The area of a rectangle is 42 square inches. the length is 7 inches.what is the perimeter of the rectangle?
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The closest point on a line, to another point, will be a point that's on a normal of that line, or a line that is perpendicular to it, notice picture below
so, y = 2x, has a slope of 2, a perpendicular line to it, will have a slope of negative reciprocal that, or
so, we know that line passes through the point 20,0, and has a slope of -1/2
if we plug that in the point-slope form, we get
now, the point that's on 2x and is also on that perpendicular line, is the closest to 20,0 from 2x, thus, is where both graphs intersect, as you can see in the graph
thus
solve for "x'
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not sure on the 2nd part, but sounds like, what's the distance from that point to 20,0, well, if that's the case, just use the distance equation
so, y = 2x, has a slope of 2, a perpendicular line to it, will have a slope of negative reciprocal that, or
so, we know that line passes through the point 20,0, and has a slope of -1/2
if we plug that in the point-slope form, we get
now, the point that's on 2x and is also on that perpendicular line, is the closest to 20,0 from 2x, thus, is where both graphs intersect, as you can see in the graph
thus
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not sure on the 2nd part, but sounds like, what's the distance from that point to 20,0, well, if that's the case, just use the distance equation
Eight *(a number) plus 5*(another number) is -13.
translates to:
8(x) + 5(y) = -13
The sum of (the number) and (the other number) is 1.
translates to:
(x) + (y) = 1
We have a system of two equations involving two unknowns: x and y.
We can easily solve the system using Substitution or Elimination. Let's use Elimination this time.
We'll multiply the second equation by -8 so that the x's match up.
When we add the equations together, the x's will fall out of the equation, summing to zero. The 5y and -8y will sum to -3y and the right hand side will sum to -21.
Divide by -3,
Plug back into one of your original equations to find the value of x,
Subtract 7,
translates to:
8(x) + 5(y) = -13
The sum of (the number) and (the other number) is 1.
translates to:
(x) + (y) = 1
We have a system of two equations involving two unknowns: x and y.
We can easily solve the system using Substitution or Elimination. Let's use Elimination this time.
We'll multiply the second equation by -8 so that the x's match up.
When we add the equations together, the x's will fall out of the equation, summing to zero. The 5y and -8y will sum to -3y and the right hand side will sum to -21.
Divide by -3,
Plug back into one of your original equations to find the value of x,
Subtract 7,