What is the result of dividing 48a3 + 32a2 + 16a by 4a?

A. 12a2 + 8a + 4

B. 12a2 + 4a + 8

C. 12a + 8

D. 12a2 + 4a + 4

Answer:

The required equation is .

Step-by-step explanation:

We are given,

The table showing the boiling points of water at different altitudes.

We will find the slope of the equation using .

Taking points (0,212) and (0.5,211.1) and substituting in the formula,

Slope is

i.e. Slope is

i.e. Slope is -1.8

Substituting slope and the point (0,212) in the equation , we will find the value of y-intercept 'b'.

That is, i.e. b= 212

Thus, the required equation is.

Answer:

one comic book costs $5

Step-by-step explanation:

let cost of comic book = $x

let cost of vinyl  = $y

according to the question:

6x = y + 3x

y = 6x - 3x

y = 3x                 (1)

y = $15               (2)

substituting the value of y from equation (2) into equation (1)

15 = 3x

x = 15/3 = 5

thus, cost of one comic book = $5

Answer:

5$.

Step-by-step explanation:

Let's denote the cost of one Sailor Moon comic book as x .

The cost of 6 Sailor Moon comic books is 6x.

According to the given information, the cost of a Nirvana vinyl plus 3 comic books is equal to the cost of 6 Sailor Moon comic books.

So, 15 + 3x = 6x , as the vinyl costs $15.

Now, let's solve for x :

Subtract 3x from both sides: 15 = 3x

Divide by 3: x = 5

Therefore, the cost of one Sailor Moon comic book is $5.

Answer:

Step-by-step explanation:

To maximize the area of the two identical rectangular pens, we need to find the dimensions that will allow us to enclose the largest possible area using the given 480 feet of fencing.

Let's start by assigning variables to the dimensions of the rectangular pen. Let's say the length of the pen is "L" and the width is "W". Since the two pens share one wall, we can divide the available fencing equally between the two long sides and the two short sides.

The equation for the perimeter of a rectangle is: P = 2L + 2W.

In this case, we have two pens, so the total perimeter is 480 feet: 2L + 2W = 480.

We can simplify this equation by dividing both sides by 2: L + W = 240.

To maximize the area, we need to find the dimensions that satisfy this equation while maximizing the product of L and W, which represents the area.

Since the pens are identical, we can express one dimension in terms of the other. Let's solve the equation for L: L = 240 - W.

Now, substitute this expression for L in the equation for the area: A = L * W = (240 - W) * W.

To find the maximum area, we need to find the value of W that maximizes the expression (240 - W) * W.

One way to do this is by graphing the equation or using calculus, but since this is likely a high school-level problem, we can use the concept of symmetry.

Since the equation for the area is quadratic, the maximum area will occur at the midpoint of the symmetry axis. In this case, the symmetry axis is given by W = 240/2 = 120.

So, to maximize the area, each pen should have a width of 120 feet.

Substituting this value back into the equation for the perimeter, we can find the length of each pen: L + 120 = 240, L = 240 - 120 = 120.

Therefore, the dimensions of each pen that will maximize the area are 120 feet by 120 feet.

Keep in mind that this is just one possible answer, as there may be other valid dimensions that also maximize the area. However, for a symmetrical solution, both pens should have equal dimensions.

Answer:

ASA

Step-by-step explanation:

A - The 90º angles

S - the marked sides

A - the verticle angles

Answer:

an​=−6n+2

Step-by-step explanation:

First, you need to identify the first term and the common difference of the sequence. The first term is the value of the first element, which is -4. The common difference is the amount that is added or subtracted to each term to get the next one, which is -6 in this case. You can find it by subtracting any two consecutive terms, such as -10 - (-4) = -6 or -16 - (-10) = -6.

Next, you need to use the standard explicit formula for an arithmetic sequence, which is:

an​=a1​+d(n−1)

where an​ is the Nth term, a1​ is the first term, d is the common difference, and n is any term number.

Finally, you need to substitute the values of a1​ and d that you found in the first step into the formula. This gives:

an​=−4+(−6)(n−1)

This is the explicit formula for the Nth term aN of the given arithmetic sequence. You can simplify it further by expanding and combining like terms:

an​=−4−6n+6

an​=−6n+2