Answer:
a. v.v' = v₁v₂ - v₁v₂ = 0 b. (20, -21)/29 and (-20,21)/29
Step-by-step explanation:
a. For two vectors a, b to be orthogonal, their dot product is zero. That is a.b = 0.
Given v = (v₁, v₂) = v₁i + v₂j and v' = (v₂, -v₁) = v₂i - v₁j, we need to show that v.v' = 0
So, v.v' = (v₁i + v₂j).(v₂i - v₁j)
= v₁i.v₂i + v₁i.(- v₁j) + v₂j.v₂i + v₂j.(- v₁j)
= v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j
i.i = 1, i.j = 0, j.i = 0 and j.j = 1
So, v.v' = v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j
= v₁v₂ × 1 - v₁v₁ × 0 + v₂v₂ × 0 - v₂v₁ × 1
= v₁v₂ - v₂v₁
= v₁v₂ - v₁v₂ = 0
So, v.v' = 0
b. Now a vector orthogonal to the vector v = (21,20) is v' = (20,-21).
So the first unit vector is thus a = v'/║v'║ = (20, -21)/√[20² + (-21)²] = (20, -21)/√[400 + 441] = (20, -21)/√841 = (20, -21)/29.
A unit vector perpendicular to a and parallel to v is b = (-21, -20)/29. Another unit vector perpendicular to b, parallel to a and perpendicular to v is thus a' = (-20,-(-21))/29 = (-20,21)/29
()) How do you write 250% as a fraction or mixed number? I really need help plz
Step-by-step explanation:
250% = 250/100 = 25/10 = 2 1/2
Topic: Conversion between fraction and percentage
If you like to venture further, feel free to check out my insta (learntionary). It would be best if you could give it a follow. I'll be constantly posting math tips and notes! Thanks!
Find the slope using the table!
Answer:
5/2 is the slope or 2.5
Step-by-step explanation:
you take two points and do rise over run to get the slope, Hope this helped.
how do you find the longest side of a rectangle mapped on a coordinate plane?
Is 20/15 and 4/3 equivalent
Answer:
Yes, they are equivalent.
Step-by-step explanation:
20 divided by 15 = 1.333333...
4 divided by 3 = 1.333333...
Point D is located at (7,1). What are the coordinates of Point D after a Vertical Stretch of 3?
Answer:
since it got stretched by 3 it's 4
Question 5: CONSUMER MATH
Answer:aaaaa
AAAA
Step-by-step explanation:
Solve 0.25x + 7 = 1/5 x -8
Answer:
x= -300
Step-by-step explanation:
0.25x+7 = 1/5x-8
convert the decimal into a fraction
1/4x+7 = 1/5x-8
1/4x+7+8 = 1/5x
1/4+15 = 1/5x
multiply both sides of the equation by 20
1/4x(20)+15(20) = 1/5x(20)
5x+300 = 4x
5x-4x+300 = 0
x+300 = 0
x = -300
brianliest if correct please help me
Answer:
ΔABC ≅ ΔQPR
Step-by-step explanation:
if you were to reflect it, they would line up also A ≅ Q because their angles are the same and I know that because of the markings, they both have one arc and B and P both have two arcs meaning they are congruent and C and R both have three arcs so they are congruent.
Ernie wants to be a teacher but does not want work in a school. What should Ernie probably do?
Answer: She could start a you tube channel and teach there u get way more money anyways. one of my history teachers teachs in a school and has a you tube channel.
Step-by-step explanation:
Answer:
well first
why does ernie want be a teacher in the first place if one of the main aspects of it is dealing with kids?
it also depends on what subject he'd want to teach
if he doesnt want to physically be in a school he can just do online teaching yk
Help!!! Need help. I can’t fail this!! 2222
Answer:
c
Step-by-step explanation: because the one on the bottom is smaller than the other
Simple. It’s the first one.
Which steps are included in using integer tiles to evaluate –8 ÷ 2? Check all that apply.
Answer: -4
Step-by-step explanation:
- + - = +
+ (+) += -
- (+) + = -
Answer:
a,d,e
Step-by-step explanation:
sorry if im wrong :(
Need help
Find the mode in this frequency distribution.
Number | Frequency
61 | 12
62 | 3
63 | 11
64 | 21
65 | 10
66 | 3
Answer:
64
Step-by-step explanation:
the frequency of 64 is 21 which is the highest frequency presented making it the mode. 64 is the mode
All of the information needed is in the pictures please help..
Answer:
Phone B
Step-by-step explanation:
It is around the same cost as Phone C, but has unlimited data (which means unlimited gigs)
Answer:
B
Step-by-step explanation:
Charge of 9 gigs for A
find slope:
125 - 95/5 - 3 = 30/2 = $15/month
use point slope form with point (3,95) and slope 15:
y - y1 = m(x - x1)
y - 95 = 15(x - 3)
y - 95 = 15x - 45
+ 95 +95
y = 15x + 50
put 9 for x, gigs, in the new equation:
y = 15(9) + 50
y = 135 + 50
y = 185
$185 for opt A
Charge of 9 gigs for B
slope = 0
there is the fee of 150 so the equation is:
y = 0x + 150
Next find the price for 9 gigs
y = 9(0) + 150
y = 150
$150 for opt B
Charge of 9 gigs for C
use graph and the cost is about $157
A: $185
B: $150
C: $157
I need help I’m give the most points if u help
B- you can't divide by 0
_ Is –7 + 9 positive or negative
Answer:
Positive 2
Step-by-step explanation:
its like ur subtracting 9+ (-7)
its basically 9-7=2
but not all problems r like this.
Brainlest plz
Carol earns $16.00 for 1/2 of an hour. Peter earns $15.00 for 1/3 of an hour. How much do Carol and Peter earn for 3 hours of work?
Answer:
carol and peter make $231
Step-by-step explanation:
16 x 2 = 32
15 x 3 = 45
32 + 45 = 77
77 x 3 = 231
Answer:
92 for both $48 for carol $45 for peter
Step-by-step explanation:
u/4 + 12 =18
worth 10 points
Answer:
u = 24
Step-by-step explanation:
[tex]\frac{u}{4}[/tex] + 12 = 18
-12 -12
[tex]4*\frac{u}{4}[/tex] = 6*4
u = 24
Answer:
u = 24
Step-by-step explanation:
Original Equation:
u/4 + 12 = 18
Subtract 12 from both sides
u/4 = 6
To separate the u from the 4, multiply both sides by 4
u = 24
Hope this helps :)
write in slope intercept form (-1,3) (1,-2)
Answer:
y = 5/2x + 1/2
Step-by-step explanation:
Find the slope with the formula [ y2-y1/x2-x1 ].
-2-3/1-(-1)
-5/2
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Find the y-intercept using the formula for slope-intercept form [ y = mx + b ]
y = -5/2x + b
3 = -5/2(-1) + b
3 = 5/2 + b
1/2 = b
Put everything we solved for into its final form.
y = 5/2x + 1/2
Best of Luck!
Answer:
y = -2.5x + 0.5
Step-by-step explanation:
First we must find the slope.
To do so we will use this formula:
y2 - y1 / x2 - x1
Substitute with (-1, 3) and (1, -2)
-2 - 3 / 1 + 1
-5/2
-2.5 is our slope.
Now to put this into slope-intercept form we will use Point-slope formula.
y - y1 = m(x - x1)
substitute using the ordered pair, (-1, 3):
y - 3 = -2.5(x + 1)
Distribute:
y - 3 = -2.5x + -2.5
Add 3 to both sides:
y = -2.5 + 0.5
Double check by using the other ordered pair.
(1, -2)
y + 2 = -2.5(x - 1)
Distribute:
y + 2 = -2.5x - 2.5
Add 2 to both sides:
y = -2.5x + 0.5
(-1, 3) and (1, -2) written in slope intercept form is:
y = -2.5x + 0.5
Step 1: Subtract 3 from both sides of the inequality. Step 2: __________ Step 3: Divide both sides of the inequality by the coefficient of x. What is the missing step in solving the inequality 5 – 8x < 2x + 3? Add 2x to both sides of the inequality. Subtract 8x from both sides of the inequality. Subtract 2x from both sides of the inequality. Add 8x to both sides of the inequality.
