(a) has no solutions.

(b) has infinitely many solutions.

(c) has exactly one solution.

Answers

Answer 1

Answer and Step-by-step explanation:

Given

ax + by = c

qx + ry = s

(a) the equation has no solutions if a/q = b/r ≠ c/s, when this happens, we say the system of equations has no solution. For example

x + y = 3

x + y = 5

Subtracting first equation from the second we have:

0 = 2 which is impossible.

(b) the equations have infinite solutions if a/q = b/r = c/s, for example

x + y = 2

x + y = 2

Subtracting the first equation from the second we have

0 = 0, since this is always true, then it has infinite solutions.

(c) the equations have unique solutions if a/q ≠ b/r, for example

x + y = 2

x – y = 1

Adding the first and second equation we have

2x = 3, we can get x from here and definitely y, so we have just one solution.


Related Questions

Which of the following is equivalent to 2 x (4 x 3)? *

2 + (4 + 3)
2 x (6 x 4)
(2 x 4) x 3
8

Answers

2×(4×3)?24

4×3=12

12×2=24

(2×4)×3=24

Classify the following triangle. Check all that apply. A. Scalene B. Right C. Acute D. Equilateral E. Obtuse F. Isosceles ​

Answers

Answer:

E and F

Step-by-step explanation:

The triangle given has two equal sides, and an obtuse angle that is more than 90° that measures 120°. The other two angles are of equal measure since their opposite sides are of the same length. Thus, this implies that it is an isosceles triangle because it has two equal base angles and two equal sides. It also implies that it is an obtuse triangle since one of it's angles is more than 90°.

Answer:

the correct answer is acute and scalene

What is the value of 3 in the figure shown below?
E
с
20
3.6 3.6
118°
3.8 3.8
30
D
B

Answers

9514 1404 393

Answer:

  32

Step-by-step explanation:

Angle E is congruent to angle C, so is the value required to make the sum of angles in triangle ABC be 180°.

  ∠E = 180° -118° -30° = 32°

The value of x is 32.

Consider the spreading of a rumor through a company of 1000 employees, allworking in the same building.We assume that the spreading of a rumor is similar to the spreading of a contagious disease (see Example 3, Section 1.2) in that the number of people hearing the rumor each day is proportional to the product of the number who have heard the rumor previously and the number who have not heard the rumor. This is given by
rn+1 = rn + 1000krn(1000 ? rn)
where k is a parameter that depends on how fast the rumor spreads and n is the number of days. Assume k = 0.001 and further assume that four people initially have heard rumor. How soon will all 1000 employees have heard the rumor?

Answers

Answer:

On the 12th day, the rumor would have has to all the 1000 employees

Step-by-step explanation:

Given the data in the question;

so, lets consider the rumor spreading thorough the company of 1000 employee;

the given model is; [tex]r_{n+1}[/tex] = [tex]r_{n}[/tex] + 1000k[tex]r_{n}[/tex] ( 1000 - [tex]r_{n}[/tex] )

where k is the parameter that depends on how fast the rumor spreads, n is the number of days.

now, lets assume k = 0.0001, lets also assume r₀ = 4

so to find how soon all 1000 employees  will have heard the rumor  ;

let n be;

then r1 will be;

r1 = r₀ + ( 0.001)r₀(1000-r₀ )

so

r1 = 4 + ( 0.001) × 4× (1000 - 4 )

r1 = 7.984

r2 will be;

r2 = r1 + ( 0.001)r1(1000-r1 )

r2 =  7.984 + ( 0.001) × 7.984 × (1000 - 7.984 )

r2 = 15.904255744

   

r3  will be;

r3 = r2 + ( 0.001)r2(1000-r2 )  

r3 = 15.904255744 + ( 0.001) × 15.904255744 × (1000 - 15.904255744 )

r3 = 31.555566137

Using the same formula and procedure by substituting n = 1,2,3,4,5,6,7,8,9,10,11,12.

we will have;

n        rₙ

0        4

1        7.984

2       15.904255744

3       31.555566137

4       62.1153785

5       120.372437

6       226.25535

7       401.319217

8       641.58132

9       871.53605

10     983.497013

11      999.727651

12     999.999926

Therefore, On the 12th day, the rumor would have has to all the 1000 employees

 

can you guys please help me

Answers

9514 1404 393

Answer:

  see below

Step-by-step explanation:

Each vertex has a single-letter label.

Each edge joins two vertices, and is named by naming those two vertices.

