Answer:
1/4
Step-by-step explanation:
We know two points on the line so we can use the slope formula
(0,6) and (8,8)
m = ( y2-y1)/(x2-x1)
= (8-6)/(8-0)
= 2/8
= 1/4
ANSWER
The required equation is

EXPLANATION
The given line passes through the point

The slope of this line is given by the formula,

This implies that,


The product of the slope of the two perpendicular lines should be negative one.
Thus,

This implies that,

We multiply through by

to obtain,


Therefore the slope of the line perpendicular to the given line is

We use the slope intercept formula

where

is the y-value of the y-intercept.
We therefore have,

as the required equation.
The correct answer is C.
Answer:
[A] -3(2x-2.5)
Step-by-step explanation:
<em>Given:</em>
<em>Which expression is equivalent to -6x + 7.5?</em>
<em>Solution:
Going through all answer choices:</em>
<em>[A] -3(2x-2.5)</em>
<em>Simplify</em>
<em>-6x + 7.5</em>
<em />
<em>[B] -3(2x + 2.5)</em>
<em>Simplify</em>
<em>-6x - 7.5</em>
<em />
<em>[C] -3(2x-7.5)</em>
<em>Simplify</em>
<em>-6x+22.5</em>
<em />
<em>[D] -3(2x + 7.5)</em>
<em>Simplify</em>
<em>-6x - 22.5</em>
<em />
<em>Hence, the answer is [A] -3(2x-2.5)</em>
<em />
<em />
<u><em>Kavinsky</em></u>
<em />
<em />
Answer:
Shawn is correct.
Step-by-step explanation:
Let the quadratic function is g(x) = a(x - h)² + k
Here (h, k) is the vertex of the parabola.
Since this parabola passes through (0, 0), (1, 9) and (-1, 9), axis of symmetry is x = 0 and the vertex is (0, 0).
Therefore, equation of the parabola will be,
g(x) = a(x - 0)²+ 0
g(x) = ax²
for a point (1, 9) which lies on the graph,
9 = a(1)²
a = 9
g(x) = 9x² (here a > 1)
Therefore, f(x) is vertically stretched by a factor of 9 to form g(x).
Shawn is correct.
Answer: the system of equations that represents this situation are
12x + 6y = 180
x = 2y
Step-by-step explanation:
Let x represent the number of hardcover books that were sold in a day.
Let y represent the number of paperback books that were sold in a day.
The discount bookstore sells hardcover books for $12 and paperback books for $6. The total sales that day were $180. It means that
12x + 6y = 180
The number of hardcover books sold that day was twice the number of paperback books. It means that
x = 2y