Answers
Answer:
Step-by-step explanation:
Unit vector is a vector with mangnitue 1 and we can find out the magnitude of the vector [tex]u = (x , y)[/tex] with the following formula
[tex]magnitude = \sqrt{x^{2}+y^{2}}[/tex]
So in the given options whichever vector has magnitude 1 it will be a unit vector.
So if we put the values in the above mentioned formula
1.Magnitude of option A is not 1 so it is not a unit vector
2.Magnitude of option B is 1 so it is a unit vector
3.Magnitude of option C is 1 so it is a unit vector
4.Magnitude of option D is not 1 so it is not a unit vector
A unit vector is of length 1 and is used to represent the positive direction on an axis in a Cartesian system. In mathematics, the i, j, and k unit vectors denote the positive directions on the X, Y, and Z axes, respectively. The magnitudes of all unit vectors are one, and they are crucial in representing directions in space.
Explanation:In mathematics, a unit vector is a vector of length 1. The unit vectors in a Cartesian system are typically denoted as i, j, and k. Unit vector i signifies the positive direction on the X-axis, while unit vector j represents the positive direction on the Y-axis. In three-dimensional space, unit vector k denotes the positive direction on the Z-axis.
For example, Consider any vector A in a Cartesian coordinate system (figure 2.16). The scalar x-component of vector A is its dot product with the unit vector i, while the scalar y-component of that vector is its dot product with the unit vector j. This approach effectively expresses A in terms of the unit vectors of the axes. By their very definition, these unit vectors are dimensionless, such as their direction allows precise representations of vectors in space.
In summary, unit vectors essentially establish the directions for the system of coordinates in question. These vectors assist in expressing the direction of physical entities, such as the projection of vector A onto the x-axis or the y-axis. The magnitudes of these unit vectors are always one, so their principal significance comes from the directions they represent.
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Related Questions
4. Perform the indicated operation on polynomials.
a. (4x2 + 5x - 7) + (2x2 - 7x - 3)
b. (8m - 2n - 4) - (6m - 3n + 2)
c. (30+4) (5c-2)
Answers
Answer:
A) 6x2-2x-10
B) 2m+1n-6
C) 170c-68
Step-by-step explanation:
4x2 + 2x2 = 6x2 5x -7x = -2x -7 + -3 = -10
8m - 6m = 2m -2n + 3n = 1n -4 - 2 = -6
34 x 5c = 170 34 x -2 = -68
Answer:
Step-by-step explanation:
a) (4x2 + 5x - 7) + (2x2 - 7x - 3)
This is an addition question. We have to perform addition
The first step is open the parenthesis/brackets.
4x^2+5x-7 + 2x^2 -7x-3
Arrange the terms according to the exponents:
4x^2+2x^2-7x+5x-7-3
Combine the like terms:
6x^2-2x-10
Thus the answer is 6x^2-2x-10
b) (8m - 2n - 4) - (6m - 3n + 2)
We have to perform subtraction:
There is a rule in the subtraction that when you open the brackets then the signs of 2nd bracket will be multiplied by the negative sign:
Open the brackets:
8m - 2n - 4 - 6m+3n-2
Arrange the terms:
8m-6m+3n-2n-4-2
Combine the like terms:
2m+n-6
Thus the answer is 2m+n-6
c) (30+4) (5c-2)
This expression shows the operation of multiplication:
Solve the first parenthesis.
(34)(5c-2)
Now multiply 34 by each term of 2nd bracket:
=170c-68
Thus the answer is 170c-68....
If Esther deposited $50 at the end of each month into an account with no interest, how much money would she have saved by the end of 12 months?
Answers
Answer:
she will have saved a total of $600.00
Step-by-step explanation:
$50.00 x 12=$600.00
Robin earned twice as much money this week as she did last week. Let d represent the amount of money she earned last week. Write a variable expression to represent how much money she earned this week? *
Answers
Answer:
2d=m
Step-by-step explanation:
d represents the amount of money she earned Last weekm represents the amount of money she earned this week2xd=m
The variable expression that represents the money Robin earned this week, if 'd' is the money she earned last week, is '2d'. This is because Robin earned twice as much this week as she did the previous week.
