20 edges
F=12, V=10
V -E+F=2
10-E+12=2
-E+22=2
-E=-20
E=20
Answer:
Perpendicular
Step-by-step explanation:
To tell if the lines are perpendicular/parallel, you must look at the slope, but in this case, you must first get y by itself, like so:
3x + 7y = 15
-3x - 3x
___________
7y = -3x + 15
<em><u>Divide both sides by 7:</u></em>
y = 
<em><u>Now the other equation:</u></em>
7x - 3y = 6
-7x -7x
_________
-3y = -7x + 6
<em><u>Divide both sides by -3:</u></em>
y = 
You can see that the lines are perpendicular because the slopes (
and
) are opposite reciprocals.
Answer:
(x+2)(x−10)
Step-by-step explanation:
x^2-8x-20
Factoring means something like this:
(x+_)(x+_)
Add together to get -8
Multiply together to get -20
think of the two numbers
Try 2 and -10:
2+-10 = -8
2*-10 = -20
Fill in the blanks of with 2 and -10 to get
(x+_)(x+_) = (x+2)(x−10)
I hope it's right!
To make things easier, first rewrite
<em>f(x)</em> = <em>x</em> / (<em>x</em> + 7/<em>x</em>) = <em>x</em> ² / (<em>x</em> ² + 7)
i.e. multiply <em>f</em> by <em>x</em>/<em>x</em>, which is valid because <em>x</em> can't be 0 anyway as it's outside the domain of <em>f</em>.
Now, by the quotient and chain rules, we get
<em />
<em>f '(x)</em> = ((<em>x</em> ² + 7) (<em>x</em> ²)' - <em>x</em> ² (<em>x</em> ² + 7)') / (<em>x</em> ² + 7)²
… = (2<em>x</em> (<em>x</em> ² + 7) - <em>x</em> ² (2<em>x</em>)) / (<em>x</em> ² + 7)²
… = (2<em>x</em> ³ + 14<em>x</em> - 2<em>x </em>³) / (<em>x</em> ² + 7)²
… = 14<em>x</em> / (<em>x</em> ² + 7)²
<em>f ''(x)</em> = ((<em>x</em> ² + 7)² (14<em>x</em>)' - (14<em>x</em>) ((<em>x</em> ² + 7)²)') / ((<em>x</em> ² + 7)²)²
… = (14 (<em>x</em> ² + 7)² - (14<em>x</em>) (2 (<em>x</em> ² + 7)² (<em>x</em> ² + 7)')) / (<em>x</em> ² + 7)⁴
… = (14 (<em>x</em> ² + 7)² - (14<em>x</em>) (2 (2<em>x</em>) (<em>x</em> ² + 7)²)) / (<em>x</em> ² + 7)⁴
… = (14 (<em>x</em> ² + 7)² - 4<em>x</em> (14<em>x</em>) (<em>x</em> ² + 7)²) / (<em>x</em> ² + 7)⁴
… = 14 (<em>x</em> ² + 7)² (1 - 4<em>x</em>) / (<em>x</em> ² + 7)⁴
… = 14 (1 - 4<em>x</em>) / (<em>x</em> ² + 7)²
… = (14 - 56<em>x</em>) / (<em>x</em> ² + 7)²
Answer:
Cereal A is cheaper by $0.15
Step-by-step explanation:
Cost of a 10-ounce box of Cereal A = $2.70
So,
Cost of a 1-ounce box of Cereal A = 
Cost of a 15-ounce box of Cereal A = 
Also,
Cost of a 13-ounce box of Cereal B = $3.64
So,
Cost of a 1-ounce box of Cereal B = 
Cost of a 15-ounce box of Cereal B = 
Here,
Cost of a 15-ounce box of Cereal B - Cost of a 15-ounce box of Cereal A = 
Therefore,
Cereal A is cheaper by $0.15