Jack has 20 unit cubes. How many rectangular prisms with different sized bases can he build with the cubes?

Mathematics

1 answer:

andrezito [222]4 years ago

6 0

Answer:

Jack can form four rectangular prisms with 20 unit cubes.

Step-by-step explanation:

Number of unit cubes Jack has = 20

Factors of 20 = 1, 2, 4, 5, 10, 20

The possible dimensions of a rectangular prism that can be formed by these unit cubes may be,

1 × 1 × 20 (One cube at the base)

1 × 2 × 10 (2 cubes at the base)

1 × 4 × 5 (4 cubes at base in a single row)

2 × 2 × 5 (4 cubes at the base with 2 cubes in length and 2 cubes in width)

Therefore, Jack can form four rectangular prisms with 20 unit cubes.

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Point-slope equation of the line through (6,4) and (7,2)

Nataly [62]

Answer:

Step-by-step explanation:

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m - slope

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$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (6, 4) and (7, 2). Substitute:

$m=\dfrac{2-4}{7-6}=\dfrac{-2}{1}=-2$

Using the first point

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Donna took twice as long to drive 720 miles and Maple took to drive 200 miles. Find the rates and ties of both if Donna's speed

shepuryov [24]

Answer:

Donna traveled for 8 hours at 90 mph

Maple traveled for 4 hours at 50 mph

Step-by-step explanation:

The velocity at which each person traveled is given by the distance traveled divided by the time spent (t). From the information given, the following expressions can be written

$t_d = 2t_m\\V_d = V_m+40\\V_d = \frac{720}{t_d}\\V_m = \frac{200}{t_m}\\\\V_d = \frac{360}{t_m}\\ \frac{360}{t_m}=\frac{200}{t_m}+40\\t_m = 4\ hours\\t_d=2*4 = 8\ hours\\\\V_d = \frac{720}{8}=90\ mph\\V_m = \frac{200}{4}=50\ mph\\$