(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

Does 9x mean I multiply 9 times X?

Answers

Yes, but x must equals something in order to multiply it.

Answer:

yes

Step-by-step explanation:

PLEASE HELP ITS URGENT
12. Carla is lying on the ground between two trees in her backyard. She is 67 feet from the tree to her left. The angle of elevation from her eyes to the top of the tree on the left is 50°. Carla is 75 feet from the tree to her right and the angle of elevation from her eyes to the top of that tree is 36°. a. Determine the height of each tree to the nearest foot. Show your work. b. State which tree is taller, and by how much.

Answers

Answer:

the left tree is taller

Step-by-step explanation:

shown in work above :)

The first tree is taller than the second tree by 25.3 ft.

We have to use the trigonometric ratios and angle of elevation to obtain the height of each tree as follows;

Let the height of the first tree be h1 and the height of the second tree be h2.

For the first tree;

tan 50° = h1/67

h1 = 67 tan 50° = 79.8 ft

For the second tree;

tan 36° = h2/75

h2 = 75tan 36°

h2 = 54.5 ft

The first tree is taller than the second tree by 25.3 ft.

Learn more about angle of elevation: https://brainly.com/question/12483071

what are the answers to these questions? need help asap

Answers

the correct answer is ^
1. -20-5x 3. -3x+21
5. 6y+12z 2. should be 4+x
4. -36-6d

Need Help please,
Which graph is generated by this table of values?

Answers

Answer:

y=3x-6

Step-by-step explanation:

use 2 of the points for y=a×x+b

we use (2,0) and (3,3) as an example

we get

0=2a+b & 3=3a+b

so

3-0=3a+b-(2a+b)

3=a

b=-6

3/4(8x -4) is equivalent to 3x - 2 + 3x - 1
true or flase

Answers

Answer:

true

Step-by-step explanation:

5. Five-eighth of a number is 15. What is the number?
Your answer

Answers

Answer:

I think it is 24

Step-by-step explanation:

15÷5=3

3×8=24

Answer:

24

Step-by-step explanation:

divide 15 by 5 to get 3 which is equal to 1/8 of the number. then just multiply 3 by 8 to get 24.

If a pound of coffee costs 12. How many ounces can be brought for 3.90

Answers

32.5 is the right answer I believe

The length of a subway is 385 miles. If 3 cm represents 35 miles on the map, then what is the length of the subway on the map in cm?

Answers

Answer:

33cm

Step-by-step explanation:

385 / 35 = 11

11 times 3 = 33

Lisa makes $78.37 per day. If she works 8 12
hours, how much does she make in 1 hour?

Answers

i’m assuming the time is eight hours and 12 minutes. let me know if that’s not what it’s supposed to be

78.37 / 8.12 = 9.65

lisa makes $9.65 in 1 hour
hope this helps

9/5 -(-6/10) please helppppppppppppppp0pppppp

Answers

Answer:

[tex]\frac{12}{5}[/tex]

Can sombody plz help me?!​

Answers

Answer:

D.

Step-by-step explanation:

The posssibility that a random person will not buy any dramas is 3/4 since 1/4 is the one with drama and there's 4 types of movies.

The answer is D I think. Hopefully you get it correct!

What is the value of
the digit 9 in the
number below?
157,243

Answers

Answer:

Nine hundred

The 9 is in the hundred place. So it would stand for 9 hundred.

the 9 is in the hundreds place.

Your car repair bill was $390. You were charged $215 for parts and $35 per hour for labor.
How many hours did the repairs take?

Answers

Answer:

5 hours

Step-by-step explanation:

subtract 390 by 215 to get 175 then divide 175/35 to get 5

Diana pays $33 for 12 gallons of gas. Manny pays $37.10 for 14 gallons of gas. How much less per gallon does Manny pay than

Answers

diana pays $2.74, manny pays $2.65. therefore, many pays 10¢ less

McKenzie gets a base pay of 1,800 per month.She also earns 12% commission on the amount of car sales.If she sells 45,000 worth of cars how much money does she make in one month

Answers

9514 1404 393

Answer:

  7,200

Step-by-step explanation:

McKenzie's commission for the month is ...

  0.12 × 45,000 = 5,400

When that is added to McKenzie's base pay, she makes a total of ...

  5,400 +1,800 = 7,200

McKenzie makes 7,200 in a month when she sells 45,000 worth of cars.


Which is equivalent to 243 2/4
O 3
O 6
O9
O 12

Answers

the answer is 9 because......

The 95% confidence interval for these parts is 56.98 to 57.05 under normal operations. A systematic sample is taken from the manufacturing line to determine if the production process is still within acceptable levels. The mean of the sample is 56.96. What should be done about the production line

Answers

Answer:

Stop the line of production since the sample mean  (56.96) is outside the confidence interval [[tex]CI_{0.95}[/tex] = ( 56.98, 57.05 )]

Step-by-step explanation:

Given that;

95% confidence interval for these parts is 56.98 to 57.05

[tex]CI_{0.95}[/tex] = ( 56.98, 57.05 )

Sample mean = 56.96

We know that;

If the sample mean is within the confidence interval then, our decision is to keep the line operating as it is inside the confidence interval.

But if the sample mean is not within the confidence interval them, our decision is to stop the line of production as it is outside the confidence interval.

Now since our mean sample (56.96) does not lie between with the 95% confidence interval [tex]CI_{0.95}[/tex] = ( 56.98, 57.05 ).

