How do you know if an equation has one solution, no solutions, or infinitely many solutions?

Answers

Answer 1

Answer:

Summary. If the equation ends with a false statement (ex: 0=3) then you know that there's no solution. If the equation ends with a true statement (ex: 2=2) then you know that there's infinitely many solutions or all real numbers.

Step-by-step explanation:

Answer 2

To determine whether an equation has one solution, no solutions, or infinitely many solutions, we need to examine the relationship between the variables and the consistency of the equation.

Here are the general guidelines:

1. One Solution: An equation has one solution if the variables can be assigned specific values that satisfy the equation, resulting in a unique solution. When solving the equation, you will find a specific value or set of values for the variables that make the equation true. The solution is often a numerical value or a specific point in a coordinate system.

2. No Solutions: An equation has no solutions if there is no value or combination of values for the variables that satisfy the equation. When solving the equation, you will arrive at a contradiction or an inconsistency. For example, if you encounter a statement like 2 = 5 during the solution process, it indicates that the equation has no solutions.

3. Infinitely Many Solutions: An equation has infinitely many solutions if any value assigned to the variables will satisfy the equation. This typically occurs when the equation is an identity or when there are variables on both sides of the equation that cancel out during the solution process, resulting in the equation always being true. In such cases, any value can be substituted for the variables, and the equation will remain true.

Determining the nature of the solutions often involves algebraic manipulation, simplification, and analysis of the equation to determine if it is consistent, inconsistent, or an identity.

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Related Questions

Patty ran 3 miles in 290 minutes,
Assume Patty maintains a constant
speed. How many minutes will it take
Patty to run 1 mile?

Answers

96.666..., or about 97 minutes/every mile.

Drag a description to match each equation.

Pleaseee I am desperate!

Answers

Answer:

y is 4 times x

y is 4 more than x

Step-by-step explanation:

sorry if im wrong

Han made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa

Answers

tfff am I supposed to do about this

(4+3c^5)(4-3c^5) combine like terms

Answers

Answer:

16 − 9 c ^10

Step-by-step explanation:

Simplify the expression.

Answer:

-9c^10+16

Step-by-step explanation:

(4+3c^5)(4-3c^5)  multiply

(16 -12c^5+12c^5-9c^10) combine and rewrite

-9c^10+16

I am really behind and I REALLY need help... I am giving every point I have for this...

Answers

Answer:

Get ahead then

Step-by-step explanation:

Step-by-step explanation:

Shorts cost $16

T-shirts cost $10

So:

16x + 10y ≤ 100

or

y ≤ -1.6x + 10

Then graph y = -1.6x + 10 and x = 2

Part b:

Using the graph, we can infer that there are two possible solutions:

A. 3 pairs of shorts and 4 t-shirts

B. 4 pairs of shorts and 2 t-shirts

6a. X =  number of apples, Y = number of oranges

So:

x + y ≤ 20

0.24x + 0.8y ≤ 12

x ≤ 20 - y

0.24(20 - y) + 0.8 ≤ 12

= 4.8 - 0.24y + 0.8y ≤ 12

= 0.56y ≤ 7.2

y = 12.9 (You can use twelve because there can't be a fraction of an orange.)

x = 7.14 (again, because of fractions, round to 7.)

Therefore, she got 12 oranges and 7 apples.

Part 2:

Question 1:

Both equations are unbounded.

Question 2:

Both equations are unbounded.

Question 3:

Both equations are unbounded.

Question 4:

Both equations are unbounded.

Give me a moment to add question four's graph.

Zelie planned for a square pool to have a side length of 28 ft but found that it needs to be 14 ft long to fit in her backyard. She found the change of scale below. StartFraction 28 feet minus 7 over 14 feet minus 7 EndFraction = StartFraction 21 over 7 EndFraction Which is Zelie's error?

Answers

Answer:

Step-by-step explanation:

Find the complete question

Zelie planned for a square pool to have a side length of 28 ft but found that it needs to be 14 ft long to fit in her backyard. She found the change of scale below.

Which is Zelie’s error?

Zelie should have divided both numbers by 14.

Zelie should have written the ratio as 28/7.

Zelie should have written the ratio as 14/8.

Zelie should have subtracted 14 from both numbers.

Original length of pool = 28ft

If he found that it need to be 14ft longer then the actual measure = 14th

given equation is;

(28 - 7)/14 - 7 = 14/7

Scale constant  = original length/actual length

Scale constant = 28/14

Scale constant = 2

Hence the scale constant is 2

According to the option, Zelei should have divided both numbers by 14.

