(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

Can u help me with qustion no 5

Can u help me with qustion no 5

Answers

The I had this question last time the answer of the problem is 4

True or false: An absolute value function is an example of a piecewise function.

Answers

Answer:

True

Step-by-step explanation:

An absolute function can be re-written as:

\(|x| = \left \{ {{x} \quad \ \ \ \text{if} \ x \geq \ 0\atop {-x} \quad \text{if} \ x < 0} \right.\)

That is the form of a piecewise function.

-4x+5>-5 solve the equation is it greater than or less than

Answers

Answer:

x>5/2

Step-by-step explanation:

-4x+5>-5

-4x>-10

4x>10

x>10/4

x>5/2

Estimate 6,976 + 3,983 + 13,560 by first rounding each number to the nearest thousand.

Answers

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

how many more seconds does it take to drive 1 mile at 40 miles per hour than 60 miles per hour​

Answers

Answer:

165 seconds

Step-by-step explanation:

If you were going steadily 60 miles per hour, you would go one mile in one minute. So, if you were going steadily 40 miles per hour, without your speed going up or down, you would get through one mile in 3 3/4 minutes (which is 165 seconds more than 1 minute).

Hope this helps. Pls give brainliest! Also, pls sub to kgirl633 on yt!

Simplify 4(3v + 2)
12v + 8
12v + 2
7v - 2
5v

Simplify 4(3v + 2)12v + 812v + 27v - 25v

Answers

A) 12v + 8

Explanation: you would need to distribute (multiply) whatever is in the parentheses

Help me I need the math problem

Help me I need the math problem

Answers

Answer:

y=4x-3

Step-by-step explanation:

Answer:

DO i care... no ask your dam teacher won der why u aint pass

Step-by-step explanation:

Who can answer this question 1+2+3+4+5+6+7+8+9+10​

Answers

Answer:

I can very easily is not it 55

Answer:

I HOPE IT WILL HELP YOU.

:D

Who can answer this question 1+2+3+4+5+6+7+8+9+10

Find f(x-7) if f(x)=-3x+2

Answers

Answer:

f(x-7)=-3x+23

Step-by-step explanation:

f(x-7)= -3(x-7)+2

= -3x+21+2

f(x-7)=-3x+23

Solve using Cramer's rule. 3x + 2y = 5
x + 3y = 4
i need an answer ASAP

Answers

By applying Cramer's rule as solution method, the solution of the linear system 3 · x + 2 · y = 5 and x + 3 · y = 4 is equal to the set (x, y) = (1, 1).

How to solve a system of two linear equations with two variables

Determinants are constructions studied in linear algebra and related to matrices, one of the most common applications of determinants is the solution of linear equations, whose simplest form is known as the Cramer's rule.

Now we proceed to use this rule to get the solution of the linear system:  

\(x = \frac{\left|\begin{array}{cc}5&2\\4&3\end{array}\right| }{\left|\begin{array}{cc}3&2\\1&3\end{array}\right|}\)

\(x = \frac{(5)\cdot (3)-(4)\cdot (2)}{(3)\cdot (3) -(1)\cdot (2)}\)

x = 1

\(y = \frac{\left|\begin{array}{cc}3&5\\1&4\end{array}\right| }{\left|\begin{array}{cc}3&2\\1&3\end{array}\right|}\)

\(y = \frac{(3)\cdot (4) - (5)\cdot (1)}{(3)\cdot (3) - (1)\cdot (2)}\)

y = 1

By applying Cramer's rule as solution method, the solution of the linear system 3 · x + 2 · y = 5 and x + 3 · y = 4 is equal to the set (x, y) = (1, 1).