Explanation:In the context of this question, Robin earned twice as much money this week as she did last week. Because last week's earnings are represented by the variable, the expression to represent this week's earning becomes 2d. The number 2 is multiplied by d because Robin earned double this week of what she earned last week. Therefore, 2d accurately represents Robin's earnings for this week, if d is the amount she earned last week.
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What is the value of b?
Answers
Both chords are the same distance from the center of the circle ( the 12 inch lines are the same length).
This means that both chords are the same length. The bottom chord has a dimension of 22.5.
B id half the top chord so would be equal to half of 22.5
b = 22.5 / 2 = 11.25
Help With the problem! With picture
Answers
Answer:
Slope is 20
y-intercept is 50
Step-by-step explanation:
y=mx+b is slope-intercept form where m is the slope and b is the y-intercept where x and y are the variables.
For your equation the slope is 20 and the y-intercept is 50 where m and y are variables.
The y-intercept is what you initially start with and here that is 50. The slope is a rate. So you are getting 20 dollars added per month.
What is the remainder when 3x^4 +2x^3-x^2+2x-24)/(x+2)
Answers
Answer:
remainder = 0
Step-by-step explanation:
Using the Remainder Theorem
Given f(x) divided by (x + h) then the remainder is found by evaluating f(- h)
Here the divisor is (x + 2), hence evaluate at h = - 2
Let f(x) = 3[tex]x^{4}[/tex] + 2x³ - x² + 2x - 24, then
f(- 2) = 3[tex](-2)^{4}[/tex] + 2(- 2)³ - (- 2)² + 2(- 2) - 24
= 3(16) + 2(- 8) - 4 - 4 - 24
= 48 - 16 - 4 - 4 - 24 = 0 ← Remainder
Remainder = 0 , hence (x + 2) is a factor of f(x)
Chris lost $5.29 playing poker in one week. If this continued, what would be his net winnings or losses after five weeks ?
Answers
Answer:
$26.45
Step-by-step explanation:
If Chris lost $5.29 playing poker in one week, in five weeks he would lose $26.45.
$5.29 lost per week.
5 weeks.
$5.29 x 5 = $26.45.
The net loss of Chris after five weeks will be $26.45.
Average value per week: -$5.29
Net loss after five weeks: -$5.29 x 5 = -$26.45
Is the line for the equation y = -8 horizontal or vertical? What is the slope of this
Answers
Answer:
Horizontal and it's slope is 0.
Step-by-step explanation:
y=a number is horizontal while x=a number is vertical.
The slope of horizontal lines are 0 because there is no rise.
The slope of vertical lines are undefined because there run is 0.
Slope is equal to rise over run.
y=-8 is horizontal because it represents all the points in the form (x,-8) where x is any real number.
Graph as many points as you want in the form (x,-8), you should see a horizontal line formed. The slope of y=-8 is 0.
Example of points in the form of (x,-8):
(-10,-8)
(-5,-8)
(-1,-8)
(0,-8)
(1,-8)
(5,-8)
(10,-8)
All of these go down 8 units after going left or right however many.
This is a horizontal line 8 units below the x-axis.
Answer:
Horizontal
0
Step-by-step explanation:
No matter what the x value is, the y value is - 8. Make a small table to see what that means.
x y
2 -8
0 -8
- 2 -8
See what's happening?
Look at the y intercept. The y value is - 8 when x = 0. It is also - 8 when x = 2.
Make a rough drawing on a scrap piece of paper. Plot just those 2 points. Roughly. You don't even need a ruler.
What do you see? The line must be going horizontally.
The next question is a little harder. It is not obvious, but you do know that this line either goes horizontally or vertically. So the slope can either be 0 or undefined. There is no third choice.
The general equation is y = mx + b
There is no x in y = - 8
Therefore the slope is 0. That's the only way you could get rid of the x.
Jason deposits $5 into his savings account twice a week for 6 weeks. How much money will he have saved after 6 weeks?
Let s stand for the amount of money saved.
Equation:
How much money did he save?
Show your work.
First person who answers gets to be followed and marked brainliest.
