How do I factor 5n^2 +19n+12

Mrs. Bhatia's closet consists of two sections, each shaped like a rectangular prism. She plans to buy mothballs to keep the moth

AveGali [126]

Answer:

6.5 boxes

Step-by-step explanation:

Given

See attachment for closet

Required

Determine the number of boxes needed to fill the closet

First, we calculate the volume of the two section.

According to the attachment

The first section has the following dimension:

$Width = 5ft$

$Length = 4ft$

$Height = 8ft$

The second has the following dimension:

$Width = 3ft$ ---- see the last label at the top

$Length = 2ft$ --- This is calculated by subtracting the length of the first section (4ft) from the total length of the closet (6ft) i.e. 6ft - 4ft

$Height = 8ft$

So: The volume of the closet is:

$Volume = W_1 * L_1 * H_1 + W_2 * L_2 * H_2$

$Volume = 5ft * 4ft * 8ft + 3ft * 2ft * 8ft$

$Volume = 160ft^3 + 48ft^3$

$Volume = 208ft^3$

The number of box needed is then calculated by dividing the volume of the closet (208ft^3) by the volume of each box (32ft^3)

$Boxes = \frac{208ft^3}{32ft^3}$

$Boxes= \frac{208}{32}$

$Boxes = 6.5$

7 0

2 years ago

Find the vertex and length of the latus rectum for the parabola. y=1/6(x-8)^2+6

Ivan

Step-by-step explanation:

If the parabola has the form

$y = a(x - h)^2 + k$ (vertex form)

then its vertex is located at the point (h, k). Therefore, the vertex of the parabola

$y = \dfrac{1}{6}(x - 8)^2 + 6$

is located at the point (8, 6).

To find the length of the parabola's latus rectum, we need to find its focal length <em>f</em>. Luckily, since our equation is in vertex form, we can easily find from the focus (or focal point) coordinate, which is

$\text{focus} = (h, k +\frac{1}{4a})$

where $\frac{1}{4a}$ is called the focal length or distance of the focus from the vertex. So from our equation, we can see that the focal length <em>f</em> is