Hey there!
Your answer is C.
If you take the lengths of the legs of the triangle, which are 12 and 4, we can multiply them by the scale factor to see what the legs of our new triangle is.
12 x 1/4 = 3
4 x 1/4 = 1
So, the legs of our new triangle have lengths of 1 and 3.
We can see that option C has the correct triangle in red.
If we're looking at the ratio of rise to run of each triangle, it is 1/3 for both the large triangle and the small triangle.
The rise for the larger triangle is 4, and the run is 12. That is 4/12, which can be simplified to 1/3.
The rise for the smaller triangle is 1, and the run is 3. That is 1/3, which is all the way simplified already.
These triangles are similar because the first one was dilated to get the second one, which explains why the ratios are the same.
Hope this helps!
Answer:
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).
We are dividing:
So, a polynomial by a binomial factor.
Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.
We want our remainder to be 3. So, P(a)=P(-k)=3.
Therefore:
Simplify:
Solve for <em>k</em>. Subtract 3 from both sides:
Factor:
Zero Product Property:
Solve:
So, either of the two expressions:
Will yield 3 as the remainder.
Answer:2.26796
Step-by-step explanation:
