1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
In-s [12.5K]
3 years ago
11

Please help. Don’t understand this math problem!

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
5 0

Answer:

  { 4 }

Step-by-step explanation:

First you need to solve the equation. Then you need to write the solutions as a set.

__

I like to use a graphing calculator to solve equations involving roots. That helps avoid extraneous solutions. Here, the graph of the left side intersects the graph of the right side at x=4. There is exactly one solution, so the solution set is ...

  { 4 }

__

Solving this algebraically, you would isolate the radical, then "undo" it by squaring both sides of the equation. Then solve the resulting quadratic. That will have 2 solutions, only one of which will work in the original equation.

  √(5x +16) -2 = 3x -8 . . . . given

  √(5x +16) = 3x -6 . . . . . .  add 2

  5x +16 = (3x -6)^2 . . . . .  square both sides

  5x +16 = 9x^2 -36x +36 . . . . expand the square

  9x^2 -41x +20 = 0 . . . . . . subtract (5x+16) to put into standard form

Factors of 9·20 = 180 that have a sum of 41 are 5 and 36, so we can rewrite this equation as ...

  9x^2 -36x -5x +20 = 0

  9x(x -4) -5(x -4) = 0 . . . . . . factor by pairs

  (9x -5)(x -4) = 0

The values of x that make this equation true are the values that make the factors be zero: 5/9 and 4. Trying these in the equation, we find ...

  √(5(5/9) +16) -2 = 13/3 -2 = 2 1/3 . . . . value of the left side for x = 5/9

  3(5/9) -8 = -6 1/3 . . . . . . value of the right side for x=5/9; not the same

  x = 5/9 is NOT A SOLUTION

__

  √(5(4)+16) -2 = √36 -2 = 4 . . . . value of the left side for x = 4

  3(4) -8 = 12 -8 = 4 . . . . . . value of the right side for x=4. These are the same, so ...

  x = 4 is a solution

The set of solutions is then ...

  { 4 } . . . . . solution set

You might be interested in
Please Help With all 3! Will Give 100 Points + Brainliest!
koban [17]

Answer: I don't see anything. Maybe upload some images?

Step-by-step explanation:

3 0
2 years ago
HELPP ASAPP!!!!!!!!!!!!!!!!
kati45 [8]

Answer:

y = 18

Step-by-step explanation:

7 0
3 years ago
What is the first quartile (Q1) of the data set?
KATRIN_1 [288]
Sequence = 40, 45, 48, 51, 59, 62, 69, 74

Median = 51+59 / 2 = 55
First quartile = 40, 45, 48, 51 
So, it would be: 45 + 48 / 2 = 46.5

In short, Your Answer would be Option C

Hope this helps!
8 0
3 years ago
I need these done as quick as possible and i have no clue what to do.
Korvikt [17]

Answer:

1. y = 4

2. x = 10

3. n = 6

4. m = 4

5. h = 2

Step-by-step explanation:

Hope this helps!!

3 0
3 years ago
Read 2 more answers
Which dot plot three TVs in two houses
Bogdan [553]

Answer:

A

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • 5(y5x4+1) simplify please answer now!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    10·1 answer
  • Translate the sentence into an equality
    15·1 answer
  • What is the result when two or more are added<br>​
    12·1 answer
  • Find dy/dx implicitly and find the largest interval of the form −a &lt; y &lt; a or 0 &lt; y &lt; a such that y is a differentia
    12·1 answer
  • The camera was $824.99 but I had to pay the additional 10% tax. What did I pay in total for my camera?
    11·1 answer
  • The first five terms of a sequence are:
    13·2 answers
  • Isabella is travelling in Brazil during the summer, She knows that a 15-minute phone call home to her family costs $45.85 and a
    12·1 answer
  • Select the correct difference.<br> -3z^7- (-5z^7)
    15·2 answers
  • Lean systems coupled with statistical process control (spc) requires a high degree of regimentation which in turn can lead to:__
    13·1 answer
  • Question Subtract. 3 1/3−5 Enter your answer as a simplified mixed number by filling in the boxes.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!