What is the image of (4,−7) after a dilation by a scale factor of 2 centered at the origin?

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough

answer: john is 20, mary is 15

step-by-step explanation:

x³ - 13x + 12

step-by-step explanation:

if you are familiar with the distributive property

a(b+c) = a·b + a·c

then you can apply this here with the binomials.

since multiplication over the real numbers is commutative, we can multiply these binomials in any order. suppose we want to focus on the product (x - 1)(x + 4)

using the distributive property, we can distribute (x - 1) into (x+4):

(x - 1)(x + 4) = x(x - 1)+ 4(x - 1)

and then we apply the distributive property again:

  = x² - x + 4x - 4

combining like terms -x and 4x, we get that

  = x² + 3x - 4

hence we have that (x - 1)(x + 4) = x² + 3x - 4. in this original product, this means that

  (x - 1)(x + 4)(x - 3) = (x² + 3x - 4)(x - 3)

now we can take (x - 3) to the front

  = (x - 3)(x² + 3x - 4)

and then distribute (x-3) inside

  = x²(x - 3) + 3x(x - 3) - 4(x - 3)

now distribute again

  = x³ - 3x² + 3x² - 9x - 4x + 12

and combine like terms to get a final answer of

  = x³ - 13x + 12