If A, B, and C are the vertices of a triangle, find AB + BC + CA.

Answers

Answer 1

Answer:

0

Step-by-step explanation:

When drawing a triangle, note that the vectors can be drawn either in a clockwise or anticlockwise direction. For a triangle with vertices A, B and C, te vectors are AB, BC and CA

In vector notation CA = - AC (length CA is equal to AC but acting in opposite direction to AC)

and AB+BC = AC

To evaluate AB + BC + CA, we will substitute the vector expression above into the given expression and simplify as shown;

= (AB + BC) + CA

= AC + (-AC)

open the parenthesis

= AC-AC

= 0

Hence the sum of the vector expression AB + BC + CA is a zero vector


Related Questions

please simplify 1+3^2⋅2−5

Answers

Answer:

[tex]-2.2[/tex]

Step-by-step explanation:

Let's simplify the expression.

[tex]1+3^2.2-5[/tex]

And the answer is

[tex]-2.2[/tex]

Hope this helps!

Answer:

14

Step-by-step explanation:

I took the test~~~~

Are lines GH and G'H' perpendicular? Why or why not? Yes, they intersect at one point. Yes, their slopes are negative reciprocals. No, their slopes are not negative reciprocals. No, their slopes are not equal.

Answers

Answer:

Step-by-step explanation:

B yes their slopes are negative reciprocals

Answer:

b

Step-by-step explanation:

on edge

A magic square is a square array of numbers arranged so that the numbers in all​ rows, all​ columns, and the two diagonals have the same sum. Create a​ 3-by-3 magic square using nine of the ten​ numbers, 20,​ 21, 22,​ 23, 24,​ 25, 26,​ 27, 28, and 29. Explain your solution and reasoning. List the strategies used.

Answers

Answer:

strategies used are : identifying a sub-goal and Guess and check

Step-by-step explanation:

To create a 3 by 3 magic square using nine of the ten numbers

20,21,22,22,23,24,25,26,27,28 and 29

In order to achieve a 3 by 3 magic square table we will pick Nine consecutive numbers out of the ten numbers given and apply the format below

n+1,n-4,n+3,n+2,n,n-2,n-3,n+4,n-1

we will take n = 24

attached below is the magic square

Find the unit rate and use it answer the question
35 copies in 7 minutes, how may copies in 10 minutes

Answers

Answer:

50 copies in 10 minutes

Step-by-step explanation:

becuase it takes 7 minutes for 35 copies and 5 copies times 7 is 35 so 5 copies per minute and it would take 10 minutes for 50 copies

10/2i?
(dividing complex numbers)​

Answers

Note that; i = √-1

Divide using the rule

10/2i = -5i

Best of Luck!

Given f(x) = 3x – 5, solve for x when f(x) = 1

Answers

Answer: f(1) = -2

Explanation:

f(x) = 3x - 5
f(1) = 3(1) - 5
f(1) = 3 - 5
f(1) = -2

The value of x when f(x) = 1 is  x = 2.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

The function,

f(x) = 3x – 5.

Solving for x when f(x) = 1,

1 = 3x - 5

3x = 6

x = 2

Therefore, the value is x = 2.

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what's the solution of the equation 4[x+2(3x-7)]=22x-65

Answers

Answer:

x = -3/2

Step-by-step explanation:

Let's solve your equation step-by-step.

4(x+2(3x−7))=22x−65

Step 1: Simplify both sides of the equation.

4(x+2(3x−7))=22x−65

(4)(x)+(4)(2(3x−7))=22x+−65(Distribute)

4x+24x+−56=22x+−65

(4x+24x)+(−56)=22x−65(Combine Like Terms)

28x+−56=22x−65

28x−56=22x−65

Step 2: Subtract 22x from both sides.

28x−56−22x=22x−65−22x

6x−56=−65

Step 3: Add 56 to both sides.

6x−56+56=−65+56

6x=−9

Step 4: Divide both sides by 6.

