4) r = √[v/(πh)]; d ≈ 5 in
5) 1.25x + 2.50y = 25.00 ; 11 combinations
4) (a) formula for radius
v = πr²h divide each side by πh
v/(πh) = r² take the square root of each side.
r = √[v/(πh)]
(b) diameter of tuna can
v = 66 in³
h = 3.3 in
r = √[v/(πh)]
= √[66/(π × 3.3)]
d = 2r
≈ 5 in
5) hot dogs and hamburgers
(a) the equation
let x = the number of hot dogs
and y = the number of hamburgers
1.25x + 250y + 7 × 0.50 = 28.50
1.25x + 250y + 3.50 = 28.50 subtract 3.50 from each side
1.25x + 2.50y = 25.00
(b) plot the graph
let x = 0. then
2.50y = 25.00 divide each side by 2.50
y = 10
plot a point at (0, 10).
let y = 0. then,
1.25x = 25.00 divide each side by 1.25
x = 20
plot a point at (20, 0).
draw a straight line between the two points.
your graph should look like the one below.
(c) hot dog/hamburger combinations
the possible hot dog/hamburger (x/y) combinations are:
0x + 10y, 2x + 9y, 4x + 8y, 6x + 7y, 8x + 6y, 10x + 5y, 12x + 4y, 14x + 3y, 16x + 2y, 18x + 1y, 20x + 0y
thus, there are 11 different combinations that zeke and his friends can buy for $28.50.
it works like this, because one hamburger costs $2,50 and a hamburger half as much.
you can replace one hamburger with two hot dogs (or vice versa) and still spend the same amount of money,.
105×35m = 35(3 + m)
x = 4
note the exact value of tan60° =
since the triangle is right use the tangent ratio to find x
tan60° = =
multiply both sides by x
x × = 4
divide both sides by
x = = 4 × = 4