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
dybincka [34]
1 year ago
8

Solve your answers using inequalities using a number line strategy or a factor table strategy. Express your answers using set no

tation. a) (x+3)^2 (x+1)(x-1) > 0b) (x+1)(x+3) ≥ 0
Mathematics
1 answer:
PtichkaEL [24]1 year ago
5 0

S=\lbrace x\parallel x1\rbrace

Explanation

(x+3)^2(x+1)(x-1)>0

Step 1

solve for each factor:

set each factor equal to zero

\begin{gathered} (x+3)^2=0 \\ x=-3 \end{gathered}\begin{gathered} x+1=0 \\ x=-1 \end{gathered}\begin{gathered} x-1=0 \\ x=1 \end{gathered}

so, we have 3 critical numbers

-3,-1 and 1

Step 2

now, let's make a table to evaluate each interval , (select a number from the interval)

\begin{gathered} a)(x+3)^2 \\ \text{for x=-5} \\ (x+3)^2=(-5+3)^2=4 \\ so\text{ }\Rightarrow positive \\ \text{for x= -2} \\ (x+3)^2=5^2=25\Rightarrow positive \\ \text{for x= 0} \\ (0+3)^2=9\Rightarrow positive \\ for\text{ x= 2} \\ (2+3)^2=(2+3)^2=25\Rightarrow positive \end{gathered}

b) (x+1)

\begin{gathered} x+1 \\ \text{for x=-4} \\ -4+1=-3\Rightarrow negative \\ \text{for x=-2} \\ -2+1=-1\Rightarrow negative \\ \text{for x=0} \\ 0+1=1\Rightarrow positive \\ \text{for x= 2} \\ 2+1=3\Rightarrow positive \end{gathered}

c)(x-1)

\begin{gathered} x-1 \\ \text{for x=-4} \\ -4-1=-\Rightarrow negative \\ \text{for x=-2} \\ -2-1=-3\Rightarrow negative \\ \text{for x=0} \\ 0-1=-1\Rightarrow\text{negative} \\ \text{for x= 2} \\ 2-1=1\Rightarrow positive \end{gathered}

Step 3

now, make th multiplication of the signs ( check the table in step 2)

so, we got

(-infi, -1) U (1, inf)

as we need that the product of the factors is greater than zero ( positive) , the solution is( set notation)

S=\lbrace x\parallel x1\rbrace

I hope this helps you

You might be interested in
Question 2(Multiple Choice Worth 4 points) (08.02)A pair of equations is shown below. x + y = 5 y = one halfx + 2 If the two equ
8_murik_8 [283]

Answer:

(2,3)

Step-by-step explanation:

The first equation is  x+y=5

The second equation is y=\frac{1}{2}x+2

When we graph these two equations, <em>they will meet at a point which represent the solution of the two equations</em>.

We can solve the two equations simultaneously to determine their point of intersection.

Let us substitute the second equation into the first equation to get;

x+\frac{1}{2}x+2=5

Multiply through by 2 to get;

2x+x+4=10

Group similar terms to obtain;

2x+x=10-4

Simplify;

3x=6

Divide both sides by 3;

\Rightarrow x=2

Put x=2 into the second equation;

y=\frac{1}{2}(2)+2

\Rightarrow y=1+2

\Rightarrow y=3

Therefore the graphs of the two functions intersect at (2,3)

See graph in attachment.

3 0
3 years ago
4. Using the graph at right, determine how long it<br> takes to mow an acre of grass.
kirill115 [55]

Answer:

I think 0.7

Step-by-step explanation:

3 0
2 years ago
WILL CHOOSE BRAINLIEST!!!
dsp73

Answer:

Step-by-step explanation:

Percentage without triazine resistance

Start 21,200%

End  9,900%

Percentage with triazine resistance

Start 28,800%

End 35,100%

7 0
2 years ago
Alexis has a rectangular piece of red paper that is 4 centimeters wide. it's length is twice it's width. she glues a rectangular
Sergio039 [100]
The area of the red piece of paper is A= 4(2*4)= 4*8= 32 in^2.
The area of the blue piece of paper is A= 3*7=21 in^2. You subtract 21 from 32 and the difference is 11. So 11in^2 is visible.
5 0
3 years ago
Solve : 4x+10=14 for x<br> x=___
valentinak56 [21]

Answer:

x=1

To make it 20 characters long.....

a lehougwoeljghhwi;eklt gyfbkqw.jlguyvgsajbqkjr.nltGUDVYAGSIB;GILBUSDVYHAGIBU;JKLTGRIUVHAGIBJKtlgrUVSDAGUIFqbjktnlGARWJUHIGFUWQHJRRGEF

6 0
3 years ago
Other questions:
  • Solve for a in terms of b and c:3a+4b=c
    13·1 answer
  • The longest side of an obtuse triangle measures 20 cm. The two shorter sides measure x cm and 3x cm. Rounded to the nearest tent
    9·2 answers
  • Given: ∠N ≅ ∠S, line ℓ bisects at Q.
    7·1 answer
  • Kayla drove 13 miles in 20 minutes. What's her average rate in miles per hour
    5·1 answer
  • You are buying a house for 158,950 you have an annual intrest rate of 4.83% over the next 25 years. How much us the final cost o
    12·1 answer
  • Trent attaches his A+ test to the refrigerator with a circular magnet. Out of curiosity, he measures the magnet and calculates t
    11·1 answer
  • A right triangular prism has a base with perimeter 12 cm and area 6 cm2.
    10·2 answers
  • using the equation G = 10-1.25t. What is the x-intercept of the equation and what is its interpretation in the context of the pr
    5·1 answer
  • Need help asap i’ll vote brain liest
    13·2 answers
  • This is another 5 questions
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!