Answer:
When we have a set of N elements, the number of combinations of K elements (such that N ≤ K) from these N elements is:
Then if we have 8 different types of carpet, and we want to see how many different samples of 3 types we can choose, we just need to replace N by 8, and K by 3 in the above equation:
So there are 56 different samples.
Now we can do the same, but this time we want to use 5 types of carpet, then we will have K = 5.
Again, we have 56 different samples.
The correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.
<h3>What is congruency?</h3>The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
According to the SAS theorem which means Side Angle Side, The angle which is included between the two sides must be congruent.
Here we are given that
KL = NR
JL = MR
Now in the figure, we can clearly see that the angle included between JL & KL is L & the angle included between NR & MR is R.
So for the triangles to be congruent by SAS, angle L must be congruent to angle R.
∠L=∠R
Therefore the correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.
Learn more about congruency at
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Answer:
a = -0.32
b = 16
c = - 168
Step-by-step explanation:
In the figure attached, the quadratic function is shown. We can model it as follows:
y = a*(x - x1)*(x - x2)
where (x1, 0) and (x2, 0) are its roots
From the picture, roots are (15, 0) and (35, 0), replacing them into the equation:
y = a*(x - 15)*(x - 35)
and the vertex is at (25,32), replacing into the equation:
32 = a*(25 - 15)*(25 - 35)
32 = a*(-100)
a = 32/(-100)
a = -0.32
Applying distributive property:
y = -0.32*(x - 15)*(x - 35)
y = -0.32*(x² - 35x - 15x + 525)
y = -0.32x² + 16x - 168
which corresponds to the general form:
y = ax² + bx + c
Answer:
Step-by-step explanation:
the first one is correct
