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Sveta_85 [38]
3 years ago
12

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

Mathematics
1 answer:
SOVA2 [1]3 years ago
4 0

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).

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Find the value of k for which the line y = kx + 6 is a tangent to the curve x^2 + y^2 – 10x + 8y = 84
guajiro [1.7K]

Answer:

k = 1/2

Step-by-step explanation:

input y = kx +6 into the equation of the curve x² + y² – 10x + 8y = 84

x² + (kx + 6)² - 10x + 8(kx + 6) = 84

expand:

x² + k²x² + 12kx + 36 - 10x + 8kx + 48 = 84

simplify by collecting like terms:

x² + k²x² + 20kx - 10x + 84 = 84

subtract 84 on both sides to bring it to the left:

x² + k²x² + 20kx - 10x + 84 - 84 = 0

x² + k²x² + 20kx - 10x = 0

factorise out x:

x²(1 + k²) + x(20k - 10) = 0

using the discriminant b² - 4ac where b is 20k - 10, a is 1 + k² and c is 0, substitute them in the formula b² - 4ac:

b² - 4ac

(20k - 10)² - 4(1 + k²)(0) = 0

the part highlighted in bold is gone because it's all multiplied by 0, so we are left with (20k - 10)² = 0

(20k - 10)² is the same as

(20k - 10)(20k - 10)

equate both to 0

20k - 10 = 0 and 20k - 10 = 0

add 10 on both sides

20k = 10 and 20k = 10

divide 20 on both sides

k = 10/20 and k = 10/20 which are both the same

10/20 is simplified to 1/2

k = 1/2

5 0
2 years ago
6) Manert's grandfather put $8000 in the bank for him when he was 5. The account has been
Firdavs [7]
He earned $199,423 in interest.

His total would be $207,423.
4 0
3 years ago
How do I solve this?
andreev551 [17]

Answer:

x is in the range [-1,4]

Step-by-step explanation:

I haven't worked with absolute value inequalities in awhile, but let's take a wack at this.

We are given the following inequality:

| 2x - 3 | <= 5

This implies two possible cases:

[1] -5 <= 2x -3

Or

[2] 2x - 3 <= 5

So let's solve x for both of these cases:

[1] -5 <= 2x - 3

 -2 <= 2x

 -1  <= x

[2]  2x - 3 <= 5

 2x <= 8

  x <= 4

So from these cases, we can say the following is true:

x >= -1  and x <= 4

Thus, we can write this in the form

-1 <= x <= 4

Or in interval notation:

{ x is element of reals | -1 <= x <= 4}

Also written as

x is in the range [-1,4]

Where the closed brackets represent 1 and 4 as possible answers whereas parenthesis would imply they were not.

Cheers.

4 0
3 years ago
Point O is the incenter of ΔABC.<br><br> What is mQBO?<br><br> mQBO is ___ degrees.
natta225 [31]
The answer is 12 degrees
5 0
3 years ago
Read 2 more answers
Which graph represents x - 1 ≤ 3
MAVERICK [17]
The first graph. 

The  equation is x - 1 \leq 3
In order to solve it, you need to get x by itself.
Add 1 to both sides.  3+1=4
x \leq 4

Since this is your sign \leq the arrow has to point towards the left, and the circle needs to be colored in.
3 0
3 years ago
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