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
zavuch27 [327]
3 years ago
14

For which values of x is the inequality 2(1 + x) > x + 8 true?

Mathematics
1 answer:
Arlecino [84]3 years ago
4 0

Answer:

\large\boxed{\text{For}\ x>6\to x\in(6,\ \infty)}

Step-by-step explanation:

2(1+x)>x+8                 <em>use distributive property</em>

2+2x>x+8       <em>subtract 2 from both sides</em>

2x>x+6           <em>subtract x from both sides</em>

x>6

You might be interested in
Write the standard form of the equation for the circle that passes through the points (2,31),(-15,14),(33,0)
stepladder [879]

Answer:

Step-by-step explanation:

Begin with the standard form of a circle as a conic:

Ax^2+Bxy+Cy^2+Dx+Ey+F=0

For a circle, A and C will be the exact same, and B will equal 0.  If B is non-zero, the equation represents a rotation of a conic, which is reserved for college-level courses.  Shortening this, then:

x^2+y^2+Dx+Ey+F=0 is good enough for us for this.  Start with the first point on the circle, (2, 31) and fill in the equation above with x and y:

2^2+31^2+2D+31E+F=0 which simplifies down to:

(1):2D+31E+F=-965

Do the same with the next point on the circle, (-15, 14):

-15^2+14^2-15D+14E+F=0 which simplifies down to:

(2):-15D+14E+F=0

Do the same with the last point, (33, 0):

33^2+0^2+33D+0E+F=0 which simplifies down to:

(3):33D+F=-1089

Now we will add (1) and (2) to get (4):

 2D + 31E + F = -965

-15D + 14E + F = -421

Multiply the top equatio by -1 to get rid of the F terms:

 -2D - 31E - F = 965

-15D + 14E + F = -421

which simplifies to

(4): -17D - 17E = 544

Now add (2) and (3) to get (5):

-15D + 14E + F = -421

33D           + F = -1089

Multiply the bottom equation by -1 to get rid of the F terms:

-15D + 14E + F = -421

-33D          - F = 1089

which simplifies to

(5): -48D + 14E = 668

Now add (4) and (5) together and eliminate the E terms:

-17D - 17E = 544

-48D + 14E = 668

In order to eliminate the E terms, multiply the top equation by 14 and the bottom equation by 17 to solve for D:

-238D - 238E = 7616

-816D + 238E = 11356

Which gives you that

D = -18

Now plug the value for D into (4) to find E:

-17(-18) - 17E = 544 and

306 - 17E = 544 and

-17E = 238 so

E = -14

Now plug the values for both D and E into (1) to find F:

2(-18) + 31(-14) + F = -965 and

-36 - 434 + F = -965 and

-470 + F = -965 so

F = -495

Now we can fill in the standard form of the conic:

x^2+y^2-18x-14y=495

but we're not done til we complete the square on both the x terms and the y terms (and I am assuming you know how to complete the square):

(x^2-18x+81)+(y^2-14y+49)=495+81+49 which simplifies to

(x-9)^2+(y-7)^2=625

The second choice down matches that equation, but the center they have there is not correct.  The center of that circle is (9, 7) and they have it as being (7, 10) with a radius of 5.  The radius is 25.  The center is wrong in the equation that represents the circle as is the radius.  Maybe let someone know that...

4 0
3 years ago
Read 2 more answers
Ax+by+c=0 solve for y
kvv77 [185]

Answer: \large\boxed{y=\frac{-ax}{b} -\frac{c}{b}}

Step-by-step explanation:

ax+by+c=0\\ax+by=-c\\by=-ax-c\\y=\frac{-ax-c}{b}\\y=\frac{-ax}{b} -\frac{c}{b}

8 0
2 years ago
1) 130 words in 5 mins. How many words in an hour?
FinnZ [79.3K]

Answer:

Part 1) 1,560 words

Part 2) 161 miles

Step-by-step explanation:

Part 1) 130 words in 5 mins. How many words in an hour?

Remember that

1\ hour=60\ min

so

using proportion

Find out how many words in 60 minutes (one hour)

\frac{130}{5}\ \frac{words}{min}= \frac{x}{60}\ \frac{words}{min}\\\\x=130(60)/5\\\\x=1,560\ words

Part 2) 322 miles in 2 hours. How many miles in 60 minutes?

Remember that

1\ hour=60\ min

so

2\ hours=120\ minutes

using proportion

Find out how many miles in 60 minutes

\frac{322}{120}\ \frac{miles}{min}= \frac{x}{60}\ \frac{miles}{min}\\\\x=322(60)/120\\\\x=161\ miles

8 0
3 years ago
How many positive integers less than 500 are equal to 5 times an even integer?
arlik [135]

Answer:

490/10=49

Every 10 numbers is one number. I divided by 490 because it says less then 500

Step-by-step explanation:

4 0
3 years ago
N + N - 35000=833000
adell [148]

Answer:

N + 434000

Step-by-step explanation:

N + N - 35000 = 833000

(add 35000 to both sides)

N + N = 868000

(N + N is equivalent to 2N)

2N = 868000

(divide both sides by 2)

N = 434000

8 0
3 years ago
Other questions:
  • The sales tax on a $350 computeris $22.75. find thr sales tax rate
    15·1 answer
  • If you have an x-intercept = 3 and a y-intercept = 5 find the slope and the y-intercept.
    7·1 answer
  • What is the product? (3.4)(-7.8<br> a.-26.52<br> b.11.2<br> c.-11.2<br> d.-21
    7·1 answer
  • HELP URGENT 5 STAR RATING AND BRANLY!
    6·2 answers
  • Please help with a math problem. Please explain how you got the answer
    8·1 answer
  • What is one word descriptor for sustituye and solve?
    15·1 answer
  • Hello please help posted picture of question
    6·1 answer
  • select all the correct answers which expressions are equal to 6^3.2^6/2^3 A. 2^3.3^3 B. 12^6 C. 2^6.3^3 D.6^3 E. 12^3​
    8·1 answer
  • 4. 1 less than twice the square of a number
    10·1 answer
  • A right pyramid has a height of 3 inches and a square base with side length of 5 inches. What is the volume of the pyramid?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!