Step-by-step explanation:
y = ax^n + bx^(n-1) ... + z
(0, 1) tells us that the constant term z = 1.
because x = 0 eliminates all other terms. and as the sum is 1, that means z = 1.
for the other pairs I strongly suspect
(-1, 3) : 2×(-1)² + 1 = 2×1 + 1 = 3
(-2, 9) : 2×(-2)² + 1 = 2×4 + 1 = 9
so, the fitting equation is
y = 2x² + 1
Answer:

Step-by-step explanation:
The equation of the line in Slope-Intercept form is:

Where "m" is the slope and "c" is the y-intercept.
By definition:
1. If the lines of the System of equations are parallel (whrn they have the same slope), the system has No solutions.
2. If the they are the same exact line, the System of equations has Infinite solutions.
(A) Let's solve for "y" from the first equation:

You can notice that:

In order make that the System has No solutions, the slopes must be the same, but the y-intercept must not. Then, the values of "a" and "b" can be:

Substituting those values into the second equation and solving for "y", you get:

You can idenfity that:

Therefore, they are parallel.
(B) In order make that the System has Infinite solutions, the slopes and the y-intercepts of both equations must be the same. Then, the values of "a" and "b" can be:

If you substitute those values into the second equation and then you solve for "y", you get:

You can identify that:

Therefore, they are the same line.
She would have $7160.86 left over in cash here's why.....
she starts off with $8,322.65 and spends $830.98 on rent $8,322.65-$830.98= $7,491.67
then spends $210.36 on food and another $120.45 on gas
$7,491.67-$210.36= $7,281.31 - $120.45= $7,160.86 <---- Left over $
The new perimeter of the rectangle if the dimensions are quadrupled would be 72 inches.
<h3>What are the side lengths of the first triangle?</h3>
The perimeter is always obtained by adding all the sides. This means the possible side lengths of the original rectangle are:
- 5 inches + 5 inches + 4 inches + 4 inches
<h3>What are the side lengths of the new triangle?</h3>
5 inches x 4 = 20 inches
4 iches x 4 = 16 inches
<h3>What is the new perimeter?</h3>
20 + 20 + 16 +16= =72 inches
Learn more about perimeter in: brainly.com/question/6465134