Determine whether the following relationship is a linear inequality or not

1. Y < 3

2. x ≥ 6

3. x² > -3

4. x -3 > 1/2

5. xy + 5 ≤ 7​

Answers

Answer 1

Answer:

What is a linear inequality ? A linear inequality has the same condition as a linear equality, but instead of the equal sign, we have for example this one ≤ wish means less than or equal to.

But what are the condition of a linear equality ? There are many ways of writing linear equations but they usually have constants (like "2" or "c") and must have simple variables (like "x" or "y") BUT the variables (x and y) on a linear equation do NOT have Exponents (like the 2 in x²) and square roots,

1. y < 3

Yes, this is a linear inequation. Frequently, the term linear equation refers implicitly to the case of just one variable (here y).

2. x ≥ 6

Yes.

3. x² > - 3

No, remember the rule the variable (here x) must not have exponents.

4. x - 3 > 1/2

Yes.

5. xy + 5 ≤ 7

This one is nice. If both x and y are variables then the answer is no, it's not a linear inequation. Why ?The linear equation is a sum of terms like "Ax" where x is a variable, and A is a number or a constant. On the other hand if x or y was a constant (like e or π), it could be treated as a number and the whole expression would become linear.

You can also have fun and write :

xy ≤ 2

for y > 0 we write:

x ≤ 2/y

x ≤ 2[tex]y^{-1}[/tex]

and then simply say exponents are not allowed so not a linear inequation.


Related Questions

SOVE, REDUCE TO LOWEST TEERMS SIMPLIFY IMPROPER FRACTIONSAS MIXED FRACTIONS

Answers

I don’t see a picture

A research report claims that 20% of all individuals use Firefox to browse the web. A software company is trying to determine if the proportion of their users who use Firefox is significantly different from 0.2. In a sample of 200 of their users, 26 users stated that they used Firefox.

Required:
Using this data, conduct the appropriate hypothesis test using a 0.01 level of significance.

Answers

Answer:

Reject H0

Step-by-step explanation:

Z  = -2.474873734

 

survey (positive) 26

n (total) 200

p 0.2

 

p /point est. 0.13

POPULATION(min) 4000

np        >= 5 ? YES 40

n(1-p)  >= 5 ? YES 160

Sample is valid  

Confidence Level - "P" values  

99% 2.58

Confidence Interval - "P" values  

(0.0686 , 0.1914 )  

Reference=0.2 Reject H0

3(8a - 5b) – 2(a + b); use a = 3 and b = 2

Answers

Answer:

32

Step-by-step explanation:

3(8(3)-5(2))-2((3)+(2))

3(24-10) -2(5)

3(14) -10

42-10

32

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{3(8a - 5b) - 2(a + b)}\\\\\huge\textsf{= 3(8(3) - 5(2)) - 2(3 + 2)}\\\\\huge\textsf{= 3(24 - 10) - 2(3 + 2)}\\\\\huge\textsf{= (3)(14) - 2(3 + 2)}\\\\\huge\textsf{= 42 - 2(3 + 2)}\\\\\huge\textsf{= 42 - 2(5)}\\\\\huge\textsf{= 42 - 10}\\\\\huge\textsf{= 32}}[/tex]

[tex]\huge\boxed{\textsf{Answer: 32}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]


Which expression is the best estimate of the product of 7/8and 8 1/10?

Answers

Answer:

7 7/80 or 7.0875

Step-by-step explanation:

product is the result of multiplication

7/8 * 81/10 = 567/80 = 7 7/80 or 7.0875

Find the measure of angle x in the figure below:

A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 57 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 61 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 67 degrees. The interior angle on the left is labeled as x.

35°
47°
51°
62°

Answers

I think is 62 but I’m not sure

Your answer iss...

It is 51º

A circular water fountain in the town square has a 112-foot circumference. How far is the center of the fountain from the outer edge? Round to the nearest whole number.

Answers

Answer:

18 feet

Step-by-step explanation:

The distance of the center of the fountain from the enter edge is equal to the radius of the circular fountain.

Use the circumference formula, c = 2[tex]\pi[/tex]r, to find the radius.

c = 2[tex]\pi[/tex]r

112 = 2[tex]\pi[/tex]r

18 = r

So, to the nearest whole number, the distance between the center of the fountain and outer edge is 18 feet.

