Answer:
The length of the model is 21 inches
Step-by-step explanation:
we have
The scale factor
That means
1 unit in the model represent 12 units in the actual
1 inch in the model represent 12 inches in the actual
Remember that
so
1 inch in the model represent 1 ft in the actual
The scale factor is
therefore
21 ft in the actual represent 21 inches in the model
Part A.
The set of equations can be solved by substitution. Use the expression one equation gives for y as the value of y in the other equation. This gives
2x²-15 = 3x-6
Subtracting the right side gives a quadratic in standard form that can be solved by any of several methods.
2x² -3x -9 = 0
(2x+3)(x-3) = 0 . . . . factor the above equation
x = -3/2, x = 3 . . . . .use the zero product rule to find x
Now, these x-values can be substituted into either equation for y. The linear equation is often easier to evaluate.
y = 3(-3/2) -6 = -10.5
y = 3(3)-6 = 3
The solutions to the system are (-1.5, -10.5) and (3, 3).
Part B.
The two equations can be graphed. The solutions are where the graphs intersect. The graphs intersect where the (x, y) values that satisfy one equation are the same (x, y) values that satisfy the other equation. Those points of intersection are (-1.5, -10.5) and (3, 3).
It would be half of the coefficient of x squared added to both sides:
So half of 8 ( the coefficient of 8x) is 4;
The number 4 squared is 16, so you would add that to both sides.
You do this so that you can easily factor the left side: x^2 + 8x + 16 = 4 + 16
(x + 4)(x+4) = 20
$75.77 × 0.25 = $18.94
The correct answer is B.
