Answer:
the answer is a.
Step-by-step explanation:
I plugged your data into a graphing calculator, and got a quad reg in the picture.
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)
Answer:
see explanation
Step-by-step explanation:
Parallel lines have equal slopes.
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 5x + 1 ← is in slope- intercept form
with slope m = 5
Rearrange 2y - 10x + 3 = 0 into this form
Add 10x to both sides
2y = 10x ( subtract 3 from both sides )
2y = 10x - 3 ( divide all terms by 2 )
y = 5x - ← in slope- intercept form
with slope m = 5
Since both lines have a slope of 5 then they are parallel.
<span>Expression- arithmetic or algebraic expression (ex, 12, 5 + 3x)
Terms- number of independent items in an expression
Coefficient- number or constant multiplied by a variable (ex. 3x....3 is coefficient)
Equivalent expression- two or more expressions with the same numerical value</span>
Answer:
L = 6, w = 2
Step-by-step explanation:
Let w = width of rectangle
Let L = length of rectangle
w = L - 4
Area of rectangle = Lw
L (L - 4) = 12
L^2 - 4L = 12
L^2 - 4L - 12 = 0
(L - 6)(L + 2) = 0
L - 6 = 0
L = 6 (the other option doesn't work because dimensions can't be negative)
w = L - 4
w = 6 - 4
w = 2
Double check
A = Lw
A = 6 x 2
A = 12
It matches so we are right.