Answer:

Zelei should have divided both numbers by 14

Step-by-step explanation:

A hot air balloon was flying at an altitude of 300 meters when the pilot decided to land by descending at a rate of 2 meters per second. For which of these rules does y represent the altitude of the hot air balloon, if x represents the number of seconds since the pilot started her landing?

Answers

Answer:

The answer is "150 seconds".

Step-by-step explanation:

[tex]\to distance = 300 \ meter\\\\\to speed = 2 \ \frac{m}{s} \\\\\ formula: \\\\ \bold{speed = \frac{distance}{time}}\\\\[/tex]

[tex]time= \frac{distance}{speed}\\\\[/tex]

        [tex]=\frac{300}{2}\\\\=150 \ seconds[/tex]

Quien quiere ser mi amigo o amiga? Manden soli si quieren XD

Answers

si me gustaria ser tu amiga :)

Which statement about the ordered pairs (2, −9) and (3, −6) is true for the equation 5x−y3=13?


Neither ordered pair is a solution.

(3, −6) is a solution to the equation.

Both ordered pairs are solutions.

(2, −9) is a solution to the equation.



ABEGGG HELP ME OO , WITH THIS QUESTION , A.S.A.P!!!

Answers

(2, −9) is a solution to the equation.

i took the quiz lol

what is 64x64? and I know if you use a calculator =)

Answers

Answer:

4096

Step-by-step explanation:

The tree in Ravinder’s drawing is 12 cm tall. The ratio of the drawing to the tree is 0.5:15. What is the height of the tree in the park?

Answers

Answer:

In cm 360

In meters 3.6

Step-by-step explanation:

had the same question but had to answer in both and got em right

In 2011, the winner of the Peachtree Road Race ran the 7-kilometer event in 28 minutes. What is the runner's unit rate? If the runner completed ina 14-kilometer race, what would be the expected time?

Answers

Answer:

unit rate= 4-kilometers/minute   expected time= 56 minutes

Step-by-step explanation:

14 kilometers x 4 kilo/minute = 56 minutes

I NEED HELP PLEASE!!!!!!!!!! O///O
How can you look at the equation of two lines and determine if they will be parallel?

Answers

Answer:

If the slope is the same but the intercept is different

i.e.

y=2x+1

y=2x+2

Step-by-step explanation:

If the slope is the same the lines are parallel, but if the y-intercept is also the same the lines have infinite solutions.

Divide. 495 ÷ 10,000 = _____ 4.950 0.0495 0.4950 0.00495

Answers

Answer:

0.0495

Step-by-step explanation:

used a calculator

0.0495.

[tex]495 / 10000 = 0.0495.[/tex]

B)

Consider the two different types of elections. Which statement is true?
А
The candidates in the general election earn Electoral College votes.
B.
There is only one primary election but multiple general elections.
с
The general election decides who will run as a presidential candidate.
D
The primary election decides who will be the next president.

Answers

Answer:

D

The primary election decides who will be the next president.

Step-by-step explanation:

Answer:

the candidates in the general election earn electoral college vote

If 4 pounds of bologna cost $5.04, how much will it cost
per pound?

Answers

Divide $5.04 by 4 to get the solution $1.26/pound

Answer:

$1.26

Step-by-step explanation:

To get the cost of one pound you need to divide the cost of 4 pounds by 4.

5.04/4=1.26

$1.26 per pound.

-8x + 3y = 18
-7x – 2y= 25
(-3,-2)

Answers

Answer: what is the question though

Step-by-step explanation:

What is 3,050 divided by 75 with a remainder?

Answers


3050 dived by 75 is 40.6 Decimal Form

The quotient from the given division is 46 and the remainder is 50.

Given that, 3500 divided by 75.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Here, 3500/75

75|3500|46

     300

    _____

       500

       450

   ______

        50

Thus, quotient = 46 and remainder=50

Therefore, the quotient from the given division is 46 and the remainder is 50.

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Deal 1: $16.05 for 5 Caramel apples Deal 2: $19.14 for 6 caramel

Answers

Deal 2 is the best deal. Deal 1 is $3.21 per apple but Deal two is $3.19 per apple.

Which of these is it ?..

