Answer:
should be correct!
Step-by-step explanation:
First choice in the upper left corner.
It is the same shape with same proportions, just dilated.
2/5 = 0.4
8/20 = 0.4
The Pythagorean theorem can be used to find the straight-line distance between the starting point and an ending point that is 4.5 km south and 12.0 km east of there.
d² = 4.5² + 12.0² = 20.25 + 144.0 = 164.25
d = √164.25 ≈ 12.816 . . . km
(2x - y)(x - 8y + 7) =
2x(x - 8y + 7) - y(x - 8y + 7) =
2x^2 - 16xy + 14x - xy + 8y^2 - 7y =
2x^2 - 17xy + 8y^2 + 14x - 7y <===
The first number is positive, so the second has to be positive too so that their product can be a positive number which is 48.
Suppose the first number is x and the second number is y.
We know that:
y = 4 + 2x (4 more meaning adding 4 to sthing and that sthing is twice x hence the 2x)
Moving on, we have x.y = 48 (we replace y by its other value that has x in it so that we have only one unknown variable that we need to find)
<=> x.(4 + 2x) = 48
<=> 4x + 2x^2 = 48
<=> 2x^2 + 4x - 48 = 0 (we add (-48) on both sides)
Now we have to solve the second degree equation, I don't know the exact names of things since I didn't study math in English, but we have to calculate the value of, say, b^2 - 4ac (ax^2 + bx + c)
in this case b = 4 , a = 2, c = -48
so b^2 - 4ac = 16 + 384 = 400, so the square root of that equals 20
now, we have two possible values for x, suppose x1 and x2
x1 = (-4 + 20)/2.a = (-4 + 20)/4 = 16/4 = 4
x2 = (-4 - 20)/2.a = (-4 - 20)/4 = (-24)/4 = (-6) (which is impossible giving that the two numbers must be positive)
So x has to be equal to x1 => x = 4
We find x, and since y = 4 + 2x <=> y = 4 + 2.4 = 4 + 8 = 12
As a conclusion, x = 4 , y = 12
