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Dafna11 [192]
3 years ago
9

What is the equation of the plane that contains the triangle shown in the diagram?

Mathematics
2 answers:
Anastaziya [24]3 years ago
6 0
The first equation

2x + 3y + 6z = 12
kolezko [41]3 years ago
3 0

Answer:

Option A is correct.

2x + 3y +z = 6

Step-by-step explanation:

The intercept form of the equation of plane is given by:

\frac{x}{l}+\frac{y}{m} +\frac{z}{n} =1            .....[1]

where

l is the intercept of x-axes

m is the intercept of y-axes and

n is the intercept of z-axes respectively;

From the given figure;

we have;

The intercepts of coordinates axes are;

l = 3

m = 2

n = 6

Substitute these values in the equation [1]; we have;

\frac{x}{3}+\frac{y}{2} +\frac{z}{6} =1  

Taking LCM of 3, 2 and 6 is 6

2x + 3y +z = 6

therefore, the equation of plane that contains the triangle as shown in the diagram is, 2x + 3y +z = 6

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3 years ago
1. Simplify the expression below.<br> 2(x + 2) + 3(-x-7) -5 ( 2x - 4)
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5 0
3 years ago
In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horiz
BabaBlast [244]

Answer:

C (2, -1)

Step-by-step explanation:

C has the same x coordinate as A = 2

that eliminates A and B.

and the y value of C has to be closer to the y value of B than to the y value of A (due to the 5:3 ratio).

so, without spending unnecessary effort on actual calculation, we can directly derive the correct answer to be C.

but to show in numbers, the "coordinate triangle" of the difference between D and B is a similar triangle to ACD. and so, the ratio of one side pair applies then to all other sides too. including the individual coordinate differences.

so, also the y difference of A to D relates to the y difference between D and B in the same ratio of 5:3 of the overall y difference of A to B.

the y difference A to B is 2 - -6 = 8

the 5/3 split of 8 units is actually 5 and 3.

so, the y coordinate of D is -6 + 5 = -1

and C must have the same y coordinate.

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4 0
3 years ago
An equation and the first step in its solution are shown: Equation: x2 + 8x - 9 = 0
Novay_Z [31]
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2 years ago
If the mass of a material is 45 grams and the volume of the material is 11 cm^3, what would the density of the material be?
Nuetrik [128]

Answer:

Density of material would be 4.09 g/cm^3

units is g/cm^3

Step-by-step explanation:

Given: The mass of a material is 45 grams and the volume of the material is 11 cubic centimeter

Density is defined as mass per unit volume.

It is given by:

p= \frac{m}{V} where p is the density , m is the mass and V is the volume of the material respectively.

Here, Density is expressed in grams per centimeter cubed (g/cubic cm)

Here, m = 45 g , V = 11 cubic cm

We get;

p= \frac{45}{11} = 4.09 g/cm^3

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2 years ago
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