We can find roots by setting f(x) = 0 --> x^4 - x^3 - 13x^2 + x + 12 = 0.
Factoring f(x) to make things easier for us gives us (x - 1)(x + 1)(x - 4)(x + 3), which, equal to 0, gives us the ability to set each set of parentheses = 0.
x - 1 = 0 gives us x = 1.
x + 1 = 0 --> x = -1.
x - 4 = 0 --> x = 4.
x + 3 = 0 --> x = -3.
our roots are x = 1, -1, 4, and -3.
Answer:
e = 7.5
Step-by-step explanation:
Hi,
15 = e/0.5
You need to find what e equals. To do that, you need e all by itself. So to get e by itself in this equation, you need to multiply by 1/2 (same thing as 0.5). 15 x 0.5 is equal to 7.5.
To check your work, 7.5/0.5 is equal to 15.
So you know it's correct.
I hope this helps you :)
The answer is chicken $8, duck $5
x - the cost of a chicken
y - the cost of a duck
<span>he sold 50 chickens and 30 ducks for $550: 50x + 30y = 550
</span><span>he sold 44 chickens and 36 ducks for $532: 44x + 36y = 532
</span>50x + 30y = 550 divide by 10
44x + 36y = 550 divide by 4
______________
50x/10 + 30y/10 = 550/10
44x/4 + 36y/4 = 532/4
______________
5x + 3y = 55 Multiply by (-3)
11x + 9y = 133
______________
5x * (-3) + 3y * (-3) = 55 * (-3)
11x + 9y = 133
______________
-15x - 9y = -165
11x + 9y = 133
______________
Sum up:
-4x + 0y = -32
-4x = -32
x = -32/-4
x = 8
Since 5x + 3y = 55 and x = 8, then:
5 * 8 + 3y = 55
40 + 3y = 55
3y = 55 - 40
3y = 15
y = 15/3
y = 5
Answer: 267.947 (or 267.95) inches^3
Step-by-step explanation:
The formula for the volume of a sphere is 
.
To find your radius (r), divide the diameter of 8 inches by 2. <em>The radius is 4 inches.</em>
Plug in your numbers to the volume equation to get 
. The first step is to cube 4 (4*4*4) to get <em>64</em>. Now your equation is 
.
Multiply 3.14 and 64 to get <em>200.96</em>. The equation is now 
or 
.
Multiply the numerators (4 * 200.96) and denominators (1 * 3) to get a final equation of 
.
Finally, divide 803.84 by 3 to get the final answer of 267.947 in^3.
