There are mnemonic acronyms out there for reminding you how to do this. I think of it simply as using the distributive property.
(4x-3)(x+5) = 4x(x+5) -3(x+5)
then again
= (4x² +20x) + (-3x -15)
= 4x² + (20-3)x -15 . . . . . . . combine like terms
= 4x² +17x -15
The Pythagorean Theorem is used to find the unknown length of a side of a triangle or (in your case) a pyramid. The Pythagorean theorem is a^2 + b^2 = c^2 with c being the hypotenuse (longest side). Use this theorem to find each of the lengths of the sides of the pyramids that you need to find the volume of each respective pyramid.
Hope this helps!
Answer:
C. 42
Step-by-step explanation:
<em>Since the triangle making up the base of the right triangular pyramid is equilateral, the three lateral triangles will have equal areas. To find the surface area of the pyramid, find the area of one of the lateral triangles and multiply it by 3. Then, add that to the area of the triangle that forms the base.</em>
<em>Area of Lateral Triangle = 1/2 · base · height</em>
<em> = 1/2 · X · Z</em>
<em> = 1/2 · 4 units · 6 units</em>
<em> = 12 square units</em>
<em>Area of Base Triangle = 1/2 · base · height</em>
<em> = 1/2 · X · Y</em>
<em> = 1/2 · 4 units · 3 units</em>
<em> = 6 square units</em>
<em>Now, use the method described above to find the surface area of the pyramid.</em>
<em>Surface Area = 3( Area lateral ) + ( Area base )</em>
<em> = 3 ( 12 square units ) + ( 6 square units )</em>
<em> = 42 square units</em>
Let B be the event that Andrea passes her test, and let A be the event
<span>that she studies. We are given that P(A and B) = 17/20, and that P(A) = 15/16. </span>
<span>Now the probability that Andrea passes her test given that she has studied </span>
<span>is represented by P(BlA). The formula your teacher gave you can be written as </span>
<span>P(BlA) = P(A and B) / P(A). </span>
<span>So P(BlA) = P(A and B) / P(A) = (17/20) / (15/16) = (17/20)*(16/15) = 68/75.</span>
63degrees
Step-by-step explanation:
there are multiple ways to do this
for one, angle a = angle e (corresponding angles)
angle f + angle e = 180 degrees (angles on a straight line)
angle f = 180 degrees - angle e where angle e = angle a = 117degrees
so angle f = 63 degrees.
