x-intercept = (15, 0) y-intercept = (0, 3)
slope (m) = (y₂ - y₁)/(x₂ - x₁) = (0 - 3)/(15 - 0) = -3/15 = -1/5
Point-Slope formula: y - y₁ = m(x - x₁) ; where (x₁, y₁) is one of the given points
y - 0 = (-1/5)(x - 15)
-5y = x - 15
x + 5y = 15
Answer: x + 5y = 15
Part a), solve this system of equations:
x + y = 5
x - y = 2.25
2x = 7.25
x = 3.625
y = 1.375
part b), solve this system of equations:
x + y = 5
x = 3y
y = 1.25
x = 3.75
Answer:
T=4B+10C
Step-by-step explanation:
for every bag there are 4 doughnuts
for every carton there are 10 doughnuts
Start with the equation,
V = 2s^3
Now substitute s with 3.5 units and evaluate the expression.
V = 2 * (3.5 units)^3
V = 2 * 42.875 units^3
V = 85.75 units^3
Answer: The volume is 85.75 cubic units
Step-by-step explanation:
b is per the identity of angles on parallel lines when intersected by one inclined line the same as the 40° angle.
so,
b = 40°
due to the parallel nature of the 2 lines there is a symmetry effect for such shapes inscribed a circle. the upper and the lower triangle must be similar. and when applying a vertical line through the central crossing point, everything to the left is mirrored by everything on the right.
so, angle c must be equal to angle b.
c = 40°
and as the sum of all angles in a triangle is always 180°, d is then
d = 180 - 40 - 40 = 100°
the interior angle of the arc angle a is the supplementary angle of d (together they are 180°), because together with d they cover the full down side of the top-left to bottom-right line.
interior angle to a = 180 - 100 = 80°
due to the symmetry again, the arc angle opposite to a is the same as a.
as we know, the interior angle to a pair of opposing arc angles is the mean value of the 2 angles.
so, we have
(a + a)/2 = 80
2a/2 = 80
a = 80°
there might (and actually should) be some more direct approaches for "a" out of the other pieces of information, but that was the most straight one right out of my mind, and I don't spend time on finding additional shortcuts, when I have already a working approach.