MATHEMATICS HIGH SCHOOL

Find the area of the polygon with the given vertices W(0,0), X(0, 3), Y(-3,3), Z(-3,0)

Answers

Answer 1

Answer:

The area of the polygon is 9.

Calculating the area of triangle WXY

The area of a triangle can be calculated using the following formula:

Area of triangle = 1/2 * base * height

In triangle WXY, the base is XY and the height is WX.

The length of XY is equal to the distance between the two points (0, 3) and (-3, 3). This distance can be calculated using the distance formula:

Distance between two points = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of the two points into the distance formula, we get:

Distance between (0, 3) and (-3, 3) = sqrt((-3 - 0)^2 + (3 - 3)^2) = sqrt(9) = 3

Therefore, the length of XY is 3.

The length of WX is equal to the y-coordinate of point X, which is 3.

Therefore, the area of triangle WXY is:

Area of triangle WXY = 1/2 * 3 * 3 = 4.5

Calculating the area of triangle YXZ

The area of triangle YXZ can be calculated in the same way as the area of triangle WXY.

The length of YZ is equal to the distance between the two points (-3, 3) and (-3, 0). This distance can be calculated using the distance formula:

Distance between (-3, 3) and (-3, 0) = sqrt((-3 - (-3))^2 + (3 - 0)^2) = sqrt(9) = 3

Therefore, the length of YZ is 3.

The length of XZ is equal to the x-coordinate of point Z, which is -3.

Therefore, the area of triangle YXZ is:

Area of triangle YXZ = 1/2 * 3 * 3 = 4.5

Calculating the area of the polygon

The area of the polygon is the sum of the areas of the two triangles:

Area of the polygon = Area of triangle WXY + Area of triangle YXZ = 4.5 + 4.5 = 9

Therefore, the area of the polygon is 9.

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Answer 2

Answer:

Final answer:

The area of a rectangle with vertices at W(0,0), X(0,3), Y(-3,3) and Z(-3,0) is 9 square units.

Explanation:

The question asks to find the area of a polygon given its vertices. The polygon in this question is a rectangle with vertices at W(0,0), X(0,3), Y(-3,3) and Z(-3,0). The formula to find the area of a rectangle is Length x Width. In this case, the length of the rectangle is WX or XZ which is 3 units (from 0 to 3) and the width is X to Y or W to Z which is 3 units (from 0 to -3). So, the area of the rectangle is 3 x 3 = 9 square units.

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Answers

3x = 12 - x because they are vertical angles.
+x +x
4x = 12
/4 /4
x = 3

Brandon uses the steps below to solve the equation 15x+6=14x+5 using algebra tiles. Step 1 Add 14 negative x-tiles to both sides. Step 2 Add 5 negative unit tiles to both sides Step 3 The solution is x=1 Which explains whether Brandon is correct?

Answers

Answer:

No he was not correct

Step-by-step explanation:

The Equation is 15 x + 6 = 14 x + 5

now By the steps brandon used let us solve the question

Step 1 : Add 14 negative x tile to both sides

which will make the equation

15x + 6 - 14x = 14x + 5 - 14 x

x + 6 = 5 .......(ii)

Step 2: Add 5 negative unit tiles to both sides of equation (ii)

which will make the equation

x +6 - 5 = 5 - 5

x + 1 = 0 .........(iii)

Step 3: x =1 is the answer

but from equation (iii) we see that

x + 1 =0

by adding -1 on both sides

x + 1 -1 = 0-1

x = -1

So the step three done by Brandon is wrong which explains he was not correct

Answer:

D.) Brandon is not correct because he should have added 6 negative unit tiles to isolate the variable in step 2.

Step-by-step explanation:

YOUR WELCOME!! I took the test on Edge!! :)

Diagonals AC and BD of a rhombus ABCD meet at O . If AC=8cm and BD=6cm , find sin √OCD.

Answers

Answer:

Hi,

Step-by-step explanation:

AC=8 => AO=OC=AC/2=4

BD=6 => BO=OD=3

$sin(\widehat{OCD})\n\n=(OD)/(√(OD^2+OC^2))\n\n=(3)/(√(3^2+4^2) )\n\n\n=\boxed{(3)/(5)}$

Length of a rectangle is 2.5 cm and it’sarea is 12.5cm2. Ram found that the breadth of the rectangle is 5 cm while Rahim found that the breadth is 10 cm. Who is correct? Justify your answer.