8) Absolute value is the distance from zero on a number line (and has no reference to which direction left/right from zero), so this means the value is always positive:
<u><em> abs(2) = 2</em></u>
<u><em>abs(-2) = 2</em></u>
9) Solve the equation for x
(3x + y)/z = 2
*multiply both sides by z
(3x + y) = 2z
*subtract y from both sides
3x = 2z - y
*divide both sides by 3
x = (2z - y)/3
10) Which point is a solution to the equation 6x - 5y = 4? Justify your choice
A. (1, 2)
B. (1, -2)
C. (-1, -2)
D. (-1, 2)
*plug (x, y) coordinates into equation and see if the result is a valid equation:
*start with A. (1, 2):
6(1) - 5(2) = 4
6 - 10 = 4
-4 = 4 [NO GOOD]
*now try B. (1, -2):
6(1) - 5(-2) = 4
6 - (-10) = 4
6 + 10 = 4
16 = 4 [NO GOOD]
*now try C. (-1, -2):
6(-1) - 5(-2) = 4
-6 - (-10) = 4
-6 + 10 = 4
<u><em> 4 = 4 [OK]</em></u>
*just for fun let's also verify D. (-1, 2) is not the solution, since we found that C. was:
6(-1) - 5(2) = 4
-6 - 10 = 4
-16 = 4 [NO GOOD]
<u><em>The answer is C. (-1, -2) (and the justification is that we solved for it to be true)</em></u>
11) Domain is all values 'x' (i.e. input)
Range is all values 'y' (i.e. output)
a.) y = 2x + 1 is a line with a slope of 2:1 (vert:horiz) and a y-intercept of y = 1, but because it is a line, it extends from -infinty to +infinity for both 'x' and 'y', so . .
<u><em>Domain = (-infinity ≤ x ≤ +infinity)</em></u>
<u><em>Range = (-infinity ≤ y ≤ +infinity)</em></u>
b.) This table on shows discrete values of input/output, so the domain/range is also discrete . .
<u><em>Domain = (3, 7, 11)</em></u>
<u><em>Range = (-1, -3, -5)</em></u>
c.) Just from visual confirmation of the plot's extents . .
<u><em>Domain = (-5 ≤ x ≤ 5)</em></u>
<u><em>Range = (-1 ≤ y ≤ 1)</em></u>
d.) Again using visual confirmation of the plot's extents . .
<u><em>Domain = (-2 ≤ x ≤ 2) *note extents are limited by vertical asymptote</em></u>
<u><em>Range = (-infinity ≤ y ≤ +infinity)</em></u>
12) There are <u><em>2 lines of symmetry</em></u> (they are the vertical line drawn at x = 0, and the horizontal line drawn at y = 0 that bisect the ellipse)
Cost of Rings = 3 x $21
= $63
Cost of Bracelets = $200 - $63
= $137
Cost per Bracelet = $137 / 4
= $34.25
Therefore, the answer is C
For purple, multiply pi by radius. (cylinder bottom is a circle, so area of circle is pi*r^2) for pink, the one that says cubic units (bc it is 3d shape)
Answer:
-30?
Step-by-step explanation: