Determine whether the points p1 (6,9,7), p2(9,2,0), and p3(12,-5,-6) lie on the same line

Answers

Answer 1

Answer:

They are not.

Step-by-step explanation:

Let's first calculate the vectors joining the first point to the second and the first to the third, they will be useful later.

[tex]\vec v_1_2 = \vec P_2 -\vec P_1 = <3; -7; -7>\\\vec v_1_3= \vec P_2 -\vec P_1 = <6; -14; -13>[/tex]

At this point we have at least three options:

Write down the line between P1 and P2 in vector form, and then see if we can fit the third point in there.

Calculate the cross product between the two, if it's non-zero the three point are not in a line.

Try to determine the plane passing for the 3 points: if we find one they are not in a line.

Option 1:

The vector form of the lne between the firs two points is [tex]<6+3t;9-7t;7-7t>[/tex]. Let's check the coordinates of the third point:

[tex]x_3:\ 6+3t= 12 \rightarrow t=2\\y_3:\ 9-7t = -5 \rightarrow t =2\\7z_3:\ 7-7t=-6 \rightarrow t = 13/7\ne 2[/tex]

So the three points are not in a line.

Option 2:

Let's calculate the cross product of the two vectors we found at the beginning.

[tex]\vec v_1_2 \times \vec v_1_3 = det \left[\begin{array}{ccc}\hat i&\hat j&\hat k\\3&-7&-7\\6&-14&-13\end{array}\right] = \hat i [-7(-13)-(-14)(-7)] - \hat j[3(-13)-6(-7)]+\hat k [3(-14)-6(-7)] = 7\hat i -3 \hat j + 0 \hat k \ne 0[/tex]

Since the result is not the null vector, the three points are not in a line.

Option 3:

Let's write the plane (in the [tex]z= ax+by+c[/tex] form that contain the three points. If the thre points are in a line, means that we can find only two of these parameters.

[tex]P1: 7= 6a+9b+c\\P2: 0= 9a+6b+c\\P3: -6= 12a-5b +c[/tex]

Since you can determine a, b and c ( I ended up with [tex]a=-\frac {10}3; b=-\frac18; c= \frac{123}8[/tex] but I probably messed something in there) the thre points are not in a line


Related Questions

Solve for r.
4r–3r=20
r=

Answers

Answer:

20

Step-by-step explanation:

4r - 3r = 20

r = 20

There you go.

Answer:

r = 20

Step-by-step explanation:

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

4r − 3r = 20

Step 1: Simplify both sides of the equation.

4r − 3r =20

4r + −3r =20

(4r + −3r) =20 (Combine Like Terms)

r = 20

Hope this helps

Let E be the region bounded cone z = â 6 â ( x 2 + y 2 ) and the sphere z = x 2 + y 2 + z 2 . Provide an answer accurate to at least 4 significant digits. Find the volume of E.

Answers

Answer:

       

Step-by-step explanation:

Answ
Question
Dylan went to the toy store and
bought 3 action figures for $45.
How much did 1 action figure
cost?
*Use the dollar sign"
10
Using the information from
problem #9, write the equation.


What is the equation?

Answers

Answer:

15$

Step-by-step explanation:

45 ÷ 3 = 15

7 inches 6 inches and 6 inches make a triangle?

Answers

Answer:

^

Step-by-step explanation:

The left and right sides of the triangle must be 6 and the bottom must be 7. This creates an equilateral triangle where 2 sides are equal.

The perimeter of a triangle is 71 cm. If the longest side of the triangle is 8 cm longer than five times the shortest side and the third side is 7 cm less than four times the shortest side. How long is the longest side of the triangle?

Answers

Answer:

43 cm

Step-by-step explanation:

If the longest side of the triangle is 8 cm longer than five times the shortest side

5s + 8

the third side is 7 cm less than four times the shortest side

4s - 7

The perimeter of a triangle is 71 cm

s + (4s - 7) + (5s + 8) = 71

Combine like terms

10s + 1 = 71

Subtract 1 from both sides

10s = 70

divide both sides by 10

s = 7

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

How long is the longest side of the triangle

5s + 8

5(7) + 8

35 + 8

43

What does y= when x = -1?

Answers

I think Y would equal 0

what is the value of 69 - -26

Answers

Answer:

98

Step-by-step explanation:

Answer:

95

Step-by-step explanation:

subtracting by a negative number is cancelling out the negatives which makes it a positive so it is 69+26 which is 95

Solve the given equations. PLEASE show your work. Answer if it has No solution or Infinite many solutions.




-17 + 2(1 + 3x) = x - 5(3 - x)

Answers

Answer:

Infinite.

Step-by-step explanation:

[tex]-17+2(1+3x)=x-5(3-x)[/tex]

Expand:

[tex]-17+2+6x=x-15+5x[/tex]

[tex]6x+15=6x+15[/tex]

[tex]6x=6x[/tex]

[tex]0=0[/tex]

Since 0=0 is true, then there are infinite solutions as no matter what value you put in for x, it will never affect the outcome of 0=0 which is true.

The measure of an angle is 68.2°. What is the measure of its supplementary angle?​

Answers

Answer:

x = 111.8°

Step-by-step explanation:

Supplementary angles are angles that add up to 180 degrees. Let x be the supplementary angle:

[tex]68.2+x=180\\x=111.8[/tex]

Who ever sole this problem, with step by step soloution I will mark Brainliest (No Rubbish Please, I will report)

Answers

She could use the 500ml container four times

Or she could do
750ml + 500 ml = 1250
1250 + 250ml = 1500ml
And now she can add 750ml
And add another 250 ml
It will be 2500

Step-by-step explanation:

There are a couple of ways you could do this

10, 250ml (10*250=2500)

5, 500ml (5*500=2500)

3, 750ml + 250ml (3*750=2250.... 2250+250=2500)

There are many ways you could approach this. Hope these examples help

if someone helps me with dis ill give u brainliest​

Answers

Answer:

(25, 30) = 150 ,300 450

(15, 24) = 120 225 300

Step-by-step explanation:

Prime Factorization of 15 is:

3 x 5 => 3^1 x 5^1

Prime Factorization of 24 is:

2 x 2 x 2 x 3 => 2^3 x 3^1

Prime Factorization of 25 is:

5 x 5 => 5^2

Prime Factorization of 30 is:

2 x 3 x 5 => 2^1 x 3^1 x 5^1

Write the equation of the line that passes through the given points.
(1,2.5) and (0,6.5)

Answers

let's change the decials first off to fractions and get the slope and line

[tex]2.\underline{5}\implies \cfrac{25}{1\underline{0}}\implies \cfrac{5}{2}~\hfill 6.\underline{5}\implies \cfrac{65}{1\underline{0}}\implies \cfrac{13}{2} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{\frac{5}{2}})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{\frac{13}{2}})[/tex]

[tex]\stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{13}{2}}-\stackrel{y1}{\frac{5}{2}}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{1}}}\implies \cfrac{~~ \frac{8}{2}~~}{-1}\implies \cfrac{4}{-1}\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\cfrac{5}{2}}=\stackrel{m}{-4}(x-\stackrel{x_1}{1})[/tex]

[tex]y-\cfrac{5}{2}=-4x+4\implies y=-4x+4+\cfrac{5}{2}\implies y = -4x+\cfrac{13}{2}[/tex]

the total whole numbers less than 1539 divisible by 12​

Answers

Answer:

the ancwer is 1536

Step-by-step explanation:

i used a coculater

Original price of shorts $53.95 Discount 30% Tax:4.5%

Answers

Answer:157.35

Step-by-step explanation: multiply then add the tax

Please hurry, will mark brainliest if you answer correctly

Answers

Answer:

10

Step-by-step explanation:

according to BODMAS

6÷2=3

3+3=6

4^2=16

16-6=10

16.00 is the correct answer

A group of 6 friends rent a cabin on a campsite. It costs $62.88 to rent the cabin. if they divide the cost evenly between them, how much does each friend need to pay?

Answers

Answer: Each friend needs to pay $10.48


Translate the English phrase into an algebraic expression: four times the difference of v and one.

Answers

Answer:

4(v-1)

Step-by-step explanation:

the answer is 4(V-1)

Answer:

the answer is 4(v-1)

Arranging the real number in ascending order -8,2,0,9,-10

Answers

Hello,

- 10, - 8, 0, 2, 9

The ascending order is always : negative numbers, zero, positive numbers

Answer:

-10, -8, 0, 2, 9

Is it possible for a fifth degree polynomial function with
integer coefficients to have no real zeroes?

Answers

if a polynomial function is given with degree and and and is even then it is possible toe have all complex zeros as complex zeros come in pairs in conjugated pairs, so we would always have two times the number of pairs given us and even degree.

Find the slope of the line that goes through the points (4,-3) and (5,0)

Answers

Answer:

the slope of the points (4,-3) and (5,0) is 3

Step-by-step explanation: I used the formula y2-y1 over x2-x1 will give you the answer hope this helped!

Answer:

[tex]\boxed {\boxed {\sf m=3}}[/tex]

Step-by-step explanation:

We are asked to find the slope of the line that passes through (4, -3) and (5,0).

The slope is the number that tells us the steepness and direction of a line. It is the rise over run, or the change in y over the change in x.

[tex]m= \frac{ \Delta y}{\Delta x} = \frac{y_2-y_1}{x_2-x_1}[/tex]

In the slope formula, (x₁, y₁) and (x₂, y₂) are the points the line passes through. The points we are given are (4, -3) and (5,0). If we match the value with its corresponding value, we see that:

x₁ = 4 y₁ = -3x₂ = 5 y₂ = 0

Substitute the values into the formula.

[tex]m= \frac{0 - -3}{5-4}[/tex]

Solve the numerator. Remember that 2 back to back subtraction signs become an addition sign.

0--3 = 0+3=3

[tex]m= \frac{3}{5-4}[/tex]

Solve the denominator.

5-4 =1  

[tex]m= \frac{3}{1}[/tex]

Divide.

[tex]m=3[/tex]

The slope of the line is 3.

BEST ANSWER GETS BRAINLIEST!!!!
A store is having a sale on trail mix and jelly beans. For 3 pounds of trail mix and 8 pounds of jelly beans, the total cost is $31. For 5 pounds of trail mix and pounds of 2 jelly beans, the total cost is 12. Find the cost for each pound of trail mix and each pound of jelly beans.

Answers

Answer:

trail mix costs 1.00 per pound

jelly beans costs 3.50 per pound

Step-by-step explanation:

t = cost of trail mix

b = cost of jelly beans

3t+8b = 31

5t+2b = 12

Multiply the second equation by -4

-4(5t+2b = 12)

-20t+-8b = -48

Add this to the first equation

3t+8b = 31

-20t+-8b = -48

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

-17t = -17

Divide by -17

t = 1

Now we can find b

3t+8b = 21

3(1) +8b = 31

3+8b =31

Subtract 3

8b = 31-3

8b = 28

Divide by 8

b = 28/8

b = 7/3

b = 3.50

Let trail mix be x and jelly beans be y

The equations are

3x+8y=31-(1)5x+2y=12-(2)

Multiplying (1) by 1 and (2) by 4

3x+8y=31---(3)20x+8y=48--(4)

Subtracting

[tex]\\ \sf\longmapsto -17x=-17[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

Putting in eq(2)

[tex]\\ \sf\longmapsto 5(1)+2y=12[/tex]

[tex]\\ \sf\longmapsto 2y=7[/tex]

[tex]\\ \sf\longmapsto y=7/2[/tex]

10 4/5+(8 3/4−6 1/2) no files plz you dont have to explain it either

Answers

Answer:

11

Step-by-step explanation:

10×4/5+(8×3/4-6×1/2)=8+6-3=14-3=11

Help me please ill mark you brainly

Answers

Answer:

The first one is -6x The second one is 18a to the power 3

Step-by-step explanation:

Part A: Solve −mk − 90 > 85 for m. Show your work. (4 points) Part B: Solve 3c − 5f = 55 for f. Show your work. (6 points) (10 points)

Answers

Answer:

m < -175/k

f = -11 + [tex]\frac{3}{5}[/tex]c

Step-by-step explanation:

Part A:

-mk - 90 > 85

add 90 to each side to get:

-mk > 175

divide each side by -k to get:

m < -175/k

(inequality symbol switched because we divided by a negative)

Part B:

3c - 5f = 55

subtract 3c from each side to get:

-5f = 55 - 3c

divide each side by -5 to get:

f = -(55 - 3c) / 5  or -11 + [tex]\frac{3}{5}[/tex]c

what is the measure of angle x

Answers

Answer:

180

Step-by-step explanation:

Find the value of X in triangles by subtracting known angle measurements from 180 degrees. Since the value of all angles within a triangle must equal 180 degrees, if you know at least two angles, you can subtract them from 180 to find the missing third angle.

Find the median salary of nurses in Illinois : $72500, $52000 , $88500 , $73300 , $112000

Answers

Answer:

the correct answer is $74,560 but since that's not declared go with 73300


If I paid 1/7 of the total bill and the remainder of the bill was $114, how much did I pay?

l

Answers

See answer attached in photo. I drew it out

Solve
-16+ 20

A. -36

B.-4

C. 4

D. 36

Answers

Answer:

C: 4

Step-by-step explanation:

We can rearrange the numbers:

[tex]-16+20=+20-16=20-16=4[/tex]

Answer:

C. 4

Step-by-step explanation:

-16+20 equals 4 becase:

-16 is under zero, and if we add 20 to that, it will take 16 of that 20 to fill up the negative part, and the rest part remaining will be 4. So that four will add up to be the positive number!

Thank You! Please Mark Me Brainliest!

group the first two terms by underline the first two terms 16x^3-4x^2-4x+1

Answers

Answer:

Terms are the things that are separated by a (+) or a (-).

Step-by-step explanation:

16x^3 - 4x^2 -4x+1

I don't think I'm right...

The value in cents of a nickels, The value in cents of a dimes =, The value in cents of a quarters = , The value in cents of a dimes and one quarter = ,The value in cents of 13 dimes =​

Answers

The value in cents of a nickels = 5a

     [] A nickle is worth 5 cents, so 5a is the value of a nickles

The value in cents of a dimes = 10a

     [] The value of a dime is 10 cents, so 10a is equal to a dimes

The value in cents of a quarters = 25a

     [] A quarter is worth 25 cents, so 25a is the value of a quarters

The value in cents of a dimes and one quarter = 10a + 25

     [] Up above we figured out the expression for a dimes, so we need to add 25 to it for one quarter

The value in cents of 13 dimes =​ 130

     [] A dime is worth 10 seconds, so 13 * 10 = 130

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

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