Solve this quadratic equation by completing the square.

x^2 + 6x = 18

Answer:

[tex]f(x)=3+|2x-5|=\left\{ \begin{array}{ll} 2x-2& \quad x \geq 5/2 \\ -2x+8 & \quad x < 5/2 \end{array} \right.[/tex]

Step-by-step explanation:

We are given the function:

[tex]f(x)=3+|2x-5|[/tex]

Remember that by the definition of absolute value:

[tex]\displaystyle |x|= \left\{ \begin{array}{ll} x & \quad x \geq 0 \\ - x & \quad x < 0 \end{array} \right.[/tex]

Our absolute value is:

[tex]|2x-5|[/tex]

First, we will find when it becomes 0. Set the equation equal to 0:

[tex]2x-5=0[/tex]

Solve for x:

[tex]x=5/2[/tex]

So, we can see that for all values greater than x = 5/2, 2x - 5 is positive.

For all values less than x = 5/2, 2x - 5 is negative.

Therefore (the positive case go above, and the negative case go below):

[tex]|2x-5|= \left\{ \begin{array}{ll} 2x-5 & \quad x \geq 5/2 \\ -(2x-5) & \quad x < 5/2 \end{array} \right.[/tex]

Finally, we can add a three:

[tex]f(x)=3+|2x-5|=\left\{ \begin{array}{ll} 3+(2x-5) & \quad x \geq 5/2 \\ 3+(-(2x-5)) & \quad x < 5/2 \end{array} \right.[/tex]

Simplify if desired:

[tex]f(x)=3+|2x-5|=\left\{ \begin{array}{ll} 2x-2& \quad x \geq 5/2 \\ -2x+8 & \quad x < 5/2 \end{array} \right.[/tex]

15 hours =20men

1 hour =20/15 men

1hour =4/3 men

10 hours =40/3men

Aprrox 13 men

Answer:

4= 20

Step-by-step explanation:

hope this helps.

Answer:

"in an average of" / "approximately"

Step-by-step explanation:

these clue words do not hold any definite value. therefore, it can be used for estimating.

Answer:

51720

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Answer:

18/35

Step-by-step explanation:

Answer:

x=y-6

Step-by-step explanation:

First, flip the equation.

x+6=y

Finally, add -6 to both sides.

x+6+−6=y+−6

x=y−6

Answer:

x=17 y=3

Step-by-step explanation:

x=5y+2

(5y+2)-4y=5

5y+2-4y=5

y=3

x=5(3)+2

x=17

Answer:

3√10

Step-by-step explanation:

Answer:

10980

Step-by-step explanation:

10,000

Since the thousand is 0 you keep the ten thousand at 1 and make all other digits 0.

Answer:

b) 7

Step-by-step explanation:

Answer:

To make the sentences true the answer is 7

Step-by-step explanation:

8*7=56

56/8=7

Answer:

2500

Step-by-step explanation:

25% of 10 000= 2500

Answer:

5555555

Step-by-step explanation:

I really dont know

Answer:

C

Step-by-step explanation:

first

let 3x-y= -2

here after rearranging fin the different values of x and y w. r. t the equation then shade the upper region of the line

similarly do with the second one equation and then mark the line as dotted and shade the below part of the equation of the line and then find the common shaded area

c=8

Hope it helps Hve a nice day

Answer:

c=8

Step-by-step explanation:

[tex]28+c=36\\ 36-28=8\\ c=8[/tex]

nAnswer:

32??? i think dont kill me if its wrong

Step-by-step explanation:

Answer:

women=x=65%

so men=100-65=35%=1820

let total workers be y

atq....y×35/100=1820=y=5200workers

Answer:

Triangle F G E is similar to Triangle J K L

Step-by-step explanation:

I AM A GOAT

Answer:

F G E  J K L

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

use demos online graphing calculator to check and for future graph problems

0.6*3.98+1.8*2.49 =6.87 total cost

Answer:

8

Step-by-step explanation:

The numbers in order

1, 2, 3,4,4,6,7,[8,]10,11,12,12,15,15,22

Answer:

Step-by-step explanation:

Y = mx +b        / Slope intercept form

  mx - y = -b      / Standard form

6m -2 = -b   / Plug in ( 6,2)

-9m -10 = -b / Plug in  ( -9, 10)

 Solve the system of equation for m and b.

 6m -2 = -9m -10  , then   15m = -8      m = -8/15

     b = -6m +2     ,then         b= -6 ( -8/ 15) +2 = 78/15

    -8/15 X -  y = - 78/15

     8X +15y = 78  / Equation of in standard form

Note: This is a different methods of solving this problem. All methods find their roots coming from the basic premises.

Equation of a line in the slope intersect form is

   Y = mx +b

   To convert to standard form of ax + by =c

      Simply move over the parameters

       mx - y = -b        where a = m , and c = -b

      Then we feed coordinates of 2 points in there

       make a 2 equation with 2 unknown( m,b) to

       solve.

Answer:

can you translate to english

Step-by-step explanation:

I can't understand

Answer:

We conclude that:

[tex]-8x\le \:32\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]

The solution graph on the number line is also attached.

Step-by-step explanation:

Given the inequality

[tex]-8x\:\le 32[/tex]

Solving the inequality

[tex]-8x\:\le 32[/tex]

Multiply both sides by -1 (reverse the inequality)

[tex]\left(-8x\right)\left(-1\right)\ge \:32\left(-1\right)[/tex]

Simplify

[tex]8x\ge \:-32[/tex]

Divide both sides by 8

[tex]\frac{8x}{8}\ge \frac{-32}{8}[/tex]

Simplify

[tex]x\ge \:-4[/tex]

Therefore, we conclude that:

[tex]-8x\le \:32\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]

The solution graph on the number line is also attached.

Step-by-step explanation:

cross-multiply

4y = -2

y = -2/4

y = -1/2

Answer-

y=-1/2

Multiply each side by -2 to isolate the variable.

1/4 x -2 = -1/2