Answer:
Step-by-step explanation:
We can use the quadratic formula to factor this expression
For a quadratic function of the form:
Whe have:
Then:
The quadratic formula is:
Then the solutions are:
Finally The factored expression is:
and
Then
A- 756 in^2
B- Box A and Box B both have the same surface are
Separate the vectors into their <em>x</em>- and <em>y</em>-components. Let <em>u</em> be the vector on the right and <em>v</em> the vector on the left, so that
<em>u</em> = 4 cos(45°) <em>x</em> + 4 sin(45°) <em>y</em>
<em>v</em> = 2 cos(135°) <em>x</em> + 2 sin(135°) <em>y</em>
where <em>x</em> and <em>y</em> denote the unit vectors in the <em>x</em> and <em>y</em> directions.
Then the sum is
<em>u</em> + <em>v</em> = (4 cos(45°) + 2 cos(135°)) <em>x</em> + (4 sin(45°) + 2 sin(135°)) <em>y</em>
and its magnitude is
||<em>u</em> + <em>v</em>|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)
… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))
… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))
… = √(16 + 16 cos(135° - 45°) + 4)
… = √(20 + 16 cos(90°))
… = √20 = 2√5
Step-by-step explanation:
the average rate of change is
(f(x2) - f(x1)) / (x2 - x1)
so, for x = 1 and 2
(4×3² - 4×3¹) / (2 - 1) = 36 - 12 = 24
for x = 3 and 4
(4×3⁴ - 4×3³) / (4 - 3) = 324 - 108 = 216
so the second rate is 216/24 = 9 times greater than the first rate.
Answer:
10 stickers.
Step-by-step explanation:
Let's say that Mandy has m stickers, and Priscilla has p stickers.
m = 1/4p
6/5(m + 28) = p + 28
6/5(1/4p + 28) = p + 28
1/4p + 28 = 5/6p + 23 and 1/3
5/6p - 1/4p = 28 - 23 and 1/3
10/12p - 3/12p = 84/3 - 70/3
7/12p = 14/3
p = (14/3)(12/7)
p = 8
At the beginning, Priscilla had 8 stickers. That means that Mandy had 1/4 * 8 = 8 / 4 = 2 stickers.
So, in the packet, there were 8 + 2 = 10 stickers.
Hope this helps!
