The error is that -2 times -5 is 10 not -10. Then carry on from there because that error meant the rest is wrong as well.
Let 
, so that differentiating both sides wrt 
gives
If 
and 
, the above reduces to
This is the slope of the tangent line, which has equation
Answer:
B) 1.078 < 1.23 (T)
Step-by-step explanation:
A) 1.23 < 1.203 (F)
B) 1.078 < 1.23 (T)
C) 1.17 > 1.203 (F)
D) 1.078 > 1.17 (F)
Let's call the three numbers a, b, and c.
Now we can turn the information we are given into equations.
The sum of the three numbers is 26:
a + b + c = 26
Twice the first (2 times a) minus the second (2 times a minus b) is 2 less than the third:
2a - b = c - 2
The third is the second minus three times the first:
c = b - 3a
Counting what we have here, we now have three equations and three variables: enough to solve the whole system of equations.
The third equation gives us c directly, so we can start there and substitute into the second equation:
2a - b = (b - 3a) - 2
2a + 3a = b + b - 2
5a = 2b - 2
Let's get one of these variables on its own so we can continue with the substitution:
5a + 2 = 2b
b = (5a + 2) / 2
Now we have c in terms of a and b, and b in terms of just a. So let's use the first equation and substitute to find out what a is:
a + b + c = 26
a + (5a + 2) / 2 + (b - 3a) = 26
a + (5/2)a + 1 + (5a + 2) / 2 - 3a = 26
7/2a + 1 + 5/2a + 1 - 3a = 26
12/2a + 2 - 3a = 26
6a - 3a = 26 - 2
3a = 24
a = 8
At last, we have solved for one of the variables. Now, plug this into the equation for b to find b:
b = (5a + 2) / 2 = (5(8) + 2) / 2 = (40 + 2) / 2 = 42 / 2 = 21
Now we have a and b. Time to find c!
a + b + c = 26
(8) + (21) + c = 26
29 + c = 26
c = 26 - 29
c = -3
<span>So our values for a, b, and c are 8, 21, and -3.</span>
Answer:
C
Step-by-step explanation:
first of all, the correct factorization is
y = (x - 3)(x + 6)
because when we do the multiplication
y = x² + 6x - 3x - 18 = x² + 3x - 18
and then, the factorization tends us also directly the zero points, because y is only 0, when one of the factors is 0.
so, either x-3 or x+6 has to be 0 to make the whole expression 0.
and that is only for x=3 or x=-6
