HELP, WILL MARK BRANLIEST<br><br> The graph shown represents which of the following polar equations?

notka56 [123]

Answer:

x = -3, 0, or 7

Step-by-step explanation:

After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.

__

Write the equation in standard form.

4x³ -16x² -84x = 0

Factor out the common factor from all terms.

= 4x(x² -4x -21) = 0

Compare to the factored form of a quadratic:

(x +a)(x +b) = x² +(a+b)x +ab

This tells you the constants 'a' and 'b' in the factors can be found by considering ...

(a+b) = -4 . . . . the coefficient of the x term of the quadratic

ab = -21 . . . . . the constant term of the quadratic

It is often helpful to list factor pairs of the constant:

-21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum

The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...

a = -7, b = 3

Put it all together.

4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation

Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:

4x = 0 ⇒ x = 0

x -7 = 0 ⇒ x = 7

x +3 = 0 ⇒ x = -3

Solutions to the equation are x ∈ {-3, 0, 7}.

_____

<em>Additional comment</em>

What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.

A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.

3 0

3 years ago

George is folding a piece of paper to make an origami figure. Each time he folds the paper, the thickness of the paper is double

Rudiy27

Answer to part A; Folding the paper once makes the thickness 2mm. Folding it twice makes it 4mm thick. Folding it 3 times makes it 8mm thick. Folding it 4 times makes it 16mm thick. Folding it 5 times makes it 32mm thick. Folding 6 times makes it 64mm thick.
Answer to part B; This relation is a function, because every time you fold the paper, you double how thick it was before the most recent fold. For example, if you had already folded the paper 4 times, which makes it 16mm thick, folding it a 5th time will make it 32mm, double 16mm.

6 0

3 years ago

Read 2 more answers

Identify the expression for calculating the mean of a binomial distribution.

Gre4nikov [31]

A random variable $X$ following a binomial distribution with success probability $p$ across $n$ trials has PMF

$\mathbb P(X=x)=\begin{cases}\dbinom nxp^x(1-p)^{n-x}&\text{for }x\in\{0,1,\ldots,n\}\\\\0&\text{otherwise}\end{cases}$

where $\dbinom nx=\dfrac{n!}{x!(n-x)!}$ .

The mean of the distribution is given by the expected value which is defined by

$\mathbb E(X):=\displaystyle\sum_xx\mathbb P(X=x)$

where the summation is carried out over the support of $X$ . So the mean is

$\displaystyle\sum_{x=0}^nx\binom nxp^x(1-p)^{n-x}$

Because this is a proper distribution, you have

$\displaystyle\sum_x\mathbb P(X=x)=1$

which is a fact that will be used to evaluate the sum above.

$\displaystyle\sum_{x=0}^nx\binom nxp^x(1-p)^{n-x}$
$\displaystyle\sum_{x=1}^nx\binom nxp^x(1-p)^{n-x}$
$\displaystyle\sum_{x=1}^n\frac{xn!}{x!(n-x)!}p^x(1-p)^{n-x}$
$\displaystyle np\sum_{x=1}^n\frac{(n-1)!}{(x-1)!(n-x)!}p^{x-1}(1-p)^{n-x}$
$\displaystyle np\sum_{x=1}^n\frac{(n-1)!}{(x-1)!((n-1)-(x-1))!}p^{x-1}(1-p)^{(n-1)-(x-1)}$

Letting $y=x-1$ , this becomes

$\displaystyle np\sum_{y=0}^{n-1}\frac{(n-1)!}{y!((n-1)-y)!}p^y(1-p)^{(n-1)-y}$

Observe that the remaining sum corresponds to the PMF of a new random variable $Y$ which also follows a binomial distribution with success probability $p$ , but this time across $n-1$ trials. Therefore the sum evaluates to 1, and you're left with $np$ as the expression for the mean for $X$ .

3 0

4 years ago

Why do the kindergartener take her books to the zoo?

SpyIntel [72]

Probably because their teacher asked them or if they did something bad they would probably have to sit and read.

5 0

3 years ago

Write the slope-intercept form of the equation of each line?

Ivenika [448]

Problem 1

It appears the line is going through the points (-1,-4) and (0,5)

Let's find the slope

$(x_1,y_1) = (-1,-4) \text{ and } (x_2,y_2) = (0,5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{5 - (-4)}{0 - (-1)}\\\\m = \frac{5 + 4}{0 + 1}\\\\m = \frac{9}{1}\\\\m = 9\\\\$

The slope is 9

The y intercept is b = 5 as this is where the graph crosses the y axis.

We go from y = mx+b to y = 9x+5

<h3>Answer: y = 9x+5</h3>

=======================================================

Problem 2

This line goes through the points (0,4) and (5,5)

We'll follow the same exact steps as before

First we need the slope

$(x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (5,5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{5 - 4}{5 - 0}\\\\m = \frac{1}{5}\\\\$

The y intercept is the y coordinate of (0,4) so it's b = 4

<h3>Answer: $y = \frac{1}{5}x+4$ </h3>

4 0

2 years ago

HELP, WILL MARK BRANLIEST The graph shown represents which of the following polar equations?