Answer:
Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another. In our attempt to prove all circles are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.
Step-by-step explanation:
17) replace the given number for "x" and evaluate
a) x² + 2x + 1 ; when x = 3
3² + 2(3) + 1
= 9 + 6 + 1
= 16
b) x² + 2x + 1 ; when x = -4
(-4)² + 2(-4) + 1
= 16 - 8 + 1
= 9
c) x² + 2x + 1 ; when x = 3
(-22.872)² + 2(-22.872) + 1
= 523.128384 - 45.744 + 1
= 478.384384
18) The dependent variable is affected by the other variable and is the "output" The independent variable is the input.
a) y = 3x - 5; "x" is the independent variable
b) the time of day is the independent variable (you would input the time of day to calculate the temperature).
19) Let the x-axis represent the length of the lumber cut off and the y-axis represent the length of the lumber remaining.
Answer:
see explanation
Step-by-step explanation:
I don't have graphing facilities but can give you the vertex and 1 other point.
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
x = - 
y = - x² - 2x + 8 ← is in standard form
with a = - 1 and b = - 2 , then
x = - 
= - 1
Substitute x = - 1 into the equation for corresponding value of y
y = - (- 1)² - 2(- 1) + 8 = - 1 + 2 + 8 = 9
vertex = (- 1, 9 )
To obtain another point substitute any value for x into the equation
x = 0 : y = 0 - 0 + 8 , then (0, 8 ) is a point on the graph
x = 2 : y = - (2)² - 2(2) + 8 = - 4 - 4 + 8 = 0 then (2, 0 ) is a point on the graph
Answer:
8
Step-by-step explanation:
