Answer:
Step-by-step explanation:
Step 1: Sum of angles on a straight line is 180
Step 2:
2x + 25 + y = 180
2x + y = 180 - 25
2x + y = 155 (1)
Step 3:
3x - 10 + y = 180
3x + y = 180 + 10
3x + y = 190 (2)
Step 4: Substract equation 1 from 2
3x + y - 2x - y = 190 - 155
x = 35
Step 5:
Substitute x in equation 1 to find y
2x + y = 55
2(35) + y = 155
70 + y = 155
y = 155 - 70
y = 85
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (2, 1)
m = 
= - 5, hence
y = - 5x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 6), then
6 = - 5 + c ⇒ c = 6 + 5 = 11
y = - 5x + 11 → A
Simplify the following:
(3 sqrt(2) - 4)/(sqrt(3) - 2)
Multiply numerator and denominator of (3 sqrt(2) - 4)/(sqrt(3) - 2) by -1:
-(3 sqrt(2) - 4)/(2 - sqrt(3))
-(3 sqrt(2) - 4) = 4 - 3 sqrt(2):
(4 - 3 sqrt(2))/(2 - sqrt(3))
Multiply numerator and denominator of (4 - 3 sqrt(2))/(2 - sqrt(3)) by sqrt(3) + 2:
((4 - 3 sqrt(2)) (sqrt(3) + 2))/((2 - sqrt(3)) (sqrt(3) + 2))
(2 - sqrt(3)) (sqrt(3) + 2) = 2×2 + 2 sqrt(3) - sqrt(3)×2 - sqrt(3) sqrt(3) = 4 + 2 sqrt(3) - 2 sqrt(3) - 3 = 1:
((4 - 3 sqrt(2)) (sqrt(3) + 2))/1
((4 - 3 sqrt(2)) (sqrt(3) + 2))/1 = (4 - 3 sqrt(2)) (sqrt(3) + 2):
Answer: (4 - 3 sqrt(2)) (sqrt(3) + 2)
Answer:x=-1
Step-by-step explanation:
Answer:
Step-by-step explanation:
Formula for the volume of a sphere is V = (4/3) (π) r³
3V 4²
and so the cube of the radius, "r," is r³ = ------------- * -----
4 4²
Taking the cube root of both sides, we get
∛[3V / 4²] 3V
and so the radius, "r," is r = ------------------ = ∛ ( --------- ) = (1/4)*∛(3*v)
∛[4³] 4³
Then
r = (1/4)*∛(3*V), after substituting 500/(3π) for V, becomes:
r = (1/4)*∛[ 3*500/3π ] = (1/4)*∛[ 500/π ]
