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katrin2010 [14]
3 years ago
13

9/29/2020

Mathematics
2 answers:
Contact [7]3 years ago
8 0

Answer:  -2x + 5y = 8

Step-by-step explanation:

Since the lines must be parallel, the slopes must be the same, so keep the coefficients of x and y

Substitute the values of x and y from the given coordinate  (6,4) to find the new constant, b, the y-intercept.

-2x + 5y = b

-2(6) + 5(4) = b

-12 + 20 = b

8 = b

Rewrite the original equation substituting the new b for the original -15

-2x + 5y = 8

vovangra [49]3 years ago
8 0

Answer:

  • y = 2/5x + 8/5

Step-by-step explanation:

<u>Slope - intercept form</u>

  • y = mx + b

<u>Given line</u>

  • -2x + 5y = -15

<u>Converting the equation into slope-intercept form</u>

  • -2x + 5y = -15
  • 5y = 2x - 15
  • y = 2/5x - 3

<u>Parallel lines have same slope of 2/5</u>

  • y = 2/5x + b

<u>Using point (6, 4) lets find it's y-intercept (b)</u>

  • 4 = 2/5*6 + b
  • b = 4 - 12/5 = 8/5

<u>So the line is</u>

  • y = 2/5x + 8/5
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The binomial factor of the equation \rm 9x^2 -64 is 3x-8.

<h3>What is a binomial factor?</h3>

The algebraic expression which contains only two terms is called binomial. It is a two-term polynomial. Also, it is called a sum or difference between two or more monomials.

Factoring binomials means breaking down a binomial expression into its simplest form.

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\rm 9x^2 -64

The binomial is determined in the following steps given below.

\rm =9x^2 -64\\\\= (3)^2x^2-8^2\\\\= (3x)^2-8^2\\\\= (3x-8)(3x+8)

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Mary walks a certain distance up a road that climbs a hill. The vertical component of her displacement is 17.63 meters, and the
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Find the distance from the point to the line. (-1,-2,1);x=4+4t, y=3+t, z=6-t .The distance is ____ Typn exact answer, using radi
lawyer [7]

Answer:

The distance is<u>  4.726 </u>

Step-by-step explanation:

we need to find the distance from the point to the line

Given:- point (-1,-2,1) and line ; x=4+4t, y=3+t, z=6-t .

used formula d=\frac{|a\times b|}{|a|}

Let point P be (-1,-2,1)

using value t=0 and t=1

The point Q (4 , 3, 6) and R ( 8, 4, 5)

Let a be the vector from Q to R :   a = < 8 - 4, 4 - 3, 5 - 6 > = < 4, 1, -1 >

Let b be the vector from Q to P:    b = < -1 - 4, -2 - 3, 1 - 6> = < -5, -5, -5 >

The cross product of a and b is:

a \times b= \begin{vmatrix} i & j & k\\ 4 &1&-1\\-5 &-5&-5\\ \end{vmatrix}

= -6i+15j-15k

The distance is : d=\frac{\sqrt{(-6)^{2}+(15)^{2}+(-15)^{2}}}{\sqrt{(4)^{2}+(1)^{2}+(-1)^{2}}}

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≈4.726

Therefore, the distance is<u>  4.726 </u>

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