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Tanzania [10]
2 years ago
5

Combine the like terms to create an equivalent expression: 3 + 2 + (52) + 6

Mathematics
1 answer:
devlian [24]2 years ago
3 0
It would be -2z+8. Because 3z+-5 is -2 and 2+6 is 8.
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An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corne
lawyer [7]

Answer:

The dimensions of the resulting box that has the largest volume is 1.3 inches x 1.3 inches

Step-by-step explanation:

Card board size is L= 14 inches and

W = 6 inches

Let x be the size of equal squares cut from 4 corners and bent into a box whose size is now;

L = 14 − 2x , W = 6 −2x and h = x inches.

Volume of the box is given as;

V = (14 −2x)(6−2x)x

V =(4x² − 40x + 84)x

= 4x³ − 40x² + 84x.

Now, for the maximum value,

dV/dx =0

Thus,

dv/dx = 12x² - 80x + 84 = 0

Using quadratic formula

x = [-(-80) ± √(-80²) - 4(12 x 84)]/(2 x 12)

x = [80 ± √(6400 - 4032)]/24

x = (80 + 48.66)/24 or (80-48.66)/24

x = 5.36 or 1.31

Looking at the two values, 1.31 would be more appropriate because if we use 5.36,we will get a negative value of the width (W).

Thus, x = 1.31 inches

Let us use the Second Derivative Test to verify that V has a local maximum at x = 1.31.

Thus;

d²v/dx² = 24x - 80 = 24(1.31) - 80 = -48.56

This is less than 0 and therefore, the volume of the box is maximized when a 1.31 inch by 1.3 inch square is cut from the corners of the cardboard sheet.

3 0
3 years ago
Definition the value of a number regardless of its sign Definition
kumpel [21]
Are you asking for a definition
4 0
3 years ago
1
Inessa [10]

Answer:

Approximately 920.324 p/m

Step-by-step explanation:

so to figure this out, we need to simply divide 6,688 people by 7.267 square miles. 6,688/7.267=920.324.... So we have approximately 920.324 people per square mile

5 0
3 years ago
What is the area of the composite figure?<br> units
Pani-rosa [81]

Answer:

Step-by-step explanation:

You have to decompose the figure. Cut it into different sections like squares, triangles, and rectangles so you can find the area. Once you have decomposed it, multiply the sides of each section to find the separate area of each  square, triangle, rectangle, etc then add up those areas.

3 0
3 years ago
Read 2 more answers
Solve for the roots in simplest form using the quadratic formula: x^2+14x=-45
Natalija [7]

Answer:

x = − 5 − 9

Step-by-step explanation:

Solve the equation for  x  by finding  a ,  b , and  c  of the quadratic then applying the quadratic formula. x = − 5 − 9

6 0
2 years ago
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