Answer 169
This is because 13x13=169
Answer:
Distributive property
Step-by-step explanation:
The rule being shown here is the distributive property, because the first binomial is taken apart and separately multiplied with the other binomial.
Y = 500(1 + r)^x; where r is the rate and x is the number of years.
500(1 + r)^2 = 551.25
(1 + r)^2 = 551.25/500 = 1.1025
1 + r = sqrt(1.1025) = 1.05
Therefore, the equation that represents y, the value of the item after x years is
y = 500(1.05)^x
Points (1, 7) and (-3, 2)
Slope for a line between (x₁, y₁) and (x₂, y₂) , m = (y₂ -y₁) / (x₂- x₁)
The slope for the line joining the two points = (2 - 7) / (-3 - 1) = -5/-4
Slope = 5/4
Hence the perpendicular bisector would have a slope of -1/(5/4) = -4/5
By condition of perpendicularity
For points (1, 7) and (-3, 2),
Formula for midpoints for (x₁, y₁) and (x₂, y₂) is ((x₁ +x₂)/2 , (y₁+ y₂)/2)
Midpoint for (1, 7) and (-3, 2) = ((1+ -3)/2 , (7+2)/2) = (-2/2, 9/2)
= (-1, 9/2)
Since the slope of perpendicular bisector is -4/5 and passes through the midpoint (-1, 9/2)
Equation y - y₁ = m (x - x₁)
y - 9/2 = (-4/5) (x - -1)
y - 9/2 = (-4/5)(x + 1)
5(y - 9/2) = -4(x + 1)
5y - 45/2 = -4x - 4
5y = -4x - 4 + 45/2
5y + 4x = 45/2 - 4
5y + 4x = 22 1/2 - 4 = 18 1/2
5y + 4x = 37/2
10y + 8x = 37
The equation of the line to perpendicular bisector is 10y + 8x = 37
18) Let x be the number of coins in the pouch:
3x + 3 = 9; subtract 3 from each side:
3x + - 3 = 9 -3
3x = 6 . Now divide both side by 3:
x = 2 (in each pouch we have 2 coins)
19) SAME logic:
4x + 1 = 2x + 7; subtract 1 from each side:
4x + 1 - 1 = 2x + 7 - 1
4x = 2x + 6; now subtract 2x from each side:
4x - 2x = 2x + 6 - 2x
2x = 6 and x = 3 (each pouch contains 3 coins)
