Mathematics High School

(1 point) Solve the following system of linear equations: 2x-6y=-25
-3x+9y=36
(a) How many solutions are there to this system? OA. None OB. Exactly 1 OC. Exactly 2 OD. Exactly 3 OE. Infinitely many OF. None of the above (b) State the solution to the system of equations. [x] [x]
[x] = [(x+4)/3]
NOTES: If there is/are:
-> one solution, give its coordinates (point) in the spaces above. This is how most solutions will be entered on this assignment. -> infinitely many solutions, enter x in the space for and enter an expression in terms of a (that represents y) in the space for y. -> no solutions, enter None in each of the spaces.

Answers

Answer 1

The solution is given by [x, (1/3)x + 4], where x can be any real number. To determine the number of solutions, we can examine the coefficients of the variables.

In the first case, the system can be written as:

2x - 6y = -25

-3x + 9y = 36

We notice that both equations are scalar multiples of each other, meaning they represent the same line in the coordinate plane. Therefore, the system has infinitely many solutions (E. Infinitely many).

Let's solve the system using the second equation:

-3x + 9y = 36

Rearranging the equation, we have:

9y = 3x + 36

y = (1/3)x + 4

Now, we can express the solution as [x, y] = [x, (1/3)x + 4]. The variable x can take any value, and y is determined by the equation y = (1/3)x + 4. Therefore, the solution is given by [x, (1/3)x + 4], where x can be any real number.

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Related Questions








Find dy/du, du/dx, and dy/dx. y = u, u³, u = 2x2 - 4 dy / du = du / dx = dy / dx =

Answers

So, the derivatives are: dy/du = 1, du/dx = 4x, dy/dx = 4x.

To find dy/du, du/dx, and dy/dx, we can use the chain rule of differentiation.

Given:

y = u

u = u³

u = 2x² - 4

dy/du:

Since y = u, the derivative of y with respect to u is simply 1.

dy/du = 1

du/dx:

To find du/dx, we need to differentiate the equation u = 2x² - 4 with respect to x.

du/dx = d/dx(2x² - 4)

= 4x

dy/dx:

To find dy/dx, we can use the chain rule by multiplying dy/du and du/dx.

dy/dx = (dy/du) * (du/dx)

= (1) * (4x)

= 4x

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If f(x)=3x^(5)+4x^(3)+3, then what is the remainder when f(x) is divided by x-3 ?

Answers

The Remainder when dividing f(x) by x - 3 is 840

The remainder when dividing the polynomial f(x) = 3x^5 + 4x^3 + 3 by the binomial x - 3, we can use the polynomial remainder theorem. According to the theorem, if we substitute the divisor, x - 3, into the polynomial f(x) and evaluate it at x = 3, the resulting value will be the remainder.

Let's calculate the remainder using this approach:

Substituting x = 3 into the polynomial f(x), we have:

f(3) = 3(3)^5 + 4(3)^3 + 3

    = 3(243) + 4(27) + 3

    = 729 + 108 + 3

    = 840

Therefore, when f(x) = 3x^5 + 4x^3 + 3 is divided by x - 3, the remainder is 840.

In summary, the remainder when dividing f(x) by x - 3 is 840.

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According to a recent poll, 80% of adults enjoy watching TV. Choose a group of 3 adults at random. The probability that all of them enjoy watching TV is: O a. 0.267 Ob. 0.512 c. 0.333 d. 2.400

Answers

Answer:

B) 0.512

Step-by-step explanation:

Use the binomial probability formula

[tex]P(X=x)=C(n,x)p^xq^{n-x}\\P(X=3)=C(3,3)(0.80)^3(0.20)^0\\P(X=3)=(0.80)^3\\P(X=3)=0.512[/tex]

Therefore, B is the correct option.

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