88%
19. What is the solution X in this equation? 2(3x - 7) + 4(3x + 2) = 6(5x+9) + 3

Answers

[tex]\\ \sf\longmapsto 2(3x-7)+4(3x+2)=6(5x+9)+3[/tex]

[tex]\\ \sf\longmapsto 6x-14+12x+8=30x+54+3[/tex]

[tex]\\ \sf\longmapsto 6x+12x-14+8=30x+57[/tex]

[tex]\\ \sf\longmapsto 18x+6=30x+57[/tex]

[tex]\\ \sf\longmapsto 30x-18x=6-57[/tex]

[tex]\\ \sf\longmapsto 12x=51[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{51}{12}[/tex]

a company has decreased the weight of its boxes of macaroni by 8 %. if the new weight of the box is 13.1ounces, what was the original weight of the​ box?

Answers

Answer:

실례합니다 ?

Step-by-step explanation:

이것이 무엇을 의미하는 질문입니까?

회사는 마카로니 상자의 무게를 8% 줄였습니다. 상자의 새 무게가 13.1온스인 경우 상자의 원래 무게는 얼마였습니까? 오른쪽 ?

Answer:

x*0.92 = 13.1

x = 14.24

Step-by-step explanation:

r-(-4x - (y + y)); use x = -4, and y = -3 evaluate ​

Answers

Answer:

insert values of x and y

r - ( -4(-4) - ( -3-3))

r - ( 16 +6 )

r - 22

Doneeeeeeeeeeeeeeeeee3

Does the point (7,34) satisfy the equation y = 2x + 8

Answers

Answer:

no

Step-by-step explanation:

Substitute the point into the equation and see if it is true

34 = 2(7) +8

34 = 14+8

34 = 22

Since this is not true, the point does not satisfy the equation

Answer:

No

Step-by-step explanation:

because 7 is X and 34 is Y

So its 2 *7 +8=22

so no

A certain positive integer has exactly 20 positive divisors.

What is the largest number of primes that could divide the integer?

thx for the help in advance

Answers

9514 1404 393

Answer:

  3

Step-by-step explanation:

20 has at most 3 proper factors greater than 1: 2×2×5. Each of these can represent a prime factor of the number of interest, and is 1 more than that prime's power. That is, the number of interest (n) will have at most 3 prime factors p, q, r, and will be ...

  n = p·q·r^4

_____

For some prime factorization ...

  [tex]\displaystyle n=\prod_{k=1}^m{p_k^{q_k}}[/tex]

The total number of divisors of n is ...

  [tex]\displaystyle\prod_{k=1}^m{(q_k+1)}[/tex]

7. Kylie bikes at a speed of 100 yards per minute. Robert bikes at a speed of 240 feet per minute. In feet per second, how much faster does Kylie bike than Robert?​

Answers

440 feet she get equal

Simplify the following by removing parentheses and combining terms
- (2x + 8) + 3(2x + 8) - 2x

Answers

Answer:

2x+16

Step-by-step explanation:

PEMDAS

A football team has a probability of 0.76 of winning when playing any of the other four teams in its conference. If the games are independent, what is the probability the team wins all its conference games

Answers

Answer:

0.33362176

Step-by-step explanation:

Probability is the ratio of the number of possible outcomes to the number of total outcomes.

Given that a football team has a probability of 0.76 of winning when playing any of the other four teams in its conference, the probability that the team wins all its conference games

= 0.76 * 0.76 * 0.76 * 0.76

= 0.33362176

This is the probability that the teams wins the 4 matches played against the other teams in the conference.

how do you tell how many times greater is the 5 in 458,039 than the 5 in 271,145

Answers

Answer:

count the number of places it is. The 5 in 458,039 is in the 10,000 place and the 5 in 271,145 is in the ones place so the 5 in 458,039 is 10,000 times greater

1,000
the 5 in 45,039 has a value of 1,000 while the 5 in 271,145 has a value of 1 and 1,000/1=1,000

Please help I need the answer ASAP!!

Answers

The hypotenuse will always be the longest side of the triangle. Option C is correct: AB > DC.

AB is the hypotenuse of triangle ABC. Therefore, it is greater than leg AC. AC is the hypotenuse of triangle ACD. If AC is less than AB, then DC must also be less than AB because DC is less than AC.

Hope this helps!

a² +6²
a-b
if a = 3 and b = 4
Evaluate each expression using the variable replacements.

Answers

Knowing what the variables are means that all we have to do is substitute:
[ ( 3 ) ^2 + ( 4 ) ^2 ] / 4 - 3 =
( 9 + 16 ) / 1 =
25

Answer:

-45

Step-by-step explanation:

let a= 3 and b= 4a² + 6² / a - b= 3² + 6² / 3 - 4= 9 + 36 / -1= 45 / -1= -45

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Please help me, by completing this proof!

