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4 years ago

For f(x)=4x+1 and g(x)=x^2-5 find (g/f)(x)

Mathematics

2 answers:

Ipatiy [6.2K]4 years ago

6 0

$f(x)=4x+1\\\\g(x)=x^2-5\\\\(g/f)(x)=\dfrac{g(x)}{f(x)}=\dfrac{x^2-5}{4x+1}$

Rama09 [41]4 years ago

3 0

Answer:

$(\frac{g}{f})(x)=\frac{x^2-5}{4x+1}$

Step-by-step explanation:

We have been given two function formulas $f(x)=4x+1$ and $g(x)=x^2-5$ .

By the definition of composition $(\frac{g}{f})(x)=\frac{g(x)}{f(x)}$ .

Upon substituting our given values we will get,

$(\frac{g}{f})(x)=\frac{x^2-5}{4x+1}$

Since we can not simplify our expression further, therefore, $(\frac{g}{f})(x)=\frac{x^2-5}{4x+1}$ .

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Alyssa draws a ray in her notebook. what is the minimum number of points through which the ray is drawn? 2 0 1 3

marshall27 [118]

Answer:

Step-by-step explanation:

Definition of ray in mathematics

A part of a line with a start point but no end point (it goes to infinity)

However to draw a ray, you need the start point and at least one other point on the ray.

So the answer is minimum number of points needed for a ray is 2

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2 years ago

What is the arrow way to show your strategy in math

dangina [55]

<------------------>. Need a question to do more

7 0

3 years ago

Read 2 more answers

aniked [119]

$\huge \frak \red{question}$

The Great Pyramids of Khufu is located in El Giza, Egypt. Pyramids were built to serve as tombs for the pharaohs of ancient Egypt. The Great Pyramid is 481 feet high and has a square base with a base edge length of 756 feet. What is the approximate surface area (to the nearest hundredth) of the pyramid.

(HINT: Is the base on the surface?)

$\huge \frak \green{answer}$

Square with edge length = 756 feet

Square= 1/2 × 297.45 × 481

= 286,146.9ft

= 1,037,709,9ft. base with edge length =756 feet

area of square,

= Side² = 756 × 756 = 571,563ft²

⇒ area of base = 1/2 = 756/2 = 378ft

By pythagorean theorem,

H² = P²+B²

(481)² = P²+(378)²

P² = (481)²-(378)²

P² = 231,361-142,884

P² = 88,477

P = √88,477

P = 297.45

Area of triangle =1/2 × b × h

= 1/2x297.45*481

= 148.725×481

= 71,536.725

Now 4 area of triangle = 4×71,536.725

= 286,146.9ft

total surface area of pyramid + square

= 751,563+286,146.

= 1,037,709,9ft.

$\\ \\$

$\bold \pink{TheExtraterrestrial}$

6 0

3 years ago

One root of f(x) = 2x3 9x2 7x – 6 is –3. explain how to find the factors of the polynomial.

m_a_m_a [10]

We have the following polynomial:

$f(x)=2x^{3}+9x^{2}+7x-6$

The problem states that one root is -3. Thus, it is true that $(x+3)$ is a factor of the polynomial. Given that this is fulfilled, it is also true that:

 $f(x)=(x+3)Q(x) \therefore Q(x)=\frac{f(x)}{x+3} \\ \\ where \ Q(x) \ has \ a \ degree \ of \ 2$ 

We can find Q(x) by applying Ruffini's rule, thus:

 $\ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ 9 \ \ \ \ \ \ \ \ 7 \ \ \ \ \ \ -6 \\ -3 \\ \rule{50mm}{0.1mm} \\ \ {} \ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ 3 \ \ \ \ \ -2 \ \ \ \ \ \ \ \ 0$ 

Therefore:

$Q(x)=2x^{2}+3x-2$

The roots of this polynomial can be get as follows:

$x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \rightarrow x_{12}=\frac{-3\pm\sqrt{3^2-4(2)(-2)}}{2(2)}\\x_{1}=\frac{1}{2};\ x_{2}=-2$

These are the roots along with $-3$ . Finally, the factored polynomial can be written as follows:

$f(x)=(x+3)(x+2)(2x-1)$

4 0

4 years ago

Read 2 more answers

On a true-false quiz, the probability of achieving a perfect score by guessing is halved for each additional question on the qui

Crank

For each question, there is a 1/2 chance at getting the question correct by guessing.

Let's take a scenario to better understand.
Suppose the true-false paper has 5 questions. For a perfect score by guessing, you'd need to get all 5 correct (ie (1/2)⁵)
The reason why you multiply is because you need each 1/2 simultaneously for a perfect score, which is an important concept when doing binomial probability later on.

Thus, let's use this knowledge to answer the question.
We need the minimum amount of questions such that the probability is less than 1/10.

We can write an inequality for this:

$\frac{1}{10} < \frac{1}{2}^{n}$
Now, we need to log both sides to find n.
$log_(\frac{1}{2}) \frac{1}{10} < n$
n > 3.3219...
n ≈ 4

Thus, 4 questions is the minimum number of questions needed.

6 0

3 years ago