Answers
Answer:
(5x2)6=60
60
Step-by-step explanation:
Answer:
Let s stand for the amount of money saved.
[tex]2*5(6)=s[/tex]
He saved $60.
[tex]s=2*5(6)=10*6=60[/tex]
Calculate the area of rhombus ABCD where diagonal AC = 66 units and diagonal BD = 26 units
Answers
Answer:
858 sq. units
Step-by-step explanation:
Area of a rhombus is found by A=ab/2 where a and b are the diagonals of the rhombus and A is the area.
AC is a and BD is b
A= (AC.BD)/2
=(66×26)/2
=858 Sq units
The area of the rhombus is therefore 858 sq. units.
A diameter is a line segment whose endpoints are on a circle. It is a special type of chord because it must contain the _____ of the circle HELP!!!!!!!!!!
Answers
A diameter is a special type of chord that passes through the center of a circle. It has its endpoints on the circle's circumference, with the center of the circle as its midpoint.
Explanation:In the field of mathematics, a diameter is indeed a special type of chord. The unique characteristic of a diameter, differentiating it from other chords, is that it must contain the center of the circle - that is the definition finds its completion. As a line segment, a diameter has its endpoints on the circumference of the circle and its middle point is the center of the circle. So, when referring to a diameter, you are essentially talking about the largest chord in a circle that passes through the center.
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What is the total surface area of a rectangular prism that is 4 inches deep, 5 inches high, and 15 inches across?
Answers
Answer:
The total surface area of a rectangular prism is 310 inches
Step-by-step explanation:
The surface area of rectangular prism can be found using formula
Surface Area = 2(lw+hl+hw)
Where l = length
h = height
w = width
We are given:
l = 4
h = 5
w = 15
Putting values in the formula:
Surface Area = 2(lw+hl+hw)
Surface Area = 2((4*15)+(5*4)+(5*15))
Surface Area = 2(60+20+75)
Surface Area = 2(155)
Surface Area = 310 inches
So, The total surface area of a rectangular prism is 310 inches
Answer:
The total surface area of a rectangular prism is 310 inches
Step-by-step explanation:
The surface area of rectangular prism can be found using formula
Surface Area = 2(lw+hl+hw)
Where l = length
h = height
w = width
We are given:
l = 4
h = 5
w = 15
Putting values in the formula:
Surface Area = 2(lw+hl+hw)
Surface Area = 2((4*15)+(5*4)+(5*15))
Surface Area = 2(60+20+75)
Surface Area = 2(155)
Surface Area = 310 inches
So, The total surface area of a rectangular prism is 310 inches
HELP!!!!!!!!
Which expressions are equivalent to -7+3(-4e-3)?
Choose all answers that apply:
(Choice A)
-4(3e+4)
(Choice B)
12e
(Choice C)
None of the above
Answers
ANSWER
(Choice A)
-4(3e+4)
EXPLANATION
The given expression is
[tex] - 7 + 3( - 4e - 3)[/tex]
We expand to get:
[tex] - 7 - 12e - 9[/tex]
We regroup the terms to get:
[tex] - 12e - 9 - 7[/tex]
Simplify now to get:
[tex] - 12e - 16[/tex]
We now factor -4 to obtain:
[tex] - 4(3e + 4)[/tex]
The correct choice is A.
The expression simplifies to -16 - 12e. None of the given choices match this expression. Therefore, the correct answer is (C) None of the above.
To determine which expressions are equivalent to -7+3(-4e-3), let's simplify the given expression step-by-step:
Start by distributing the 3:
-7 + 3(-4e - 3) = -7 + (3 * -4e) + (3 * -3)
= -7 - 12e - 9
Now, combine the constants:
-7 - 12e - 9 = -16 - 12e
None of the provided choices are equivalent to -16 - 12e:
Choice A: -4(3e + 4) simplifies to -12e - 16, which is close but not equivalent.Choice B: 12e is not equivalent to -16 - 12e.Choice C: None of the above is the correct answer.If two angles are complementary, they are complements of each other.
True or False
Answers
True
Explanation:
If a pair of angles are complementary, their sum adds up to 90°. When two angles add to 90°, it is generally known as the angles being "complements" of each other, or in other words, "complement" each other.
