Answer:
A and c
Step-by-step explanation:
multiply the 3 to both parts of equation
![\bf f(x)=(x-6)e^{-3x}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}=1\cdot e^{-3x}+(x-6)-3e^{-3x}\implies \cfrac{dy}{dx}=e^{-3x}[1-3(x-6)] \\\\\\ \cfrac{dy}{dx}=e^{-3x}(19-3x)\implies \cfrac{dy}{dx}=\cfrac{19-3x}{e^{3x}}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%3D%28x-6%29e%5E%7B-3x%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%3D1%5Ccdot%20e%5E%7B-3x%7D%2B%28x-6%29-3e%5E%7B-3x%7D%5Cimplies%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3De%5E%7B-3x%7D%5B1-3%28x-6%29%5D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%3De%5E%7B-3x%7D%2819-3x%29%5Cimplies%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3D%5Ccfrac%7B19-3x%7D%7Be%5E%7B3x%7D%7D)
set the derivative to 0, solve for "x" to get any critical points
keep in mind, setting the denominator to 0, also gives us critical points, however, in this case, the denominator will never be 0, so... no critical points from there
there's only 1 critical point anyway, and do a first-derivative test on it, check a number before it and after it, to see what sign the derivative has, and thus, whether the graph is going up or down, to check for any extrema
In this question, you're solving for x.
Solve for x:
x + 4.2 = 7
You need to get x by itself, to do so, you would need to subtract 4.2 from both sides:
x = 2.8
Answer:
x = 2.8
Answer:
b
c
Step-by-step explanation:
First question: x - 6 means there is a shift to the right.
Second Question: substitute the given values into the original equation for appropriate transformations.
Answer: 3 |x-4| + 2, because vertical stretch multiplies x, horizontal shifts are subtracted or added to x, and vertical shifts are added or subtracted to the entire function.
Answer:
6) 15
7)5
8)120 degrees
9)60 degrees
10)9
Step-by-step explanation:
GHIJ is a parallelogram.
Opposite sides of a parallelogram are congruent.
3y - 1 = 2y + 1
3y - 2y = 1 + 1
y = 2
Opposite sides of a parallelogram are congruent.
4x + 3 = x + 12
4x - x = 12 - 3
3x = 9
x = 9/3
x = 3
6)GH = ?
GH = 4x + 3
GH = 4(3) + 3
= 12 + 3
= 15
therefore, GH = 15
7) HI = ?
HI = 2y + 1
= 2(2) + 1
= 4 +1
= 5
therefore, HI = 5
Opposite angles of a parallelogram are equal.
8) m(angle I) = 120 degrees...... (given)
therefore, measure of angle G = measure of angle I
therefore, m(angle G) = 120 degrees
Consecutive angles of a parallelogram are supplementary.
9) m(angle I) + m(angle J) = 180 degrees
120 + m (angle J) = 180
m(angle J) = 180 - 120
= 60 degrees.
The diagonals of a parallelogram bisect each other.
10) JK = 9 .........( given)
JK = HK
therefore, HK = 9