6x = -9

6       6

x =  -3/2

If 46 people can fit into 64 square teet. Which proportion should you use to estimate how many people are in a 600
square foot area?

Answers

Answer:

431.25 approximately 431

Step-by-step explanation:

one way of calculating it would be to get the measure per one person which would be equal to 46 / 64 = 0.7 people in one square feet

then multiply 0.7 by the total distance = 431.25 approximated to 431

Add an apple orchard, small bags contain 7 apples. Alexa and her family bought 91 apples for a party. How many small bags did they buy? I need the problem solved out thanks

Answers

In this problem, we'll need to divide the number of apples by the amount of apples in a small bag. This will leave us with the number of small bags needed for the amount of apples.

91 / 7 = 13

Therefore, Alexa and her family bought 13 small bags of apples.

(4x - 2) + (6x - 2). Please help brainly

Answers

Answer:

2 (5 x - 2) = 10 x - 4 or x = 2/5 (if you need to solve for x)

Step-by-step explanation:

Simplify the following:

4 x - 2 + 6 x - 2

Hint: | Group like terms in 4 x - 2 + 6 x - 2.

Grouping like terms, 4 x - 2 + 6 x - 2 = (4 x + 6 x) + (-2 - 2):

(4 x + 6 x) + (-2 - 2)

Hint: | Add like terms in 4 x + 6 x.

4 x + 6 x = 10 x:

10 x + (-2 - 2)

Hint: | Group the negative terms in -2 - 2 together and factor out the minus sign.

-2 - 2 = -(2 + 2):

10 x + -(2 + 2)

Hint: | Evaluate 2 + 2.

2 + 2 = 4:

10 x - 4

Hint: | Factor out the greatest common divisor of the coefficients of 10 x - 4.

Factor 2 out of 10 x - 4:

Answer: 2 (5 x - 2)

________________________________

if you need to solve for x then:

Solve for x:

10 x - 4 = 0

Add 4 to both sides:

10 x + (4 - 4) = 4

4 - 4 = 0:

10 x = 4

Divide both sides of 10 x = 4 by 10:

(10 x)/10 = 4/10

10/10 = 1:

x = 4/10

The gcd of 4 and 10 is 2, so 4/10 = (2×2)/(2×5) = 2/2×2/5 = 2/5:

Answer:  x = 2/5

x/9 + 7 ≥ 10

A. x ≤ 83

B. x ≥ 27

C. x ≤ 27

D. x ≥ 83

Answers

Answer:

its B.x> 27

Step-by-step explanation:

Solving by Completing the Square

Answers

Answer:

16

Step-by-step explanation:

Hello,

[tex]x^2-8x=10 \text{ *** we complete the square ***}\\ \\(x-4)^2-4^2=10 <=> (x-4)^2-16=10 \text{ *** we add 16 to both sides ***}\\\\(x-4)^2-16\boxed{+16}=(x-4)^2=10\boxed{+16}=26[/tex]

Thanks

Carrie has $87 left in her bank account. If she writes a check for $99, what will Carrie’s balance be?

Answers

Answer:

[tex] -12 [/tex]

Step-by-step explanation:

You start with 87 dollars.

[tex] 87 [/tex]

You write a check for 99 dollars.

Writing a check means taking money out of the bank.

[tex] 87 - 99 [/tex]

[tex] -12 [/tex]

She will have -12 dollars.

She is in debt for 12 dollars.

She owes the bank 12 dollars.

Simplify 3 + (b + 8) = 3 + (8 + b)

Answers

Answer:

−3b /8

​  

 

Step-by-step explanation:

Answer:

b + 11 = 11 + b

Step-by-step explanation:

Combine like terms. Note that because you are adding for all terms, you can technically disregard the parenthesis:

3 + (b + 8) = b + 3 + 8 = b + 11

3 + (8 + b) = 3 + 8 + b = 11 + b

b + 11 = 11 + b (True).

Help, please! College precalc! TIA.

Answers

Answer:

I believe that the answer is 0

Step-by-step explanation:

All you have to do is add f and g and substitute -2 for x. When you substitute -2, simplify.

