-<br> What is g(x)= -4(x - 5)2 + 8 in standard form

Sergio039 [100]

Answer:

$\displaystyle 4.\overline{15} = \frac{137}{33}$ .

Step-by-step explanation:

Start by separating this decimal number into its integer part and its fraction part:

$4.151515\cdots = 4 + 0.151515\cdots$

The most challenging task here is to express $0.151515\cdots$ as a proper fraction. Once that fraction is found, expressing the original number $4.151515\cdots$ will be as simple as rewriting a mixed number as an improper fraction.

Let $x = 0.151515\cdots$ . $(x + 4)$ would then represent the original number.

Note that the repeating digits appear in groups of two. Therefore, if the digits in $x$ are shifted to the left by two places, the repeating part will continue to match:

$\begin{aligned}x = 0.&151515\cdots && \\ 100\, x = 15.& 151515\cdots \end{aligned}$ .

Note, that this "shifting" is as simple as multiplying the initial number by $100$ (same as $10$ raised to the power of the number of digits that needs to be shifted.)

Subtract the original number from the shifted number to eliminate the fraction part completely:

$\begin{aligned}&(100\, x) - x \\ &= 15.151515\cdots\\ & \phantom{=}- 0.151515\cdots\\&=15 \end{aligned}$ .

In other words:

$99\, x = 15$ .

$\displaystyle x = \frac{15}{99} = \frac{5}{33}$ .

Therefore, the original number would be:

$\displaystyle x + 4 = \frac{5}{33} = \frac{132 + 5}{33} = \frac{137}{33}$ .

4 0

3 years ago

Find the value of x.

PIT_PIT [208]

Answer:

Step-by-step explanation:

180 = 7x +2 + 7x + 2 + 180 - (17x -23)

180 = 14x +4 + 180 -17x +23

180 = -3x +207

3x = 27

x = 9

4 0

3 years ago

which undefined geometric term can be described as a one dimensional set of point that has no beginning or end?

user100 [1]

A line-----------------

3 0

3 years ago

Read 2 more answers

How many complex roots does the polynomial equation have?<br><br> 3x5−2x+1=0

dmitriy555 [2]

Answer : The given polynomial equation can have 0,2 or 4 complex roots.

Explanation:-

Given polynomial equation is $3x^5-2x+1=0$ which is a polynomial of degree 5.

We know that the complex roots always occur in pair ,therefore the number of complex roots in any polynomial must be an even number but less than equal to the degree of polynomial.

Thus, the given polynomial equation has 4 complex roots.

3 0

3 years ago

Read 2 more answers

What is the factorization of the polynomial below? x^3 + 8x^2 + 17x + 10

faltersainse [42]

Answer:

This is your answer.

Step-by-step explanation:

Hope is helps!!