Let the faculties be X and the number of students be Y.
X/Y = 17/3
3X= 17Y
X=17Y/3
Let that be equation 1
We also know that X+Y = 740. Let it be equation 2
Substitute equation 1 in equation 2
(17Y/3)+Y= 740
20Y/3 = 740
Y=111
Since the total is 740, then X equal 740-111 =629.
The number of faculties is 111 and the number of students is 629.
Answer:
Volume ≈ 33.33 cubic feet
Step-by-step explanation:
The question is:
<em>Find the volume of a right square pyramid with base square edges measuring 5 feet each and a height of the pyramid be 4 feet.</em>
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So, the base is a square with side length 5 feet.
And the height of the pyramid is 4 feet.
The volume of a pyramid is given by the formula:

Where
a is the square base side length (given as 5)
h is the height of the pyramid (given as 4)
Now we substitute and find the value:

The volume is around 33.33 cubic feet
Answer:
Second option: On a coordinate plane, rectangle A'B'C'D' prime has points
(See the graph attached)
Step-by-step explanation:
For this exercise it is importnat to know that a Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) has the same shape as the Pre-Image (which is the original figure before the transformation), but they have different sizes.
In this case, you know that the vertices of the rectangle ABCD ( The Pre-Image) are the following:

Therefore, to find the vertices of the rectangle A'B'C'D' (The Image) that results of dilating the rectangle ABCD by a factor of 4 about the origin, you need to multiply the coordinates of each original vertex by 4. Then, you get:

Finally, knowing those points, you can identify that the graph that shows the result of that Dilation, is the one attached.
Answer:
See proof below
Step-by-step explanation:
Two triangles are said to be congruent if one of the 4 following rules is valid
- The three sides are equal
- The three angles are equal
- Two angles are the same and a corresponding side is the same
- Two sides are equal and the angle between the two sides is equal
Let's consider the two triangles ΔABC and ΔAED.
ΔABC sides are AB, BC and AC
ΔAED sides are AD, AE and ED
We have AE = AC and EB = CD
So AE + EB = AC + CD
But AE + EB = AB and AC+CD = AD
We have
AB of ΔABC = AD of ΔAED
AC of ΔABC = AE of ΔAED
Thus two sides the these two triangles. In order to prove that the triangles are congruent by rule 4, we have to prove that the angle between the sides is also equal. We see that the common angle is ∡BAC = ∡EAC
So triangles ΔABC and ΔAED are congruent
That means all 3 sides of these triangles are equal as well as all the angles
Since BC is the third side of ΔABC and ED the third side of ΔAED, it follows that
BC = ED Proved