What are inequality? When do we use inequalities?

What type of inequalities are there? Which symbols are used for each type?


Are the following expressions variable inequalities? Why?
a. 13z=27
b. x<0
c 3x+5x>11
d. y+5≤11
e. 7-1>- 32​

Answer:

B,C,D, and E

Step-by-step explanation:

Inequality tells us about the relative size of two values.

Mathematics is not always about "equals", sometimes we only know that something is greater or less than.

Example: Alex and Billy have a race, and Billy wins!

What do we know?

We don't know how fast they ran, but we do know that Billy was faster than Alex:

Billy was faster than Alex

We can write that down like this:

b > a

(Where "b" means how fast Billy was, ">" means "greater than", and "a" means how fast Alex was)

Inequalities: Symbols and Vocabulary

Algebra rules / General Rules:

 Isolate a positive x on the left side using algebra

 Reverse the inequality sign when mult/divide by a negative

 Less than: The symbol that:  Looks like an L () for ess than

< ○ )  Points to the Left



● ]  Caps the arrow pointing towards smaller numbers

on the number line

 Points towards the smaller of two numbers (4 < 7)

> Greater than: The symbol that: Looks like the top of an R ( >

)for GReater than

> ○ (  Points to the Right



● [  Caps the arrow pointing towards larger numbers on

the number line

 Open end is by the larger number (7 > 4)

Compound inequalities: usually in the form -4 < x < 4

but can also be x > -4 and x < 4

A researcher predicts that listening to music while solving math problems willmake a particular brain area more active. To test this, a research participant hasher brain scanned while listening to music and solving math problems, and thebrain area of interest has a percentage signal change of 58. From many previousstudies with this same math problems procedure (but not listening to music), it isknown that the signal change in this brain area is normally distributed with amean of 35 and a standard deviation of 10.
(a) Using the .01 level, what shouldthe researcher conclude? Solve this problem explicitly using all five steps of hypothesistesting, and illustrate your answer with a sketch showing the comparisondistribution, the cutoff (or cutoffs), and the score of the sample on this distribution.(b) Then explain your answer to someone who has never had a course in statistics(but who is familiar with mean, standard deviation, and Z scores).

What is the opposite of 4:3?

Please help me if you know the correct answer, thank you

f(x)=3x^2+6x-18 , find f(10)

3 + 8 + 6 + 6 + 6 = 58 + 6
How do we solve this

(Score for Question 1: ___ of 6 points)
Refer to the equation 4x+3y=24
A Complete the table of values for at least 2 points. Show your work.
B How did you find these two values? Answer in complete sentences.
C Use the table of values to graph the line.
You must complete all parts to receive full credit.



Answer:
x y



(Score for Question 2: ___ of 5 points)

Which term describes the relationship between L A and 2 B, if the m LA= 84º and m 2 B = 96º7
A
vertical
В.
adjacent
С
supplementary
D
complementary

Mai's new bedroom has a walk-in closet with a floor that measures 20 square
feet. Her closet ceiling is 9 feet from the floor.
What is the volume of her closet?

guys help me 3(x−4)≥−2x+3

need help not sure ​

Write an algebraic expression for the difference of 5 from b .

what is the value of 2.5x+17+21x-25=180

Please help me with this question? ​

Suppose that two balanced dice are tossed repeatedly and the sum of the two uppermost faces is determined on each toss. a) What is the probability that we obtain a sum of 3 before we obtain a sum of 7? Hint: Let A denote the event of a sum of 3. Let B denote the event of no sum of 3 or 7. Now, begin to list the out the sample space in terms of A and B - it should be recognizable in the lecture notes. Hint: A useful infinite series result when |z| < 1: 1 + z + z 2 + z 3 + z 4 + . . . = 1 1 − z

what is the answer to this question?

A system of equation is shown: 2x = -y + 6 -4x + 3y =8 what is the solution tonthis system of equations? (-1, -4) (1, 4) (4, 4) (-4, -1)

A diagram of a swimming pool is shown.
3.5 m
What is the approximate circumference of the swimming pool? Use 3.14 as an estimate for t.
Ο Α. 7 m
Ο Β. 11 m
Ο Ο Ο Ο
Ο C. 22 η
O D. 28 m

Jane wants to buy carpet for her room measuring 400 square feet. She purchased carpet that costs $20 per square yard. How much will it cost to have her room carpeted? (1 square yard = 9 square feet) Explain how you solved it.

What is the value of 3/4 divided by 3/8

The price of a stock steadily decreased by a total of $123 over the past 14 months.

Write as a product:

25a^2−0.01b^10

Hope is n years old. Interpret the following expression if the expression represents Hunter's age.

3n -8

A.
Hunter is 8 years younger than Hope's age.

B.
Hunter is 8 years older than 3 more than Hope's age.

C.
Hunter is 8 years younger than 3 times Hope's age.

D.
Hunter is 8 years older than 3 times Hope's age.

Help plz asap I really need help with this

Having trouble with finding the rise over run and simplifying the fraction

If f(x) = 3x2 + 2x - 2, find f(8) - f(-5)

I need help with this problem (THIS IS NOT FROM A TEST)

1/2 mi = 880 yd
True
O False

A 33 pound bag of grass seed holds 2 pounds less than 5 smaller bags of seed. Find the weight of the smaller bag of seed.

The angle represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t = 0. If the weight is at its maximum positive position (weight is above equilibrium) at t = 0, then = 0. If the weight is at its maximum negative position (spring is stretched and weight is below equilibrium) at t = 0, then . If the weight is traveling in the negative direction and passing through equilibrium at t = 0, then . In the response box, describe the initial condition of our experiment; specifically, describe the position of the weight and the direction in which it was traveling.

5(r-10)=51 what is r equal to?