What is the y-coordinate of the solution to the system of equations? 5x-y=25 4x+3y=1
1 answer:
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Slope-intercept form is <em>y</em><em> = </em><em>mx</em> + <em>b</em>, where <em>m</em> is the slope and <em>b</em> is the <em>y</em>-intercept. To write this in slope-intercept form we must isolate the <em>y</em>:
2x + 3y = 1470
2x + 3y - 2x = 1470 - 2x (subtraction will cancel the positive 2x on the left side of the equation)
3y = -2x + 1470 (since they are not like terms we cannot combine them, we leave them separate)
3y/3 = -2/3x + 1470/3 (cancel the 3 by dividing; EVERYTHING gets divided to keep it equal)
y = -2/3x + 490
The slope of this equation is -2/3 and the <em>y</em>-intercept is 490.
To graph this equation, plot 490 on the <em>y</em>-axis first, since it is the intercept. Then count over to the right 3 and down 2 to find the next point; continue this for all successive points.
In function notation this would be <em>f</em>(<em>x</em>) = -2/3<em>x</em> + 490. This function shows how the profit on wrap specials changes as the number of sandwich specials sold increases. The graph of the function is attached.
The next month, when Sal's profit increased, the function changes because the <em>y</em>-intercept changes. The slope stays the same.
2x + 3y = 1470
2x + 3y - 2x = 1470 - 2x (subtraction will cancel the positive 2x on the left side of the equation)
3y = -2x + 1470 (since they are not like terms we cannot combine them, we leave them separate)
3y/3 = -2/3x + 1470/3 (cancel the 3 by dividing; EVERYTHING gets divided to keep it equal)
y = -2/3x + 490
The slope of this equation is -2/3 and the <em>y</em>-intercept is 490.
To graph this equation, plot 490 on the <em>y</em>-axis first, since it is the intercept. Then count over to the right 3 and down 2 to find the next point; continue this for all successive points.
In function notation this would be <em>f</em>(<em>x</em>) = -2/3<em>x</em> + 490. This function shows how the profit on wrap specials changes as the number of sandwich specials sold increases. The graph of the function is attached.
The next month, when Sal's profit increased, the function changes because the <em>y</em>-intercept changes. The slope stays the same.
Answer:
see explanation
Step-by-step explanation:
(f + g)(x) = f(x) + g(x), so
f(x) + g(x)
= x² + 5x + 6 + x + 3 ← collect like terms
= x² + 6x + 9
-------------------------------------------------
(f - g)(x) = (f(x) - g(x), so
f(x) - g(x)
= x² + 5x + 6 - (x + 3) ← distribute by - 1
= x² + 5x + 6 - x - 3 ← collect like terms
= x² + 4x + 3
---------------------------------------------------
(f • g)(x)
= f(x) × g(x)
= (x² + 5x + 6)(x + 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x²(x + 3) + 5x(x + 3) + 6(x + 3) ← distribute parenthesis
= x³ + 3x² + 5x² + 15x + 6x + 18 ← collect like terms
= x³ + 8x² + 21x + 18
---------------------------------------------------------------
( )(x)
=
= ← factor the numerator
= ← cancel common factor (x + 3) on numerator/ denominator
= x + 2