Answer:
see explanation
Step-by-step explanation:
consecutive even integers have a difference of 2 between them
for example 2, 4, 6 are 3 consecutive even integers
In general if we let the first integer be k then the next 2 integers are
k + 2 and k + 4
the sum of these equals 4 times the first integer, that is 4k, hence
k + k + 2 + k + 4 = 4k
3k + 6 = 4k ( subtract 3k from both sides )
6 = k
the 3 consecutive integers are
k = 6
k + 2 = 6 + 2 = 8
k + 4 = 6 + 4 = 10
that is 6, 8 and 10
note that sum = 6 + 8 + 10 = 24
and 4 × 6 = 24
confirming the sum of the 3 integers equals 4 times the first integer
You can use factors to solve. Determine all the factor pairs of 24, find the two that are two numbers apart.
1, 24 X
2, 12 X
3, 8 X
4, 6 YES!
Algebraic way to solve using Quadratics:
l = 2 + w
A = lw
A = (2 + w)w Substitute (2 + w) for l
24 = (2 + w)w Substitute 24 in for the area
24 = 2w + w^2 Distribute
w^2 + 2w - 24 = 0 Set equal to 0 (put in standard form)
(w + 6) (w - 4) = 0 Factor
w + 6 = 0 and w - 4 = 0 Set each factor equal to 0.
So w= -6 or w = 4 ... -6 makes no sense for a length! So the width must be 4 and the length will be 4 + 2, which is 6.
To rewrite as a function of x (f(x)), write the equation so that y is by itself on one side of the equal sign and an expression involving only x is on the other side.
f (x) = - x^4
Answer:
34$
Step-by-step explanation:
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