1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gelneren [198K]
2 years ago
12

Which of the following is an equation for the plane through the point (1, 1, −1) and parallel

Mathematics
1 answer:
Bas_tet [7]2 years ago
6 0

The given plane, x-y+z=3, has normal vector \vec n = \langle1,-1,1\rangle. Any plane parallel to this one has the same normal vector.

Let (x,y,z) be any point in the plane we want. The plane contains the point (1, 1, -1), so an arbitrary vector in this plane is

\langle x,y,z\rangle - \langle 1,1,-1\rangle = \langle x-1, y-1, z+1 \rangle

and this is perpendicular to \vec n.

So the equation of the plane is

\langle x-1, y-1, z+1 \rangle \cdot \vec n = 0 \implies (x-1) - (y-1) + (z+1) = 0 \implies \boxed{x - y + z = -1}

or equivalently,

\boxed{-x + y - z = 1}

You might be interested in
A trapezoid has a perimeter of 14 feet. What will the perimeter be if each side length is increased by a factor 7? 21 feet 98 fe
natka813 [3]

Answer:

Correct choice is B

Step-by-step explanation:

Let a, b, c and d be the trapezoid's sides lengths.

The perimeter of the trapezoid is the sum of all sides lengths, thus,

a+b+c+d=14\ ft.

If each side length is increased by a factor 7, then new sides have lengths 7a, 7b, 7c and 7d. The perimeter of new trapezoid is

7a+7b+7c+7d.

Use the distributive property for this expression:

7a+7b+7c+7d=7(a+b+c+d).

Since a+b+c+d=14\ ft, then

7a+7b+7c+7d=7(a+b+c+d)=7\cdot 14=98\ ft.

7 0
3 years ago
Read 2 more answers
- 2(x+5) = -2<br> Directions say solve for the equation
erik [133]

Answer:

x = -4

Step-by-step explanation:

Distribute:

-2(x + 5) = -2

-2(x) -2(5) = -2

Multiply:

-2(x) -2(5) = -2

-2x - 10 = -2

Add 10 on both sides:

-2x - 10 = -2

      +10    +10

-2x = 8

Divide by -2 on both sides:

-2x = 8

/-2     /-2

x = -4

3 0
3 years ago
Please help! Will mark best answer!!!
tatyana61 [14]
Area = Pi x r (r + v)
v is h^2 + r^2 under radical (couldn't write it in the equation above so I wrote it here)
The answer is the 1st choice, 1944 pi
4 0
3 years ago
After school carnival Daniel won 6 chocolate cream pies. He plans to share them with his 7 friends . If all 8 people get the sam
Mariana [72]
6 pies split up into 8 people would make 6÷8, or 6/8. if you simplify the fraction you would get 3/4, meaning everyone got 3/4 pie, or .75 pie.
3 0
3 years ago
Building A is 150 feet shorter than Building B. The total height of the two buildings is 1490 feet. Find the height of each buil
Phantasy [73]

c is the   correct

answer


6 0
3 years ago
Other questions:
  • Elizabeth and Mini are playing a factor game. Elizabeth told Mimi that she was thinking of a mystery number that had 2, 7, and 9
    9·2 answers
  • The roots of 6 corn plants had depths of -3.54 feet? /2 4/5 feet, /3.86 feet, -3 2/5 feet. How many corn plants had roots betwee
    10·1 answer
  • 28 1/2% covert the percent to a decimal
    10·1 answer
  • What’s the answer for this
    7·1 answer
  • A property was assessed at 25% of value with a tax rate of $12 per hundred. if the taxes totaled $11,400, what was the value? 1
    9·1 answer
  • What is the solution set to this equation? Log2(x - 2) + log2x = 3
    10·2 answers
  • Plz help due tomorrow ill give Brainlyest if ur correct
    14·2 answers
  • Alana runs 4 laps around the track in 10 minutes. If Alana runs 17 laps at the same rate how long does it take her​
    5·2 answers
  • Triangle X Y Z is shown. The length of X Z is 12, the length of Y Z is 11, and the length of Y X is 6.
    6·2 answers
  • What is the area of this rectangle? 10units 20units 24units 48 units
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!