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3 years ago

Factor completely 4x4 − 24x3 + 36x2.

Mathematics

1 answer:

ipn [44]3 years ago

6 0

The previous answer from another person got deleted, so I'm here to put it back in my own words.

(Edit: The answer is A)

First of all, you can take 4 out of each, so simplify everything by 4.

4(x^4 - 6x^3 + 9x^2)

Next, you can see that you're able to take out x^2

4x^2(x^2 - 6x + 9)

You can see that both x^2 and 9 are perfect squares, meaning you can crunch them together like this

(x+3)^2 or (x-3)^2

Of course, only one would work, and as fate has it, (x-3)^ produces x^2 - 6x + 9

This would turn the now factored equation into :

4x^2(x-3)^2 or 4x^2(x-3)(x-3), this means the answer is A

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Simplify $\frac{1+\sqrt{2}}{2+\sqrt{3}}$. Your solution can be converted to the form $A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})$, where

Zina [86]

Answer:

A+B+C+D = 13

Step-by-step explanation:

The given expression is:

$\dfrac{1+\sqrt{2}}{2+\sqrt{3}}$

We have to simply it and express it in the form of:

$A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})$

Multiply and divide the given expression with $2-\sqrt 3$ :

$\dfrac{1+\sqrt{2}}{2+\sqrt{3}} \times \dfrac{2-\sqrt 3}{2-\sqrt 3}\\\Rightarrow \dfrac{(1+\sqrt{2}) \times (2-\sqrt 3)}{(2+\sqrt{3})\times (2-\sqrt 3)}\\\Rightarrow \dfrac{2+2\sqrt2-\sqrt3-\sqrt6}{2^2-(\sqrt{3})^2}\\\Rightarrow \dfrac{2+2\sqrt2-\sqrt3-\sqrt6}{4-3}\\\Rightarrow \dfrac{2(1+\sqrt2)-(\sqrt3+\sqrt6)}{1}\\\Rightarrow 2(1+\sqrt2)-(\sqrt3+\sqrt6)$

It is the simplified form of given expression.

Formula used:

$(a+b)(a-b) = a^{2} -b^{2}$

Comparing the simplified expression with $A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})$

$2(1+\sqrt2)-(\sqrt3+\sqrt6)=A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})\\\Rightarrow A =2, B=2, C=3\ and\ D=6$

So, value of

$A+B+C+D = 2+2+3+6 = 13$

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4 years ago

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The answer is the third option.

m = 7.5h

The h value multiplied by 7.5 will give you the m value.

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3 years ago

Given the two functions, which statement is true? fx = 3^4, g(x) = 3^x + 5

Neko [114]

Answer:

third option

Step-by-step explanation:

Given f(x) then f(x) + c represents a vertical translation of f(x)

• If c > 0 then shift up by c units

• If c < 0 then shift down by c units

Given

g(x) = $3^{x}$ + 5 ← this represents a shift up of 5 units

Thus g(x) is the graph of f(x) translated up by 5 units

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3 years ago

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During samuels experiment, the experimental probability was 0.25. What else must be true about the experiment?

cupoosta [38]

Answer: the experimental probability of the outcome is 1/4

Step-by-step explanation:

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A parallelogram has a base of length xplus 7 and a height of xplus 2 and has an area of 50 square units. Find the base and heigh

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Hello,

$(x+7)(x+2)=50\\\Rightarrow\ x^2+9x+14=50\\\Rightarrow\ x^2+9x-36=0\\\Rightarrow\ x^2+12x-3x-36=0\\\Rightarrow\ x(x+12)-3(x+12)=0\\\Rightarrow\ (x+12)(x-3)=0\\\Rightarrow\ x=-12\ or\ x=3\\If \ x=-12\ then\ x+7$

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4 years ago