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2 years ago

Graphf(x)=x and g(x)=5x+1.

Mathematics

1 answer:

matrenka [14]2 years ago

4 0

Blue line is g(x) and red line is x

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Four students are trying to determine what number must replace the question (x^2)^7=x^4*x^8 in order to make it true

tiny-mole [99]

Answer:

Joe is correct

Step-by-step explanation:

Given equation:

$(x^2)^?=x^4 \cdot x^8$

The exponent outside the bracket is a question mark and the students are trying to determine the value of the question mark.

For ease of answering, let y be the unknown number (question mark):

$\implies (x^2)^y=x^4 \cdot x^8$

First, simplify the equation by applying exponent rules to either side of the equation:

$\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}\quad\textsf{to the left side}:$

$\implies (x^2)^y=x^4 \cdot x^8$

$\implies x^{2y}=x^4 \cdot x^8$

$\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c} \quad \textsf{to the right side}:$

$\implies x^{2y}=x^4 \cdot x^8$

$\implies x^{2y}=x^{4+8}$

$\implies x^{2y}=x^{12}$

Now, apply the exponent rule:

$x^{f(x)}=x^{g(x)} \implies f(x)=g(x)$

Therefore,

$x^{2y}=x^{12}\implies 2y=12$

Finally, solve for y:

$\implies 2y=12$

$\implies 2y \div 2 = 12 \div 2$

$\implies y=6$

Therefore, <u>Joe is correct</u> as the unknown number is 6.

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1 year ago

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By which matrix should you multiply vector [1 3] to rotate it 180°?

Ksivusya [100]

Answer:

Step-by-step explanation:

Rotation 180° is accomplished by negating both the x- and y-coordinates. That is, you multiply each of them by -1. You want the opposite of the identity matrix, so matrix B.

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The subtraction model to the left

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INCREASE THE AMOUNT OF 1;37500

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Where’s the image? I don’t see it

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