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marysya [2.9K]
2 years ago
14

An equation allows you to find the x- and y-coordinates of any point on the xy-plane.

Mathematics
2 answers:
Assoli18 [71]2 years ago
8 0

Answer:

True, An equation allows you to find the x- and y-coordinates of any point on the xy-plane.

Step-by-step explanation:

Given : An equation allows you to find the x- and y-coordinates of any point on the xy-plane.

We have to check whether the given statement is true or not.

Since, An equation in xy- plane is of the form ax + by = c , where a, b and c are real numbers.

Then, we can put different values of x and get values of y  and similarly , by putting different values of y and get values of x.

Thus, we obtain the x- and y-coordinates of any point on the xy-plane.

Example : 2x + 3y = 6

Put x = 0

And solve for y

We have , 3y = 6 ⇒ y = 2

Put y = 0

And solve for x

We have , 2x = 6 ⇒ x = 3

Thus, Points are (0,2) and (3,0)

Thus, An equation allows you to find the x- and y-coordinates of any point on the xy-plane.

 

     

monitta2 years ago
6 0

Answer:

The give statement is true.

Step-by-step explanation:

Yes, we can find the coordinates of any point on the xy-plane for any given equation.

For the given equation, we can take random values of x and then find the corresponding y values.

Let us prove this statement with an example.

Let us suppose, we have the equation y=x^2+4

For x= 1, we have

y=1^2+4\\\\y=5

Thus, the coordinate of the point is (1,4)

Similarly for other values of x, we can find the y values and can find the coordinate.

Thus, we can say that an equation allows us to find the x- and y-coordinates of any point on the xy-plane.

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The base of a pentagonal prism is regular with an apothem of 4 cm. The height of the prism is 16 cm. Find the volume of the pris
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Answer:

volume ≈ 930 cm³ (nearest cubic cm)

Step-by-step explanation:

The base of the prism which is a pentagon is regular. The apothem which is a line drawn from the center to any side of the pentagon is 4 cm. The height of the prism is 16 cm.

The volume of a prism = Bh

where

B = base area

h = height of the prism

The base of the prism can be divided into 5 congruent triangles.But the base of the triangles is unknown.

The sum of interior angle of a pentagon is 540°. That means each angle is 108° . The triangle divide the angle into 2. Making the 2 base angle as 54° each. The last angle of the triangle at the center is 72°(remember sum of angle in a triangle is 180° which is 54° + 54° + 72° = 180°) .

The angle form the center can be divided by the line of height of the triangles. The angle will then be 36°. Using tangential ratio half of the length of the base of the triangle can be known. Therefore,

tan 36° = opposite/adjacent

tan 36° = opposite/4

opposite = 4 tan 36°

The full base of the triangles = 2(4 tan 36°)

area of each triangle = 1/2 × 2(4 tan 36°) × 4 = 16 tan 36°

Base area of the prism(pentagon) = 5 × 16 tan 36° = 80 tan 36°

Volume of the prism = Bh

where

h = 16 cm

B = 80 tan 36°

volume =  80 tan 36° × 16 = 1280  tan 36° = 1280  × 0.726542528

volume = 929.974435847  cm³

volume ≈ 930 cm³ (nearest cubic cm)

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