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Find the coordinates of the fourth vertex that completes the construction of the rectangle on the coordinate plan

SOVA2 [1]

The coordinates of the fourth vertex are (2, -4).

Step-by-step explanation:

Step 1:

The opposite sides of a triangle are always equal.

First, we plot the three given points of the rectangle.

Assume the top left corner is A, the top right corner is B, the bottom left corner is C and the bottom right corner is D.

We need to determine the coordinates of point D.

Step 2:

The coordinates of the given three points are

A (-2, 5), B (2, 5), and C (-2, -4).

A and C are the same side i.e. the left side, they have the same x coordinate of -2.

So B and D will have the same x coordinate of 2.

A and B are on the same side too i.e. the top side so they both have the same y coordinate of 5.

The points C and D are two ends of the bottom side so they must have the same y coordinate of -4.

So the coordinates of the fourth vertex are (2, -4).

4 0

3 years ago

The height in feet above the water of a diver can be modeled by ℎ() = −16*2 − 16 + 192, where t is the time in seconds after the

Maurinko [17]

h(t) is the height of the diver in feet above the water

Now it asks about the time at which diver reaches the water

When diver reaches the water , the height of diver from water should be zero

So we plug h(t) =0

So

$-16t^2 -16 t +192 =0$

divide whole equation by -16

$t^2 +t -12 =0$

we can now factor the quadratic equation

So we get

(t+4)(t-3) =0

plug each factor equal to zero and solve for t

t+4 =0 and t-3 =0

So t=-4 and t=3

Now time cannot be negative , So t=3

So time = 3 seconds

It takes 3 seconds for the diver to reach the water

3 0

4 years ago

What is the sum of the series?

Mamont248 [21]

Answer:

45

Step-by-step explanation:

Since the values are relatively small substitute i = 1 to 5 into 3i and sum

(3 × 1) + (3 × 2) + (3 × 3) + (3 × 4) + (3 × 5)

= 3 + 6 + 9 + 12 + 15

= 45

6 0

4 years ago

The measures of three angles of a triangle are given by (8x - 5), (2x)º, and (3x – 10). What is the measure of the largest angle

zhannawk [14.2K]

Answer: 115°

Step-by-step explanation:

We should note that the sum of the angles that are in a triangle is equal to 180°, therefore we will add the angles given and equate them to 180°. This will be:

(8x - 5) + (2x) + (3x - 10) = 180

8x - 5 + 2x + 3x - 10 = 180

Collect like terms

8x + 2x + 3x = 180 + 5 + 10

13x = 195

x = 195/13

x = 15

The angles are:

8x - 5 = 8(15) - 5 = 120 - 5 = 115°

2x = 2(15) = 30°

3x - 10 = 3(15) - 10 = 45 - 10 = 35°

Therefore, the largest angle is 115°

3 0

3 years ago

What is the relationship between 7 and —7?

Alex73 [517]

Answer: absolute value

Step-by-step explanation:

Sorry for my writing it’s horrible ik I’m in a hurry rn lol

4 0

3 years ago