equations is:
y = 2x + 4
y = 3x + 2
To solve it, we use the fact that the variable y is already isolated in both equations, so we can write:
2x + 4 = y = 3x + 2
2x + 4 = 3x + 2
Solving for x we get:
4 - 2 = 3x - 2x
2 = x
After 2 hours, Elise and Jacob drink the same amount of water.
If you want to learn more about systems of equations, you can read:
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help and walk me thru pleasee
Answer:
Your answer is 63
Step-by-step explanation:
First lets find the area of the rectangle:
To find the area of a rectangle your multiply the length by the width. In this case it is 5 and 9 so..
5 x 9 = 45
Now to find the area of the triangle:
Formula for triangle: 1/2(bh)
9 is your height to find the base subtract 5 from 9:
9 - 5 = 4
Now divide that by 2:
4 / 2 = 2
2 is your base
Now we know the base and height solve:
1/2(2 x 9)
1/2(18)
18 / 2 = 9
multiply 9 by 2
9 x 2 = 18
Now add your areas to find the final area:
45 + 18 = 63
Use the graph or table to find the equation that represents the relationship.
Using the information given in any graph or table, find the slope (m) and y-intercept (b) and substitute their values into y = mx + b, which represents the linear equation.
What is the Equation that Represents a Linear Graph?If we have a graph or table that represents a linear relationship between x and y, we can use a linear equation to represent the graph or table as, y = mx + b.
The graph or table is missing, however, here's how to find the linear equation that represnts the table or graph.
We would find the following:
Slope (m) = chnage in y/change in x = unit rate.y-intercept (b) = the initial value or the vaue of y when the value of x is 0.Therefore, using the information given in any graph or table, find the slope (m) and y-intercept (b) and substitute their values into y = mx + b, which represents the linear equation.
Learn more about linear equation on:
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Answer:
Here you go
Step-by-step explanation:
Just use a slope calculator
-3(10)
Simplify
[Multiplication with integers]
Answer:
[tex]\boxed{\sf{-30}}[/tex]
Step-by-step explanation:
To solve this problem, all you have to do is solve by order of operations.
PEMDAS stands for:
ParenthesisExponentsMultiplyDivideAddSubtract-3(10)First, remove parenthesis.
Multiply.
-3*10
Solve.
[tex]\sf{-3*10=\boxed{\sf{-30}}[/tex]
-30
Therefore, the correct answer is -30.I hope this helps you! Let me know if my answer is wrong or not.
Answer:
-30
Step-by-step explanation:
it is adding 10 three times, but then you add the negative after
so it is 10+10+10 because you are multiplying it by 3
you could also add 3 ten times because the communitive property
so 3+3+3+3+3+3+3+3+3+3
you would do the same whether the -3 was in parentheses or not
Write an equation of the line in the slope-intercept form from each of the following. the y-intercept of 2, the slope is 4
Answer:
y=4x+2
Step-by-step explanation:
Hi there!
We are given that a line has a y intercept of 2, and a slope of 4
We want to write the equation of that line in slope-intercept form
Slope-intercept form can be written as y=mx+b, where m is the slope and b is the y intercept
As we are already given these values, we can substitute the values as needed into the formula to find the equation of the line.
First, substitute 2 as the y intercept (b)
y=mx+2
Now substitute 4 as the slope (m)
y=4x+2
We have found the equation of the line.
Hope this helps!
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Magan has a bag that contains pineapple chews, cherry chews, and lime chews. He performs an experiment. Magan randomly removes a chew from the bag, records the result, and returns the chew to the bag. Magan performs the experiment 68 times. The results are shown below:
A pineapple chew was selected 59 times.
A cherry chew was selected 3 times.
A lime chew was selected 6 times.
Based on these results, express the probability that the next chew Magan removes from the bag will be cherry chew as a decimal to the nearest hundredth.
Answer:
The Answer is 0.04
Step-by-step explanation:
Write the absolute value equations in the form x−b =c (where b is a number and c can be either number or an expression) that have the following solution sets:
two solutions: x=1/2, x=-1/3
one solution: x=-3
all numbers such that x≤5
all numbers that x ≥-1.3
anything helps!