Answer:
the answer is d add 8x to both sides
Step-by-step explanation:
The missing step in step 2 is to add 8x to both sides of the inequality.
What is inequality?An inequality shows the relationship between two mathematical expressions which is denoted by the inequality signs such as (<, >, ≤, ≥).
The inequality given is expressed as:
5 - 8x < 2x + 3
Step 1 says to minus 3 from both sides.5 - 8x - 3 < 2x + 3 - 3
2 - 8x < 2x
We are required to determine what to do in step 2.So, we need to add + 8x to both sides, in order to eradicate the variable (8x) from the left-hand side.
i.e.
2 - 8x + 8x < 2x + 8x
2 < 10x
In step 3, we divide both sides by the coefficient of x.
i.e.
[tex]\mathbf{\dfrac{2}{10} < \dfrac{10x}{10}}[/tex]
[tex]\mathbf{0.2 < x}[/tex]
Learn more about solving inequalities here:
https://brainly.com/question/24372553
#SPJ2
find the value of
g(−2) if g(x)=x3−x
[tex]g(x)=x^3-x\\g(-2)=(-2)^3-(-2)\\g(-2)=-8+2\\g(-2)=-6[/tex]
Therefore, g(-2) = -6
Basically substitute x = -2 in the equation.
CAN SOMEONE PLEASE HELP I WILL GIVE BRAINLIEST TO HOWEVER ANSWERS FIRST!!
Write an equation in point-slope form of the line that passes through the point (7,-5)with slope -1/7. Fill in the blanks.
y-|_|=|_|(x-|_|)
-4*7=
Please hel p...................
Answer:
-28
Step-by-step explanation:
Answer:
-28
Step-by-step explanation:
idk how to do this
At bargain store. Tanya bought 3 items each cost same amount. Tony bought 4 items that each cost the same amount, but each was $2.25 less than the items Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items?
Answer:
$4.30
Step-by-step explanation:
2.25 + 2.25= 4.30
write an equation using the following numbers in the chart in point slope form
Answer:
A
Step-by-step explanation:
Change 95.61 to degrees, minutes, and seconds.
a.95° 43´ 44´´
c.95' 36´ 36´´
b.95° 41´ 43´´
d.95° 44´ 60´´
Answer:
95 ° 36 ′ 36 ′′
Step-by-step explanation:
To convert 95.61 into degrees, minutes and seconds, you'll have to leave the whole units of degrees alone. You have to multiply the decimal by 60. The whole number becomes the minutes.
Then, you multiply 0.61 by 60, in which you get 36.6.
Take the remaining decimal and multiply by 60 and take the whole number portion to find the seconds.
Multiply 0.6 by 60. You get 36.
And lastly, Take the three sets of whole numbers and combine them, using the symbols for degrees ( ° ) , minutes ( ′ ) , and seconds ( ′′ ) .
This is how you get 95 ° 36 ′ 36 ′′.
7. Bobby wants to check if (4,2) is on the line y = 5x - 18. Lisa also wants to check if (3,-3) is on the
same
line. Show your work, and write a statement (sentence) about who's point is on the line. (8 pts)
Answer:
Both Bobby's and Lisa's points are on the line.
Step-by-step explanation:
You just have to plug the points into the equation.
Bobby:
(4,2)
2 = 5(4) - 18
2 = 20 - 18
2 = 2
Lisa:
(3,-3)
-3 = 5(3) - 18
-3 = 15 - 18
-3 = -3
So they both are correct.
s1 = 20, s1 = 15, s1 = 9, and s1 = 6 what is the sum of the balance column
Answer:
51
Step-by-step explanation:
Two sides of a triangle are equal in length, and the third side is 5 less than the length of the equal sides. If the perimeter of the triangle is 49, how long are it's sides?
Answer:
let the length of each of the 2 equal sides= n
then n+n+(n-5)=49
3n=44
n=44/3
Answer:
let the length of each of the 2 equal sides= n
then n+n+(n-5)=49
3n=44
n=44/3
If you read 4/9 of a page in 3/5 minutes what’s your unit rate page per minute
Answer:
12/45
Step-by-step explanation:
The unit rate is 12/45, because 4 times 3 is 12, and 9 times 5 is 45.
