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Nostrana [21]
3 years ago
5

On paper, make a rectangle that has points A and B as two of its vertices and has a perimeter of 40 units. Draw and label the tw

o other vertices as points C and D on the coordinate plane. Draw line segments to show the rectangle. What are the coordinates for points C and D.
Mathematics
1 answer:
Westkost [7]3 years ago
8 0

Answer:

A(x,y),B(x+10,y),C(x+10,y-10) \:and\: D(x,y-10)

Step-by-step explanation:

If a Rectangle has a perimeter of 40 units, then we can write that formula and find the a formula for the coordinates:

\left\{\begin{matrix}w+l=20 & \\ w*l=100 & \end{matrix}\right.\Rightarrow w=20-l\Rightarrow (20-l)l=100\Rightarrow -l^2+20l-100=0\Rightarrow l^2-20l+100\Rightarrow (l-10)(l-10)\Rightarrow l=10\therefore l=10\: and\: w=10

Therefore we can say:

A(x,y),B(x+10,y),C(x+10,y-10) \:and\: D(x,y-10)

Technically when w=lin this rectangle is a square, a degenerate square.

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Solve 2(3-a)=18 for a
Alinara [238K]

Answer:

a=-6

Step-by-step explanation:

2(3-a)=18

3-a=18/2

3-a=9

a=3-9

a=-6

7 0
3 years ago
Read 2 more answers
Given that x and y are positive integers, solve the equation x² - 4y² = 13​
zvonat [6]
<h3>Answer:  x = 7 and y = 3</h3>

=====================================================

Explanation:

Apply the difference of squares rule

x² - 4y² = 13

x² - (2y)² = 13

(x - 2y)(x + 2y) = 13

Since x and y are positive integers, this means x-2y and x+2y are both integers as well.

The value 13 is prime. Its only factors are 1 and 13

Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:

  • A) x-2y = 1 and x+2y = 13
  • B) x-2y = 13 and x+2y = 1

----------------

Let's consider case A

We have this system of equations

\begin{cases}x-2y = 1\\x+2y = 13\end{cases}

Add the equations straight down

  • x+x becomes 2x
  • -2y+2y becomes 0y = 0 which goes away
  • 1+13 becomes 14

Therefore we have 2x = 14 solve to x = 7

From here, plug this into either equation to solve for y

x-2y = 1

7 - 2y = 1

-2y = 1-7

-2y = -6

y = -6/(-2)

y = 3

You should get the same result if you used x+2y = 13

----------------

Since we've found that x = 7 and y = 3, notice how case B is not possible

Example:  x-2y = 13 becomes 7-2(3) = 13 which is false.

Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.

-----------------

Let's check those x and y values in the original equation

x² - 4y² = 13

7² - 4*(3)² = 13

49 - 4(9) = 13

49 - 36 = 13

13 = 13

The answer is confirmed.

4 0
2 years ago
The weights of 67 randomly selected axles were found to have a variance of 3.85. Construct the 80% confidence interval for the p
VLD [36.1K]

Answer:

3.13

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 67

Variance = 3.85

We have to find 80% confidence interval for the population variance of the weights.

Degree of freedom = 67 - 1 = 66

Level of significance = 0.2

Chi square critical value for lower tail =

\chi^2_{1-\frac{\alpha}{2}}= 51.770

Chi square critical value for upper tail =

\chi^2_{\frac{\alpha}{2}}= 81.085

80% confidence interval:

\dfrac{(n-1)S^2}{\chi^2_{\frac{\alpha}{2}}} < \sigma^2 < \dfrac{(n-1)S^2}{\chi^2_{1-\frac{\alpha}{2}}}

Putting values, we get,

=\dfrac{(67-1)3.85}{81.085} < \sigma^2 < \dfrac{(67-1)3.85}{51.770}\\\\=3.13

Thus, (3.13,4.91) is the required 80% confidence interval for the population variance of the weights.

8 0
3 years ago
Can somebody please help
horsena [70]

Step-by-step explanation:

x + 90⁰ + 90⁰ + 120⁰ = 360 ....sum of angles of quadrilatral is 360⁰

x = 60⁰...

7 0
3 years ago
david ran on a straight track. every time he ran 480m, he took a break. After 2 breaks, he still had to run 120 m to complete th
kipiarov [429]

Answer:

The distance of the playground is 540m

Step-by-step explanation:

Here, we are interested in calculating the length of the playground given the information in the question.

Where to attack the question from is the segment that states that he took a break after 480m and also had 2 breaks. Thus, the distance traveled would be 480 * 2 = 960 m

Now, to find the length of the track, we add the distance covered plus the distance uncovered. Mathematically that would be 960m + 120m = 1,080m

In the last part of the question, we are told that the track is twice as long as the playground. This means that the length of the playground or the distance of the playground is 1080/2 = 540 m

4 0
3 years ago
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