Answer: 235 cm^2
Explanation: you can cut the shape into two smaller ones and then solve for each smaller shapes area. to find out the length of the top piece with 11 as length you can subtract nine from fourteen. from their you calculate the area of the top shape (11x5=55) and then the bottom shape (9x20=180). from their just add the two areas to get 235.
The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;
- Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.
- Maximum volume of the box is approximately 1048.6 in.³
<h3>How can the dimensions and volume of the box be calculated?</h3>
The given dimensions of the cardboard are;
Width = 18 inches
Length = 35 inches
Let <em>x </em>represent the side lengths of the cut squares, we have;
Width of the box formed = 18 - 2•x
Length of the box = 35 - 2•x
Height of the box = x
Volume, <em>V</em>, of the box is therefore;
V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x
By differentiation, at the extreme locations, we have;

Which gives;

6•x² - 106•x + 315 = 0

Therefore;
x ≈ 4.55, or x ≈ -5.55
When x ≈ 4.55, we have;
V = 4•x³ - 106•x² + 630•x
Which gives;
V ≈ 1048.6
When x ≈ -5.55, we have;
V ≈ -7450.8
The dimensions of the box that gives the maximum volume are therefore;
- Width ≈ 18 - 2×4.55 in. = 8.89 in.
- Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.
- The maximum volume of the box, <em>V </em><em> </em>≈ 1048.6 in.³
Learn more about differentiation and integration here:
brainly.com/question/13058734
#SPJ1
The system of equations has infinite solutions.
<h2>Given to us,</h2>
<h3>Equation 2,</h3>
The value of y is already given in equation 1,

substituting the value of y in equation 2,

The solution of the two equations is 0. Also, we can see that both the equations are in ratio.
Further, the image also shows that the line of the two equations are coinciding.
Hence, the system of equations has infinite solutions.
Learn more about System of solutions:
brainly.com/question/14264175
Answer:
g(-1) = -5
g(2a+1) = 16a+11
Step-by-step explanation:
Substitute the given value into the function and evaluate.
So for g(x) = 8x+3
You substitute g(-1)
So g(-1) = 8(-1)+3
That is how you get -5
Then g(2a+1)
So g(2a+1) = 8(2a+1)+3
Thats how you get 16a+11
Hope this helps. Mark as brainlist