A system of equations for this would be
19x + 11y = 273
and
12x + 17y = 283.
X is the amount of minutes to solve one long division problem and y is the amount of minutes to solve a graphing problem.
How To Solve This System of Equations.
Multiply both by 17 and 11 respectively for them to have the greatest common factor for y. So now both equations are:
323x + 187y= 4641
132x + 187y= 3113.
Subtract both equations and you have left:
191x = 1528.
Divide both sides by 191 and you find x.
X = 8.
Answer
It takes Sally 8 minutes to do one Long Division Problem.
Hope this helped. ;)
y = x³ + 3x² - x - 3
0 = x³ + 3x² - x - 3
0 = x²(x) + x²(3) - 1(x) - 1(3)
0 = x²(x + 3) - 1(x + 3)
0 = (x² - 1)(x + 3)
0 = (x² + x - x - 1)(x + 3)
0 = (x(x) + x(1) - 1(x) - 1(1))(x + 3)
0 = (x(x + 1) - 1(x + 1))(x + 3)
0 = (x - 1)(x + 1)(x + 3)
0 = x - 1 or 0 = x + 1 or 0 = x + 3
+ 1 + 1 - 1 - 1 - 3 - 3
1 = x or -1 = x or -3 = x
Solution Set: {-3, -1, 1}
So hmm notice the picture below
that's the 30-60-90 rule, notice your triangle, the bottom-left-angle is a right angle, 90°, the angle atop is 30°, so the angle on the bottom-right has to be 60°, thus is a 30-60-90 triangle, and as you can see on the triangle on the left in the picture, those are the ratios for it
so 8 will be x, what is the longer leg or side in yours then? well, is
Answer:
Step-by-step explanation:
Question (1)
x² + 10x + 12
= x² + 2(5x) + 5² - 5² + 12
= [x² + 2(5x) + 5²] - 5² + 12
= (x + 5)² - 25 + 12 [Since, a² + 2ab + b² = (a + b)²]
= (x + 5)² - 13
Question (2)
y² - 6y - 15
= y² - 2(3y) - 15
= y² - 2(3y) + 3² - 3² - 15
= [y² - 2(3y) + 3²] - 3² - 15 [Since, a² - 2ab + b² = (a - b)²]
= (y - 3)² - 3²- 15
= (y - 3)² - 9 - 15
= (y - 3)² - 24
Angle C prime D prime and A prime
