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Law Incorporation [45]
3 years ago
11

Find an equation of the plane. The plane through the points (0, 7, 7), (7, 0, 7), and (7, 7, 0).

Mathematics
1 answer:
Nookie1986 [14]3 years ago
7 0

Answer:

  x + y + z = 14

Step-by-step explanation:

If the points are designated A, B, C, then ...

  AB × AC = (7, -7, 0) × (7, 0, -7) = (49, 49, 49).

That is, a vector perpendicular to the plane is (1, 1, 1), so the equation of the plane can be ...

  (1, 1, 1)·(x, y, z) = (1, 1, 1)·A

  x + y + z = 14

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How do you solve this equation: -2m+3=|15+m|
Elden [556K]

Any number inside the modulus sign becomes positive. This means |15+m|=|-(15+m)|=|-15-m| and so we have,

-2m+3=|15+m| \Rightarrow \left \Big\{ {{-2m+3=15+m} \atop{-2m+3=-15-m}} \right

Solving these gives us

-2m+3=15+m \Rightarrow m=-4

-2m+3=-15-m \Rightarrow = m=18

However if we check the second solution in the original equation we obtain -2(18)+3=|15+18| \Rightarrow -33=33. This is false and so m=18 can't be a solution.

Therefore the only solution is m=-4.

(Note: I'm not sure why the second solution didn't work but when there's a modulus sign involved it always pays to check your final answers to be sure. I'll have a think about it but in case you find out before I do, I'd be interested to know in the comments.)

8 0
3 years ago
Find the commission.
juin [17]

Answer:

63.9

Step-by-step explanation:

Convert 9% to a decimal: 0.09

710×.09=63.9

Please give me brainliest

3 0
2 years ago
The population of a city has increased by 33% since it was last measured. If the current population is 39,900, what was the prev
Ksju [112]

Answer:

26,733

Step-by-step explanation:

39,900 - Percentage decrease =

39,900 - (33% × 39,900) =

39,900 - 33% × 39,900 =

(1 - 33%) × 39,900 =

(100% - 33%) × 39,900 =

67% × 39,900 =

67 ÷ 100 × 39,900 =

67 × 39,900 ÷ 100 =

2,673,300 ÷ 100 =

26,733

Hope this helps :)

5 0
3 years ago
Hope someone help.me​
zvonat [6]

x = r sin θ cos Ф

x² = r² sin² θ cos² Ф

y = r sin θ sin Ф

y² = r² sin² θ sin² Ф

z = r cos θ

z² = r² cos²  θ

x² + y² + z²

= r² sin² θ cos² Ф  +  r² sin² θ sin² Ф +  r² cos²  θ

= r² sin² θ (cos² Ф + sin² Ф) +  r² cos²  θ

= r² sin² θ + r² cos²  θ

= r² (sin² θ + cos²  θ)

= r²       √

7 0
3 years ago
Help pls fast
Andrews [41]

Answer:

32.40cm²

Step-by-step explanation:

Given the parallelogram ABCD ;

side AB is always Parallel to CD, hence ;

AB = CD = 7.2cm

Perpendicular from C on AB is the height of the parallelogram = 4.5cm

Area of a parallelogram : base * height

Area of a parallelogram = length base * height

Area of a parallelogram = 7.2 cm * 4.5cm

Area of parallelogram = 32.40cm²

6 0
2 years ago
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