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3 years ago

Please help I’m a bit confused on this I appreciate answers!

Mathematics

1 answer:

Afina-wow [57]3 years ago

5 0

Answer:

$(2x^3)^3=8\cdot x^{9}$

Step-by-step explanation:

Properties of Exponents

The property called Power to a Power shows us how to simplify expressions of the type:

$(x^n)^m=x^{n*m}$

Similarily the property called Power of a product simplifies expressions like:

$(x.y)^n=x^n.y^n$

The company mentioned in the question uses the expression

$(2x^3)^3$

millimeters per second to calculate the maximum capacity of a photocell with an area of x^3 square millimeters.

First, use the power of a product property:

$(2x^3)^3=2^3\cdot (x^3)^3$

Now use the power to a power property:

$(2x^3)^3=2^3\cdot x^{3*3}$

Operate:

$\mathbf{(2x^3)^3=8\cdot x^{9}}$

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3 years ago

Write 2x+y=17 in slope-intercept form

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Answer:

Step-by-step explanation:

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Step 1: Add -y to both sides.

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3 years ago

how do you rewrite : y=x^2-5x+9 in standard form using complying the square? I keep getting to : x^2-5x-25/4 but I’m not allowed

yawa3891 [41]

I presume with this you meant to say you want this equation in general form, also known as vertex form, which is y = a(x - h)² + k, instead of standard form, which is y = ax² + bx + c, which is what the original equation is already in.

So with completing the square, you first have to isolate the x-terms. To do this, subtract 9 on both sides of the equation:

$y-9=x^2-5x$

Next, we want to make the right side of the equation a perfect square. To find the constant of this soon-to-be perfect square, divide the x-coefficient by 2 and square that quotient. In this case:

$-5\div 2 = -\frac{5}{2}\\\\(-\frac{5}{2})^2=-\frac{5}{2}\times-\frac{5}{2}=\frac{25}{4}$

Now add 25/4 on both sides of the equation:

$y-9+\frac{25}{4}=x^2-5x+\frac{25}{4}$

Now to combine -9/1 and 25/4, they must have the same denominator, and to find it you must find the LCD, or lowest common denominator, of 1 and 4. To find it, list the multiples of both and the lowest one they share is their LCD. In this case, the LCD is 4. Multiply both sides of -9/1 by 4/4 and then add the numerators up:

$-\frac{9}{1}\times \frac{4}{4}=-\frac{36}{4}\\\\-\frac{36}{4}+\frac{25}{4}=-\frac{11}{4}\\\\y-\frac{11}{4}=x^2-5x+\frac{25}{4}$