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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.

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Can someone tell me what the small circles on the angles of the triangles mean and what they are called?
kozerog [31]
The semi-circles in the triangles represent the verteces or different angles on certain points of the triangle.

-Hope this helped! :D
4 0
2 years ago
Read 2 more answers
A trapezoid has an area of 329 square feet. If the bases are 30 feet and 17 feet, what is the height of the trapezoid in feet? F
ExtremeBDS [4]

Answer:

The correct option is C.  14 ft

Step-by-step explanation:

To calculate the height, we will follow the steps below;

Formula is given to be:  h = 2A / b1 +b2

where h = height of the trapezoid   b1 and b2 are the bases of the trapezoid    and A is the area of the trapezoid

From the question given;

Area A =329 feet²      b1 = 30 feet    b2 =17 feet  

We can now proceed to insert the values into the formula

h = 2A / b1 +b2

h= 2(329)  / 30 + 17

h = 658 /47

h=14 feet

6 0
2 years ago
Joanna made a table and a graph for the equation y = 2x.
Leokris [45]
B. both r correct

when it’s 2x it goes up two over one. rise/run, 2/1
for the table if you look at the graph when x=1 then y=2 and if x=2 then y=4

5 0
2 years ago
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Estimate the amount of time the trip will take. 100 miles at 40 mph 8 and 1/2 hours 2 and 1/2 hours 4 hours 6 and 1/4 hours
Natasha_Volkova [10]

Answer:

2 1/2 hours

Step-by-step explanation:

Divide 100 by 40 and you get 2.5

7 0
2 years ago
May I please receive help?
Yuki888 [10]

Answer:

9.2 ft

Step-by-step explanation:

The shape is a triangle, the 11 ft is your hypotenuse

You need to use the Pythagorean Theorem!

a^2 + b^2 = c^2 (solve for a, the missing length that they ask for)

so --->

a^2 + (6^2) = 11^2

      a^2 + 36 = 121

             ~subtract 36 to the right side~

               a^2 = 85

now find the square root of 85:

               a = 9.21954

        round it to the nearest tenth:

                   a = 9.2

final answer: 9.2 ft

hope this helpsss

3 0
2 years ago
Read 2 more answers
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