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Which point is represented by 6 times the quantity cosine 11 pi over 6 plus i times sine 11 pi over 6 end quantity question mark

Which point is represented by 6 times the quantity cosine 11 pi over 6 plus i times sine 11 pi over 6

Answers

\(6\left[\cos\left( \frac{11\pi }{6} \right) +i\sin\left( \frac{11\pi }{6} \right) \right] \\\\\\ 6\left[\cfrac{\sqrt{3}}{2}~~,~-\cfrac{1}{2}i \right]\implies (3\sqrt{3}~~,~-3i) ~~ \approx ~~ \stackrel{ \textit{\LARGE S} }{(5.2~~,~-3i)}\)

What is the volume of the sphere shown below with a radius of 3? ​

Answers

Answer: 113.1

Step-by-step explanation: v=4/3(pie)r^3=4/3•(pie)•3^3= 113.09734

The quotient of 8 and the cube of a number.

Answers

By using division, it is obtained that

The Quotient of 8 and cube of 2 is 1

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division.

Divisor x Quotient + Remainder = Dividend.

Let the number be 2

cube of 2 = \(2^3 = 8\)

Quotient of 8 and 8 = \(\frac{8}{8}\) = 1

The Quotient of 8 and cube of 2 is 1

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How can 85% be broken down with friendly percents to find 85% of a number?

Answers

Answer:

it would be  C

Step-by-step explanation:

5(10%)+25%

Answer: options:

2(25%) + 3(10%)

3(25%) + 10%

5(10%) + 25%

4(10%) + 2(25%)

b.  the answer is 3(25%)+ 10%

Step-by-step explanation:

hope this helps!

Hosting a dinner party for 38 people, you plan to serve peach pie for desert.
Each pie has 8 slices.
How many slices are in each pie?

Answers

Answer:

40 slices

Step-by-step explanation:

I rounded 38 to 40 and divided by 8

In circle EE, the length of \overset{\LARGE\frown}{FG} = 4\pi
FG

=4π and m\angle FEG=80^\circ∠FEG=80

. Find the area shaded below. Express your answer as a fraction times \piπ.
PLEASE HELP IM STUCK

In circle EE, the length of \overset{\LARGE\frown}{FG} = 4\pi FG =4 and m\angle FEG=80^\circFEG=80 .

Answers

\(\bold{ANSWER:}\)
18pi SQUARE UNITS

\(\bold{EXPLANATIONS:}\)
In circle EE, the length of \overset{\LARGE\frown}{FG} = 4\pi FG =4 and m\angle FEG=80^\circFEG=80 .

Professor A.B.C company opens his own company, Electronic Tutorial Services, and completes the following transactions in June:
6/1 A.B.C company invests 20,000 in the business.
6/3 Purchased 12,100 of equipment.
6/4 Paid 220 premium for an insurance policy.
6/6 Purchased office supplies on Account 140.
6/9 Purchased a new computer for 9,000. Paid 40% cash agreed to pay the remainder Later.
6/10 Billed student Omar 58 for tutorial services that were performed.
6/14 Paid for the supplies purchased on June 6th.
6/15 the owner suggested to purchased new Building for his company by 22,000
6/25 Received 85 cash from student Salim Ali for tutorial services performed.
6/30 Student billed on June 10 pays the amount due to A.B.C company.
6/30 A.B.C company withdraws 60 for personal use.
Required: Prepare the all Accounting Cycles

Answers

In June, A.B.C company invested $20,000, purchased equipment, paid insurance premium, bought office supplies, billed students for tutorial services, received cash, paid for supplies, withdrew personal funds.

Accounting Cycles:

1. June 1:

  - A.B.C company invests $20,000 in the business.

  - Prepare the journal entry:

    - Debit: Cash ($20,000)

    - Credit: Capital ($20,000)

2. June 3:

  - Purchased equipment for $12,100.

  - Prepare the journal entry:

    - Debit: Equipment ($12,100)

    - Credit: Cash ($12,100)

3. June 4:

  - Paid $220 premium for an insurance policy.

  - Prepare the journal entry:

    - Debit: Insurance Expense ($220)

    - Credit: Cash ($220)

4. June 6:

  - Purchased office supplies on account for $140.

  - Prepare the journal entry:

    - Debit: Office Supplies ($140)

    - Credit: Accounts Payable ($140)

5. June 9:

  - Purchased a new computer for $9,000. Paid 40% in cash and agreed to pay the remainder later.

  - Prepare the journal entry for the cash payment:

    - Debit: Computer ($3,600) [40% of $9,000]

    - Credit: Cash ($3,600)

  - Prepare the journal entry for the remaining amount:

    - Debit: Computer ($5,400)

    - Credit: Accounts Payable ($5,400)

6. June 10:

  - Billed student Omar $58 for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Accounts Receivable ($58)

    - Credit: Tutorial Services Revenue ($58)

7. June 14:

  - Paid for the supplies purchased on June 6th ($140).

  - Prepare the journal entry:

    - Debit: Accounts Payable ($140)

    - Credit: Cash ($140)

8. June 15:

  - The owner suggested purchasing a new building for the company for $22,000.

  - No journal entry is required at this point. It is a decision made by the owner.

9. June 25:

  - Received $85 cash from student Salim Ali for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Cash ($85)

    - Credit: Accounts Receivable ($85)

10. June 30:

   - Student billed on June 10 pays the amount due ($58).

   - Prepare the journal entry:

     - Debit: Cash ($58)

     - Credit: Accounts Receivable ($58)

11. June 30:

   - A.B.C company withdraws $60 for personal use.

   - Prepare the journal entry:

     - Debit: Withdrawals ($60)

     - Credit: Cash ($60)

These transactions represent the accounting cycles for the given period.

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Rewrite as a piece wise function y=1/2 |x-6| +4

Answers

Answer:

  y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}

Step-by-step explanation:

You want y = 1/2|x -6| +4 written as a piecewise function.

Domains

The absolute value function changes its definition when its argument is negative:

  y = |x|   ⇒   y = -x for x < 0, and y = x for x ≥ 0

This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.

For x -6 < 0

The argument is negated in this domain, so we have ...

  y = -1/2(x -6) +4

  y = -1/2x +3 +4

  y = -1/2x +7

For x -6 ≥ 0

The absolute value function is an identity function in this domain:

  y = 1/2(x -6) +4

  y = 1/2x -3 +4

  y = 1/2x +1

Piecewise function

Combining these descriptions into one, we have ...

  \(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)

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Rewrite as a piece wise function y=1/2 |x-6| +4

Find the perimeter of this shape

Find the perimeter of this shape

Answers

The perimeter of the given shape as represented in the task content is; 29 cm.

What is the perimeter of the given shape?

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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Using the answers below where would -6.0 be placed?

A. Rational Number

B. Integer

C. Whole Number​

Answers

Answer:

b

Step-by-step explanation:

integer because is a negative number

BONJOUR AIDEZ MOI SIL VOUS PLAIT

BONJOUR AIDEZ MOI SIL VOUS PLAIT

Answers

The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

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what is the sum of 7/9 plus 3/5

Answers

Answer:

\(\frac{62}{45}\)

Step-by-step explanation:

what is the sum of 7/9 plus 3/5
62/45 your welcome girl or boy lol

Answer the following questions based on the spinner below.


Find P(5) as a fraction. ____
Find P(number > 2) as a percentage. _____%

Answer the following questions based on the spinner below.Find P(5) as a fraction. ____Find P(number

Answers

The probability P(5) as a fraction is 1/8 and P(number > 2) as a percentage is 75%

P(5) represents the probability of landing on the number 5 when spinning the spinner.

Since there is only one 5 on the spinner and a total of eight possible outcomes, the probability of landing on 5 is 1/8.

Therefore, P(5) as a fraction is 1/8.

To find P(number > 2) as a percentage, we need to calculate the probability of landing on a number greater than 2.

The numbers greater than 2 on the spinner are 3, 4, 5, 6, 7, and 8.

There are six favorable outcomes out of eight possible outcomes.

P(number > 2) = 6/8 = 3/4

To express this as a percentage, we multiply the fraction by 100:

P(number > 2) as a percentage = (3/4) × 100 = 75%

Therefore, P(number > 2) as a percentage is 75%.

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Determine probability of selecting at least 1 marble that is not red

Answers

The probability of selecting at least one marble that is not red is given as follows:

1.

What is the hypergeometric distribution formula?

The mass probability formula is presented as follows:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.

Considering a success as selecting non-red marbles, the values of these parameters are given as follows:

N = 4, n = 2, k = 3.

The probability of at least one not red is given as follows:

P(X > 0) = 1 - P(X = 0).

In which:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,4,3,2) = \frac{C_{3,0}C_{1,2}}{C_{4,2}} = 0\)

Hence the probability is of:

P(X > 0) = 1 - P(X = 0) = 1 - 0 = 100%.

Missing Information

The problem is given by the image shown at the end of the answer.

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Determine probability of selecting at least 1 marble that is not red

If you double a number and then add 28 ​, you get 4/9
of the original number. What is the original​ number?

Answers

Answer: -124/9 or -13.778

Step-explanation: You may not have any idea how to approach this problem but I can help. We are given some information about a number and asked to find out what number it is. Since we don't know what the number is, we can say that it is X (a variable).

If you double X and add 28 you get 4/9. Doubling X can be represented as 2X. If we add 28 to that, we get 2X+28. We are told we get 4/9 which means that 2X + 28 is equal to 4/9 or 2x + 28 = 4/9.

We have now built an algebraic equation for X. We can now simply solve for X.

2X + 28 = 4/9

2X + 252/9 = 4/9   Rewrite 28 as 252/9 so we have common denominators

2X = -248/9            Subtract 252/9 from both sides

X = -124/9               Divide by 2 on both sides and we get X

Whenever you are given a problem similar to this one, try to create an algebraic equation or expression that can model the problem. A variable can represent the number you are trying to find.

Hope this helps!

find an equation of the line passing through the following points (-8, 4) and (-5, -5)

Answers

Answer:

y= -3x-20

Step-by-step explanation:

°First find the gradient between the two points

Gradient= - 3

°Using the formula y= mx+c substitute the gradient into the equation. You'll get something like this: y=-3x+c

°Substitute the point (-8;4) in the above equation. You'll get something like this : 4=-3(-8) +c

°Calculate the value of c. It'll give you c=-20

°Substitute c=-20 in the equation

Final answer is y= - 3x-20

2x-3\(\geq\) 0

Answers

Answer:

x ≥ 1.5

Step-by-step explanation:

2x - 3 ≥ 0 ( add 3 to both sides )

2x ≥ 3 ( divide both sides by 2 )

x ≥ 1.5

The net of a triangular pyramid is shown.

Each triangle in the net has a base length that measures 6 inches and a height that measures 4 inches. What is the surface area of the pyramid that can be formed from this net?

The net of a triangular pyramid is shown.Each triangle in the net has a base length that measures 6 inches

Answers

Answer:

48 in²

Step-by-step explanation:

4x1/2x4x6=48

If u have 40 dollars which is 8 times more money than Jefferson has how much money does Jefferson have

Answers

Write it as an equation, letting the amount Jefferson has equal x:

40 = 8x

Solve for x by dividing both sides by 8:

X = 40/8

X = 5

Jefferson has $5

identify the domain of the relation s={(2,4), (5,-3), (2,3), (0,-6),(1,0)}

Answers

Answer: Domain is {2,5,0,1}

Answer:

2, 5, 0, 1

Step-by-step explanation:

The domain is the first coordinate in a set of ordered pairs. This means that  the domain is going to be the x coordinate. In this set of ordered pairs the domain is 2, 5, 0, and 1.

Hope This Helps :)

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