Each polygon is named by listing the vertices at its corners. It is a plane figure.

The base is the polygon opposite the point where all of the triangles come together.

__

16. figure: pentagonal pyramid ABCDEF

17. base: ABCDE

18. faces: ABF, BCF, CDF, DEF, AEF, ABCDE (the bottom face, or base)

19. edges: AB, BC, CD, DE, AE, FA, BF, CF, DF, EF

20. vertices: A, B, C, D, E, F

Select five numbers that have 7, 13, and 3 as prime factors.
А
1,092
B
897
с
2,093
D
819
483
F
1,365
G
273
H
546

Answers

Answer:

ADFGH

Step-by-step explanation:

Good luck on your test!

The numbers having the prime factors 7, 13, and 3 are 1,092,819,1,365,273, and 546.

What is a prime factor?

A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth. Now, we may also apply the so-called prime factorization, which actually involves using factor trees, for numbers.

The numbers having the prime factors 7, 13 and 3 are 1,092,819,1,365,273, and 546. Because all the numbers are completely divisible by the numbers 7, 13, and 3.

Therefore, the numbers having the prime factors 7, 13, and 3 are 1,092,819,1,365,273, and 546.

To know more about prime factors follow

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The volume of a cube is 1.5 mº. Find the length of its edge to the nearest tenth of a meter.

Answers

Answer:

About 1.1 meters.

Step-by-step explanation:

Hope this helps! :D

BONUS QUESTIONS 1. The number of books featured at the local library is shown below: MYSTERY BOOKS: 32 NOVELS: 16 NON-FICTION BOOKS: 12 The library is hosting a book fair that features the mystery books. All the authors discuss the same number of mystery books and each will discuss more than 1 book. How many authors could be featured in the show?​

Answers

Answer:

I don't get the question

Step-by-step explanation:

Erin wants to buy a set of paint brushes:

Store A sells a set for $25.00 and offers a 10% discount
Store B sells a set for $27.00 and offers a 20% discount
Store C sells a set for $26.00 and offers a 15% discount
I NEED THIS ASAP! worth 20 points!

Answers

Answer:

m

Step-by-step explanation:

Nicole swims 6 times as many laps as Evan. What multiplication equation compares the laps Nicole and Evan swim?

Answers

Answer:

6E

Step-by-step explanation:

If Evan swims 5 laps (for example) that automatically means that Nicole sawm 6 more laps, so it would be 6 times "E" as in Evan

Hope this helps! :D

Easy
5
If 3x + 5y = 15 and x – 2y = 10, what is the value of 2x
+7y?

Answers

Answer:

5

Step-by-step explanation:

dont really understand why you answered your own question?

Identify the parent function.
A. Square root B. Cube root C. Absolute value D. Reciprocals

Answers

The answer is cubic root

Bella's bedroom is 3 meters wide and 6 meters
long. Gina's bedroom is a 5-meter square. Who has
the bigger bedroom?

Answers

Answer:

Gina

Step-by-step explanation:

Bella's bedroom is 3m x 6m = 18m^2

Gina's bedroom is 5m x 5m = 25m^2

3
What is the solution to the equation 9x = 54?
x = 6
B) x = 7
C
X = 8
x = 9

Answers

Answer:

6

Step to Step:

9x6=54

Answer:

Option A

Step-by-step explanation:

In order to find the answer to this equation you must remember to divide if there is a variable right next to the number.

[tex]9x=54[/tex]

[tex]\div9[/tex]

[tex]54\div9=6[/tex]

[tex]x=6[/tex]

Hope this helps.

What expression is equivalent to (-18) - 64n ?

A -2 (9 - 32n)
B 2 (9 - 32n)
C 2 (9 + 32n)
D -2 (9 + 32n)

Answers

Answer:

D

Step-by-step explanation:

Distribute the -2 to the 9 to get -18 and then to the 32n giving you -64n

16^5/4 times 16^1/4/(16^1/2)^2

Answers

Answer:

4

Step-by-step explanation:

its four trust me

Answer:

4

Step-by-step explanation:

:)

What is 5% of 40? Need help please.

Answers

Answer:

it is 2

Step-by-step explanation:

Write the equation for the horizontal line passing through (3, 4).

Answers

Answer:

equation for a straight horizontal line passing through the coordinates (3,4):

y=4

Step-by-step explanation:

Please Help Me Asapp

Answers

The answer for the first question is s-14=25.

