Answer:
y = 5
Step-by-step explanation:
The triangles will be congruent when corresponding sides are congruent. __
We already have ...
KL ≅ NP . . . = 15 mm
JL ≅ MP . . . = 22 mm
So, we need ...
JK ≅ MN
4y +12 = 32 . . . . substitute given values
This will be the case when ...
4y = 20 . . . . . subtract 12
y = 5 . . . . . . . divide by 4
The value of y that makes the triangles congruent is 5.
Answer:
110 students
Step-by-step explanation:
The number of students who have only taken calculus is given by the number of students who have taken calculus minus the students who have taken both classes:

The number of students who have only taken discrete mathematics given by the number of students who have taken discrete mathematics minus the students who have taken both classes:

The number of students that have taken a course in either calculus or discrete mathematics is:

Step-by-step explanation:
Use the form (a + b)(a - b) = a^2 - b^2:
(2x^4 + 3x^3)(2x^4 - 3x^3) = 4x^8 - 9x^6.
<span>z^2-z(z+3)+3z
z^2 - z^2 - 3z + 3z
0 + 0
0
</span><span>z^2-z(z+3)+3z = 0</span>