Hope this helps!
lim-0
(1 + 3x)/x =?????
Answers
Answer:
not existStep-by-step explanation:
[tex]\lim\limits_{x\to0}\dfrac{1+3x}{x}\\\\\lim\limits_{x\to0^+}\dfrac{1+3x}{x}=\dfrac{1+(3)(0)}{(+)}=\dfrac{1}{(+)}=+\infty\\\\\lim\limits_{x\to0^-}\dfrac{1+3x}{x}=\dfrac{1+(3)(0)}{(-)}=\dfrac{1}{(-)}=-\infty[/tex]
Answer:
See below.
Step-by-step explanation:
The two sided limit does not exist.
As x approaches 0 from negative values the limit is -∞.
As x approaches 0 from positive values the limit is ∞.
the quote for usd/jpy is listed as 119.68/75 as shown. how many japanese yes does it cost to buy 1 U.S. dollar?
Answers
the quote for usd/jpy is listed as 119.68/75 as shown. how many japanese yes does it cost to buy 1 U.S. dollar?
Answer:
the correct answer is 119.75
Answer:
the guy above is right
Step-by-step explanation: i took the test and it was
Which is a rational function?
a. y= x-3^x / x^2. b. y= x^2 - x + 4. c. y= x-5/ 2. d. y= 2/x
Answers
ANSWER
d.
[tex]y = \frac{2}{x} [/tex]
EXPLANATION
A rational function is of the form:
[tex]r(x) = \frac{p(x)}{q(x)} [/tex]
where p(x) and q(x) are polynomial functions and q(x)≠0.
The first option contains the exponential function
[tex] {3}^{x} [/tex]
This disqualifies it from being a rational function.
The second and third options are polynomial functions.
By definition, all polynomials are rational functions.
The last option is a typical rational function because it has at least an asymptote.
The most correct choice is
[tex]y = \frac{2}{x} [/tex]
What’s the answer to this problem? (Photo included) thanks!
Answers
Answer:
C
Step-by-step explanation:
85+92+78+93=348
348/4=87
Answer:
.the answer is 93
Step-by-step explanation:
85 + 92 + 78 + 93= 348
348/4= 87 average
PLEASE HELP ME !! I need it ..
Answers
Answer:
D
Step-by-step explanation:
The Rational root theorem states that the possible roots ( zeros) of a polynomial are of the form
( plus or minus ) factors of the constant term divided by the factors of the leading coefficient.
For x³ - 3x² + 27x - 8
The factors of constant term (- 8) are ± 1, 2, 4, 8
The coefficient of the leading term x³ is 1
Hence possible zeros are
± ([tex]\frac{1,2,4,8}{1}[/tex]) = ± 1, ± 2, ± 4, ± 8 → D
You roll a 6-sided die with faces numbered 1 through 6, and toss a coin. What is the probability of rolling a 2 or getting heads
Answers
P(2 or H) = P(2) + P(H) - P(2 and H)
What is the probability of getting a 2 P(2)? = 1/6
What is the probability of getting heads P(H)? = 1/2
P(2 and H) is the product of those two events since the events are independent. = 1/6 * 1/2 = 1/12
P(2 or H) = P(2) + P(H) - P(2 and H)
P(2 or H) = 1/6 + 1/2 - 1/12 = 7/12
If a parallel b and e parallel f what is the value of y
Answers
Answer:
C
Step-by-step explanation:
Answer:
92
Step-by-step explanation:
(x+1) + (x-3) = 180
2x-2=180
2x=182
x=91
(x+1) = 92
(x+1) and y are equal angles
y = 92
edge 2023
Graph the data in the table below. Which kind of function best
models the data? Write an equation to model the data. Please help ASAP
Answers
Answer:
C
Step-by-step explanation:
Try to plug in the first pair of numbers to eliminate some equations, all but C fail to satisfy the equation. So C is the answer.
Answer:
CStep-by-step explanation:
Notice that the table doesn't have an exponential behaviour. Because an exponential function has the point (0,1), because all powers with a null exponent are equal to 1.
