Factor the numerator and denominator...
(n^4-5n^2-6n^2+30)/(n^4-2n^2-5n^2+10)
[n^2(n^2-5)-6(n^2-5)]/[n^2(n^2-2)-5(n^2-2)]
[(n^2-5)(n^2-6)]/[(n^2-5)(n^2-2)] notice the (n^2-5)s cancel out
(n^2-6)/(n^2-2)
We could further factor this because each is a difference of squares to:
[(n+√6)(n-√6)]/[(n+√2)(n-√2)
2x - y = -24
x + 7y = 3
Solve one equation for a variable and plug the resulting value into the second equation.
x + 7y = 3 Subtract 7y from both sides
x = -7y + 3
Now, plug that x-value into the x of the first equation.
2x - y = -24 Plug in the x-value
2(-7y + 3) - y = 24 Use the Distributive Property
-14y + 6 - y = -24 Combine like terms (-14y and -y)
-15y + 6 = -24 Subtract 6 from both sides
-15y = -30 Divide both sides by 15
y = 2
Next, plug the y-value back into the second equation.
x + 7y = 3 Plug in the y-value
x + 7(2) = 3 Multiply
x + 14 = 3 Subtract 14 from both sides
x = -11
y = 2 and x = -11
Answer:
10,404/334,084
Step-by-step explanation:
Given the polynomial
289r^2 - 102r + c
We are to find the value of c that will make it a perfect square
Divide through by 289
289r²/289 - 102r/289 + c/289
Half of the coefficient of r is 1/2(102/289)
Half of the coefficient of r = 102/578
Square the result
r² = (102/578)²
r² = 10,404/334,084
Hence the required constant is 10,404/334,084
In the equation: -6x - 19 - 4x replace x with -2
-6(-2) - 19 - 4(-2)
Use your rules of PEMDAS to evaluate
12 - 19 + 8
-7 + 8
1
Hope this helped!
~Just a girl in love with Shawn Mendes
<span>N + D = 55 coins (1) (N stands for nickels,
5N + 10D = 390 cents (2) D stands for dimes)
Simplify (2) by canceling the factor 5 in both sides:
N + 2D = 78 (3)
Subtract eq(1) from eq(3). You will get
D = 78 - 55 = 23.
Answer. 23 dimes and 55-23 = 32 nickels.
Check. 23*10 + 32*5 = 390 cents</span>