Answers

Answer:

D) all of the above

Step-by-step explanation:

If a line bisects another line, that means the length of the lines are equal

The lines are perpendicular because angle APR is 90 degrees

If the lines are perpendicular, then angle RPB is 90 degrees

Identify each part of the algebraic expression as the coefficient, constant, or variable.
1. 4x - 12
4 is a(n) ___________________
x is a(n) ___________________
12 is a(n) __________________

2. a + 3b
a is a(n) ___________________
3 is a(n) ___________________
b is a(n) __________________

3. 6y
6 is a(n) ___________________
y is a(n) ___________________







TRANSLATIONS
DIRECTIONS: Highlight and Translate, Then type the final translation.

1. Three less than “x” is equal to 13. ________________________



2. The product of 9 and “m” is 45. ________________________



3. A number divided by 6 is 18. ________________________



4. A number plus 17 is 25. ________________________



5. Seven times a number is 28. ________________________



6. A number divided by 7 is 9. ________________________



7. A number minus 12 is 20. ________________________




8. The quotient of “y” and 3 is 25. ________________________



9. One-fifth of “r” is 15. ________________________



10. Six less than 2 times “y” is 34. ________________________



11. Five more than “n” is equal to 9. ________________________



12. A number increased by 3 is 19. ________________________




13. The difference of “p” and 7 is 30. ________________________



14. Fifteen multiplied by “k” is 75. ___________________________



15. The sum of 3y and 5 is 47. ________________________


Answers

Answer:

1. coefficient,variable, constant

2. variable,coefficient,variable

3. coefficient, variable

Translations:

1. x-3=13

2. 9m=45

3. x/6=18

4. x+17=25

5. 7x=28

6. x/7=9

7. x-12=20

8. y/3=25

9. r/5=15

10. 2y-6=34

11. 5+n=9

12. x+3=19

13. p-7=30

14. 15k=75

15. 3y+5=47

18-4y=42 help, please?

Answers

18-4y=42

4y = 18-42

4y=-24

y = - 6

HELP!! igzitzgiziztztizu​

Answers

Answer:

57 miles in 1 hr

Step-by-step explanation:

171/3 = 57

I need help!!!!!! I only have 5 minutes!!!
use two unit multipliers to convert:
A. 90 yards to inches

Answers

Answer:

The yards and the feet will "cancel" out, and you will be left with the answer in inches.

I hope this helps!

Step-by-step explanation:

The distance required to stop a car varies
directly as the square of its speed. If 250
feet are required to stop a car traveling 60
miles per hour, how many feet are required to
stop a car traveling 96 miles per hour?

Answers

Answer:

400

Step-by-step explanation:

Find the total distance from Mercury to Earth. HELP!

Answers

Answer:

5.67*10^7

Step-by-step explanation:

Since the distance from mercury to venus is 30,700,000, and the distance from venus to earth is 26,000,000, we can simply add these together to find the distance from mercury to earth:

 30,700,000

+26,000,000

__________

 56,700,000

Now, to convert it to scientific form, just multiply 10^7 (which is the number of digits-1) and 5.67. Therefore, the answer is 5.67*10^7

At 8:00, the temperature was -6°. Three hours later, the temperature dropped 13°. What is the temperature at 11:00?

Answers

Answer:

-19 degrees

Step-by-step explanation:

13+6=19

you would need to add the negative since it said dropped in temperature and the temperature was already negative.

2÷5 × -4 what Is the answer please? ​

Answers

Answer:

-1 3/5

Step-by-step explanation:

2÷5 × -4

Work from left to right

2/5 * -4

-8/5

-1 3/5

The concentrates were pooled from the blood of about 1000 donors per lot. If the prevalence of HIV in donor blood in the early 1980s was 1 in 3,000, what was the probability that a hemophiliac would contract HIV from a single infusion of clotting factors?

Answers

Answer:

The required probability is "0.0003".

Step-by-step explanation:

Throughout the early 1980s, reconstructed coagulation factors concentrate extracted from individual blood was collected by hemophiliacs. The concentrate was obtained from either the blood of approximately 1000 donors every lot. The occurrence of hepatitis C throughout donated blood reached 1 in 3000 throughout the early 1980s.

Therefore, the risk though from a single injection of clotting factors, a hemophiliac would contracted hepatitis C seems to be:

= [tex]\frac{1}{3000}[/tex]

= [tex]0.0003[/tex]

Write four different equations that have –3 as the solution

Answers

1 + -4

2 + -5

3 + -6

4 + -7

Answer:

5 + -8

6 + -9

7 + -10

8 + -11

Step-by-step explanation:

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