Answer: The slope is 5.
Step-by-step explanation: Use formula: (y2-y1)/(x2-x1)
(7-2)/(4-3)
5/1 = 5
Have a nice day! :)
Answer:
(Explanation)
Step-by-step explanation:
Part A:
The graph of y = + 2 will be translated 2 units up from the graph of y = .
If you plug in 0 for x, you get a y-value of 2. The 2 is also not included with the , which is why it doesn't translate left.
This is what graph A should look like:
[Attached File]
Part B:
The graph of y = - 2 will be translated 2 units down from the graph of y = .
If you plug in 0 for x, you get a y-value of -2. The 2 is also not included with the , which is why it doesn't translate right.
This is what graph B should look like:
[Attached File]
Part C:
The graph of y = 2 is a stretched version of the graph y = . Numbers that are greater than 1 stretch and open up and numbers less than -1 stretch and open down.
This is what graph C should look like:
[Attached File]
Part D:
The graph of y = 
is a compressed version of the graph y = . Numbers that are in-between 0 and 1, and -1 and 0 are compressed.
This is what graph D should look like:
[Attached File]
Answer:
(a) square: L; triangle: 0.
(b) square: L·(-16+12√3)/11; triangle: L·(27-12√3)/11
Step-by-step explanation:
<u>Strategy</u>: First we will write each area in terms of its perimeter. Then we will find the total area in terms of the amount devoted to the square. Differentiating will give a way to find the minimum total area.
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In terms of its perimeter p, the area of a square is ...
A_square = p^2/16
In terms of its perimeter p, the area of an equilateral triangle is ...
A_triangle = p^2/(12√3)
Then the total area of the two figures whose total perimeter is L with "x" devoted to the square is ...
A_total = x^2/16 + (L-x)^2/(12√3)
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(a) We know when polygons are regular, the one with the most area for the least perimeter is the one with the most sides. Hence, the total area is maximized when all of the wire is devoted to the square.
__
(b) The derivative of A_total with respect to x is ...
dA/dx = x/8 -(L-x)/(6√3)
This will be zero when ...
x/8 = (L-x)/(6√3)
x(6√3) = 8L -8x
x(8 +6√3) = 8L
x = L·8/(6√3 +8) = 8L(6√3 -8)/(64-108)
x = L·(12√3 -16)/11
The total area is minimized when L·(12√3 -16)/11 is devoted to the square, and the balance is devoted to the triangle.
Because if you multiply 2 different irrational numbers (like the following)
You will get an irrational answer.
BUT
if you multiply the same square root (which are both irrational, you get a rational number)
Answer:
2(x+3)=2x+6
2x+6=2x+6
Step-by-step explanation:
2(x+3)=2x+6
2x+6=2x+6
