Answer:
5
Step-by-step explanation:
We are asked to find the value of A. We know from the question that we need to have the sum of -3x and (A)x equal the third term of the original polynomial, which is 2x. written out in an equation, it looks like this.

We can simplify the equation if we add 3x to both sides, which then leaves us with this.

We can further simplify the equation by dividing both sides by x. This leaves us with our last equation for this problem.

Finally, we have our answer. We can also verify that this is a valid integer by multiplying our, now completed, quotient by the divisor and adding the remainder, which in this case, our remainder is 0, so we will not be including it in our operation.

If our calculations were all correct, the product of these polynomials should equal our dividend, verifying our integer is valid; lo' and behold, it is.


I only know this because I remember the common fractions, and 1/3 is .3333 repeating.
Answer: 380 ft^2
Step-by-step explanation:
Length of sides of square=25
Diameter of semicircle=25
Radius=r=25/2=12.5
π=3.14
Area of square=length x length
Area of square=25 x 25=625
Area of semicircle=0.5 x π x r x r
Area of semicircle=0.5 x 3.14 x 12.5 x 12.5
Area of semicircle=245.3125
Area of shaded portion=area of square - area of semicircle
Area of shaded portion=625-245.3125
Area of shaded portion=379.6875
Area of shaded portion=380ft^2
approximately
Answer:

Step-by-step explanation:
Let
Side of square base=x
Height of rectangular box=y
Area of square base=Area of top=
Area of one side face=
Cost of bottom=$9 per square ft
Cost of top=$5 square ft
Cost of sides=$4 per square ft
Total cost=$204
Volume of rectangular box=
Total cost=



Substitute the values of y

Differentiate w.r.t x







It takes positive because side length cannot be negative.
Again differentiate w.r. t x

Substitute the value

Hence, the volume of box is maximum at x=2.2 ft
Substitute the value of x

Greatest volume of box=
Answer:
<u><em>y = 63</em></u>
Step-by-step explanation:
<em>y is directly proportional to x²</em>
<em>As given,</em>
<em>when y = 3 => x = 2</em>
<em>So, 3 = 4 - 1</em>
<em>Which means the relation can be written as :-</em>
<em>y = x² - 1</em>
<em></em>
<em>Substituting x = 8</em>
<em>y = (8)² - 1</em>
<em>y = 64 - 1</em>
<u><em>y = 63</em></u>