Answer:
13,000 pounds
Step-by-step explanation:
simple addition
There are 6 faces in this prism. Each pair of opposite faces is two congruent faces.
The front and back faces have dimensions x by x + 4.
The right and left faces have dimensions x + 2 by x + 4.
The top and bottom faces have dimensions x by x + 2.
Let's find the area of each different face.
Front & back:
A = LW = x(x + 4) = x^2 + 4x
Right and left:
A = LW = (x + 2)(x + 4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8
Top & bottom:
A = LW = x(x + 2) = x^2 + 2x
Now we add the three areas:
x^2 + 4x + x^2 + 6x + 8 + x^2 + 2x =
=3x^2 + 12x + 8
The polynomial above is the sum of the areas of three different faces.
Each of the three different faces has a congruent opposite face with the same area, so we double this area to find the total surface area of all 6 faces.
2(3x^2 + 12x + 8) = 6x^2 + 24x + 16
The answer is option A.
Answer:
"I can find the maximum or minimum by looking at the factored expression of a quadratic function by reading off its roots and taking the arithmetic average of them to obtain the -coordinate of the quadratic function, and then substituting that value into the function."
Step-by-step explanation:
Because of the symmetry of quadratics (which is the case here because we have two factors of degree 1, so we are dealing with a <em>polynomial</em> of degree 2, which is a fancy way of saying that something is a quadratic), the -coordinate of the extremum (a fancy way of saying maximum or minimum) is the (arithmetic) average of the two roots.
In the factored form of a quadratic function, we can immediately read the roots: 3 and 7. Another way to see that is to solve , which gives (the 'V' stands for 'or'). We can take the average of the two roots to get the -coordinate of the minimum point of the graph (which, in this case, is ).
Having the -coordinate of the extremum, we can substitute this value into the function to obtain the maximum or minimum point of the graph, because that will give the -coordinate of the extremum.
Answer:
Y=20x+15 & 175 dollars
Step-by-step explanation:
The word problems says $20 per hour, so that means 20 times the amount of hours. If yo multiply 20 times 8 you get 160. Add 15 to 160, you end up with $175.