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3 years ago

2. Simplify. 10(x + 2)(x – 3) 5(x - 3)(x + 6)

Mathematics

2 answers:

Mariana [72]3 years ago

8 0

Answer:

$10(x + 2)(x - 3) \\ 10x + 20 \times x - 3 \\ 10 {x}^{2} + 17$

$5(x - 3)( x + 6) \\ 5x - 15 \times x + 6 \\ 5 {x}^{2} - 9$

Basile [38]3 years ago

7 0

Answer:

If it's all one multiplication problem:

50x^4 + 100x^3 − 1350x^2 + 5400

Just 50x to the 4th power

plus 100x to the 3rd power

plus 1350x to the 2nd power

plus 5400

If it's two separate problems:

10x^2 - 10x - 60

5x^2 + 15x - 90

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The Amount of sales tax on a new car varies directly to the purchase price of the car. On a 25,000 car, sales tax is 1,750. What

Gekata [30.6K]

Answer:

50,000

Step-by-step explanation:

1st car had $1,750 tax

2nd car has $3,500 tax

1750(2) = 3500

so your tax doubled so the price must be doubled.

The car is $50,000

Algebraically using direct variation:

t = kp where t=tax, p = purchase price,

and k is constant of variation

1750 = 25000k

k = 1750/25000

k = 0.07

Your equation is: t = 0.07p

3500 = 0.07p

p = 3500/0.07

p = $50,000

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2 years ago

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The type of data that contains results from other people that are of similar age and gender is known as normative data.

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To learn more about data, please check: brainly.com/question/20841086

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2 years ago

Question 1: Use the image and your knowledge of the isosceles triangle to find the value of x

pochemuha

Answer:

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Step-by-step explanation:

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3 years ago

Lim (n/3n-1)^(n-1) n → ∞

n200080 [17]

Looks like the given limit is

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1}$

With some simple algebra, we can rewrite

$\dfrac n{3n-1} = \dfrac13 \cdot \dfrac n{n-9} = \dfrac13 \cdot \dfrac{(n-9)+9}{n-9} = \dfrac13 \cdot \left(1 + \dfrac9{n-9}\right)$

then distribute the limit over the product,

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \lim_{n\to\infty}\left(\dfrac13\right)^{n-1} \cdot \lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}$

The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.

For the second limit, recall the definition of the constant, e :

$\displaystyle e = \lim_{n\to\infty} \left(1+\frac1n\right)^n$

To make our limit resemble this one more closely, make a substitution; replace 9/(n - 9) with 1/m, so that

$\dfrac{9}{n-9} = \dfrac1m \implies 9m = n-9 \implies 9m+8 = n-1$

From the relation 9m = n - 9, we see that m also approaches infinity as n approaches infinity. So, the second limit is rewritten as

$\displaystyle\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8}$

Now we apply some more properties of multiplication and limits:

$\displaystyle \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m} \cdot \lim_{m\to\infty}\left(1+\dfrac1m\right)^8 \\\\ = \lim_{m\to\infty}\left(\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = e^9 \cdot 1^8 = e^9$

So, the overall limit is indeed 0:

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \underbrace{\lim_{n\to\infty}\left(\dfrac13\right)^{n-1}}_0 \cdot \underbrace{\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}}_{e^9} = \boxed{0}$

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3 years ago

What is the relationship between the lines determined by the following two equations?

oksano4ka [1.4K]

Answer:

C. They are the same line.

Step-by-step explanation:

In order to compare the linear equations given, they need to be in the same form. The best form in order to evaluate slope and y-intercept is slope-intercept form, y = mx + b. Since the second equation is already in slope-intercept form, we need to use inverse operations to convert the first equation:

6x - 2y = 16 ---- 6x - 2y - 6x = 16 - 6x ---- -2y = -6x + 16

-2y/-2 = -6x/-2 + 16/-2

y = 3x - 8

Since both equations are in the form y = 3x - 8, then they are both the same line.

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3 years ago