Answer:
The correct answer us 9/15<4/4
Can I please have a brainliest? I want to rank up :)
Answer:
The second option
Step-by-step explanation:
For this problem, there are multiple ways to solve. The easiest here is the cross method. For ax²+bx+c, you find 2 numbers that multiply to ac and add to b, which you replace b with.
ac in this case is -8×3, which is -24. b in this case is 23.
You can go through the factor pairs of -24 to find the ones that add to b. These pairs are (1 and -24, -1 and 24, 2 and -12, -2 and 12, 3 and -8, -3 and 8, 4 and -6, -4 and 6). The only pair that adds to 23 is 24 and -1.
You sub this into the original equation, making 3x²+24x-x-8.
From there, you factorise, making 3x(x+8)-x(x+8).
This can be factorised further to (3x-x)(x+8) by collecting like terms.
**This question involves factorising quadratics, which you may wish to revise. I'm always happy to help!
Answer:
Step-by-step explanation:
First, simplify each term:
Then given expression is equivalent to
![\cos ^3\alpha+(-\sin \alpha)^3-(-\sin \alpha)+(-\cos \alpha)\\ \\=\cos ^3\alpha-\sin^3 \alpha+\sin \alpha-\cos \alpha\\ \\=(\cos\alpha-\sin\alpha)(\cos^2\alpha+\cos\alpha\sin\alpha+\sin^2\alpha)-(\cos\alpha-\sin\alpha)\\ \\=(\cos\alpha-\sin\alpha)(1+\cos\alpha\sin\alpha-1)\ \ [\cos^2\alpha+\sin^2\alpha=1]\\ \\=\cos\alpha\sin\alpha(\cos\alpha-\sin\alpha)](https://tex.z-dn.net/?f=%5Ccos%20%5E3%5Calpha%2B%28-%5Csin%20%5Calpha%29%5E3-%28-%5Csin%20%5Calpha%29%2B%28-%5Ccos%20%5Calpha%29%5C%5C%20%5C%5C%3D%5Ccos%20%5E3%5Calpha-%5Csin%5E3%20%5Calpha%2B%5Csin%20%5Calpha-%5Ccos%20%5Calpha%5C%5C%20%5C%5C%3D%28%5Ccos%5Calpha-%5Csin%5Calpha%29%28%5Ccos%5E2%5Calpha%2B%5Ccos%5Calpha%5Csin%5Calpha%2B%5Csin%5E2%5Calpha%29-%28%5Ccos%5Calpha-%5Csin%5Calpha%29%5C%5C%20%5C%5C%3D%28%5Ccos%5Calpha-%5Csin%5Calpha%29%281%2B%5Ccos%5Calpha%5Csin%5Calpha-1%29%5C%20%5C%20%5B%5Ccos%5E2%5Calpha%2B%5Csin%5E2%5Calpha%3D1%5D%5C%5C%20%5C%5C%3D%5Ccos%5Calpha%5Csin%5Calpha%28%5Ccos%5Calpha-%5Csin%5Calpha%29)
Answer:
a trapezoid
Step-by-step explanation:
A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Characteristics of a trapezoid
It has 4 vertices and edges
If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogram
Area of a trapezoid = x (sum of the lengths of the parallel sides) x height
Perimeter = sum of lengths of sides of a trapezoid
Answer:
Step-by-step explanation:
So initially you have a square piece of metal, 15" x 15". You cut out squares from the corners of each side with side length x.
So you'll have a sheet that looks something like this now (assuming the formatting works):
_____
__| |__
| |
|__ __|
|____|
Your original side length was 15, but it has now been reduced by x on each side, so you're now going to have a new side length of 15 - 2x
When you fold the box up, the box will have a height of just x.
So you have a base with lengths (15 - 2x) and (15 - 2x), and a height which is just x.
V = l*w*h
So
V = (15 - 2x)(15 - 2x)(x)
= 225x - 60x^2 + 4x^3
Hope this helps
