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yuradex [85]
2 years ago
12

Which statement describes if there is an extraneous solution to the equation √x-3 = x-5? A. there are no solutions to the equati

on, B. the extraneous solution is x = 7, C. the valid solutions are x = 7 and x = 4, or D. the extraneous solution is x = 4
Mathematics
1 answer:
Brrunno [24]2 years ago
7 0
Remember that <span>an extraneous solution of an equation, is the solution that emerges from solving the equation but is not a valid solution.
 
Lets solve our equation to find out what is the extraneous solution:
</span>\sqrt{x-3} =x-5
(\sqrt{x-3})^2 =(x-5)^2
x-3=x^2-10x+25
x^2-11x+28=0
(x-4)(x-7)=0
x-4=0 and x-7=0
x=4 and x=7
<span>
So, the solutions of our equation are </span>x=4 and x=7. Lets replace each solution in our original equation to check if they are valid solutions:
- For x=7
\sqrt{x-3} =x-5
\sqrt{7-3} =7-5
\sqrt{4} =2
2=2
We can conclude that 7 is a valid solution of the equation.

- For x=4
\sqrt{x-3} =x-5
\sqrt{4-3} =4-5
\sqrt{1} =1
1 \neq 1
We can conclude that 4 is not a valid solution of the equation; therefore, 4 is a extraneous solution.

We can conclude that the correct answer is: <span>D. the extraneous solution is x = 4</span>
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7 0
3 years ago
In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that eac
VARVARA [1.3K]

Answer:

Total number of ways will be 20

Step-by-step explanation:

We have given three identical green shirts and three identical red shirts

So total number of shirts = 3+3 = 5

We have to distribute these shirts to 6 children so that each children got one shirt

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5 0
3 years ago
A vertical radio tower is 645 feet high above level ground. How far would you need to be from the base of the tower so that the
WITCHER [35]

Answer:

921.165 feet

Step-by-step explanation:

Ok we are looking for the length of the base.

Now let's take the question and picture it as a triangle, we will find out that it looks like a right angle triangle.

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Angle of elevation= 35°

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To find the base

We recall that tan of angle

= opposite/adjacent

In this case

Angle= 35°

Opposite= height= 645

Adjacent= base

Tan 35 = 645/adj

Adj =645/tan 35

Adj =645/0.7002

Adj = 921.165

The base is 921.165 feet

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MaRussiya [10]
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mel-nik [20]

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6.66666666667

Step-by-step explanation:

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7 0
3 years ago
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