Hi there!
The question here is asking us to multiply two functions together - j(x) and k(x). First, we need to determine the expressions for j(x) and k(x). Since this is given, we can move straight onto multiplying the two functions together, which will give us our answer.
j(x) × k(x)
Substitute expressions -
(x⁴ - 81)(x + 3)
Simplify -
(x⁴ - 81)(x + 3)
x⁵ + 3x⁴ - 81x - 243
Therefore, the answer is x⁵ + 3x⁴ - 81x - 243. Hope this helped!
Answer:
Step-by-step explanation:
V = L * W * H
L = 4
W = 3
H = 2
V = 4 * 3 * 2
V = 24
Density = mass / Volume
density = 11.34
volume = 24
mass = ?
11.34 = mass / 24 Multiply both sides by 24
11.34 * 24 = 24 * mass /24
mass = 272.16 grams
Functions can be used to represent real-life models
The complete table is:
![\mathbf{\left[\begin{array}{ccccccccccccc}{Months}&1&2&3&4&5&6&7&8&9&10&11&12&{Boat\ dealers}&60&75&90&105&120&105&90&75&60&45&30&15\end{array}\right] }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccccccccccc%7D%7BMonths%7D%261%262%263%264%265%266%267%268%269%2610%2611%2612%26%7BBoat%5C%20dealers%7D%2660%2675%2690%26105%26120%26105%2690%2675%2660%2645%2630%2615%5Cend%7Barray%7D%5Cright%5D%20%7D)
The function is given as:
![\mathbf{B = -15|t - 5| + 120}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%20%3D%20-15%7Ct%20-%205%7C%20%2B%20120%7D)
The value of the function from t = 1 to 12 is as follows:
![\mathbf{B(1) = -15|1 - 5| + 120 = 60}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%281%29%20%3D%20-15%7C1%20-%205%7C%20%2B%20120%20%3D%2060%7D)
![\mathbf{B(2) = -15*|2 - 5| + !20 = 75}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%282%29%20%3D%20-15%2A%7C2%20-%205%7C%20%2B%20%2120%20%3D%2075%7D)
![\mathbf{B(3) = -15|3- 5| + 120 = 90}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%283%29%20%3D%20-15%7C3-%205%7C%20%2B%20120%20%3D%2090%7D)
![\mathbf{B(4) = -15|4- 5| + 120 = 105}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%284%29%20%3D%20-15%7C4-%205%7C%20%2B%20120%20%3D%20105%7D)
![\mathbf{B(5) = -15|5- 5| + 120 = 120}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%285%29%20%3D%20-15%7C5-%205%7C%20%2B%20120%20%3D%20120%7D)
![\mathbf{B(6) = -15|6- 5| + 120 = 105}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%286%29%20%3D%20-15%7C6-%205%7C%20%2B%20120%20%3D%20105%7D)
![\mathbf{B(7) = -15|7- 5| + 120 = 90}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%287%29%20%3D%20-15%7C7-%205%7C%20%2B%20120%20%3D%2090%7D)
![\mathbf{B(8) = -15*|8 - 5| + !20 = 75}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%288%29%20%3D%20-15%2A%7C8%20-%205%7C%20%2B%20%2120%20%3D%2075%7D)
![\mathbf{B(9) = -15|9 - 5| + 120 = 60}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%289%29%20%3D%20-15%7C9%20-%205%7C%20%2B%20120%20%3D%2060%7D)
![\mathbf{B(10) = -15|10 - 5| + 120 = 45}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%2810%29%20%3D%20-15%7C10%20-%205%7C%20%2B%20120%20%3D%2045%7D)
![\mathbf{B(11) = -15|11 - 5| + 120 = 30}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%2811%29%20%3D%20-15%7C11%20-%205%7C%20%2B%20120%20%3D%2030%7D)
![\mathbf{B(12) = -15|12 - 5| + 120 = 15}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%2812%29%20%3D%20-15%7C12%20-%205%7C%20%2B%20120%20%3D%2015%7D)
So, the complete table is:
![\mathbf{\left[\begin{array}{ccccccccccccc}{Months}&1&2&3&4&5&6&7&8&9&10&11&12&{Boat\ dealers}&60&75&90&105&120&105&90&75&60&45&30&15\end{array}\right] }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccccccccccc%7D%7BMonths%7D%261%262%263%264%265%266%267%268%269%2610%2611%2612%26%7BBoat%5C%20dealers%7D%2660%2675%2690%26105%26120%26105%2690%2675%2660%2645%2630%2615%5Cend%7Barray%7D%5Cright%5D%20%7D)
See attachment for the function of ![\mathbf{B = -15|t - 5| + 120}](https://tex.z-dn.net/?f=%5Cmathbf%7BB%20%3D%20-15%7Ct%20-%205%7C%20%2B%20120%7D)
Read more about functions, tables and graphs at:
brainly.com/question/18588430
Answer: 110 square cm
=======================================================
Explanation:
All sides of a regular polygon are the same length. So the bottom side is also 8 cm.
Draw lines from the center to each vertex of the pentagon. Five triangles form. Each triangle has a base of 8 and a height of 5.5 (since all five triangles are congruent)
area of one triangle = 0.5*base*height = 0.5*8*5.5 = 22
area of five triangles = 5*(area of one triangle) = 5*22 = 110