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2 years ago

What is the equation of the vertical asymptote of the graph of f(x) = 2 log3(x + 1) – 3?

Mathematics

1 answer:

hammer [34]2 years ago

4 0

Set the argument (x+1) equal to zero.
$x + 1 = 0 \\ x = - 1$

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Preform the indicated operation 17 + (-5)

alisha [4.7K]

Answer:

Step-by-step explanation:

17 + (-5) =

17 - 5 = 12

This the explanation

8 0

2 years ago

Use an induction proof to prove this statement:<br> For n≥1, 4^n+5 is divisible by 3.

Tpy6a [65]

Answer:

See below

Step-by-step explanation:

We shall prove that for all $n\in\mathbb{N},3|(4^n+5)$ . This tells us that 3 divides 4^n+5 with a remainder of zero.

If we let $n=1$ , then we have $4^{1}+5=9$ , and evidently, $9|3$ .

Assume that $4^n+5$ is divisible by $3$ for $n=k, k\in\mathbb{N}$ . Then, by this assumption, $3|(4^n+5)\Rightarrow4^k+5=3m,\: m\in\mathbb{Z}$ .

Now, let $n=k+1$ . Then:

$4^{k+1}+5=4^k\cdot4+5\\=4^k(3+1)+5\\=3\cdot4^k+4^k+5\\=3\cdot4^k+3m\\=3(4^k+m)$

Since $3|(4^k+m)$ , we may conclude, by the axiom of induction, that the property holds for all $n\in\mathbb{N}$ .

3 0

1 year ago

A video game is on sale for 20% off. The sale price of the game is $35.00. How much did the game ORIGINALLY cost?

Elena-2011 [213]

Answer:

$43.75

Step-by-step explanation:

To find how much the game would have been 20% off from 43.75, you would have needed the expression

43.75*0.8

So to go from 35 to 43.75, you need the expression

35/0.8.

This expression in simpler terms means What is 38, 80% of?

That is how we get 43.75.

35/0.8 = 43.75.

7 0

2 years ago

A rectangle has a height of 2x^4 with a width of x^2+8x+15. Express the area of the rectangle.

Amiraneli [1.4K]

Hi there!

We know that the formula for the area of a rectangle is height * width. Thus, we can multiply these two expressions together:

$2x^4\cdot (x^2+8x+15)\\$

Now, we know through the distributive property that we can distribute the $2x^4\\$ to everything in the parenthesis. Once this is done, we get:

$2x^4 \cdot x^2+2x^4\cdot8x+2x^4\cdot15$

Now, we know through the power rule that when two exponents are multiplied together with the same base, the exponent can be added together $(x^a \cdot x^b = x^{a+b})$ . This then would make our equation:

$2x^{4+2}+16x^{4+1}+30x^4\\$

Giving us for our final answer:

$2x^{6}+16x^{5}+30x^4\\$

Hope this helps!

8 0

2 years ago

What is the value of the 8 in the number 8,644.58

Masja [62]

It is in the thousands place.

8 0

2 years ago

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