Given:
A(16, 4)
B(34, 40)
Line segment AB partition in the ratio 1 : 5.
To find:
The coordinate of a point that partitions AB.
Solution:
Section formula:
![$P(x,y)=\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+m y_{1}}{m+n}\right)](https://tex.z-dn.net/?f=%24P%28x%2Cy%29%3D%5Cleft%28%5Cfrac%7Bm%20x_%7B2%7D%2Bn%20x_%7B1%7D%7D%7Bm%2Bn%7D%2C%20%5Cfrac%7Bm%20y_%7B2%7D%2Bm%20y_%7B1%7D%7D%7Bm%2Bn%7D%5Cright%29)
Here
and m = 1, n = 5
![$P(x,y)=\left(\frac{1\times 34+5 \times 16}{1+5}, \frac{1\times 40+5 \times4}{1+5}\right)](https://tex.z-dn.net/?f=%24P%28x%2Cy%29%3D%5Cleft%28%5Cfrac%7B1%5Ctimes%2034%2B5%20%5Ctimes%2016%7D%7B1%2B5%7D%2C%20%5Cfrac%7B1%5Ctimes%2040%2B5%20%5Ctimes4%7D%7B1%2B5%7D%5Cright%29)
![$P(x,y)=\left(\frac{ 34+80}{6}, \frac{40+20}{6}\right)](https://tex.z-dn.net/?f=%24P%28x%2Cy%29%3D%5Cleft%28%5Cfrac%7B%2034%2B80%7D%7B6%7D%2C%20%5Cfrac%7B40%2B20%7D%7B6%7D%5Cright%29)
![$P(x,y)=\left(\frac{ 114}{6}, \frac{60}{6}\right)](https://tex.z-dn.net/?f=%24P%28x%2Cy%29%3D%5Cleft%28%5Cfrac%7B%20114%7D%7B6%7D%2C%20%5Cfrac%7B60%7D%7B6%7D%5Cright%29)
![$P(x,y)=(19, 10)](https://tex.z-dn.net/?f=%24P%28x%2Cy%29%3D%2819%2C%2010%29)
The coordinate of point that partitions the segment AB is (19, 10).
Answer:
Maggie is 13
Step-by-step explanation:
Honestly, I just kept trying ages starting from 10 because I knew it wasn't going to be less than that. Then I did whatever age, in this case 13, and multiply it by 4. Then minus 11 from that number. Then take that end number and add it to the beginning number(maggies age) and you should get 54.
Math Equation Explanation:
13*4 = 52 (Maggies Age) x 4
52-11= 41 The question stated that Maggie's brother was 11 -------------------------------------years younger than her age times 4.
41 + 13 =54 The sum of both their ages.
Answer:
1.
a. 20 m²: barn door is 5m x 4m
b. 468 m²:surface area of barn
i. left and right barn walls: 2(15 x 7) = 210
ii. back wall: 7 x 8 = 56
iii. front wall: (7 x 8) - 20* = 36
*20 for the barn door
iv. front of roof: (4 x 4) / 2 = 8 x 2* = 16
*I split the triangle into 2 smaller triangles
v. sides of roof: 2(5 x 15) = 150
2.
a. 15 m²: silo door is 3m x 5m
b. 244.18 m²: surface area of silo
i. SA(silo)=2πrh+2πr²
ii. SA(silo) = 2π(2.5)(14) + 2π(2.5)²
iii. SA(silo) = 259.18
iv. SA(silo - door) = 259.18 - 15
v. SA(silo - door) = 244.18
3.
a. 712.18 m²: total surface area painted red
i. add both surface areas: 468 + 244.18 = 712.18 m²
hope this helps :)
Five and one-fourth divided by one and one-half is equal to three and one-fifth.
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