Choose the system of equations that matches the following graph:

Mathematics

1 answer:

Flura [38]3 years ago

8 0

Answer:

3x - y = 12 and x + 2y = - 10

Step-by-step explanation:

The first straight line passes through the points (2,-6) and (4,0).

Therefore, the equation of the straight line from two point form

$\frac{y - 0}{0 - (- 6)} = \frac{x - 4}{4 - 2}$

⇒ y = 3(x - 4) = 3x - 12

⇒ 3x - y = 12 .......... (1)

Again, the second straight line passes through the points (2,-6) and (0,-5).

Therefore, the equation of this straight line will be

$\frac{y - (- 5)}{- 5 - (- 6)} = \frac{x - 0}{0 - 2}$

⇒ - 2(y + 5) = x

⇒ x + 2y = - 10 ......... (1)

Therefore, (1) and (2) are the system of equations. (Answer)

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Serga [27]

Answer:

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Step-by-step explanation:

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8 0

2 years ago

A square carpet of side length 9 feet is designed with one large shaded square and eight smaller, congruent shaded squares, as s

Pepsi [2]

Answer:

$3\sqrt{3} + 72$

Step-by-step explanation:

I attached an image to aid the understanding of the question.

Looking at the image, we see that the 8 shaded parts are congruent, as affirmed in the question as well. And we are told that T = 3, this implies that the area of the square with T as it's side is 9ft². Since all the 8 squares are congruenrt, it means each square has its area to be 9. Therefore, the total area of the 8 shaded squares will be:

$9 \times 8 = 72ft^{2}$

It remains the area of the shaded square with side S.

From the question, we have the following ratio:

$\frac{9}{S} = \frac{S}{T}[\tex]But[tex]\frac{9}{S} = \frac{S}{3}[\tex]Multiplying through by 3S we have27 = S² and this gives:[tex]S = \sqrt{27} = 3\sqrt{3}$