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
Zina [86]
3 years ago
13

X + 4(x-1) = 9-2(x+3)

Mathematics
1 answer:
Genrish500 [490]3 years ago
3 0
Collect like terms
x + 4x - 4 = 9 - 2 x - 6
move the terms
5x - 4 = 3 - 2x
collect like terms calculate
5x + 2x = 3 + 4
7x = 7
answer is x = 1
You might be interested in
Evaluate Dx / ^ 9-8x - x2^
Solnce55 [7]
It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for \sqrt x.

In that case, you want to find the antiderivative,

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}

Complete the square in the denominator:

9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2

Now substitute x+4=5\sin y, so that \mathrm dx=5\cos y\,\mathrm dy. Then

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy

which simplifies to

\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy

Now, recall that \sqrt{x^2}=|x|. But we want the substitution we made to be reversible, so that

x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)

which implies that -\dfrac\pi2\le y\le\dfrac\pi2. (This is the range of the inverse sine function.)

Under these conditions, we have \cos y\ge0, which lets us reduce \sqrt{\cos^2y}=|\cos y|=\cos y. Finally,

\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C

and back-substituting to get this in terms of x yields

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C
4 0
3 years ago
Eric starts with 10 milligrams of a radioactive substance. The amount of the
Ulleksa [173]

Answer: Eric: The 10 is the initial amount, the 1/2 is the decay factor or the rate at which it decreases, and the exponent w is the number of weeks it decreases by factor 1/2, or the time. Andrea, 1 is the initial amount, 0.2 is the decay factor or rate of decrease, w is time passed or number of weeks it's decayed by the factor.

Step-by-step explanation: Answer is explanation

5 0
3 years ago
These data show the age in years of 9 members of the youth orchestra. 12 14 16 17.5 10 18 15 15.5 19 What is the IQR (interquart
ryzh [129]
The interquartile range is 4.75.
8 0
3 years ago
Read 2 more answers
7. What are the solutions of the equation? x2 = 11x − 24
mote1985 [20]
Assuming you typed this correctly, and how you wanted it, then the answer(s) would be x=3, or x=8. Both answers are correct. If it were multiple choice, then the answer would look something like: X=3 or 8.
If you meant 2x, then the answer would be x=8/3. This is a fraction
7 0
3 years ago
Which statement is true about this equation?
Karolina [17]

Answer:

infinite solutions

Step-by-step explanation:

-9(x+3) +12 = -3(2x+5)-3x

Distribute

-9x-27 +12 = -6x-15-3x

Combine like terms

-9x -15 = -9x-15

Add 9x to each side

-9x-15+9x = -9x-15+9x

-15 = -15

This is a true statement so it is true for all x

5 0
3 years ago
Other questions:
  • Which of these numbers is composite? 3,5,19,71,85
    11·2 answers
  • True or false a system of equations including a line and a parabola can have only 2 solutions
    15·1 answer
  • in a box of 12 fuses, there are 3 that are defective. if a quality control engineer tests 4 of these fuses at random, what is th
    8·1 answer
  • The diagonals of a rhombus are _____
    6·1 answer
  • Please help worth 25 points
    9·1 answer
  • Tobin is solving the equation 3 (x minus 1.25) = 11.25. His work is shown below.
    12·2 answers
  • The nth term of a sequence is 2n-6 find the first three terms <br><br> need help plzzzz
    13·1 answer
  • I realy need help please​
    14·2 answers
  • James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements ar
    7·1 answer
  • Out of 290 racers who started the marathon, 259 completed the race, 28 gave up, and 3 were disqualified. What percentage did not
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!