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3 years ago

Factoring: All Techniques Combined

1 answer:

Ber [7]3 years ago

8 0

$x^{6} + 2 x^{4} - 16 x^{2} - 32 =x^4(x^2+2)-16(x^2+2)=(x^2+2)(x^4-16)=\\ \\=(x^2+2)(x^4-4^2)=(x^2+2)(x^2-4)(x^2+4) =\\ \\=(x^2+2)(x^2+4)(x+2)(x-2) \\ \\ \\a^2-b^2 =(a-b)(a+b)$

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You have 200 items that cost $20 and you are selling them at the price of $100.

allochka39001 [22]

Your total profit is $13,000. First you bought the 200 items for $20 each. That costs $4,000. Then you sold $50 of the items at $100 each. That’s $5,000. So already you’re in the green. You’ve already made $1,000 profit. Then you sold the rest of the items at a 20% discount. 150 items multiplied by $80 is $12,000. $12,000 plus the $1,000 equals $13,000 total.

3 0

3 years ago

Read 2 more answers

Two prisms are similar and their ratio of similarity is 3:8.

trapecia [35]

Answer:

8.63 square units

Step-by-step explanation:

you must set up a proportion.

3 x

- = -

8 23

after you set up that proportion, cross multiply to find x.

8x = 69

divide by 8

x = 8.625, rounded to 8.63

5 0

2 years ago

A model for tumor growth is given by the Gompertz equation dV dt = a (In b-, In V) V where a >0 and b >0 are constants and

Xelga [282]

Answer:

$V(t) = b^{(1-e^{-at})}$

Step-by-step explanation:

We are given the following information in the question:

$\displaystyle\frac{dV}{dt} = a (In b - In V) V$

where a > 0 and b > 0.

$\displaystyle\frac{dV}{dt} = a (In b-In V) V\\\\\displaystyle\frac{dV}{dt} = -aV(ln\frac{V}{b})\\\\\frac{dV}{V(ln\frac{V}{b})} = (-a)dt\\\\\text{Put } ln\frac{V}{b} = z\\\\\text{Integrating both sides}\\\\\int \frac{dV}{V(ln\frac{V}{b})} = \int (-a)dt\\\\\text{We get}\\\\\int \frac{dz}{z} = \int (-a)dt\\\\\\\text{where C is the constant of integration}$

$V(0) = 1~ mm^3\\V(t) = b.e^{e^{-at+C}}\\\text{Putting t =0, V(0) = 1}\\\\V(0) = 1 = b.e^{e^{C}}\\\\V(t) = b^{(1-e^{-at})}$

where v(t) is the required tumor volume as a function of time that has an initial tumor volume of V(0) = 1 cubic mm.

5 0

3 years ago

-8 -8x + 10 + 6x = 19

hram777 [196]

Answer:

x = -8.5

Step-by-step explanation:

Let's rearrange the question to find x :)

-8x + 6x + 10 - 8 = 19

-2x + 2 = 19

-2 -2

-2x = 17

/-2 /-2

x = -8.5

4 0

3 years ago

Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushe

Ugo [173]

Answer: it was probably more chocolaty because he added 5 teaspoons instead of 4 which is 2 doubled

Step-by-step explanation:

4 0

3 years ago