We have
![81-49n^4=9^2-(7n^2)^2](https://tex.z-dn.net/?f=81-49n%5E4%3D9%5E2-%287n%5E2%29%5E2)
so this is indeed a difference of squares. Factorizing would give
![81-49n^4=(9-7n^2)(9+7n^2)](https://tex.z-dn.net/?f=81-49n%5E4%3D%289-7n%5E2%29%289%2B7n%5E2%29)
making the answer D.
We can further factor the first term here and write
![9-7n^2=3^2-(\sqrt 7\,n)^2=(3-\sqrt7\,n)(3+\sqrt7\,n)](https://tex.z-dn.net/?f=9-7n%5E2%3D3%5E2-%28%5Csqrt%207%5C%2Cn%29%5E2%3D%283-%5Csqrt7%5C%2Cn%29%283%2B%5Csqrt7%5C%2Cn%29)
but that's clearly out of the scope of this question.
Answer: Width = 3cm
Length = 8cm
Step-by-step explanation:
Length = x+5 cm
Width = xcm
Area = 24cm²
Area of a rectangle = length × width
x × (x + 5) = 24
x² + 5x = 24
x² + 5x - 24 = 0
x² + 8x - 3x - 24 = 0
x(x + 8) - 3(x + 8) = 0
x - 3 = 0
x = 3
Width = 3cm
Since length = x + 5 = 3 + 5 = 8cm
Length = 8cm
Answer:
2 exponents (2) times 5 exponents (3)
Step-by-step explanation:
To find the prime factors you start by dividing the number by the first prime number which is 2 if there is not a remainder meaning you can divide evenly anymore write down how many 2's you were able to divide by evenly now try dividing by the the next prime factor which is 3 the goal is to get to a quotient of 1
Answer:
3.14 square units
Step-by-step explanation:
Circumference of a circle = 2πr
2πr = 6.28
r = 6.28/2π
r = 3.142/π
Area of a circle = πr^2
slot in the value of r
Area of the circle = π( 3.142/π)^2
" = π(9.87/ π^2)
" = 9.87/π
π = 3.14
Area of a circle = 9.867/ (3.14)
" = 3.14 square units
Answer:
x=-5 or x=3
Step-by-step explanation:
when multiplying anything by 0, the answer will be zero
In this case, one of the two factors has to be equal to 0
start by splitting into
(x+5) = 0
solve the equation
subtract 5 from both sides
x = -5
now, repeat for the other binomial
x-3 = 0
add 3 to both sides
x=3