Step-by-step explanation:

(f+g)=(x-4)+(x^2-x)=x^2+x-x-4=x^2-4

when x=-2

(f+g)(-2)=(-2)^2-4=0 ans.

A bag contains three types of candy (gumdrops, jelly beans, and jawbreakers). If
chosen at random, the probability of getting a gumdrop is, and the probability
of getting a jellybean is 3. What is the probability of getting a jawbreaker?

Answers

Answer:

1/2

Step-by-step explanation:

First, I added the two numbers tat we had already.

1/6+1/3=1/6+2/6=3/6=1/2

Then, I subtracted the sum (1/2) from the total (1).

1-1/2=1/2

So, the probability of getting a jawbreaker is 1/2.

what would be the slope of y=3x.?

Answers

Answer:

3

Step-by-step explanation:

The slope is the coefficient to the x variable.

In the equation y = 3x, this means 3 is the slope because it is the coefficient to x.

So, the slope is equal to 3.

Answer:

[tex]3[/tex] or [tex]\frac{3}{1}[/tex]

Step-by-step explanation:

Remember slope-intercept form.

[tex]y=mx+b[/tex]

~

[tex]m=slope[/tex]

[tex]b=y-intercept[/tex]

In the case of [tex]y=3x[/tex]:

[tex]m=3[/tex]

Help me please with this question

Answers

Answer:

C.

Step-by-step explanation:

His initial cost of the phone bill was  $25.90, which is the constant. He is charge $0.18 for each text. So you will have to add the initial bill and costs of the texts to get final cost on the phone bill, which is $30.40.

On a number line where is the number 14 relative to the number -23

Answers

Answer:

14 is to the right of -23

Step-by-step explanation:

On the number line, the number 14 will appear on the right side of -23 with respect to zero from front.

What is a number line?

Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series.

Number line is a graphical representation of whole numbers, natural numbers, rational and irrational numbers. which represents both negative and positive numbers such that, positive numbers from 1 to infinity lie on the right-hand side of zero and negative numbers from (- 1) to (- infinity) lie on the left-hand side of zero.

Therefore, zero is considered as the reference point.

Number 14 is positive natural number, it appears on the right side of zero and (-23) appears on the left side of zero.

Thus, On a number line, the number 14 lies to the right of number -23.

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solve the given triangles by finding the missing angle and other sides lengths.

Answers

Answer:

75+48+x=180

x=180-123

=57degree

side length=3+3+3=9

Write an improper fraction and a mixed number for the shaded portion of the group of figures.

Answers

Answer:

I will do a random number

2/3=1 2/3

Step-by-step explanation:

And I think that is what u want

[tex]2\frac{1}{3}[/tex] is a mixed fraction and 7/3 is a improper fraction.

What is Fraction?

A fraction represents a part of a whole.

We need to write a improper fraction and a mixed number for the shaded portion of the group of figures

Fractions are three types proper, improper and mixed fraction

A proper fraction is a fraction which has its numerator value less than the denominator.

A improper fraction is a fraction which has its numerator value greater than the denominator.

A fraction represented with its quotient and remainder is a mixed fraction.

[tex]2\frac{1}{3}[/tex] is a mixed fraction

7/3 is a improper fraction.

Hence, [tex]2\frac{1}{3}[/tex] is a mixed fraction and 7/3 is a improper fraction.

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What is the quotient of 8,688 ÷ 24?
362
434
450
8,664

Answers

Answer:

362

Step-by-step explanation:

Answer:

362

Step-by-step explanation:

An equivalent fraction to 5/16 is
a. 5/32
b. 10/32
c.1/2
d. 10/16

Answers

Answer:

B is the answer..................

