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:
The equation is: <em>y</em> = 15·<em>x</em>
Step-by-step explanation:
It is provided that at the Speedy Bike Works, 15 bicycles are produced each hour.
Consider the table below.
Number of Hours: 1 3 6 10
Number of Bicycles Produced: 15 45 90 150
Compute the ratio of number of bicycles produced and number of hours for every data above as follows:
The ratio of the number of bicycles produced and number of hours is same for every data value.
Thus, the relationship between the number of bicycles produced and number of hours is proportional.
The equation for the relationship is:
<em>y</em> = 15·<em>x</em>
<em>y</em> = number of bicycles produced
<em>x</em> = number of hours
Answer:35 minutes
Step-by-step explanation:
$30.00 - $25.45= $4.55/$.13= 35 minutes
Answer:
METHOD 1:
5x+7(x+1)=5x-21
5x+7x+7=5x-21
12x+7=5x-21
12x-5x=-21-7
7x=-28
x=28/7
x=4
METHOD 2:
5x+7(x+1)=5x-21
5x+7(x+1)=5x-21-5x
7(x+1)=-21
7x+7=-21
7x=-28
x=4
Step-by-step explanation:
METHOD 1:
5x+7(x+1)=5x-21
5x+7x+7=5x-21
12x+7=5x-21
12x-5x=-21-7
7x=-28
x=28/7
x=4
METHOD 2:
5x+7(x+1)=5x-21
5x+7(x+1)=5x-21-5x
7(x+1)=-21
7x+7=-21
7x=-28
x=4
Answer:
- 35 grams of 11.43% solution
Step-by-step explanation:
The end solution has same volume as initial volumes of mixture.
The concentration of solution is calculated as below
- 10*0.15 + 25*0.1 = 4 g
- 4 / 35*100% = 11.43% (rounded)
