Answer:
A = 62.35 cm²
Step-by-step explanation:
Use the area formula A =
, where a is the side length.
Plug in the values:
A = ![\frac{\sqrt{3}(12^2)}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%2812%5E2%29%7D%7B4%7D)
A = ![\frac{\sqrt{3}(144)}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%28144%29%7D%7B4%7D)
A = 62.35 cm²
The coordinates of other endpoint S is (3, 2)
<h3><u>Solution:</u></h3>
Given that midpoint of RS is M
Given endpoint R(23, 14) and midpoint M(13, 8)
To find: coordinates of the other endpoint S
<em><u>The formula for midpoint is given as:</u></em>
For a line containing containing two points
and
midpoint is given as:
![m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)](https://tex.z-dn.net/?f=m%28x%2C%20y%29%3D%5Cleft%28%5Cfrac%7Bx_%7B1%7D%2Bx_%7B2%7D%7D%7B2%7D%2C%20%5Cfrac%7By_%7B1%7D%2By_%7B2%7D%7D%7B2%7D%5Cright%29)
Here in this problem,
m(x, y) = (13, 8)
![(x_1, y_1) = (23, 14)\\\\(x_2, y_2) = ?](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%20%3D%20%2823%2C%2014%29%5C%5C%5C%5C%28x_2%2C%20y_2%29%20%3D%20%3F)
Substituting the given values in above formula, we get
![(13,8)=\left(\frac{23+x_{2}}{2}, \frac{14+y_{2}}{2}\right)](https://tex.z-dn.net/?f=%2813%2C8%29%3D%5Cleft%28%5Cfrac%7B23%2Bx_%7B2%7D%7D%7B2%7D%2C%20%5Cfrac%7B14%2By_%7B2%7D%7D%7B2%7D%5Cright%29)
Comparing both the sides we get,
![\begin{aligned}&13=\frac{23+x_{2}}{2} \text { and } 8=\frac{14+y_{2}}{2}\\\\&26=23+x_{2} \text { and } 16=14+y_{2}\\\\&x_{2}=3 \text { and } y_{2}=2\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%2613%3D%5Cfrac%7B23%2Bx_%7B2%7D%7D%7B2%7D%20%5Ctext%20%7B%20and%20%7D%208%3D%5Cfrac%7B14%2By_%7B2%7D%7D%7B2%7D%5C%5C%5C%5C%2626%3D23%2Bx_%7B2%7D%20%5Ctext%20%7B%20and%20%7D%2016%3D14%2By_%7B2%7D%5C%5C%5C%5C%26x_%7B2%7D%3D3%20%5Ctext%20%7B%20and%20%7D%20y_%7B2%7D%3D2%5Cend%7Baligned%7D)
Thus the coordinates of other endpoint S is (3, 2)
Answer:
-45
Step-by-step explanation:
(4.5)(5)(-2)=-45
therefore the answer would be the fourth option which is -45
Answer and explanation:
Farmer's number of apples = 96 apples
Given that Farmer needs to bag the apples so that there are at least 4 apples in each bag(not less than 4 apples in each bag) and not more than 10 apples in each bag
And also all apples in each bag are equal
We need to find the numbers between 4 and 10(including 4 and 10) that can divide 96 without a remainder
4 can divide 96= 24
5 cannot divide 96 without remainder
6 can divide 96 =16
7 cannot divide 96 without remainder
8 can divide 96=12
9 cannot divide 96 without remainder
10 cannot divide 96 without remainder
From the above we see that the factors of 96 = 4, 6, 8 between 4 and 10
4 apples = 24 bags
6 apples = 16 bags
8 apples = 12 bags
Therefore, there can be 3 possible ways of having equal number of apples in each bag between 4 and 10 apples
Answer:
6.37%
Step-by-step explanation:
A deck of cards have 52 cards. There are 4 suits of 13 card each, those suits are Hearts, Clubs, Diamond and Spades.
The probability that the first card is a heart is:
![P(Hearts) = \frac{13}{52}](https://tex.z-dn.net/?f=P%28Hearts%29%20%3D%20%5Cfrac%7B13%7D%7B52%7D)
Now, the probabily that the second card is a diamond is:
![P(Diamond | First card is Heart) = \frac{13}{51}](https://tex.z-dn.net/?f=%20P%28Diamond%20%7C%20First%20card%20is%20Heart%29%20%3D%20%5Cfrac%7B13%7D%7B51%7D)
The Probability that the first card is a heart and the second one a diamond is given by:
×![P(Diamond | First card is Heart)](https://tex.z-dn.net/?f=P%28Diamond%20%7C%20First%20card%20is%20Heart%29)
![= \frac{13}{52}\frac{13}{51}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B13%7D%7B52%7D%5Cfrac%7B13%7D%7B51%7D)
%