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DanielleElmas [232]
3 years ago
8

I’ll give brainliest

Mathematics
1 answer:
mrs_skeptik [129]3 years ago
3 0

Answer:

Step-by-step explanation:

4) Angles opposite to equal sides are equal

45 + 45 + x = 180     {Angle sum property}

        90 +x = 180       {Subtract 90 from both sides}

               x = 180 - 90  

               x = 90

120 +y + y = 180        {Angle sum property}

      120 +2y = 180       {Subtract 120 from both sides

              2y =180 - 120

               2y = 60      {Divide both sides by 2}

                 y = 60/2

y = 30

5)All sides are equal. so this is a equilateral triangle.

So each angle of equilateral triangle = 60

4x = 60

x = 60/4

x = 15

y = 60 +60   {Exterior of triangle equal sum of opposite interior angles}

y = 120

6) All sides are equal. so this is a equilateral triangle.

So each angle of equilateral triangle = 60

y - 10 = 60    {add 10 to both side}

y = 60 + 10

y = 70

x + 5 = 60    {Subtract 5 from both sides}

x = 60 - 5

x = 55

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Which statement best reflects the solution(s) of the equation?
Inessa [10]

x=2 is only solution while x=1 is extraneous solution

Option C is correct.

Step-by-step explanation:

We need to solve the equation \frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1} and find values of x.

Solving:

Find the LCM of denominators x-1,x and x-1. The LCM is x(x-1)

Multiply the entire equation with x(x-1)

\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}\\\frac{1}{x-1}*x(x-1)+\frac{2}{x}*x(x-1)=\frac{x}{x-1}*x(x-1)\\Cancelling\,\,out\,\,the\,\,same\,\,terms:\\x+2(x-1)=x^2\\x+2x-2=x^2\\3x-2=x^2\\x^2-3x+2=0

Now, factoring the term:

x^2-2x-x+2=0\\x(x-2)-1(x-2)=0\\(x-1)(x-2)=0\\x-1=0\,\,and\,\, x-2=0\\x=1\,\,and\,\, x=2

The values of x are x=1 and x=2

Checking for extraneous roots:

Extraneous roots: The root that is the solution of the equation but when we put it in the equation the answer turns out not to be right.

If we put x=1 in the equation, \frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}  the denominator becomes zero i.e

\frac{1}{1-1}+\frac{2}{1}=\frac{1}{1-1}\\\frac{1}{0}+2=\frac{1}{0}

which is not correct as in fraction anything divided by zero is undefined. So, x=1 is an extraneous solution.

If we put x=2  in the equation,

\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}

\frac{1}{2-1}+\frac{2}{2}=\frac{2}{2-1}\\\frac{1}{1}+1=\frac{2}{1}\\1+1=2\\2=2

So, x=2 is only solution while x=1 is extraneous solution

Option C is correct.

Keywords: Solving Equations and checking extraneous solution

Learn more about Solving Equations and checking extraneous solution at:

  • brainly.com/question/1626495
  • brainly.com/question/2959656
  • brainly.com/question/2456302

#learnwithBrainly

5 0
3 years ago
What’s #14&15 and I also need help in #2
gulaghasi [49]
#2= +$700 I couldn't see #14 and 15
4 0
3 years ago
Consider the parent function f(x) = x^2 and the transformed function f(x) =- 5(x - 4)^2 – 8. Identify the
madam [21]

Given:

The parent function is

f(x)=x^2

Consider the transformed function is g(x) instead of f(x) because both functions are different.

g(x)=-5(x-4)^2-8

Step-by-step explanation:

We have,

f(x)=x^2

g(x)=-5(x-4)^2-8

It can be written as

g(x)=-5f(x-4)-8            ...(i)

The translation is defined as

g(x)=kf(x+a)+b                .... (ii)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<|k|<1, then the graph compressed vertically by factor k and if |k|>1, then the graph stretch vertically by factor k.

If k is negative, then f(x) is reflected across the x-axis to get g(x).

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (i) and (ii), we get

a=-4, f(x) shifts 4 units right.

b=-8, f(x) shifts 8 units down.

k=-5, it is negative so f(x) reflected across the x-axis.

|k|=|-5|=5>1, so f(x) stretched vertically by factor 5.

Therefore, the function f(x) reflected across the x-axis, stretched vertically by factor 5 and shifted 4 units right 8 units down to get g(x).

8 0
3 years ago
What is the difference between 34,162 and 12,531
mixas84 [53]

Answer:

23346.5

Step-by-step explanation:

add them together and divide by 2

4 0
3 years ago
Jan pick 3/4 of a gallon of strawberries in a half an hour. If she keeps picking strawberries at the same rate, how many gallons
krek1111 [17]
2 divided by 1/2
2 x 2/1 = 4
3/4 x 4/1 = 12/3
12/3 = 4
4 gallons, Hope this helps!
8 0
3 years ago
Read 2 more answers
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