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Dmitrij [34]
3 years ago
10

A line passes through the point (-2, 4), and its y-intercept is (0,6). What is the equation of the line that is

Mathematics
1 answer:
MatroZZZ [7]3 years ago
8 0

Answer:

y = -x + 9

Step-by-step explanation:

The line that passes through the points (-2,4) and (0,6) has a slope of 1, and a y intercept of 6. The equation to the first line is y = x + 6. and perpendicular lines always have the opposite, reciprocal slope of the other line. So the slope for the second line would be -1. A line with the slope of -1 and a point of (5,4) would contain the points (5,4) , (4,5) , (3,6) , (2,7) , (1,8) , and (0,9) , which is the y intercept for the second line. So the equation for the second line would be y = -x + 9

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Do even numbers have more factors in odd numbers or do i numbers have more factors than even numbers
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<span>It is because even numbers always have a factor of two, and therefore, larger composite even numbers will have factors of two and other even numbers based around two, such as 4, 8, 16, 32, and so on. On the other hand, numbers which are odd can have factors of 3, 5, and 7 for example, and their numbers based around them(3, 9, 27; 5, 10, 15; 7, 49, 343; and so on). If we look into it, notice how for odd numbers the space between the numbers based around 3, 5, and 7 are increasingly further apart. This is the reason why less large odd integers to have numerous factors. It is because odd numbers cannot have the prime factor 2, this will reduce their factor number. And is is also because even numbers are already divided by 2, this will give them more factors over the odd numbers.</span>
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3 years ago
Verify Sin^4x+2cos^2x-cos^4=1
Alenkasestr [34]

Answer:

Proven .  We get a true statement of 1 = 1  by transforming the expression on the left side to make it look like the right side.   See below.

Step-by-step explanation:

This  is missing some notation:  Sin^4x+2cos^2x-cos^4=1

We want to prove : (Sin x ) ^ 4   +   2  (cos x)^2   -   (cos x)^4   =    1  

Replace the  (cos x)^4   with  ((cos x)^2)^2  same with the (sin x)^4 with

((sin x)^2)^2

(Sin x ) ^ 4   +   2  (cos x)^2   -   (cos x)^4   =    1  

( ((sin x)^2) ^2  -  ( (cos x)^2)^2   +   2 (cos x)^2   +  1  - 1   = 1

Factor the  trinomial   -((cos x)^2)^2  +   2 (cos x)^2   +  1 .  

considering  ((cos x)^2) is the variable

( ((sin x)^2) ^2  -  ( (cos x)^2)^2   +   2 (cos x)^2   - 1   +  1   = 1

( ((sin x)^2) ^2   + [-  ( (cos x)^2)^2   +   2 (cos x)^2   - 1 ]  +  1   = 1

( ((sin x)^2) ^2   -  [  ( (cos x)^2) - 1 ]^2  +  1   = 1

But also notice that  (sin x)^2  =  1  -  (cos x)^2  from the trig identity:

 (sin x)^2  +  (cos x)^2 =  1  

( (1  -  (cos x)^2) ^2   -  [  ( (cos x)^2) - 1 ]^2  +  1   = 1

here we see that   (1  -  (cos x)^2) ^2  =  [  ( (cos x)^2) - 1 ]^2

so  we  get     ( 0     +  1) = 1

 1 = 1   true.

Proven .  We are done proving this identity because we get a true statement.

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What are the coordinates?

  • A coordinate system in geometry is a system that uses one or more numbers, or coordinates, to determine the position of points or other geometric elements on a manifold such as Euclidean space.
  • Coordinates are numerical distances or angles that uniquely identify points on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicians, scientists, and engineers use a variety of coordinate schemes.

Learn more about coordinates here: brainly.com/question/24513436

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