Answer:
4.
a) ![4x^4-4x^3-16x^2+16x](https://tex.z-dn.net/?f=4x%5E4-4x%5E3-16x%5E2%2B16x)
b) ![4x^4-4x^3-16x^2+16x](https://tex.z-dn.net/?f=4x%5E4-4x%5E3-16x%5E2%2B16x)
5. Yes
Step-by-step explanation:
The distributive property is:
![(a+b)(c+d)=ac+ad+bc+bd](https://tex.z-dn.net/?f=%28a%2Bb%29%28c%2Bd%29%3Dac%2Bad%2Bbc%2Bbd)
It can be extended to a lot of terms as well.
We will use this to multiply both of the probelms shown.
4 a)
![(4x^2-4x)(x^2-4)=(4x^2)(x^2)-(4)(4x^2)-(4x)(x^2)+(4x)(4)=4x^4-16x^2-4x^3+16x=4x^4-4x^3-16x^2+16x](https://tex.z-dn.net/?f=%284x%5E2-4x%29%28x%5E2-4%29%3D%284x%5E2%29%28x%5E2%29-%284%29%284x%5E2%29-%284x%29%28x%5E2%29%2B%284x%29%284%29%3D4x%5E4-16x%5E2-4x%5E3%2B16x%3D4x%5E4-4x%5E3-16x%5E2%2B16x)
The answer is ![4x^4-4x^3-16x^2+16x](https://tex.z-dn.net/?f=4x%5E4-4x%5E3-16x%5E2%2B16x)
4 b)
![(x^2+x-2)(4x^2-8x)=(x^2)(4x^2)-(8x)(x^2)+(x)(4x^2)-(8x)(x)-(2)(4x^2)+(2)(8x)=4x^4-8x^3+4x^3-8x^2-8x^2+16x=4x^4-4x^3-16x^2+16x](https://tex.z-dn.net/?f=%28x%5E2%2Bx-2%29%284x%5E2-8x%29%3D%28x%5E2%29%284x%5E2%29-%288x%29%28x%5E2%29%2B%28x%29%284x%5E2%29-%288x%29%28x%29-%282%29%284x%5E2%29%2B%282%29%288x%29%3D4x%5E4-8x%5E3%2B4x%5E3-8x%5E2-8x%5E2%2B16x%3D4x%5E4-4x%5E3-16x%5E2%2B16x)
The answer is ![4x^4-4x^3-16x^2+16x](https://tex.z-dn.net/?f=4x%5E4-4x%5E3-16x%5E2%2B16x)
5. Yes
9514 1404 393
Answer:
y = -5x³
Step-by-step explanation:
The point of inflection of the parent cubic function f(x) = x³ is at the origin, the same place it is shown on the graph. So, there is no translation involved in creating the graph.
We know the parent function gives f(1) = 1, but here, we have (x, y) = (1, -5). This suggests a vertical scale factor of -5. So, the transformed function is ...
y = -5x³
Given the vertices of a triangle as A(2, 5), B(4, 6) and C(3, 1).
a.) A transformation, R_x-axis means that the vertices of the rectangle were reflected across the x-axis.
When a point on the coordinate axis is refrected across the x-axis, the sign of the y-coordinate of the point changes.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule R_x-axis are A'(2, -5), B'(4, -6), C'(3, -1)
b.) A transformation, R_y = 3 means that the vertices of the rectangle were reflected across the line y = 3.
When a point on the coordinate axis is refrected across the a horizontal line, the distance of the point from the line is equal to the distance of the image of the point from the line.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule are A'(2, 1),
B'(4, 0), C'(3, 5)
c.) A transformation, T<-2, 5> means that the vertices of the rectangle were shifted 2 units to the left and 5 units up.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<-2, 5> are A'(0, 10),
B'(2, 11), C'(1, 6).
d.) A transformation, T<3, -6> means that the vertices of the rectangle were shifted 3 units to the right and 6 units down.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<3, -6> are A'(5, -1),
B'(7, 0), C'(6, -5).
e.) A transformation, r(90°, o) means that the vertices of the rectangle were rotated 90° to the right about the origin.
When a point on the coordinate axis is rotated about the origin b 90°, the quadrant of the point changes to the right with the x-value and the y-value of the point interchanging.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule r(90°, o) are A'(5, -2),
B'(6, -4), C'(1, -3)
The number of unique combinations that can be formed by picking one object from each set is =960. That is option C.
<h3>Calculation of unique combinations of a number set</h3>
Number combination is a mathematical technique that shows the number of possible arrangements in a collection of items.
The first set of objects = 4. There are a total of 4 possibilities.
The second set of objects = 5. There are a total of 5 possibilities
Therefore from first and second set, the total number of possibilities = 4×5 = 20
For the whole set, the total possibilities;
= 4×5×6×8
= 960
Learn more about number combination here:
brainly.com/question/295961
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