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3 years ago

Combine like terms: 7x^2−5x^3+8x^2−6x^3

Mathematics

1 answer:

Romashka-Z-Leto [24]3 years ago

7 0

Final answer is:

15x^2-11x^3

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3 years ago

Please help!! What Find the Error and explain why it is wrong!

Nata [24]

Answer:

First image attached

The error was done in Step E, because student did not multiply $2\cdot x -8$ by the negative sign in numerator. Step E must be $\frac{2\cdot x -5}{(x+4)\cdot (x-4)}$ .

Second image attached

The error was done in Step C, because the student omitted the $2\cdot a \cdot b$ of the algebraic identity $(a+b)^{2} = a^{2}+2\cdot a\cdot b +b^{2}$ . Step C must be $5\cdot x = x^{2}+4\cdot x + 4$

Step-by-step explanation:

First image attached

The error was done in Step E, because student did not multiply $2\cdot x -8$ by the negative sign in numerator. The real numerator in Step E should be:

$3-(2\cdot x -8)= 3-2\cdot x+8 = 11-2\cdot x$

Hence, Step E must be $\frac{2\cdot x -5}{(x+4)\cdot (x-4)}$ .

Second image attached

The error was done in Step C, because the student omitted the $2\cdot a \cdot b$ of the algebraic identity $(a+b)^{2} = a^{2}+2\cdot a\cdot b +b^{2}$ . Step C must be $5\cdot x = x^{2}+4\cdot x + 4$

And further steps are described below:

Step D

$x^{2}-x+4 = 0$

Which according to the Quadratic Formula, represents a polynomial with complex roots. That is: ( $a = 1$ , $b = -1$ , $c = 4$ )

$D = b^{2}-4\cdot a\cdot c$

$D = (-1)-4\cdot (1)\cdot (4)$

$D = -17$ (Conjugated complex roots)

Step E

$(x-0.5-i\,1.936)\cdot (x-0.5+i\,1.936) = 0$

Step F

$x = 0.5+i\,1.936\,\lor\,x = 0.5-i\,1.936$

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3 years ago

What is the solution of the equation e^xe^2x = 4? Round your answer to the nearest hundredth.

Stells [14]

The equation is:

[e^x] [e^(2x)] = 4

1) Applying property of multiplication of powers wiith same base =>

e ^ (x + 2x) = 4

=> e ^ (3x) = 4

2) Applying logarigth properties

3x = ln(4)

=> x = ln(4) / 3 ≈ 1.38629 / 3 ≈ 0.4621

Answer: x = ln(4) / 3 ≈ 0.4621

8 0

3 years ago