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3 years ago

Please help for number 25

Mathematics

1 answer:

Phantasy [73]3 years ago

8 0

The correct answer is: [C]: " inverse variation; xy = 40 " .
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Explanation:
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Examine the table given, and plug in the value:
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In the equation for Answer choice: [C]: " xy = 40 ".

When x = 1 , y = 40.

xy = 40 ; 1*40 = 40. Yes.

When x = 2, y = 20.

xy = 40; 2*20 = 40. Yes.

When x = 5, y = 40.

xy = 40. 8* 5 = 40. Yes.

When x = 10, y = 4.

xy = 40. 10*4 = 40. Yes.
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So the equation makes sense ;

"inverse variation; xy = 40".
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since; "xy = 40" ; which is "answer choice: [C]".
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We know that the other choices do NOT make sense; if we plug in any of the corresponding x and y values for any of the equations provided in any of the other answer choices, the equations will not equal, and as such, the answer choices are incorrect.
_________________________________________

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The corners of a meadow are shown on a coordinate grid. Ethan wants to fence the meadow. What length of fencing is required?

Nuetrik [128]

Answer:

34.6 units

Step-by-step explanation:

The lenght of fencing required is the total distance between point A to B, B to C, C to D, and D to A. That is the distance between all 4 corners of the meadow.

The coordinates of the corners of the meadow is shown on a coordinate plane in the attachment. (See attachment below).

Let's use the distance formula to calculate the distance between the 4 corners of the meadow using their coordinates as follows:

Distance between point A(-6, 2) and point B(2, 6):

$AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$A(-6, 2)) = (x_1, y_1)$

$B(2, 6) = (x_2, y_2)$

$AB = \sqrt{(2 - (-6))^2 + (6 - 2)^2}$

$AB = \sqrt{(8)^2 + (4)^2}$

$AB = \sqrt{64 + 16} = \sqrt{80}$

$AB = 8.9$ (nearest tenth)

Distance between B(2, 6) and C(7, 1):

$BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$B(2, 6) = (x_1, y_1)$

$C(7, 1) = (x_2, y_2)$

$BC = \sqrt{(7 - 2)^2 + (1 - 6)^2}$

$BC = \sqrt{(5)^2 + (-5)^2}$

$BC = \sqrt{25 + 25} = \sqrt{50}$

$BC = 7.1$ (nearest tenth)

Distance between C(7, 1) and D(3, -5):

$CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$C(7, 1) = (x_1, y_1)$

$D(3, -5) = (x_2, y_2)$

$CD = \sqrt{(3 - 7)^2 + (-5 - 1)^2}$

$CD = \sqrt{(-4)^2 + (-6)^2}$

$CD = \sqrt{16 + 36} = \sqrt{52}$

$CD = 7.2$ (nearest tenth)

Distance between D(3, -5) and A(-6, 2):

$DA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$D(3, -5) = (x_1, y_1)$

$A(-6, 2) = (x_2, y_2)$

$DA = \sqrt{(-6 - 3)^2 + (2 - (-5))^2}$

$DA = \sqrt{(-9)^2 + (7)^2}$

$DA = \sqrt{81 + 49} = \sqrt{130}$

$DA = 11.4$ (nearest tenth)

Length of fencing required = 8.9 + 7.1 + 7.2 + 11.4 = 34.6 units

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kogti [31]

3a+4x=29 (1st)
2a-3x=-9 (2nd)

multiply (1st) by 3 and (2nd) by 4

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8a - 12x = -36 (2nd)
---------------------add
17a = 51
a = 3

2a-3x=-9
2(3)-3x=-9
6 - 3x = -9
-3x = -15
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answer
x = 5 and a = 3

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Answer:

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