Answer: B) 10/32

==================================================

Explanation:

Multiply top and bottom of the original fraction by 2

[tex]\frac{5}{16} = \frac{5*2}{16*2} = \frac{10}{32}[/tex]

Or you could go in reverse to divide each part of 10/32 by the GCF 2

[tex]\frac{10}{32} = \frac{10\div 2}{32\div 2} = \frac{5}{16}[/tex]

-------------------

Another alternative is to use your calculator to find the decimal version of each answer choice

5/32 = 0.15625

10/32 = 0.3125

1/2 = 0.5

10/16 = 0.625

And compare these results with 5/16 = 0.3125

Both 5/16 and 10/32 have the same decimal value 0.3125, which makes them equal.

Solve the equation, P= n+k+m for n

Answers

Answer:

n = p-k-m

Step-by-step explanation:

You would just say, like k and m and 1 and 2. But instead of adding them you just bring the to the other side like

p = n+1+2

-1         -1

p-1 = n+2

-2        -2

p-1-2 = n

p-k-m-n

Three quarters make up what fraction of a dollar?

Answers

Answer: 0.75 cents is 3/4 of a dollar

A message can follow different paths through servers on a network. The sender’s message can go to one of five servers for the first step; each of them can send to five servers at the second step; each of those can send to four servers at the third step; and then the message goes to the recipient’s server.
a. How many paths are possible?
b. If all paths are equally likely, what is the probability that a message passes through the first of four servers at the third step?

Answers

Answer:

Number of way s= N=100

The probability that it passes through  first of four servers at the third step is 0.25

Step-by-step explanation:

The total number of possible ways can be found out by multiplying the possibilities so the possibilities at the

1st stage is  5

2nd stage is 5

3rd stage is  4

4th stage is 1

So Number of way s= N= 5*5*4= 100

This can be solved by drawing a tree diagram as well.

Now the probability of finding the  that a message passes through the first of four servers at the third step.

There are five paths

And we have to find the probability of four

So 5C1*5C4/100= 0.25

The probability that it passes through  first of four servers at the third step is 0.25

Find the sum 46 +47 +48 +49+...+138 + 139.

Answers

Answer:

8695

Step-by-step explanation:

Took forever on calculator but I did it!

Answer:

8695

Step-by-step explanation:

There is a formula for adding all integers from 1 to some integer n.

[tex] 1 + 2 + 3 + ... + n = \dfrac{n(n + 1)}{2} [/tex]

In other words, to add all integers from 1 to an integer, multiply the integer by the next greater integer and divide by 2.

For example, what is

1 + 2 + 3 + 4 ?

Multiply 4 by the next integer, 5, and divide by 2.

(4 * 5)/2 = 20/2 = 10

Check: 1 + 2 + 3 + 4 = 3 + 3 + 4 = 6 + 4 = 10

We see that the formula works.

Now we need to apply that formula to this problem, but there's a little more to it.

If the problem were

1 + 2 + 3 + ... + 138 + 139, then we'd apply the formula and that would be it.

In this problem, though, we don't start the sum at 1. We start the sum at 46.

The trick here is to add all integers from 1 to 139, and then we subtract the sum of all integers from 1 to 45, so we are left with only the sum of the integers from 46 to 139.

Sum of integers from 1 to 139:

[tex] 1 + 2 + 3 + ... + 139 = \dfrac{139(139 + 1)}{2} = \dfrac{139(140)}{2} = 9730 [/tex]

Sum of integers from 1 to 45:

[tex] 1 + 2 + 3 + ... + 45 = \dfrac{45(45 + 1)}{2} = \dfrac{45(46)}{2} = 1035 [/tex]

Now we subtract the sum to 45 from the sum to 139.

46 + 47 + 48 + ... 138 + 139 = 9730 - 1035 = 8695

Answer: 8695

X/3+1=7/15 WHAT IS THE ANSWER​

Answers

Answer:

x=-8/5

Step-by-step explanation:

5x+15=7

5x=7-15

5x=-8 divide

-8/5

Estimate. Then find the difference 456,912 -37,800

Answers

The answer is 419,100 if you round to the hundreds place.

If (6, 1) is dilated by a scale factor of 3 the new point would be:
A(3,3)
B (18,3)
C (15,3)
D (9.4)

Answers

The answer is B (18,3)
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