Answer:
(1, - 2 )
Step-by-step explanation:
Given the equations
9x + 2y = 5 ( subtract 9x from both sides )
2y = 5 - 9x ( divide terms by 2 )
y = 2.5 - 4.5x → (1)
7x - 3y = 13 → (2)
Substitute y = 2.5 - 4.5x into (2)
7x - 3(2.5 - 4.5x) = 13
7x - 7.5 + 13.5 = 13 , that is
7x + 6 = 13 ( subtract 6 from both sides )
7x = 7 ( divide both sides by 7 )
x = 1
Substitute x = 1 into (1) and evaluate for y
y = 2.5 - 4.5(1) = 2.5 - 4.5 = - 2
solution is (1, - 2 )
19 thousands is 19 x 1000 = 19,000
7 tens is 7 x 10 = 70
19 thousands plus 7 tens is 19,000 + 70 which is 19,070.
Answer:
y = -5x +23
Step-by-step explanation:
If the line is parallel it has the same slope, so we only have to solve for the y-intercept.
To get from (5,-2) the y increases by 25
So y = -5x +23
Answer:
Step-by-step explanation:
We want to find the minimum-degree polynomial with real coefficients and zeros at:
As well as a <em>y-</em>intercept of 64.
By the Complex Root Theorem, if <em>a</em> + <em>b</em>i is a root, then <em>a</em> - <em>b</em>i is also a root.
So, a third root will be 4 - 4i.
The factored form of a polynomial is given by:
Where <em>a</em> is the leading coefficient and <em>p</em> and <em>q</em> are the zeros. More factors can be added if necessary.
Substitute:
Since we want the minimum degree, we won't need to add any exponents.
Expand the second and third factors:
Hence:
Lastly, we need to determine <em>a</em>. Since the <em>y-</em>intercept is <em>y</em> = 64, this means that when <em>x</em> = 0, <em>y</em> = 64. Thus:
Solve for <em>a: </em>
Our factored polynomial is:
Finally, expand: