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3 years ago

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How many linear equations in x and y can have a solution as (x = 1, y = 3)?

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Mathematics

2 answers:

Shkiper50 [21]3 years ago

6 0

Answer:

infinite

Step-by-step explanation:

Let the linear equation in two variables be ax+by+c=0

Put values

$\\ \sf\longmapsto 1a+3b+c=0$

$\\ \sf\longmapsto a+3b+c$

Hence for any values it has infinite number of solutions .

including x=1 and y=3

Ilia_Sergeevich [38]3 years ago

4 0

Answer:

<h3>infinitely many equations</h3>

A linear equation in two variable is of the form ax+by+c=0.

We have x=2 and y=3 but we can choose a,b,c accordingly and they can attain infinite values. So, Infinite such equations exist.

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Suppose you and your friends form a band and you want to record a demo. Studio A rents for $75 plus $75 an hour and Studio B

Ganezh [65]

Answer:

Step-by-step explanation:

Studio A rents for $75 plus $75 an hour .

Studio B rents for $150 and $50 an hour.

Let t = the number of hours and c = cost.

Part A

Write a system of equations to represent the cost at each studio.

Studio A: c = 75 +75·t

Studio B: c = 150 +50·t

Part B

Solve the system of equations from Part A. Explain your method.

We solve the system of equation using substitution method, where we substitute c in the first equation with 150 +50t.

150 +50·t = 75 +75·t, subtract 75 and 50t from both sides

150 -75 = 75t -50t, combine likes terms

75 = 25t, divide both sides by 25

3 = t

Now we know that t = 3 so we find c by substituting t with 3 in the second equation.

c = 150 +50·t

c = 150 +50·3

c = 300

The solution of the system of equations is c = 300 and t = 3

Part C

Explain what the solution to the system means in terms of where your band will rent a studio.

The solution of the system of equation tells us that if we rent either studio A or B for 3 hours will pay the same price $300.

The price will be different if we rent studio A then studio B if we rent it for a different amount of time than 3 hours.

7 0

2 years ago

Given the degree of measure of angle KJH is 66 degrees find the measure in radians

Mrrafil [7]

9514 1404 393

Answer:

E) 0.366π

Step-by-step explanation:

There are π/180 radians in a degree.

66° = 66°(π/180°) = (66/180)π = 11/30π ≈ 0.366π radians

11/30 = 0.366... repeating, so would normally be rounded to 0.367

3 0

3 years ago

Read 2 more answers

What's 5 divided by 47

Katen [24]

5 ÷ 47 equals .106 :)

4 0

3 years ago

Which lines are perpendicular to the line y - 1 = 1/3 (x+2)? Check all that apply.

ioda

Answer: Options 1, 3, 5

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so since the slope of the given line is 1/3, we need to find lines with a slope of -3.

Option 1 has a slope of -3.
Option 2 has a slope of 3.
Option 3 has a slope of -3.
Option 4 has a slope of 1/3.
If we subtract 3x from both sides, we get y=-3x+7, so option 5 has a slope of -3.

7 0

2 years ago

Let T:R²->R² be a linear transformation ,and assume that T (1,2)=(-1,1) and T(1,-1)=(2,3)

zavuch27 [327]

Answer:

(-4,-1)

Step-by-step explanation:

We are given T(1,2)=(-1,1) and T(1,-1)=(2,3) and T is a linear transformation.

This implies for scalars a and b that

T(a(1,2)+b(-1,1))=aT(1,2)+bT(-1,1)

T((a,2a)+(-b,b))=a(-1,1)+b(2,3)

T((a-b,2a+b))=(-a,a)+(2b,3b)

T((a-b,2a+b))=(-a+2b,a+3b)

This means we should be able to solve the system below to find a and b for T(3,3):

a-b=3 and 2a+b=3

Add equations to eliminate b and solve for a:

3a=6

Divide 3 on both sides:

a=2

If a-b=3 and a=2, then b=-1.

Plug in a=2, b=-1:

T((a-b,2a+b))=(-a+2b,a+3b)

T((2--1,2×2+-1)=(-2+2×-1,2+3×-1)

T(3,3)=(-4,-1).

4 0

3 years ago