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:
im not sure, i will try to figure it out for you
Step-by-step explanation:
y=kx+b
for (7,-8): -8=7k+b. (function 1)
for (-4,6): 6=-4k+b (function 2)
Use function 2 - function 1
we get: 14=-11k
k=-14/11------>slope is -14/11
Now we know that first two options are wrong since they have the wrong slope for the function.
Plus -14/11 back to function 1/ or 2. Both are correct and can give you the answer. In this case I would plug it back to function 2.
6=14*4/11+b
b=66/11-56/11
b=10/11
We get y=-14/11x+10/11
subtract both side by 6.
y-6=-14/11x+10/11-66/11
y-6=-14/11x-56/11
y-6=-14/11(x+4)
So C is correct
Answer:
Side D is 0.78 feet (to 2 s.f.)
Step-by-step explanation:
In the Scale Drawing, side D=24 centimeters
1 foot = 30.48cm
x foot = 24 cm
Therefore:
24 X 1 = 30.48 X x
x= 24/30.48 =0.7874 feet
Side D is 0.78 feet (to 2 s.f.)
Answer:
(a) It costs $55 at Happy Fruiterer
(b) It will cost $49.64
(c) It is cheaper at Happy Fruiterer the second week
Step-by-step explanation:
Since Fruitz shop sells as 10% less than Happy Fruiterer at $50
10% more of $50 = 50 × 10/100 + 50
= $5 + $50 = $55
(a) n Kg of grapes will cost $55 at Happy Fruiterer
(b) if Happy Fruits discounts $55 by 5%, we will have
55 × 5/100 = 2.75
that is $55 - $2.75 = $52.25
If it is discounted further at 5% more the following week, we will have
$52.25 × 5/100 = $2.6125
≈ $2.61
Then the new price for the 2nd week is $52.25 - $2.61
= $49.64
(c) at the second wee of discounting, Fruitz shop still sells at $50 will Happy Fruiterer now see at $49.64. Therefore, it is cheaper at Happy Fruiterer
