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
Volgvan
2 years ago
14

What is the solution set to the inequality 5(x – 2)(x + 4) > 0?

Mathematics
2 answers:
Sidana [21]2 years ago
7 0

Answer:

(-∞, -4) U (2,∞)

Step-by-step explanation:

5(x – 2)(x + 4) > 0

First we solve for x, we replace the inequality sign by = sign

5(x – 2)(x + 4) = 0

Divide both sides by 5

(x – 2)(x + 4) = 0

Now we set each factor =0  and solve for x

x-2 =0 , so x= 2

x+4 =0, so x= -4

Now we use number line and make three intervals

First interval -infinity to -4

second interval -4 to 2

third interval 2 to infinity

Now we check each interval with our inequality

First interval -infinity to -4, pick a number in this interval and check with our inequality. lets pick -5

5(-5 – 2)(-5 + 4) > 0

35>0 is true

second interval -4 to 2, pick a number in this interval and check with our inequality. lets pick 0

5(0– 2)(0 + 4) > 0

-40>0 is false

Third interval 2 to infinity, pick a number in this interval and check with our inequality. lets pick 3

5(3 – 2)(3 + 4) > 0

35>0 is true

solution set are the intervals that make the inequalities true

(-∞, -4) U (2,∞)

olga nikolaevna [1]2 years ago
6 0
5(x-2)(x+4)>0  For this to be true, both parenthetical terms must be both positive or both negative.

x<-4 and x>2

x=(-oo,-4),(2,+oo)


You might be interested in
A triangle has sides of lengths 8, 15, and 17. Is it a right triangle? Explain.
natta225 [31]

Answer:

Step-by-step explanation:

8^2 + 15^2 = ?

64 + 225 = 17^2

289 = 289

\sqrt{289} = \sqrt{289\\} \\ 17 = 17

4 0
2 years ago
Work in the five days?
Ghella [55]

Answer:

9.3

Step-by-step explanation:

last week she worked 45.6 hours. since 40 hours is the limit for normal working hours, she worked 45.6-40 = 5.6 hours overtime.

this week she worked 9.7+8.3+8+9.1+8.6 hours = 43.7 hours.

she worked therefore 43.7-40 = 3.7 hours overtime.

so, in total of the two weeks, she worked 5.6+3.7 = 9.3 hours overtime.

7 0
3 years ago
PLEASE HELP ASAP
Kaylis [27]

Answer:

11.1

Step-by-step explanation:

6 0
2 years ago
The graph shows the number of handbags that mandy made in one day.What are the variables? Describe how the variables are related
tankabanditka [31]
The variables are: time(the independent variable or (x) variable) and number of handbags (the dependent variable or (y) variable). The variables helps to plot an accurate points on the graph.
8 0
3 years ago
Read 2 more answers
If a basket of goods and services used to calculate CPI contains 2 pairs of socks at $2 each and 1 pair of shoes at $50, what wi
Svetach [21]

Answer:

B. 55.10

Step-by-step explanation:

Given:

1 pair of Shoes for 1st year = $50

2 pair of Sock for 1st year = $2 each = 2\times2= $4

\therefore CPI for year 1 = Price of shoes for 1st year + Price of Sock for 1st year= $50 + $4 = $54

Now

1 pair of Shoes for 2nd year = $51

2 pair of Sock for 2nd year = $2.05 each = 2 \times2.05 =$4.10

\therefore CPI for Year 2 = Price of shoes for 2nd year + Price of Sock for 2nd year= $51 + $4.1 = $55.10

Hence CPI for Year 2 is $55.10

7 0
3 years ago
Other questions:
  • 14 = 31.7 – 3x What is the solution?
    10·2 answers
  • The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, So
    6·1 answer
  • A scale drawing of a room is 6inches x4inches. Scale of 1:40. What is the square feet
    5·1 answer
  • Hello, Can someone please help me with this math problem? thanks!
    6·1 answer
  • Suzie's tulips are 6 inches shorter than her rose bush. The rose bush is 13 inches tall. Write and solve an addition equation to
    14·2 answers
  • The perimeter of a triangle with the length of x, 5x, and 6x-3
    9·1 answer
  • Show the next 2 term 5. 4,2,0,-2,-4
    15·2 answers
  • What’s the square root of 6
    6·1 answer
  • Find the value of each missing variable. PLS!!!
    9·2 answers
  • Y=in x if and only if<br>A) x=10^y<br>B) x=10^x<br>c) x=e^y<br>d) x=e^x
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!