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anygoal [31]
2 years ago
15

Not sure what to do here can someone please help

Mathematics
1 answer:
kumpel [21]2 years ago
6 0

Answer:

  x = 2

Step-by-step explanation:

These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.

__

<h3>Squaring</h3>

The usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.

  \sqrt{x+2}+1=\sqrt{3x+3}\qquad\text{given}\\\\(x+2)+2\sqrt{x+2}+1=3x+3\qquad\text{square both sides}\\\\2\sqrt{x+2}=(3x+3)-(x+3)=2x\qquad\text{isolate the root term}\\\\x+2=x^2\qquad\text{divide by 2, square both sides}\\\\x^2-x-2=0\qquad\text{write in standard form}\\\\(x-2)(x+1)=0\qquad\text{factor}

The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.

  x = -1: √(-1+2) +1 = √(3(-1)+3)   ⇒   1+1 = 0 . . . . not true

  x = 2: √(2+2) +1 = √(3(2) +3)   ⇒   2 +1 = 3 . . . . true . . . x = 2 is the solution

__

<h3>Substitution</h3>

Another way to solve this is using substitution for one of the radicals. We choose ...

  u=\sqrt{x+2}\qquad\text{requires $u\ge0$}\\\\u^2-2=x\qquad\text{solve for x}\\\\u+1=\sqrt{3(u^2-2)+3}\qquad\text{substitute for x in the original equation}\\\\(u+1)^2=3u^2-3\qquad\text{square both sides, simplify a little}\\\\2u^2-2u-4=0\qquad\text{subtract $(u+1)^2$}\\\\2(u-2)(u+1)=0\qquad\text{factor}

Solutions to this equation are ...

  u = 2, u = -1 . . . . . . the above restriction on u mean u=-1 is not a solution

The value of x is ...

  x = u² -2 = 2² -2

  x = 2 . . . . the solution to the equation

_____

<em>Additional comment</em>

Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.

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100y−39,000=55(x−800)
hoa [83]

Answer:

y = 11/20x -50

Step-by-step explanation:

100y−39,000=55(x−800)

Distribute

100y−39,000=55x−44000

Add 39000 to each side

100y−39,000+39000=55x−44000+39000

100y = 55x -5000

Divide each side by 100

100y/100 = 55x/100 - 5000/100

y = 11/20x -50

This is slope intercept form

where 11/20 is the slope and -50 is the y intercept

4 0
3 years ago
Find the slope of the line graphed below
Korolek [52]

Answer:

Slope = 1

Step-by-step explanation:

(x1, y1) = (-5, -3)

(x2, y2) = (-1, 1)

(y2 - y1) / (x2 - x1) = (1 - -3) / (-1 - -5) = 4 / 4 = 1

Slope = 1

4 0
3 years ago
Find the value of x when 6 - 4x = 6x - 8x + 12
seraphim [82]

Answer:

x = -3

Step-by-step explanation:

Step 1: Write out equation

6 - 4x = 6x - 8x + 12

Step 2: Combine like terms (x)

6 - 4x = -2x + 12

Step 3: Add 4x on both sides

6 = 2x + 12

Step 4: Subtract 12 on both sides

-6 = 2x

Step 5: Divide both sides by 2

-3 = x

Step 6: Rewrite

x = -3

8 0
3 years ago
Read 2 more answers
There are 2820 cars in Farmington. The ratio of medium size cars to compacts is 7 to 5 and the ratio of compacts to full-size ca
oee [108]

Answer:

Number of full size cars = 900

Step-by-step explanation:

The ratio of medium size cars to compacts is 7 to 5 and the ratio of compacts to full-size cars is 8 to 9. Since compact cars are  there in both ratios , we need to  make the number in the ratio for compact cars to be the same.

\frac{medium}{compact} = \frac{7}{5}

Multiply by 8 on numerator and denominator

\frac{medium}{compact} = \frac{56}{40}

\frac{compact}{full size} = \frac{8}{9}

Multiply numerator and denominator by 5.

\frac{compact}{full size} = \frac{40}{45}

Ratio of medium, compact and full size are in ratio 56,40,45.

Total number of cars =2820.

(56 + 40 + 45)x = 2820

x = \frac{2820}{141}

x = 20

Number of full size cars = 20\times 45 =900

3 0
3 years ago
Use substitution to solve for x in the system of equations.
jolli1 [7]
Equation 1) 10x + 2y = 30
Equation 2) 4x + y = 4

Multiply all of equation 2 by 2.

2)  2(4x + y = 4)

2)  8x + 2y = 8
1)  10x + 2y = 30

Subtract equations from each other.

-2x = -22

Divide both sides by -2.

x = -22/-2

x = 11

B) x = 11

~Hope I helped!~


6 0
3 years ago
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