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Sergio [31]
3 years ago
12

What is the domain, range and function of this, please help

Mathematics
1 answer:
GaryK [48]3 years ago
4 0
Domain is your x values, Range is your y values.
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What is the quotient: (6x4 + 15x3 + 10x2 + 10x + 4) ÷ (3x2 + 2)?
Kryger [21]

Answer:  Option 'C' is correct.

Step-by-step explanation:

Since we have given that

\frac{\left(6x^4+15x^3+10x^2+10x+4\right)}{\left(3x^2+2\right)}

Now, we will find the quotient by factoring the numerator:

\mathrm{Use\:the\:rational\:root\:theorem}\\a_0=4,\:\quad a_n=6\\\\\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:4,\:\quad \\\mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2,\:3,\:6\\\\\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:4}{1,\:2,\:3,\:6}\\\\-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2\\\\=\left(x+2\right)\frac{6x^4+15x^3+10x^2+10x+4}{x+2}\\\\=\frac{6x^4+15x^3+10x^2+10x+4}{x+2}=6x^3+3x^2+4x+2\\\\

Now, we will factor it again:

=\left(6x^3+3x^2\right)+\left(4x+2\right)\\\\=2\left(2x+1\right)+3x^2\left(2x+1\right)\\\\=\left(2x+1\right)\left(3x^2+2\right)

At last we get our factorised form :

=\left(x+2\right)\left(2x+1\right)\left(3x^2+2\right)\\\\=\frac{\left(x+2\right)\left(2x+1\right)\left(3x^2+2\right)}{3x^2+2}\\\\=\left(x+2\right)\left(2x+1\right)\\\\=2x^2+5x+2

Hence, Option 'C' is correct.

4 0
3 years ago
Read 2 more answers
Which of the following is true about the solution to h - 9 = 1?
Fed [463]
The solution must be larger than 9, because the answer is h=10
8 0
3 years ago
Complete the table of pork sandwiches to chicken
denis-greek [22]

Step-by-step explanation:

Pork sandwiches: 2 , 6 , 10 , 14

goes by 4

Chicken Sandwiches: 5 , 15 , 25 , 35

goes by 10

4 0
3 years ago
Given that sin theta = 1/4, 0
GaryK [48]
Answer: cos(Θ) = (√15) / 4

Explanation:

The question states:

1) sin(Θ) = 1/4

2) 0 < Θ < π / 2

3) find cos(Θ)

This is how you solve it.

1) Use the fundamental identity (in this part I use α instead of Θ, just for facility of wirting the symbols, but they mean the same for the case).

(cos \alpha )^2 + (sin \alpha )^2 =1

2) From which you can find:

(cos \alpha )^2 = 1 - (sin \alpha )^2

3) Replace sin(α) with 1/4

=> (cos \alpha )^2 = 1 - (1/4)^2 = 1 - 1/16 = 15/16

=> cos \alpha =+/- \sqrt{15/16} = +/- (\sqrt{15} )/4

4) Given that the angle is in the first quadrant, you know that cosine is positive and the final answer is:

cos(Θ) = \sqrt{15} /4.

And that is the answer.
6 0
3 years ago
What is the angle measure of an arc bounding sector with an area of 5pie square miles?
Snowcat [4.5K]

if the diameter is 20, the its radius must be half that or 10.

\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=5\pi \\ r=10 \end{cases}\implies \begin{array}{llll} 5\pi =\cfrac{\theta \pi (10)^2}{360}\implies 5\pi =\cfrac{5\pi \theta }{18} \\\\\\ \cfrac{5\pi }{5\pi }=\cfrac{\theta }{18}\implies 1=\cfrac{\theta }{18}\implies 18=\theta \end{array}

8 0
2 years ago
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