What is the solution set for the inequality |-3-5x|-8<-2

Answers

Answer 1

Answer: $|-3-5x|-8<-2\n|-3-5x|<6\n-3-5x<6 \wedge -3-5x>-6\n-5x<9 \wedge -5x>-3\nx>-(9)/(5) \wedge x<(3)/(5)\nx\in\left(-(9)/(5),(3)/(5)\right)$

Answer 2

Answer: The hard way:

$\left| -3-5x \right| -8<-2\n \n \left| -3-5x \right| <6\n \n { \left( -3-5x \right) }^( 2 )<{ 6 }^( 2 )\n \n \left( -3-5x \right) \left( -3-5x \right) <36$

$\n \n 9+15x+15x+25{ x }^( 2 )<36\n \n 25{ x }^( 2 )+30x+9<36\n \n 25{ x }^( 2 )+30x-27<0\n \n Say\quad f\left( x \right) =25{ x }^( 2 )+30x-27,\n \n and\quad that\quad f\left( x \right) =0$

$\n \n 25{ x }^( 2 )+30x-27=0\n \n 25{ x }^( 2 )+30x=27\n \n { x }^( 2 )+\frac { 30 }{ 25 } x=\frac { 27 }{ 25 } \n \n { x }^( 2 )+\frac { 6 }{ 5 } x=\frac { 27 }{ 25 } \n \n { \left( x+\frac { 3 }{ 5 } \right) }^( 2 )-{ \left( \frac { 3 }{ 5 } \right) }^( 2 )=\frac { 27 }{ 25 }$

$\n \n { \left( x+\frac { 3 }{ 5 } \right) }^( 2 )=\frac { 36 }{ 25 } \n \n x+\frac { 3 }{ 5 } =\pm \frac { 6 }{ 5 } \n \n x=-\frac { 3 }{ 5 } \pm \frac { 6 }{ 5 }$

$Therefore:\n \n x=\frac { 3 }{ 5 } \quad and\quad x=-\frac { 9 }{ 5 } \quad when\quad f\left( x \right) =0\n \n Now:\n \n f\left( x \right) <0,\n \n$

When:

-9/5<x<3/5

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Find all values of m so that the function y = e^mx
is a solution of the given differential equation. y' + 9y = 0

Answers

Hello,

y=e^(mx)
y'=m*e^(mx)

0=y'+9y=m*e^(mx)+9*e^(mx)
==> e^(mx)*(m+9)=0
This must be exact for every value of ,so
m=-9

How do you do...
cos2x-sin2x=1-2sin2x

Answers

$sin (2 \alpha) =2\cdot sin \alpha \cdot cos \alpha \ncos(2 \alpha )=1-2sin^2 \alpha \n-------------------- \ncos2x-sin2x=1-2sin2x\ncos2x+sin2x=1\n1-2sin^2x+2sinx\cdot cosx=1\n-2sinx(sin x-cosx)=0\n -2sinx=0\ \ \ \ or\ \ \ \ sinx-cosx=0\n\n1)\ -2sinx=0\ \ \Leftrightarrow\ \ sinx=0\ \ \Leftrightarrow\ \ x_1=k \pi \ \ and\ \ k\in I\n2)\ \ sinx-cosx=0\ \ \Leftrightarrow\ \ sinx=cosx\ /:cosx\ \ \ \ \ \wedge\ \ \ \ cos x \neq 0\ntanx=1\ \ \Leftrightarrow\ \ x_2= ( \pi )/(4) +k \pi \ \ and\ \ k\in I$

Whats the answer for 4(3) x 3

Answers

It is 12×3 = 36

4(3) = 12 and multiply with three i.e. 12×3=36

George spend $17.25 on pecans andpeanuts at a farmer's market. He bought
3 1/2 pounds of pecans
for $3.20 per pound
and 5 1/2 pounds of peanuts. What was the
price per pound for the peanuts George
purchased?

Answers

11.2 for pecans
6.05 left for peanuts
6.05 / 5.5
Therefore the answer is 1.10

Brand x cost $1.56 for 12 ounces. Brand y cost 2 ¢ more per ounce. What is The cost of 15 ounce of brandy

Answers

x = $1.56 = 12 oz
y = x + $0.02 = oz

1.56 ÷ 12 = 0.13
15 (0.13 + 0.02) = 2.25

$2.25 = 15y

Help me with this plzzz

Answers

Answer:

2/3

Step-by-step explanation:

Everytime the line moves over 3 it goes up 2, so the run is 3 and rise is 2. It is written in rise over run.

The correct answer for your question is 2/3

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