Please help asap. Look at picture

2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

5 0

4 years ago

Solve this equation <br>(3m⁴)²

earnstyle [38]

Answer:

9m⁸

Step-by-step explanation:

3^2=9

(m⁴)² = m⁸

9*m⁸

4 0

3 years ago

What is the probability of the complement of rolling a number less than 5 by using a six-sided die?

Inessa05 [86]

<h3><u>Answer:</u></h3>

Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is:

1/3

<h3><u>Step-by-step explanation:</u></h3>

Let A denote the event of rolling a number less than 5 in a six-sided die.

Now, we know that the Total outcomes are: 6

since, the sample space is given as: {1,2,3,4,5,6}

Also Number of favorable outcomes are: 4

since the numbers which are less than 5 are {1,2,3,4}

Now we have to find:

$P(A^c)$

where P denotes the probability of an event and $A^c$ denote the complement of event A.

We know that:

$P(A^c)=1-P(A)$

Now,

$P(A)=\dfrac{4}{6}\\\\P(A)=\dfrac{2}{3}$

Hence,

$P(A^c)=1-\dfrac{2}{3}\\\\P(A^c)=\dfrac{3-2}{3}\\\\P(A^c)=\dfrac{1}{3}$

Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is:

1/3

8 0

4 years ago

Read 2 more answers

14 more than the difference of r and s

aalyn [17]

(r-s)+14

Hope this helps:)))

7 0

3 years ago

find the amount each contestant would carry if the total amount carried (5 cups) was redistributed equally among all the contest

Blizzard [7]

<u>Complete Question</u>

The line plot shows the amount of green ooze (in cup) carried by ten contestants. Find the amount each contestant would carry if the total amount carried (5 cups) was redistributed equally among all the contestants.

Answer:

1/2 Cup

Step-by-step explanation:

This is a Line Plot in which:

1/4 had two Xs
3/8 had two Xs
1/2 had two Xs
5/8 had three Xs
7/8 had one Xs

Total

$=(\frac{1}{4}X2) +(\frac{3}{8}X2) +(\frac{1}{2}X2) +(\frac{5}{8}X3) +(\frac{7}{8}X1) \\\\=\frac{2}{4} +\frac{6}{8} +1 +\frac{15}{8} +\frac{7}{8}\\\\$=5 Cups$

If this amount was redistributed equally among the ten contestants:

Each contestant would carry (5/10) cups =1/2 cup.

3 0

3 years ago