Answer:
Therefore the required point A(x₁ , y₁) = A( -3 , 4 )
Step-by-step explanation:
Given:
The midpoint of segment AB is M(1,-3)
and B(5,-10),
Let
point A( x₁ , y₁)
point B( x₂ , y₂) ≡ (5 , -10)
M(x , y) = (1 , -3 )
To Find:
point A( x₁ , y₁) = ?
Solution:
M is the midpoint of segment AB. {Given}
BY Mid point Formula we have
![M(x,y)=(\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2})](https://tex.z-dn.net/?f=M%28x%2Cy%29%3D%28%5Cfrac%7Bx_%7B1%7D%2Bx_%7B2%7D%20%7D%7B2%7D%2C%20%5Cfrac%7By_%7B1%7D%2By_%7B2%7D%20%7D%7B2%7D%29)
Substituting the given values in above equation we get
![M( 1, -3)=(\frac{x_{1}+5 }{2}, \frac{y_{1}-10 }{2})\\\\\textrm{on equating the X coordinate and Y coordinate of M we get}\\1 =\frac{x_{1}+5 }{2}\\\\and\\-3=\frac{y_{1}-10 }{2}\\\\\therefore x_{1}+5=2\ and\ y_{1}-10 =-6\\\\\therefore x_{1} = 2-5=-3\ and\ y_{1}=10-6=4\\\\\therefore x_{1} = -3\ and \ y_{1}=4\\\\\therefore A(x_{1},y_{1})=A(-3,4)](https://tex.z-dn.net/?f=M%28%201%2C%20-3%29%3D%28%5Cfrac%7Bx_%7B1%7D%2B5%20%7D%7B2%7D%2C%20%5Cfrac%7By_%7B1%7D-10%20%7D%7B2%7D%29%5C%5C%5C%5C%5Ctextrm%7Bon%20equating%20%20the%20X%20coordinate%20and%20Y%20coordinate%20of%20M%20we%20get%7D%5C%5C1%20%3D%5Cfrac%7Bx_%7B1%7D%2B5%20%7D%7B2%7D%5C%5C%5C%5Cand%5C%5C-3%3D%5Cfrac%7By_%7B1%7D-10%20%7D%7B2%7D%5C%5C%5C%5C%5Ctherefore%20x_%7B1%7D%2B5%3D2%5C%20and%5C%20y_%7B1%7D-10%20%3D-6%5C%5C%5C%5C%5Ctherefore%20x_%7B1%7D%20%3D%202-5%3D-3%5C%20and%5C%20y_%7B1%7D%3D10-6%3D4%5C%5C%5C%5C%5Ctherefore%20x_%7B1%7D%20%3D%20-3%5C%20and%20%5C%20y_%7B1%7D%3D4%5C%5C%5C%5C%5Ctherefore%20A%28x_%7B1%7D%2Cy_%7B1%7D%29%3DA%28-3%2C4%29)
Therefore the required point A(x₁ , y₁) = A( -3 , 4 )
Answer:
These are two secant lines meaning we can use theorem 6-17 to find the value of x: 6x + 8x times 8x = 16 times 7
14x times 8x = 112
112x^2 = 112
x^2 = 1
x = 1
4 gallons but still have some left over
(3 1/6 gallons)
I thinks it’s 3 because 21-12=9 so you spent 9 dollars 9/3=3
Answer:
1. LCM of 18 & 12 = 36 minutes
2. 0.00095897
explanation.
2 18 2 12
____I______ ___l_________
3 9 2 6
____l_______. ___I_________
3 3 3 3
_____l________. ___l_________
l 1
18= 2×3×3 12=2×2×3
1 2 2 1
=1 × 3 =2 × 3
L.C.M= product of greatest power of each prime factor.
2 2
= 2 × 3
=4×9 = 36
hence, time taken by both to meet again
LCM of 18 & 12 =36 minutes