Answers

Answer:

Step-by-step explanation:

                 Statement                                                 Reasons

1). Line PQ is an angle bisector of ∠MPN       D). Given

2). ∠MPQ ≅ ∠NPQ                                           A). Definition of angle bisector

3). m∠MPQ = m∠NPQ                                      F). Definition of congruent

                                                                               angles.

4). m∠MPQ + m∠NPQ = m∠MPN                    C). Angle addition postulate

5). m∠MPQ + m∠MPQ = m∠MPN                   G). Substitution property of

                                                                                equality

6). 2(m∠MPQ) = m∠MPN                                 B). Distributive property

7). m∠MPQ = [tex]\frac{1}{2}(m\angle MPN)[/tex]                               E). Division property of equality  

Please help me please! I really need it! Thank you so much!!!!!!!!!!! Sorry Quality is really bad

Answers

Answer:

 7[tex]\frac{5}{6}[/tex]

Step-by-step explanation:

- 2[tex]\frac{1}{3}[/tex] - ( - 10[tex]\frac{1}{6}[/tex] ) = - 2[tex]\frac{1}{3}[/tex] + 10[tex]\frac{1}{6}[/tex] = - 2[tex]\frac{2}{6}[/tex] + 10[tex]\frac{1}{6}[/tex] = ( 10 - 2 ) + ( [tex]\frac{1}{6}[/tex] - [tex]\frac{2}{6}[/tex] ) = 8 - [tex]\frac{1}{6}[/tex] = 7 + ( [tex]\frac{6}{6}[/tex] - [tex]\frac{1}{6}[/tex] ) = 7[tex]\frac{5}{6}[/tex]

12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?

Answers

Answer:

3.75

Step-by-step explanation:

In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. Use the equation P(AUB)=P(A) + P(B) - P(ANB), where A and B are any events, to compute the probability that the number drawn is prime or greater than 12.

The probability that the number drawn is prime or greater than 12 is : ___________

Answers

Answer:

17/25

Step-by-step explanation:

The equation for the probability of two events that are not mutually exclusive is:

p(A ∨ B) = p(A) + p(B) - p(A ∧ B)

A = the number is prime

B = the number is prime

The numbers are:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25

Here are the 8 prime numbers that satisfy event A:

3, 5, 7, 11, 13, 17, 19, 23

p(A) = 8/25

Here are the 13 numbers that are greater than 12 that satisfy event B:

13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25

p(B) = 13/25

Here are the 4 numbers that satisfy both event A and event B:

13, 17, 19, 23

p(A ∧ B) = 4/25

p(A ∨ B) = p(A) + p(B) - p(A ∧ B)

p(A ∨ B) = 8/25 + 13/25 - 4/25

p(A ∨ B) = 17/25

The probability that the number drawn is prime or greater than 12 = [tex]\frac{18}{25}[/tex]

What is probability?

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

Formula of the probability of an event A is:

P(A) = n(A)/n(S)

where,  n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.

For given question,

In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25.

n(S) = 25

Let event A: the number drawn is prime

The prime numbers from 1 to 25 are:

2, 3, 5, 7, 11, 13, 17, 19, 23

So, n(A) = 9

The  probability that the number drawn is prime,

[tex]P(A)=\frac{n(A)}{n(S)}\\\\ P(A)=\frac{9}{25}[/tex]

Let event B: the number drawn is greater than 12

So, n(B) = 13

The probability that the number drawn is greater than 12,

[tex]P(B)=\frac{n(B)}{n(S)}\\\\ P(B)=\frac{13}{25}[/tex]

The number drawn is prime as well as greater than 12.

Such numbers are : 13, 17, 19, 23

n(A ∩ B) = 4

So, the probability that the number drawn is prime as well as greater than 12,

[tex]P(A\cap B)=\frac{n(A\cap B)}{n(s)}\\\\ P(A\cap B)=\frac{4}{25}[/tex]

Using the equation P(AUB) = P(A) + P(B) - P(A ∩ B) to find the probability that the number drawn is prime or greater than 12,

[tex]\Rightarrow P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow P(A\cup B)=\frac{9}{25}+ \frac{13}{25} -\frac{4}{25} \\\\\Rightarrow P(A\cup B)=\frac{9+13-4}{25}\\\\ \Rightarrow P(A\cup B)=\frac{18}{25}[/tex]

Therefore, the probability that the number drawn is prime or greater than 12 = [tex]\frac{18}{25}[/tex]

Learn more about probability here:

brainly.com/question/11234923

#SPJ2

find x and y on triangle
Also the degree is 30 and the other thing is 7sqrt3​

Answers

Answer:

y =7

x =14

Step-by-step explanation:

Since this is a right triangle we can use trig functions

tan 30 = opp /adj

tan 30 = y/ 7 sqrt(3)

