The shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be <u>heart-shaped</u>.
A prism is a polyhedron made up of n parallelogram faces that connect the n-sided polygon base, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.
In the question, we are informed that a prism with a heart-shaped base is sliced parallel to the base.
We are asked what shape is formed.
From the above discussion, we know that the bases are translated into all cross-sections that are parallel to them, that is, all cross-sections parallel to the base, will be congruent to the base.
Thus, the shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be <u>heart-shaped</u>.
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Given:
Line A: 
Line B: 
Line C: 
Line D: 
To find:
Which lines are perpendicular
Solution:
General equation of a line:
y = mx + c
where m is the slope and c is the y-intercept.
Slope of line A = 
Slope of line B = 
Slope of line C = 2
Slope of line D =
<em>Two lines are perpendicular if their slopes are negative reciprocal of one another.</em>
Negative reciprocal of is 2.
Therefore line B and line C are perpendicular lines.
Answer:
Samdy's statement is FALSE, total number of brothers and sisters is 52
Step-by-step explanation:
To organize our information we should draw a table, where group the students by how many siblings they have, and then calculate the total number of siblings.
First, I would distribute the 2 out to the (x+4).
2x+8.
Next, use the foil method to multiply together 2x+8 and (x+3).
2x^2 +14x+24.
Do the same process for the other side.
3(x+2)= 3x+6
(3x+6)(x-1)= 3x^2+3x-6
Set the remaining products of each side of the equation equal to each other.
2x^2 +14x+24=3x^2+3x-6.
Now you must cancel out one side to make the equation equal to zero. Do this by doing the inverse operation on one side of the equation (each value with their like term). I am going to subtract the left side values from the right:
This means:
3x^2 minus 2x^2 equals 1x^2 (or just x^2).
3x minus 14x equals -11x
-6 minus 24 equals -30
The equation should now look like this:
0=x^2-11x-30
Reverse the order to get zero on the right side:
x^2-11x-30=0
Hope this helps! Sorry if I made any careless mistakes (^^;)
Answer:
390 ft²
Step-by-step explanation:
The longer base of a trapezoid is 8 ft. The longer base of a similar trapezoid is 13 ft. The area of the smaller trapezoid is 240 ft² What is the area of the larger trapezoid?
We solve the above question using proportion
(Longer base/Area of trapezoid) smaller trapezoid = (Longer base/Area of trapezoid) bigger trapezoid
Let the the Area of the bigger trapezoid = x
Hence,
= 8ft/240ft = 13ft/x ft
Cross Multiply
8ft × x = 240ft × 13ft
x = 240ft² × 12 ft/8 ft
x = 390 ft²
