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
cupoosta [38]
4 years ago
12

Solve.

="TexFormula1" title=" \sqrt{3 x - 11} - \sqrt{x} + 5 = 6" alt=" \sqrt{3 x - 11} - \sqrt{x} + 5 = 6" align="absmiddle" class="latex-formula">

Mathematics
1 answer:
ICE Princess25 [194]4 years ago
5 0
Solve for x:
5 - sqrt(x) + sqrt(3 x - 11) = 6

Subtract 5 from both sides:
sqrt(3 x - 11) - sqrt(x) = 1

(sqrt(3 x - 11) - sqrt(x))^2 = -11 + 4 x - 2 sqrt(x) sqrt(3 x - 11) = -11 + 4 x - 2 sqrt(x (3 x - 11)) = 1:
-11 + 4 x - 2 sqrt(x (3 x - 11)) = 1

Subtract 4 x - 11 from both sides:
-2 sqrt(x (3 x - 11)) = 12 - 4 x

Raise both sides to the power of two:
4 x (3 x - 11) = (12 - 4 x)^2

Expand out terms of the left hand side:
12 x^2 - 44 x = (12 - 4 x)^2

Expand out terms of the right hand side:
12 x^2 - 44 x = 16 x^2 - 96 x + 144

Subtract 16 x^2 - 96 x + 144 from both sides:
-4 x^2 + 52 x - 144 = 0

The left hand side factors into a product with three terms:
-4 (x - 9) (x - 4) = 0

Divide both sides by -4:
(x - 9) (x - 4) = 0

Split into two equations:
x - 9 = 0 or x - 4 = 0

Add 9 to both sides:
x = 9 or x - 4 = 0

Add 4 to both sides:
x = 9 or x = 4

5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(4) + sqrt(3×4 - 11) = 4:
So this solution is incorrect

5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(9) + sqrt(3×9 - 11) = 6:
So this solution is correct

The solution is:
Answer:  x = 9
You might be interested in
once a week you babysit your neighbor’s toddler after school, usually going to a local playground. you notice that each swing on
Natalka [10]
You didn't include the formula.

Given that there is no data about the mass, I will suppose that the formula is that of the simple pendulum (which is only valid if the mass is negligible).

Any way my idea is to teach you how to use the formula and you can apply the procedure to the real formula that the problem incorporates.

Simple pendulum formula:

Period = 2π √(L/g)

Square both sides

Period^2 = (2π)^2 L/g

L = [Period / 2π)^2 * g

Period = 3.1 s
2π ≈ 6.28
g ≈ 10 m/s^2

L = [3.1s/6.28]^2 * 10m/s^2 =2.43 m

I  hope this helps you.
6 0
3 years ago
Movies are on sale for 3/
vredina [299]

Answer:

$7.50

Step-by-step explanation:

3/4 of the original price

Original price: $10

So we need 3/4 of $10

10 ÷ 4 = 2.5

2.5(3) = 7.5

3/4 of $10 = 7.5, so the price is now $7.50

6 0
3 years ago
Read 2 more answers
How would you write in standard form 8 thousands+1200 hundreds
Alex_Xolod [135]
It is basically 8 thousand plus one thousand two hundred so your answer would be 9200
4 0
3 years ago
Determine if the equation is linear 2x y=4,
Juliette [100K]
Determine whether each equation is a linear equation. ... –2x – 3 = y .... linear. 16. 4y. 2. + 9 = –4. SOLUTION: Since y is squared, the equationcannot be written in standard form.
4 0
3 years ago
Which equation is related to this equation? b + 17 = 52
Neporo4naja [7]

It would be d because you would subtract 52 from 17 to get the answer then add the number you got to 17 to get 52.
7 0
4 years ago
Read 2 more answers
Other questions:
  • Ben orders a case of his favorite macaroni and cheese. The case contains 18 same-
    9·1 answer
  • WILL GIVE BRAINLIEST Jorge solves the equation 4x - (x + 20) + 6 = 2(3x + 8) using the steps below. Step 1: 4x - x + 2 + 6 = 6x
    11·1 answer
  • Find the length of each leg. Leave answer in simplest radical form.
    15·1 answer
  • A 12-ounce soda can is 5 inches tall and 2.5 inches across. How much soda can it hold if it is completely full? Round your answe
    10·2 answers
  • Plz help me solve this ASAP and show the work thank you
    12·1 answer
  • Identify the time being asked.
    6·2 answers
  • If I have an 83% percentage as my grade and I got 90% or 100% in one of my tests, what would be my final grade percentage?
    12·2 answers
  • What is the value of x in the equation below? 3x - 15 = 60
    8·2 answers
  • A bag contains 120 marbles. Some are red and the rest are black.There are 19 red marbles for every black marble.How many red mar
    10·2 answers
  • If a/b = 4, a = 8c, and c = 9, what is the value of b?
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!