Also, notice that the table doesn't show a linear relation, because y-variable has all values positive.
Therefore, the only relation that follows the values of the table is
[tex]y=2.5x^{2}[/tex]
Let's evalue each x-value
[tex]y=2.5(-2)^{2} =2.5(4)=10\\y=2.5(-1)^{2}=2.5(1)=2.5\\ y=2.5(0)^{2}=2.5(0)=0\\y=2.5(1)^{2}=2.5\\y=2.5(2)^{2}=10[/tex]
Therefore, the right answer is C. The given values show a quadratic relation.
A faster way to deduct the quadratic pattern is observing that y-values are symmetric no matter if x-values are positive or negative, that meanst he function is pair, or quadratic.
HELP ASAP FIND EACH DERIVATIVE..... 7) 3x^2y^2=4x^2-4xy
8) 5x^3 + xy^2= 5x^3y^3
9)y=(3x^4+5x^3-5)/2x^4-4
Answers
Answer:
7. (4x - 3xy^2 - 2y) / (3x^2y + 2x).
Step-by-step explanation:
Implicit differentiation:
7. 3x^2 y^2 = 4x^2 - 4xy
6x * y^2 + 3x^2 * 2y y' = 8x - 4(x y' + y)
6xy^2 + 6x^2y y' = 8x - 4x y' - 4y
6x^2y y' + 4x y' = 8x - 6xy^2 - 4y
y' = (8x - 6xy^2- 4y) / (6x^2y + 4x)
y' = 2(4x - 3xy^2- 2y) / 2(3x^2y + 2x)
= (4x - 3xy^2 - 2y) / (3x^2y + 2x).
Numbers 8 and 9 are done in the same way.
We use the Chain, Product and Quotient rules where applicable.
Which of the following is three-dimensional and infinitely large?
Answers
Answer:
Option C Geometric space
Step-by-step explanation:
Which of the following is three-dimensional and infinitely large?
Verify each case
case A) A plane is two-dimensional and infinitely large.
case B) A line is infinitely large but is only one-dimensional
case C) Geometric space is three-dimensional and infinitely large
case D) A solid is three-dimensional, but not infinite
therefore
The answer is Geometric space
Answer:
Geometric Space
Step-by-step explanation:
Which of the following is three-dimensional and infinitely large?
Verify each case
case A) A plane is two-dimensional and infinitely large.
case B) A line is infinitely large but is only one-dimensional
case C) Geometric space is three-dimensional and infinitely large
case D) A solid is three-dimensional, but not infinite
therefore
The answer is Geometric space
Find the distance between the points. (-4, -2) and (5, 2) ^97 2^14 2^5 ^5
Answers
Answer:
The distance between 2 points is √97 or 9.84
Step-by-step explanation:
The distance between two points can be found using distance formula:
[tex]d(x_{1},x_{2})=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
x₁ = -4, y₁ = -2 x₂ =5 and y₂ = 2
Putting values:
[tex]d(x_{1},x_{2})=\sqrt{(5-(-4))^2+(2-(-2))^2}\\d(x_{1},x_{2})=\sqrt{(5+4)^2+(2+2)^2}\\d(x_{1},x_{2})=\sqrt{(9)^2+(4)^2} \\d(x_{1},x_{2})=\sqrt{81+16}\\d(x_{1},x_{2})=\sqrt{97}[/tex]
So, the distance between 2 points is √97 or 9.84
Answer:
=sqrt(97)
Step-by-step explanation:
The distance between the two points is found by
d = sqrt(( x2-x1)^2 + (y2-y1)^2)
= sqrt( ( 5--4)^2 + (2--2)^2)
= sqrt( ( 5+4)^2 + (2+2)^2)
= sqrt( ( 9)^2 + (4)^2)
= sqrt( 81 + 16)
=sqrt(97)
Colin surveyed his classmates about their favorite subject in school.
Colin’s Survey Results
Favorite Subject
Number of Students
Math
14
Language Arts
7
Earth Science
10
Life Science
11
Which statement is true?
The ratio of science fans to language arts fans is 10:7.
The ratio of language arts fans to science fans is 1:3.
