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nignag [31]
3 years ago
11

Compare and Contrast how you would factor x^2−9 and x^2+9. For full credit, make sure you explain why they are factored differen

tly.
Mathematics
1 answer:
marishachu [46]3 years ago
7 0

The factored form of the expression x^2 - 9 is (x+3)(x-3)

The expression x^2 + 9 has no real roots hence cannot be factored

Quadratic equations are equations with a degree of 2.

Given the quadratic function x^2-9 \ and \ x^2+9

For the function x^2 - 9

=x^2-9\\=x^2-3^2

Using the difference of two squares:

a^2-b^2=(a-b)(a+b)\\x^2-3^2=(x-3)(x+3)

For the expression x^2 + 9

The expression x^2 + 9 has no real roots hence cannot be factored

Learn more on factorization here: brainly.com/question/20293447

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Jennifer has run many marathons and keeps track of all of her finishing times. At a marathon last month, she finished in 350 min
suter [353]

Answer:

16%

Step-by-step explanation:

406 / 350 = 1.16

406 is 116% of 350

so 350 + 16% is 406

because 350 * 0.16 = 56

56 is 16%

350 + 56 = 406

:)

3 0
3 years ago
2ᵃ = 5ᵇ = 10ⁿ.<br> Show that n = <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bab%7D%7Ba%20%2B%20b%7D%20" id="TexFormula1" titl
11Alexandr11 [23.1K]
There are two ways you can go about this: I'll explain both ways.
<span>
</span><span>Solution 1: Using logarithmic properties
</span>The first way is to use logarithmic properties.

We can take the natural logarithm to all three terms to utilise our exponents.

Hence, ln2ᵃ = ln5ᵇ = ln10ⁿ becomes:
aln2 = bln5 = nln10.

What's so neat about ln10 is that it's ln(5·2).
Using our logarithmic rule (log(ab) = log(a) + log(b),
we can rewrite it as aln2 = bln5 = n(ln2 + ln5)

Since it's equal (given to us), we can let it all equal to another variable "c".

So, c = aln2 = bln5 = n(ln2 + ln5) and the reason why we do this, is so that we may find ln2 and ln5 respectively.

c = aln2; ln2 = \frac{c}{a}
c = bln5; ln5 = \frac{c}{b}

Hence, c = n(ln2 + ln5) = n(\frac{c}{a} + \frac{c}{b})
Factorise c outside on the right hand side.

c = cn(\frac{1}{a} + \frac{1}{b})
1 = n(\frac{1}{a} + \frac{1}{b})
\frac{1}{n} = \frac{1}{a} + \frac{1}{b}

\frac{1}{n} = \frac{a + b}{ab}
and thus, n = \frac{ab}{a + b}

<span>Solution 2: Using exponent rules
</span>In this solution, we'll be taking advantage of exponents.

So, let c = 2ᵃ = 5ᵇ = 10ⁿ
Since c = 2ᵃ, 2 = \sqrt[a]{c} = c^{\frac{1}{a}}

Then, 5 = c^{\frac{1}{b}}
and 10 = c^{\frac{1}{n}}

But, 10 = 5·2, so 10 = c^{\frac{1}{b}}·c^{\frac{1}{a}}
∴ c^{\frac{1}{n}} = c^{\frac{1}{b}}·c^{\frac{1}{a}}

\frac{1}{n} = \frac{1}{a} + \frac{1}{b}
and n = \frac{ab}{a + b}
4 0
3 years ago
If 3/8 of my money is $3840.00. How much did I have at first? *
NNADVOKAT [17]

Answer:

E $10240.00

Step-by-step explanation:

The total amount of money is x.

3/8 × x = 3840

Multiply both sides by the reciprocal of 3/8 which is 8/3.

x = 3840 × 8/3

x = 10240

Answer: E $10240.00

7 0
2 years ago
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V= \frac{1}{3} \pi r^2h \\  \\ 3V= \pi r^2h \\  \\ h= \cfrac{3V}{\pi r^2}
6 0
3 years ago
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Goodmorning hope you have a great day :)
zalisa [80]

Answer:

hello good morning.have a nice day

6 0
2 years ago
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