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
Sloan [31]
3 years ago
9

Solve the inequality and express in interval notation and graph its solution on a number line

Mathematics
1 answer:
vfiekz [6]3 years ago
7 0

Answer:

x ∈ (-∞, 3) U (6, ∞).

Step-by-step explanation:

x^2> 9x - 18

x^2 - 9x + 18> 0

We use factorization and optain

(x-6)(x-3)> 0

Then, we have two critical points: x=3 and x=6. Now:

(i) for x < 3 we have that x-6 <0 and x-3 <0. Then (x-6)(x-3)  > 0.

(ii) for 3 < x < 6 we have that x -6 <0 and x -3 > 0. Then (x-6)(x-3)  < 0.

(iii) for x > 6 we have that x-6 >0 and x-3 > 0. Then, (x-6)(x-3)  > 0.

conditions (i) and (iii) satisfy the inequatliy, then the solution is x ∈ (-∞, 3) U (6, ∞).

The graph is in the picture below.

You might be interested in
Determine if the given equations are parallel, perpendicular, or neither <br> 4y=3x-4 and 4x+3y=-6
Kazeer [188]

Answer:

Perpindicular

Step-by-step explanation:

Solve each equation for y, or point Slope form.

y = mx + b

4y = 3x - 4 divide both sides by 4 to isolate the y.

y = 3/4x - 1

The second equation.

4x + 3y = - 6 subtract 4x from both sides

3y = -4x - 6 divide both sides by 3

y = -4/3 - 2

If you visualize line 1 having a Slope of 3/4, that is, for every 4 we move in the positive x direction, y will increase by 3, it slopes up from left to right crossing the y axis at (0,-1). The second line moves 3 in the positive x direction and decreases in y by 4, it slopes down from left to right crossing the y axis at (0,-2}.

Because the two lines have negative inverse slopes they are perpendicular. 3/4x and - 4/3x

8 0
2 years ago
Round 3487 to the nearest thousand​
dlinn [17]

Answer:

3000

Step-by-step explanation:

the 4 next to the 3 means that you will be rounding down.

6 0
3 years ago
Read 2 more answers
How does an estimate help you place the decimal point when multiplying 3.9 ✖️5.3
Step2247 [10]
Answer: 20.67
Hope it helps
3 0
2 years ago
Please help me to fill in the blanks
Alja [10]
Oooooo child i wish i could help
5 0
2 years ago
Slope= -1/2 Line passes through the point (9,8). Write equation with point slope form
irina1246 [14]
ANSWER: y-8= -1/2(x-9)
3 0
2 years ago
Read 2 more answers
Other questions:
  • Find the amount (future value) of the ordinary annuity. (round your answer to the nearest cent.) $1500/semiannual period for 8 y
    15·1 answer
  • Combine like terms to create an equivalent expression.<br> 3.26d+9.75d-2.65
    13·2 answers
  • Bill Gates wants to construct an in ground swimming pool for his dog. he wants it's length to be 8 yards shorter than twice it's
    11·2 answers
  • What is greater 1 4/6 or 1 14/21
    15·2 answers
  • A rain gutter is made from sheets of aluminum that are 20 inches wide by turning up the edges to form right angles. Determine th
    12·1 answer
  • Solve the equations to find the number and type of solutions. The equation 8 − 4x = 0 has real solution(s).
    6·2 answers
  • 5. Which term best describes the outcome of flipping a coin as either heads or tails?
    5·1 answer
  • Hamburger sales for 3 lb for $6 if Alicia buys 10 lb of hamburger how much will she pay
    15·2 answers
  • Factor the expression p2-16
    10·1 answer
  • Would appreciate if someone helped me with this.
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!