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castortr0y [4]
3 years ago
9

I will give brainliest !!

Mathematics
1 answer:
tekilochka [14]3 years ago
6 0

Answer:

D

Step-by-step explanation:

When all the members in a domain has only but one member in the do main then function has been satisfied.

considering a situation of,

4 1

6 1

8 2

the domain has only one member in the Co domain hence which makes it a function

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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
Calculate the average rate of change from x = 0 to x = 3. Show work please
AURORKA [14]
Rate=\frac{f(b)-f(a)}{b-a}=\frac{f(3)-f(0)}{3-0}=\frac{3-(-4)}{3}=\frac{7}{3}
3 0
3 years ago
I need help ASAP!!!
Vera_Pavlovna [14]

I am 99% sure it’s B

6 0
3 years ago
1. Evaluate the expression when x=2, y = 3, and z= -9:
kupik [55]

Answer:

-7

Step-by-step explanation:

substitute the given values into the expression

xy-<em>x</em>

<em>(</em>-2 times 3<em>)</em>-1

-6 - 1 = -7

6 0
3 years ago
The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y ≤ −2x + 10 y &gt; 1 over
vlabodo [156]

Answer:

A, C, D and K

Step-by-step explanation:

First, plot the solution set to the system of two inequalities.

The inequality y\le -2x+10 determines solid line and bottom shaded region under this line.

The inequality y>\dfrac{1}{2}x-2 determines dotted line and top shaded region under this line.

The intersection of these two regions is the solution set to the system of two inequalities.

Points A, C, D and K belong to this region.

4 0
3 years ago
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