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:
D. 28.54
Step-by-step explanation:
To find the area of the shaded region, find the area of the circle and divide it in 4. This will the area of the portion with the triangle.
Now, find the area of the triangle and subtract the two. The resulting value will be the area of the shaded region.
Circle:

Divide by 4 for the area of the section with the triangle.
314/4 = 78.5
Triangle:

Subtract the two, 78.5 - 50 = 28.5.
a = 3, b= - 4 and c = - 4
expand the left side using FOIL
(2x + 1)(ax + b) = 2ax² + 2bx + ax + b = 2ax² + x(2b + a) + b
compare the coefficients of expressions on left and right sides.
compare 2ax² + x(2b +a) + b with 6x² - 5x + c
coefficients of x² terms → 2a = 6 ⇒ a = 3
coefficients of x terms → 2b + a = - 5 → 2b + 3 = - 5 → 2b = - 8 ⇒ b = - 4
constant terms c = b = - 4
Answer:
y= 8000x + 2000
Step-by-step explanation:
to find the formula we can use the points given in the question:
the slope:
to get the slope we can take the 2 points, (0,2000) and (2,18000) where x values are time and y values are bacteria
now using slope-intercept form we can get
which gives a slope of 8000 meaning for each hour there are 8000 new bacteria
intercept:
since we start with 2000 bacteria we know this is the y intercept so when x is 0
formula:
y=8000x + 2000