120 cupcakes
Even # rows
Odd # columns
12: 1, 2,3,4,6, 12 (integers?)
I see only one arrangement with odd column & even rows
3 columns, 40 rows
That's mainly because 120 is an even number.
Answer:
The first term is 3. The common difference is 2.
Step-by-step explanation:
The first term is x.
The common difference is d.
The second term is x + d.
3rd term: x + 2d
4th term: x + 3d
7th term: x + 6d
"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"
x + 3d = 3 * x Eq. 1
"the seventh term exceeds twice the third term by 1"
x + 6d = 2(x + 2d) + 1 Eq. 2
Simplify Eq. 1:
2x = 3d
Simplify Eq. 2:
x + 6d = 2x + 4d + 1
x = 2d - 1
Multiply both sides of the last equation by 2.
2x = 4d - 2
2x = 3d (simplified Eq. 1)
Since 2x = 2x, then the right sides are equal.
3d = 4d - 2
d = 2
2x = 3d
2x = 3(2)
2x = 6
x = 3
Answer: The first term is 3. The common difference is 2.
Answer:
21.6
Step-by-step explanation:
10.80/0.5=21.6
A function is differentiable if you can find the derivative at every point in its domain. In the case of f(x) = |x+2|, the function wouldn't be considered differentiable unless you specified a certain sub-interval such as (5,9) that doesn't include x = -2. Without clarifying the interval, the entire function overall is not differentiable even if there's only one point at issue here (because again we look at the entire domain). Though to be fair, you could easily say "the function f(x) = |x+2| is differentiable everywhere but x = -2" and would be correct. So it just depends on your wording really.
Answer:
x = 30 in
Step-by-step explanation:
length of rectangle is (2/3)x + 10; width is (1/3)x + 5;
perimeter is 90 in; find x:
P = 90 in = 2(2/3)x + 2(10) + 2(1/3)x + 2(5), or
90 in = (6/3)x + 30 in
Solving for x, we get (2)x = 60 in, or x = 30 in
