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-BARSIC- [3]
3 years ago
8

Simplify the following expression:,3 + 5 (9+2n)

Mathematics
1 answer:
Rasek [7]3 years ago
6 0
3 + 5(9+2n)
Distribute the 5 to the items in the parentheses 
3 + 5(9+2n)
3 + 45 + 10n
Combine like terms
48 + 10n
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Find all the zeros of the equation x^4-6x^2-7x-6=0
rusak2 [61]

Answer:

The zeros are

x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}

Step-by-step explanation:

We have been given the equation x^4-6x^2-7x-6=0

Use rational root theorem, we have

a_0=6,\:\quad a_n=1

\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:6,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1

\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:3,\:6}{1}

-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2

=\left(x+2\right)\frac{x^4-6x^2-7x-6}{x+2}\\

=x^3-2x^2-2x-3

Again factor using the rational root test, we get

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

Using the zero product rule, we have

x+2=0:\quad x=-2\\x-3=0:\quad x=3\\x^2+x+1=0\\\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\\\=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}

Therefore, the zeros are

x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}


4 0
3 years ago
Read 2 more answers
Guys Pls Help ASAP! Will Give Brainliesttt. <br><br> Thxx
Allisa [31]

Answer:

23. x= -2/5 x= -5

24. x= 3/4 x= -1/6

25. x= 7/3. x= -5/4

26. x= 3 x= -2/3

27. x= 1. x= -2/7

28. x= 9/4. x= -1/3

29. x= 2/5 x= 1/3

30. x= 2/3 x= 1/2

6 0
3 years ago
Sử dụng phép tính mệnh đề (các luật logic) để chứng minh các biểu thức sau là hằng
allsm [11]

Answer: “P hay Q” là một mệnh đề được

Step-by-step explanation: Các quy tắc tương đương logic: ... Chứng minh biểu thức mệnh đề (¬((r ∨ q) ∧ q) ∨. ¬p)∧ ((¬p

5 0
2 years ago
Factorise <br> 84xy+196x-36y-84
LenaWriter [7]

Hi,

84xy+196x-36y-84

4(21xy+49x-9y-21)

4(7x × (3y+7)-9y-21)

4(7x × (3y+7)-3(3y+7)

4(3y+7)×(7x-3)

4 0
3 years ago
The circumference of a circle is 138.16 centimeters. What is the area of the circle?
vodomira [7]
Circumference formula tells you C=2 \pi r

<span>C=2 \pi r
</span><span>138.16=2 \pi r
</span>21.99= r
<span>r=21.99cm</span>
The formula to find the area of a circle is A= \pi r^2

<span>A= \pi r^2
</span><span>A= \pi (21.99)^2
</span><span>A= \pi (483.56)
</span>A= 1519cm^2
6 0
3 years ago
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