The ratio of math and science fans to language arts fans is 24:7.
The ratio of language arts fans to math and science fans is 5:1.
Answers
Answer:
The correct answer is "The ratio of language arts fans to science fans is 1:3. "
Step-by-step explanation:
The ratio is the amount of students with a favorite subject per (compare with) the amount of students that prefer other subject.
We are going to analyze every statement
The ratio of science fans to language arts fans is 10:7. FALSE.Science fans are 21 (Earth Science +Life Science ). This ratio is 21:7 or 3:1.
The ratio of language arts fans to science fans is 1:3. TRUE.This ratio is 7:21, we can divide this numbers so that is the same of 1:3
The ratio of math and science fans to language arts fans is 24:7. FALSE.This ratio is 35:7
The ratio of language arts fans to math and science fans is 5:1. FALSE.This ratio is 7:35 or 1:5
Answer:
b :) hope this doesn't help
Step-by-step explanation:
i mean its the right answer but maby the wrong question you were looking for like what happens to me i put in the questions it goes voo doo magic to brainly i open it and its the wrong question i hate when it does that so then i have to copy and paste the question to put it on here just to find the wrong answer.
Which of the following expressions represents the distance between -1/4 and 3/4?
Answers
Answer:
[tex]\large\boxed{C.\ \left|-\dfrac{1}{4}-\dfrac{3}{4}\right|}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a distance between x and y on a number line:}\\\\d=|b-a|=|a-b|\\\\\text{We have}\ a=-\dfrac{1}{4}\ \text{and}\ b=\dfrac{3}{4}.\ \text{The distance:}\\\\d=\left|-\dfrac{1}{4}-\dfrac{3}{4}\right|=\left|\dfrac{3}{4}-\left(-\dfrac{1}{4}\right)\right|[/tex]
Answer:
The correct answer is C none of the above
Step-by-step explanation:
Drag each tile to the correct box.
Calculate the sum of each expression. Arrange the expressions in the order of their value from largest to smallest.
Answers
Answer:
6 3/5 , 3 4/5, 4/5
Step-by-step explanation:
1) -8 2/5 + 9 1/5 =
-42/5 + 46/5 = 4/5
2) 9 2/5 + (-5 3/5) =
47/5 + -28/5 = 19/5 = 3 4/5
3). 2 1/5 + 2 2/5 =
11/5 + 22/5 = 33/5 = 6 3/5
answer is tile 3 then tile 2 then tile 1
6 3/5 , 3 4/5, 4/5
The expression are arranged in the descending order, that is from largest to smallest as follows:
33/5 > 19/5 > 4/5
What are expressions?
The expressions are the combination of various constants numbers and mathematical symbols. They form a meaningful context that is in accordance to the mathematical rules and theories.
The expressions are computed as follows:
Given:
-8 2/5 + 9 1/5
Computation:
={(-8*5)+2}/5 + {(-9*5)+1}/5
=-42/5 + 46/5
= 4/5
Given:
9 2/5 + (-5 3/5)
Computation:
={(9*5)+2}/5 + {(-5*5)+3}/5
=47/5 + -28/5
= 19/5
Given:
2 1/5 + 2 2/5
Computation:
={(2*5)+1}/5 + {(2*5)+2}/5
=11/5 + 22/5
= 33/5
Therefore, the expressions will be arranged in the order; largest to smallest: 33/5 > 19/5 > 4/5
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Is cos theta=cos(-theta)
Answers
Answer:
TRUE
Step-by-step explanation:
An even function is a function that satisfies that f(x) = f(-x). Also, we know that cosine is an even function, therefore cos(theta) equals cos(-theta).
Please help, I am just so bad at this specific subject. I cannot get the hang of it, it's just so trippy to me.
Answers
Answer:
142°
Step-by-step explanation:
The angles of 38° and m<7 both make supplementary angles which equal to 180. Subtract 180 by 38.
Answer:
142
Step-by-step explanation:
Line M is a straight line. All straight lines have an angle measurement of 180 degrees.
m<7 + 38 = 180 Subtract 38 from both sides.
m<7 + 38 - 38 = 180 - 38
m<7 = 142