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mash [69]
3 years ago
5

Can anyone help me?

Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
8 0

Answer:

The factored form of 4<em>m</em>³ – 28<em>m</em>² – 120<em>m</em> is 4<em>m</em>(<em>m</em> – 10)(<em>m</em> + 3). The zeroes of the function would be <em>m</em> = 0, <em>m</em> = –3, and <em>m</em> = 10.

Step-by-step explanation:

I'll give this a shot.

4<em>m</em>³ – 28<em>m</em>² – 120<em>m</em> = 0 — The original expression

4<em>m</em>³ – 28<em>m</em>² – 120<em>m</em> — Did that 0 have any purpose? I just deleted it.

4(<em>m</em>³ – 7<em>m</em>² – 30<em>m</em>) — There's a common factor in here, 4. Let's pull that aside.

4m(<em>m²</em> – 7<em>m</em> – 30) — Actually, there's <em>two</em> common factors. The second one is <em>m</em>! Let's pull <em>that</em> out too!

To factor an expression, you have to break apart the middle term, so to speak. That's only possible if you can find two numbers whose product equals that of the outside terms and whose sum equals the middle term. Here, I'm just dealing with numbers and putting that variable aside.

–30 = 10 × –3

–30 = –10 × 3

–30 = –2 × 15

–30 = 2 × –15 — To solve for any potential factors, let's find all the numbers integers that multiply to –30

Now let's see which one adds up to –7!

15 – 2 = 13 — it's not this one

2 – 15 = –13 — nor this one

10 – 3 = 7 — we're pretty close! Let's switch that negative

3 – 10 = –7 — here we go! Here's our numbers!

4<em>m</em>[(<em>m</em>² – 10<em>m</em>) + (3<em>m</em> – 30)] — now we break apart the middle term. This is <em>all</em> multiplied by 4<em>m</em>, so that still encases everything with brackets.

4<em>m</em>[<em>m</em>(<em>m</em> – 10) + 3(<em>m</em> – 10)] — Factoring the two expressions

4<em>m</em>(<em>m</em> + 3)(<em>m</em> – 10) — simplifying to find our answer! Ta-da!

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Drag values to complete each equation.
Alex777 [14]

Answer:

1. A. 1

2. D. 17^9

Step-by-step explanation:

Properties used:

  • Power of a Power Property
  • Product Property
  • Quotient Property
  • Zero Exponent Property

1. First, let's deal with the numerator.

(17^3)^6 can be turned into 17^1^8 by using the Power of a Power Property.

And then use the Product Property, (17^1^8)(17^-^1^0) = 17^8

So now, our fraction is this: \frac{17^8}{17^8}

All number over itself in a fraction is equal to 1. But you can also do this the mathmatic way using the Quotient Property: \frac{a^m}{a^n} = a^m^-^n or \frac{1}{a^(^n^-^m^)}. Which then you plug the numbers in: \frac{17^8}{17^8} = 17^8^-^8 = 17^0. And since we know that in Zero Exponent Property: a^0 = 1, we can see that 17^0 = 1. So either way, we get 1.

So the answer is 1, which is A

2. Power of a Power Property: (a^m)^n = a^m^n

So plug the numbers in the property: (17^{6}) ^3= 17^1^8

Product Property: (a^m)(a^n) = a^m^+^n

We plug the equation in with (17^{6}) ^3 turned into 17^1^8 ---

(17^1^8)(17^-^9) = 17^1^8^-^9 = 17^9

So the answer is 17^9, which is D

I hope this helps!
Please give Brainliest!

Have a great day!

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