Answer:
15,872 mm³
Step-by-step explanation:
given:
A small square pyramid of height 6 cm was removed from the top of a large square pyramid of height 12cm forming the solid shown.
Find:
the exact volume of the solid
solution:
volume of square base pyramid = (base area)² * h/3
where total h = 12 cm
height of top pyramid (ht)= 6 cm
height of bottom pyramid (hb) = 6 cm
bottom volume = total volume - the volume on top
so,
total volume = 1/3 (base area)² h
= 1/3 (8*8)² * 12
= 16,384 mm³
volume on top = 1/3 (top base area)² h
= 1/3 (4*4)² * 6
= 512 mm³
finally: get the bottom volume:
bottom volume = total volume - the volume on top
bot. vol = 16,384 mm³ - 512 mm³
= 15,872 mm³
therefore,
the volume of the cut pyramid base = 15,872 mm³
N/4 less than or equal to 5
<span> 7 14/18 ...this is the answer
(simplest form should be 7 7/9)</span>
Answer:
(2, 1)
Step-by-step explanation:
To solve by substitution, we solve one equation for one of its variables and then substitute the solved value for that variable into the other equation. Because this system of equations already has one solved for the variable, this makes our job much easier. We only need to implement the solved value for y into the other equation and solve for x.
y = 6x - 11
-2x - 3(6x - 11) = -7 Distribute.
-2x - 18x + 33 = -7 Combine like terms.
-20x + 33 = -7 Subtract 33 from both sides of the equation.
-20x = -40 Divide by -20 on both sides of the equation.
x = 2
Then, with this value, we will place it into the equation that was already solved for y in order to get a definite value for y.
y = 6(2) - 11
y = 12 - 11
y = 1
Using this information, the coordinate pair for this equation (the point of intersection between the two lines) is (2, 1).