The answer for the second question is 4000+p=4375


Put together, Edward and Jamie have 56 total rocks. Jamie's collection has 3 times as many rocks in it as Edward's collection. How many rocks are in Jamie's collection?
How many rocks does Edward have?
Select the person with more rocks: Jamie

Answers

Answer:

How many rocks does Edward have? 14

Select the person with more rocks: Jamie

(Edward: 14, Jamie: 42)

function not a function ?

Answers

Answer:

not a function

Step-by-step explanation:

Find the Slope (9,5) (9,-3)

Answers

The slope is undefined

Bir kırtasiyeci aldığı kalemlerin tanesini
2 liradan satarsa 40 lira kâr, 1,5 liradan
satarsa 20 lira zarar ediyor.
Bu kırtasiyeci kaç kalem alıp satmış-
tır?
A) 125 B) 120 C) 115 D) 110​

Answers

Answer: Option B: 120.

Step-by-step explanation:

I will answer in English

This problem can be translated to:

A man bought N pens, (at a cost C) if he sells each pen at 2 lira, he will have a profit of 40 lira.

If he sells each pen at 1.5 lira, he will loss a total of 20 lira.

We want to find N, the number of pens that he bought.

if he sells the N pens at 2 lira each, the revenue is:

N*2 lira

And the profit is the difference between the revenue and the cost, then the profit (40 lira in this case) is:

N*2 lira - C = 40 lira.

When he sells each pen at 1.5 lira the equation is:

N*(1.5 lira) - C = -20 lira.

Then we have two equations:

N*2 lira - C = 40 lira.

N*(1.5 lira) - C = -20 lira.

To solve this we need to isolate the variable C in one of the equations, i will isolate C in the second equation:

N*(1.5 lira) + 20 lira = C.

Now we can replace this in the first equation to get:

N*(2 lira) - (N*(1.5 lira) + 20 lira) = 40 lira.

We can solve this for N.

N*(2 lira) - N*(1.5 lira) - 20 lira = 40 lira

N*(2 lira - 1.5 lira) = 60 lira

N*(0.5 lira) = 60 lira

N = (60lira/0.5lira) = 120

N = 120

This means that he bought 120 pens.

The correct option is B.

Combine like terms in the expression below.


5c + 6 + 8c - 2

Plz help

Answers

Answer:
13c+6-2

Explanation:
You combine the amount of cs with each other.

What expressions can be used to find 1/3 of 12

Answers

Answer:

The answer is this:

1/3*12=4/1=4

The expression can be written as 1/3 × 12 and its value is 4.

What are arithmetic operations?

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The given fraction is 1/3.

And, the number is 12.

Now, the expression to find the 1/3 of the given number can be written using the multiplication operation as,

⇒ 1/3 × 12

Its value can be evaluated as,

⇒ 1/3 × 12 = 4

Hence, the required expression is 1/3 × 12 and its value is 4.

To know more about arithmetic operation click on,

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Explain your answer

Thank you so much !

Will give brainlst

Answers

Answer:

Good luck with that

Step-by-step explanation:

We r to lazy to do it

Answer:

C

Step-by-step explanation:

Granite is mined worldwide but the most exotic colours are obtained from granite deposits in Brazil, India, China, Finland, South Africa and North America. Granite mining is a capital and labour intensive process. Chunks of granite are extracted from deposits by cutting or blasting procedures.

need help fast thank you​

Answers

Answer:

a

Step-by-step explanation:

the answer is a because thats the answer.

Answer:

No it is the second one because:

-    7x => x represents the number of cans to be collected in 7 days

you've already collected 668 cans, and 2000 cans is the target.

2000-668= 1332÷7- 190.30

Complete the following sentence.

The slope of the graph of y = x is

Answers

Answer:

The slope of y=x is 1

Step-by-step explanation:

Slope = 1

Find the slope, I don't know how though.​

Answers

Answer:

slope is -2

Step-by-step explanation:

Pls hurry and help!!!3X-2y=4
6x-2y = -2
Solve the equations by using elimination Adding.

Answers

Answer:

The answer will be the following :

Step-by-step explanation:

Let's solve for x.

3x−2y=46x

Step 1: Add -46x to both sides.

3x−2y+−46x=46x+−46x

−43x−2y=0

Step 2: Add 2y to both sides.

−43x−2y+2y=0+2y

−43x=2y

Step 3: Divide both sides by -43.

−43x

−43

=

2y

−43

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