Answer:
(2x-1)(2x+1)(x^2+2) = 0
Step-by-step explanation:
Here's a trick: Use a temporary substitution for x^2. Let p = x^2. Then 4x^4+7x^2-2=0 becomes 4p^2 + 7p - 2 = 0.
Find p using the quadratic formula: a = 4, b = 7 and c = -2. Then the discriminant is b^2-4ac, or (7)^2-4(4)(-2), or 49+32, or 81.
Then the roots are:
-7 plus or minus √81
p= --------------------------------
8
p = 2/8 = 1/4 and p = -16/8 = -2.
Recalling that p = x^2, we let p = x^2 = 1/4, finding that x = plus or minus 1/2. We cannot do quite the same thing with the factor p= -2 because the roots would be complex.
If x = 1/2 is a root, then 2x - 1 is a factor. If x = -1/2 is a root, then 2x+1 is a factor.
Let's multiply these two factors, (2x-1) and (2x+1), together, obtaining 4x^2 - 1. Let's divide this 4x^2 - 1 into 4x^4+7x^2-2=0. We get x^2+2 as quotient.
Then, 4x^4+7x^2-2=0 in factored form, is (2x-1)(2x+1)(x^2+2) = 0.
Answer:
There are 604,800 possible permutations.
Step-by-step explanation:
The order in which the digits are chosen is important, which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
In this question:
7 digits from a set of 10(10 digits to 0-9). So
There are 604,800 possible permutations.
Answer:
required time is here 45 minutes
Step-by-step explanation:
given data
apples = 100
bananas = 100
oranges = 100
pears = 100
solution
we have here 4 different kind of fruit
so that it is possible for each kind of fruit is
each kind of fruit is = 4 × 11 = 44
so each kind contain 11 fruit
as that 45th fruit make a dozen
now 1 fruit is pick every minute
'so we take here 45 minute to pick up 45 fruit
so that required time is here 45 minutes
37 is 25% of 148; 148 is 400% of 37
Step-by-step explanation:
Let us solve the questions one by one
"37 is ____ % of 148"
Let x be the percentage
Then
to convert in percentage, multiplying by 100
= 25%
"148 is ____ % of 37"
Let y be the percentage
then
To convert into percentage, multiplying by 100
= 400%
Hence,
37 is 25% of 148; 148 is 400% of 37
Keywords: Percentage, percent
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