All cases rewritten in the form of difference expressions are listed below:
x - 1/2 = 0, x + 1/3 = 0x + 3 = 0x - 5 ≤ 0x + 1/3 ≥ 0How to translate equalities and inequalities into difference expressionsEqualities represent relationships between two expressions, in which one expression is equal to another. An equality (x = a) is equivalent to the following difference expression:
x - a = 0 (1)
And inequalities represent relationships between two expressions, in which one expression is not necessarily to another. An inequality (x < a, x > a, x ≤ a, x ≥ a) is represented by the following difference expression:
x - a = b (2)
Where b have the following cases:
If x < a, then b < 0.If x > a, then b > 0.If x ≤ a, then b ≤ 0.If x ≥ a, then b ≥ 0.Now we proceed to rewrite each case in term of difference expressions:
x - 1/2 = 0, x + 1/3 = 0x + 3 = 0x - 5 ≤ 0x + 1/3 ≥ 0To learn more on inequalities, we kindly invite to check this verified question: https://brainly.com/question/19491153
what is the third quartile of the following data set? 24,20,35,43,28,42,25,29,44,21,37
Answer:42 is the third quartile
Step-by-step explanation:
Observations of the center of the Milky Way show the presence of a super massive black hole with a mass of 4.6 x 106 solar masses. Compute the Schwarzschild radius of this supermassive black hole. Give your answer in units of astronomical units (AU). At what distance does Mercury orbit from the Sun in AU? If we swapped out the Sun for this super massive black hole, would the event horizon extend beyond the orbit of Mercury? Be sure to show your calculations. 1 AU = 1.5 x 108 km.
The Schwarzschild radius of the black hole depends on its mass
The Schwarzschild radius of this supermassive black holeis 0.091 AU
How to determine the Schwarzschild radius?The Schwarzschild radius (r) is calculated using:
[tex]r_s = \frac{2GM}{c^2}[/tex]
Where:
G = Gravitational constant = 6.67408 × 10-11 m3 kg-1 s-2
M = Mass of the object = 4.6 x 10^6 solar masses
c = Speed of light = 299792458 m / s
Express the mass in Kg
M = 4.6 x 10^6 * 9.2 * 10^18 = 9.15 * 10^36 kg
Substitute the above values in the equation
[tex]r_s = \frac{2 * 6.67408 * 10^{-11} * 9.15 * 10^36}{299792458 ^2}[/tex]
Evaluate the expression
[tex]r_s = 13589425339.6[/tex] m
Express as km
[tex]r_s = 13589425.3396[/tex] km
Expressas AU
[tex]r_s = \frac{13589425.3396}{1.5 * 10^8}[/tex]
Evaluate the quotient
[tex]r_s = 0.09059616893[/tex]
Approximate
[tex]r_s = 0.091\ AU[/tex]
Hence, the Schwarzschild radius of this supermassive black holeis 0.091 AU
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Briana has 3/4 pound of rabbit food. She feeds her rabbit 1/12 pound each day. How many days can Briana feed her rabbit with the food she has?
find x and y. use proper postulates or theorems to justify your answer
Answer:
x = 110
y = 23
Step-by-step explanation:
For X :
100 = x -10
110 = x
Corresponding angles are equal
For Y :
180 - 110 = 70
(2y + 24) = 70
2y = 46
y = 23
Adjacent Angles on a straight line add up to 180 Degrees
Which field is required when importing vendors
Import field: Tax Identification Number, Tax Number for Customers or Vendors. Tax Identification Number (customers) or Tax ID Number (vendors).
there are 45 marbles in a blue jar. the blue jar has 9 times as many marbles as a red jar. let m be the number of marbles in the red jar.
Write an equation that relates the number of marbles in the two jars. Use 9, m, and 45
Answer:
9m = 45
Step-by-step explanation:
if the blue jar has 9 times as many marbles as the red jar (which is 45 marbles), then that means that:
9m = 45
where m is the number of marbles in the red jar.
Please help 8, 9, and 10 you don't need to explain
Answer:
8.
x
12
9
4.5
9.
3, 4, 12
3, 3, 12
6, 12
-6, -12
2
10.
plug in x to check work
Step-by-step explanation:
8.
1/2(x + 24) = 21
1/2x +12 = 21
1/2x = 9
x = 18
9.
28 - 3x - 4 = 2x + 12 + x
24 - 3x = 3x + 12
24 - 6x = 12
-6x = -12
x = 2
10.
3x - 18 + 6 = 5x - 6
3x - 12 = 5x - 6
-2x - 12 = -6
-2x = 6
x = -3
hope it help.
can you answer my question, i can help you in math, can you help me in english? please
Determine the equation of a Linear Function with a negative slope, goes through the point (0,5), and has a hole at x = -1
Answer:
[tex]y=\frac{-x(x+1)}{x+1} +5[/tex]
Step-by-step explanation:
This function has a slope of -1, a hole at x = -1, and a y-intercept of 5