You divide and simplify and get9.2875
Answer:
X= -6, Y= 3
Step-by-step explanation:
1)
- X - Y = 3
- X - 3= Y
Y= - X - 3
2)
6X + 2Y = -30
3X + Y = -15
Y = -15 - 3X
3) Combine
- X- 3 = - 15 - 3X
- X = -15 - 3X +3
-X + 3X = - 12
2X = - 12
X= - 6
4)
- X-Y=3
-(-6) - Y = 3
-Y= 3-6
-Y= - 3
Y = 3
Answer: X= -6, Y= 3
{
6x + 2y = -30, 6(-6)+2(3)= -30
}
Answer:
239
Step-by-step explanation:
The area the goat can graze is a circular segment (a circle cut by a chord), where the radius is 10 m and the distance from the center to the chord is 6 m. Here's a graph: desmos.com/calculator/qmstllv4dx
To find the area, we can split this into two shapes: a sector and an isosceles triangle. desmos.com/calculator/hvsor3mqps
To find the areas, we first must find the vertex angle of the triangle. We can do that using cosine:
cos(θ/2) = 6/10
θ/2 = 53.13°
θ = 106.26°
The area of the triangle can be found with the SAS formula:
A = ½ ab sin C
A = ½ (6) (6) (sin 106.26°)
A = 17.28
The area of the sector is:
A = πr² (θ / 360°)
A = π (10)² ((360° − 106.26°) / 360°)
A = 221.43
The total area is 17.28 + 221.43 = 238.71. Rounded to the nearest square meter, the goat can graze an area of 239 m².
Answer:
44 ft
Step-by-step explanation:
step 1
Find the length side of the square box
The area of the box is equal to
where
b is the length side of the square box
we have
substitute
solve for b
square root both sides
step 2
Find the perimeter of the square box
The perimeter of the square box is
we have
substitute
so change a value to a percentage format, we simply divide it by 100.
for example, 2% can be rewritten as 2/100 or 0.02 in decimal format.
now, let's first convert the mixed fraction to improper, and then do the percentage format and simplification.
![\bf \stackrel{mixed}{3\frac{1}{8}}\implies \cfrac{3\cdot 8+1}{8}\implies \stackrel{improper}{\cfrac{25}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~\frac{25}{8}~~}{100}\implies \cfrac{~~\frac{25}{8}~~}{\frac{100}{1}}\implies \cfrac{25}{8}\cdot \cfrac{1}{100}\implies \cfrac{1}{8}\cdot \cfrac{25}{100}\implies \cfrac{1}{8}\cdot \cfrac{1}{4}\implies \cfrac{1}{32}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%208%2B1%7D%7B8%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B25%7D%7B8%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B~~%5Cfrac%7B25%7D%7B8%7D~~%7D%7B100%7D%5Cimplies%20%5Ccfrac%7B~~%5Cfrac%7B25%7D%7B8%7D~~%7D%7B%5Cfrac%7B100%7D%7B1%7D%7D%5Cimplies%20%5Ccfrac%7B25%7D%7B8%7D%5Ccdot%20%5Ccfrac%7B1%7D%7B100%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B8%7D%5Ccdot%20%5Ccfrac%7B25%7D%7B100%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B8%7D%5Ccdot%20%5Ccfrac%7B1%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B32%7D%20)
