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sattari [20]
3 years ago
15

Helppp and explain than you

Mathematics
2 answers:
ss7ja [257]3 years ago
5 0

9514 1404 393

Answer:

  1. x = 2
  2. (-5, 4, 6)

Step-by-step explanation:

1. Substitution can work for this.

  2x +3(4x -5) = 13

  14x = 28 . . . . . add 15

  x = 2 . . . . . . . divide by 14

__

2. The equation z=6 eliminates all but the 1st and 3rd choices. Using that value in the first equation gives ...

  x + y + 6 = 5

  x + y = -1

Only the 3rd choice satisfies this equation.

  (x, y, z) = (-5, 4, 6)

Radda [10]3 years ago
3 0

Answer:

1) x = 2

Step-by-step explanation:

Hope it helps. I'll try to solve the second one too

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The point R(-3,a,-1) is the midpoint of the line segment jointing the points P(1,2,b)
wlad13 [49]

Answer:

The values are:

  • a = -5/2
  • b = -6
  • c = -7

Step-by-step explanation:

Given:

  • P = (x₁, y₁, z₁) = (1, 2, b)  
  • Q =  (x₂, y₂, z₂) = (c, -7, 4)  
  • m = R = (x, y, z) = (-3, a, -1)

To Determine:

a = ?

b = ?

c = ?

Determining the values of a, b, and c

Using the mid-point formula

m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)

  • As the point R(-3, a, -1) is the midpoint of the line segment jointing the points P(1,2,b)  and Q(c,-7,4), so
  • m = R = (x, y, z) = (-3, a, -1)

Using the mid-point formula

m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)

given

(x₁, y₁, z₁) = (1, 2, b) = P

(x₂, y₂, z₂) = (c, -7, 4) = Q

m = (x, y, z) = (-3, a, -1) = R

substituting the value of (x₁, y₁, z₁) = (1, 2, b) = P,   (x₂, y₂, z₂) = (c, -7, 4) = Q, and m = (x, y, z) = (-3, a, -1) = R in the mid-point formula

m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)

\left(x,\:y,\:z\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)

as (x, y, z) = (-3, a, -1), so

\left(-3,\:a,\:-1\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)

<u>Determining 'c'</u>

-3 = (1+c) / (2)

-3 × 2 = 1+c

1+c = -6

c = -6 - 1

c = -7

<u>Determining 'a'</u>

a = (2+(-7)) / 2

2a = 2-7

2a = -5

a = -5/2

<u>Determining 'b'</u>

-1 = (b+4) / 2

-2 = b+4

b = -2-4

b = -6

Therefore, the values are:

  • a = -5/2
  • b = -6
  • c = -7
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