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3 years ago

Through:(4,4),parallel to y=-6x +5

Mathematics

1 answer:

ad-work [718]3 years ago

6 0

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

In this case we have the following equation of the line:

$y = -6x + 5$

Where:

$m = -6$

By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will have an equation of the form:

$y = -6x + b$

Substitute the given point $(x, y) :( 4,4)$ to find "b":

$4 = -6 (4) + b\\4 = -24 + b\\4 + 24 = b\\b = 28$

Finally, the equation of the requested line is:

$y = -6x + 28$

Answer:

$y = -6x + 28$

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Answer:

$\huge\boxed{p(x)=4x^3-20x^2+4x+300}$

Step-by-step explanation:

$\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)$

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Using the probability concept, it is found that the correct statements are given as follows:

The number of possible outcomes is 8.

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<h3>What is a probability?</h3>

A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.

In this problem, there are eight letters, two of which are vowels and six of which are consonants.

Hence:

P(vowel) = 2/8 = 1/4.

P(consonant) = 6/8 = 3/4.

P(vowel) + P(consonant) = 1/4 + 3/4 = 1.

E is one out eight letters, hence the probability is drawing the tile with E written on it is 1/8.

More can be learned about probabilities at brainly.com/question/14398287

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