Answer:
![\large\boxed{LCM(x^2-2x-15,\ x^2+2x-3)=(x+3)(x-5)(x-1)}\\\boxed{=x^3-3x^2-13x+15}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7BLCM%28x%5E2-2x-15%2C%5C%20x%5E2%2B2x-3%29%3D%28x%2B3%29%28x-5%29%28x-1%29%7D%5C%5C%5Cboxed%7B%3Dx%5E3-3x%5E2-13x%2B15%7D)
Step-by-step explanation:
![x^2-2x-15=x^2+3x-5x-15=x(x+3)-5(x+3)=(x+3)(x-5)\\\\\\x^2+2x-3=x^2+3x-1x-3=x(x+3)-1(x+3)=(x+3)(x-1)\\\\LCM(x^2-2x-15,\ x^2+2x-3)=(x+3)(x-5)(x-1)\\\\=(x^2-2x-15)(x-1)\qquad\text{use FOIL}\\\\=(x^2)(x)+(x^2)(-1)+(-2x)(x)+(-2x)(-1)+(-15)(x)+(-15)(-1)\\\\=x^3-x^2-2x^2+2x-15x+15\qquad\text{combine like terms}\\\\=x^3+(-x^2-2x^2)+(2x-15x)+15\\\\=x^3-3x^2-13x+15](https://tex.z-dn.net/?f=x%5E2-2x-15%3Dx%5E2%2B3x-5x-15%3Dx%28x%2B3%29-5%28x%2B3%29%3D%28x%2B3%29%28x-5%29%5C%5C%5C%5C%5C%5Cx%5E2%2B2x-3%3Dx%5E2%2B3x-1x-3%3Dx%28x%2B3%29-1%28x%2B3%29%3D%28x%2B3%29%28x-1%29%5C%5C%5C%5CLCM%28x%5E2-2x-15%2C%5C%20x%5E2%2B2x-3%29%3D%28x%2B3%29%28x-5%29%28x-1%29%5C%5C%5C%5C%3D%28x%5E2-2x-15%29%28x-1%29%5Cqquad%5Ctext%7Buse%20FOIL%7D%5C%5C%5C%5C%3D%28x%5E2%29%28x%29%2B%28x%5E2%29%28-1%29%2B%28-2x%29%28x%29%2B%28-2x%29%28-1%29%2B%28-15%29%28x%29%2B%28-15%29%28-1%29%5C%5C%5C%5C%3Dx%5E3-x%5E2-2x%5E2%2B2x-15x%2B15%5Cqquad%5Ctext%7Bcombine%20like%20terms%7D%5C%5C%5C%5C%3Dx%5E3%2B%28-x%5E2-2x%5E2%29%2B%282x-15x%29%2B15%5C%5C%5C%5C%3Dx%5E3-3x%5E2-13x%2B15)
Step-by-step explanation:
the third angle in a triangle= 70
Answer:
There will be 916 ants alive after 4 months.
Step-by-step explanation:
Step 1
Let's change the percentage to a decimal by dividing by a 100.
6.5% / 100 = .065
Step 2
So, for the first month we will multiply the initial amount of ants by .065 and this will give us the number of ants that die.
1200 * .065 = 78
This means that after the first month, 1200 - 78 = 1122 ants will be alive.
Step 3
Now for the second month: 1122 * .065 = 72.93 (rounded to 73)
1122 - 73 = 1049 ants will be alive
Step 4
For the third month 1049 * .065 = 68.185 (rounded to 68)
1049 - 68 = 981 ants will be alive
Step 5
For the fourth month 981 * .065 = 63.765 (rounded to 64)
981 - 64 = 916 ants will be alive
Hope this helps!
Circumference = 2 x radius x Pi
Circumference = 2 x 0.8 x pi
Circumference = 1.6pi or 5.024 yards
area = r^2 x pi
Area = 0.8^2 x pi
Area = 0.64pi or 2.0096 square yards