7 sqrt(3)  tan 30 = y

7 sqrt(3) * 1/ sqrt(3) =t

7 =y

sin 30 = opp/ hyp

sin 30 = 7/x

x sin 30 =7

x = 7/ sin 30

x = 7 / 1/2

x = 14

Solve 7 ( x + 1 ) + 2 = 5x + 15

Answers

Answer:

x = 3

Step-by-step explanation:

7(x + 1) + 2 = 5x + 15

~Simplify left side

7x + 7 + 2 = 5x + 15

~Combine like terms

7x + 9 = 5x + 15

~Subtract 9 to both sides

7x = 5x + 6

~Subtract 5x to both sides

2x = 6

~Divide 2 to both sides

x = 3

Best of Luck!

Find the greatest number of students to whom 45 soccer balls and 60 tennis balls can be equally divided.

Answers

Answer:

15 students

Step-by-step explanation:

Find GCF of 45 and 60:

45 = 3*3*560 = 2*2*3*5

GCF(45,60) = 3*5 = 15

Soccer balls=45Tennis balls=60

Find Greatest common multiple or GCF

[tex]\\ \sf\longmapsto 45=3\times 3\times 5[/tex]

[tex]\\ \sf\longmapsto 60=2\times 2\times 3\times 5[/tex]

Now

[tex]\\ \sf\longmapsto GCF=3\times 5=15[/tex]

(a) If y varies directly as x, and y=24 when x=16, find y when x=12.

(b) In a formula, z varies inversely as P. If Z is 200 when P is 4, find z when P is 10.

Answers

Answer:

(a) 18

(b) 80

Step-by-step explanation:

(a) let y=kx

so, 24=16k

or, k=24/16 or, k=3/2

now, putting x=12

y=kx

or, y=(3/2)×12

or, y=3×12/2

or, y=36/2

or, y=18

(b) let P=k/z

so, 4=k/200

or, k=800

when P = 10

P=k/z

or, 10=800/z

or, z=800/10

or, z=80

Help !!!!!!!!!!!!!!!

Answers

Answer:

9/4 = 2 1/4

Hope this Helps!?

Write the quadratic function f(x) = x2 - 2x - 8 in factored form.
A) f(x) =(x - 4)(x - 2)
B) f(x) =(x + 4)(x - 2)
C) f(x) =(x - 4)(x + 2)
D) Rx) =(x + 4)(x + 2)

Answers

Answer:

Hello,

answer C

Step-by-step explanation:

[tex]f(x)=x^2+2x-8\\\\=x^2-4x+2x-8\\\\=x(x-4)+2(x-4)\\\\=(x-4)(x+2)\\\\Answer\ C[/tex]

3/4 + 20 (2/5 x 4/7) ​

Answers

Answer:

i believe the answer is 5.3

I WILL GIVE BRAINLEST FAST PLEASE ANSWER THE QUESTION IN THE IMAGE

Answers

Answer:

Cannot be determined

Step-by-step explanation:

We only know one angle and we could only compare one set of sides.

We do not have enough information to determine if the triangles are similar

Answer: D. Cannot be determined

A building 51 feet tall casts a shadow 48 feet long. Simultaneously, a nearby statue casts a shadow of 16 feet. How tall is the statue? Choose an answer

Answers

Answer: 17 feet

Step-by-step explanation:

51/48 = x/16

(51)(16)/48

The statute is 17 feet tall.

What are the similar triangles?

Similar triangles are the triangles that have the same shape, but different sizes. The corresponding angles are congruent and the sides are in proportion.

What is the ratio of any two corresponding sides of similar triangles?

The ratio of any corresponding sides in two equiangular triangles is always the same.

Let's visualize the situation according to the given question.

AB is the building ,whose height is 51f

BC is the shadow of the building AB, whose length is 48ft.

QR is the shadow of the tower statue, whose length is 16feet.

Let the height of the statue PR be h feet.

In triangle ACB and triangle PRQ

∠ACB = ∠PRQ = 90 degrees  

( the objects and shadows are perpendicular to each other)

∠BAC = ∠QPR

( sunray falls on the pole and tower at the same angle, at the same time )

ΔACB similar to ΔPRQ   ( AA criterion)

Therefore, the ratio of any two corresponding sides in equiangular triangles is always same.

⇒ AC/CB = PR/RQ

⇒[tex]\frac{51}{48} =\frac{h}{16}[/tex]

⇒ h = [tex]\frac{(51)(16)}{48}[/tex]

⇒ h = 17 feet.

Hence, the statute is 17 feet tall.    

Learn more about the similar triangle here:

brainly.com/question/25882965

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