Answer:
£389.4 (interest earned, not total amount of money in account)
Step-by-step explanation:
Interest = principal * rate * time (years)
I = 885 * 0.0275 * 16
I = 398.4
Use mental math to solve each equation:
1.). - 52 = - 52 + k
Simplify both sides.
- 52 = - 52 + k
Flip Equation:
k - 52 = - 52
Add 52 both sides:
k - 52 + 52 = -52 + 52
k = 0, Answer: K = 0
3.). x - 155 = 15
Add 155 to both sides:
x - 155 + 155 = 15 + 155
x = 170, Answer: 170
5.). 2,000 + y = 9,500
Simplify both sides:
y + 2000 = 9500
Subtract 2000 from both sides:
y + 2000 - 2000 = 9500 - 2000
y = 7500, Answer: 7500 Graph: 7500
7.). 111 + f = 100
Simplify both sides:
f + 111 = 100
Subtract 111 from both sides:
f + 111 - 111 = 100 - 111
f = - 11, Answer: f = - 11
Solve each equations:
9.). m - 17 = - 8
Add 17 to both sides:
m - 17 + 17 = - 8 + 17
m = 9, Answer: m = 9
11.). - 44 + n = 36
Simplify both sides of the equations:
n - 44 = 36
Add 44 to both sides:
n - 44 + 44 = 36 + 44
n = 80, Answer: n = 80
13.). x - 255 = 671
Add 255 to both sides:
x - 255 + 255 = 671 + 255
x = 926, Answer: x = 926
15.). x + 14 = 21
Subtract 14 from both sides:
x + 14 - 14 = 21 - 14
x = 7, Answer: x = 7
17.). - 19 = k + 9
Flip equation:
K + 9 = - 19
Subtract 9 from both sides:
k + 9 - 9 = - 19 - 9
k = - 28, Answer: k = - 28
19.). 36 + n = 75
Simplify both sides of equation:
n + 36 = 75
Subtract 36 from sides:
n + 36 - 36 = 75 - 36
n = 39, Answer: n = 39
21.). 41 + k = 7
Simplify both sides of equation:
k + 41 = 7
Subtract 41 from both sides:
k + 41 - 41 = 7 - 41
k = - 34, Answer: k = - 34
23.). - 88 + z = 0
Simplify both sides of equation:
z - 88 = 0
Add 88 to both sides:
z - 88 + 88 = 0 + 88
z = 88, Answer: z = 88
Hope that helps!!!! :)
16. 96 is 75% of 128
18. 200%
Answer:
the ingegral I=π/4
Step-by-step explanation:
From the integral
I=∫0-1∫0-sqrt(1-y^2) (x^2 + y^2) dxdy
from polar coordinates
r²=x² + y²
then for r=1
√(1- y²) = x
for y=1 → x=0 , for y=0 → x=1
then the integration area is a hemisphere or radius r=1
therefore
I= ∫0-1∫0-sqrt(1-y^2) (x^2 + y^2) dxdy = (1/2)∫2π-0 ∫1-0 r² *r drdθ ( the additional r is due to the Jacobian of the transformation to polar coordinates , 1/2 because is an hemisphere so it would be the half of the value of the total sphere)
I= (1/2)∫2π-0 ∫1-0 r³drdθ = (1/2)∫2π-0 (1⁴/4 - 0⁴/4) dθ = (1/2)∫2π-0 (1/4)*dθ = (1/2)*(1/4)*2π = π/4
By the Intersecting Secants Theorem we have
2x(2x+7)=x(x+23)
4x^2+14x=x^2+23x
3x^2=9x
3x=9
x=3
Since DY is length 2x,
the length of DY is 6.
