Answer:
<em>f(-5)=149603</em>
Step-by-step explanation:
<u>Synthetic Substitution</u>
It's a method to find the value of a polynomial for a given value of x. The polynomial we want to evaluate is
at x=-5
We can, of course, just replace x for -5 and compute the powers, products and sums and subtractions, but we can use the synthetic substitution to avoid the powers, just by multiplying and adding or subtracting. The method requires us to use only the coefficients of the ordered and complete polynomial as shown:
-1 4 -4 -6 -3 -6 -1 -2
Now we set up an arrangement where we can place some operations
-1 4 -4 -6 -3 -6 -1 -2
-5
The second row and a new third row will be filled by computing values as explained below.
The first value of the third row is the very same first coefficient (-1)
-1 4 -4 -6 -3 -6 -1 -2
-5
-1
The second value of the second row is the -5 times the first value of the third row: (-5)(-1)=5
Next value of the third row is the sum of the values above of it: 4+5=9
-1 4 -4 -6 -3 -6 -1 -2
-5 5
-1 9
Now we proceed the same with next values to get the full arrangement or synthetic substitution
-1 4 -4 -6 -3 -6 -1 -2
-5 5 -45 245 -1195 5990 -29920 149605
-1 9 -49 239 -1198 5984 -29921 149603
The very last value of the third row is the required substitution
f(-5)=149603
The formatted table can be seen in the image below
Answer:
525 x 1,050
A = 551,250 m²
Step-by-step explanation:
Let 'L' be the length parallel to the river and 'S' be the length of each of the other two sides.
The length of the three sides is given by:
The area of the rectangular plot is given by:
The value of 'S' for which the area's derivate is zero, yields the maximum total area:
Solving for 'L':
The largest area enclosed is given by dimension of 525 m x 1,050 and is:
Answer:
A dilation by a factor of three about Point T followed by a translation of two units downwards.
Step-by-step explanation:
When transforming functions, we will reflect/dilate the figure first and then translate it. This is directly from the order of operations.
Since we are trying to determine the transformation that was performed, we can try to map ΔS'T'U' onto ΔSTU. We can start by translating the figure and then determining any reflections/dilations.
First, we can translate ΔS'T'U' up two units to map T' onto T. This is represented by the black triangle in the image below. Let the black triangle be ΔS''T''U''. (T'' and T are the same point.)
Next, notice that from Point T'' to U'', we move nine units right and six units up.
From Point T to Point U, we move three units right and two units up.
Likewise, from Point T'' to S'', we move six units left and nine units up.
From Point T to Point S, we move two units left and three units up.
Therefore, to map ΔS''T''U'' onto ΔSTU, we dilate ΔS''T''U'' about Point T by a factor of 1/3.
Hence, by reversing the transformations, to acquire ΔS'T'U', we can see that we will dilate ΔSTU by a factor of three about Point T and then a perform a translation of two units downwards.