Therefore, Stop the line of production since the sample mean  (56.96) is outside the confidence interval [[tex]CI_{0.95}[/tex] = ( 56.98, 57.05 )]

What is the total interest earned in two years on an account containing $500 at 3.5% interest, compounded annually?

Answers

Answer: $35.6125

Step-by-step explanation:

3.5% = 0.035

Let's find the deposit amount with interest at the end of the first year:

500 + 500 · 0.035 = 517.5

Let's find the amount of the deposit with interest at the end of the second year:

517.5 + 517.5  · 0.035 = 535.6125

Find the total interest earned over two years:

535.6125 - 500 = 35.6125

Grace wants to participate in a dance recital. She cannot miss more than 15% of the 40 classes before the recital. What is the minimum number of classes Grace must go to in order to be in this recital?
(BUT DON'T SAY 6 I PUT IT AND IT WAS WRONG!)

Answers

Answer:

She has to attend 6 or more classes

Step-by-step explanation:

PLEASE ANSWER ASASP FOR BRAINLEST!!!!!!!!!!!!!!

Answers

Answer: 10

Step-by-step explanation:

2+4+4= 10

Total profit P is the difference between total revenue R and total cost C. Given the following​ total-revenue and​ total-cost functions, find the total​ profit, the maximum value of the total​ profit, and the value of x at which it occurs.

R(x)=1300x-x^2
C(x)=3300+20x

Will give brainliest!

Answers

Answer: Oh no... Anyway's wanna ask me a question about sex ed?

Step-by-step explanation: x=495

,P=241,525

Step-by-step explanation:

Given that

Profit=Total revenue - total cost

P= R -C

Also given that

So

Above equation is the total profit in terms if x.

Now to find maximum value of P we have to differentiate above equation with respect to x

So

⇒x=495

So total profit at x=445  ,P=241,525

Answer:

The profit function is:

[tex]P(x)=-x^2+1280x-3300[/tex]

The maximum value is 406, 300 occurring when x = 640.

Step-by-step explanation:

The revenue function is:

[tex]R(x)=1300x-x^2[/tex]

And the cost function is:

[tex]C(x)=3300+20x[/tex]

Then the total profit function will be:

[tex]P(x)=R(x)-C(x)=(1300x-x^2)-(3300+20x)=-x^2+1280x-3300[/tex]

This is a quadratic function.

Therefore, the maximum value of the total profit will occur at its vertex point.

The vertex of a quadratic is given by:

[tex]\displaystyle \Big(-\frac{b}{2a}, f\Big(-\frac{b}{2a}\Big)\Big)[/tex]

In this case, a = -1, b = 1280, and c = -3300.

Then the point at which the maximum profit occurs is at:

[tex]\displaystyle x=-\frac{1280}{2(-1)}=640[/tex]

And the maximum profit will be:

[tex]P(640)=-(640)^2+1280(640)-3300=406300[/tex]

The sale price of every item in a store is 85% of its usual price the usual price of backpack is $18 what is its sale price

Answers

Answer: the sale price is $2.70

Step-by-step explanation:

Discount = Original Price x Discount %/100

Discount = 18 × 85/100

Discount = 18 x 0.85

You save = $15.30

Final Price = Original Price - Discount

Final Price = 18 - 15.3

Final Price = $2.70

anybody know the answer to this

Answers

The answer to this is B

Solve the proportion. 2x/5 = 9/15

Answers

x = 3/2

Getting x on one side of the equation:

(2/5)x = 9/15

x = (9/15)(5/2)

x = 9/6

x = 3/2

5) Solve this system by graphing.
-2x - 4y = -8
y = x-10

Answers

The solution is (8,-2)
Plot the equations on a graph, at the point of intersection is the solution for both equations.

Geometry. What is the answer and how do I solve? Please don't waste my answers. I will mark brainliest.

Answers

Answer:

QS = 16

Step-by-step explanation:

We can find QS by using the Pythagorean Theorem for Δ SQT

ST = 24/2 or 12

QT = 20

QS² + 12² = 20²

QS² + 124 = 400

QS² = 256

QS = √256, which is 16

4 1/2 x 4 1/2? write in a decimal

Answers

Answer:

4 1/2×4 1/2=9/2×9/2=81/4=20.25

4 1/2×4 1/2=9/2×9/2=81/4=20 1/4 .

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

 

50 Points!
Prove that 327^3 + 173^3 is divisible by 500
It's a good question, and would like to see some answers

Answers

Answer:

327^3 = 34 965 783

173^3 = 5 177 717

34 965 783 + 5 177 717 = 40 143 500

40 143 500 ÷ 500 = 80 287

80 287 is a whole number, therefore, 327^3 + 173^3 is divisible by 500.

I hope this helps :)

Yes, the expression ( 327³ + 173³ ) is divisible by 500.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 327³ + 173³ and is divided by 500. The division will be calculated as,

327³ = 34 965 783

173³ = 5 177 717

34,965,783 + 5,177,717 = 40,143,500

40,143,500 ÷ 500 = 80,287

80,287 is a whole number, therefore, 327³ + 173³ is divisible by 500.

To know more about an expression follow

https://brainly.com/question/11482504

#SPJ2

what is the y- intercept for y=-2 +5

Answers

Answer:

(0,5)

Step-by-step explanation:

I'm assuming it's actually y=-2x+5. Anyway, in y=mx+b, b represents the y-int, and because b=5 (based on the placement), we know that the y-intercept is (0,5)

Answer:

no answer

Step-by-step explanation:

there's something wrong with your question, it must have x, and the equation must be in that order:

y=mx+c

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