Identify a3 of this sequence: 0.25, 0.5, 0.75, 1, 1.25, 1.5, … a3 =

The width of a box in the shape of a rectangular prism is 4 inches more than the height h . The length is the difference of 9 in

Doss [256]

Answer:

$(a)$ $V = -H^3+ 5H^2 + 36H$

$(b)$ $Length = 5in; Width = 9in; Height = 5in$ or $Length = 3in; Width = 10in; Height = 6in$

Step-by-step explanation:

Let:

$W=Width; L = Length; H = Height$

Given

$W = 4 + H$

$L = 9 - H$

Solving (a): The polynomial for the volume in terms of height

Volume (V) is calculated using:

$V = L * W * H$

$V = (9 - H) * (4 + H) * H$

Expand

$V = (9 - H) * (4H + H^2)$

Open brackets

$V = 36H + 9H^2 - 4H^2 - H^3$

$V = 36H + 5H^2 - H^3$

Rewrite as:

$V = -H^3+ 5H^2 + 36H$

Solving (b): The dimensions when Volume = 180

Substitute 180 for V in: $V = -H^3+ 5H^2 + 36H$

$180 = -H^3+ 5H^2 + 36H$

Rewrite as:

$H^3 - 5H^2 - 36H + 180 = 0$

Factorize:

$H^2(H - 5) - 36(H - 5) = 0$

$(H^2 - 36)(H - 5) = 0$

Express $H^2 - 36$ as difference of two squares

$(H - 6)(H + 6)(H - 5) =0$

This gives:

$H - 6 =0==> H = 6$

$H + 6 =0==> H = -6$

$H - 5 =0==> H = 5$

Since the height can not be negative, then H = 5 or H = 6

Recall that:

$W = 4 + H$

$L = 9 - H$

When H = 5

$W = 4 + 5 = 9$

$L = 9 - 5 = 4$

When H = 6

$W = 4 + 6 = 10$

$L = 9 - 6 = 3$

Hence, the dimensions of the box are:

$Length = 5in; Width = 9in; Height = 5in$

or

$Length = 3in; Width = 10in; Height = 6in$

3 0

3 years ago

Which method can be used to prove ABC =DEF?

12345 [234]

<h3>Answer :</h3>

ASA (Angle Side Angle) method can be used to prove ∆ABC ≅ ∆DEF

<h3>Solution :</h3>

In ∆ABC and ∆DEF

∠A ≅ ∠D (given)

AB ≅ DE (given)

∠B ≅ ∠E (given)

So, by ASA congruency criteria

∆ABC ≅ ∆DEF

8 0

3 years ago

PLEASE HELP!!! 100 PTS +Brainliest!!!Given the following values, which point would be considered an outlier?

True [87]

Answer:

Option C, (6, 8.4)

Step-by-step explanation:

It would be option C because all of the other ones, both the y and x value is almost the same. (2, 2.1) (4, 3.8) and (9, 9) are all really close in y and x values. While (6, 8.4) has a y value that is over 2 more than x.

Answer: Option C, (6, 8.4)

3 0

3 years ago

3x – 19 = 24.5<br> Your answer

ryzh [129]

Answer:

24.5 × 3 = 73.5

73.5=x

Step-by-step explanation:

here

4 0

3 years ago

Consider a finite population with five elements labeled A, B, C, D, and E. Ten possible simple random samples of size 3 can be s

ASHA 777 [7]

Answer:

10% probability that each sample of size 3 is selected

Step-by-step explanation:

Each sample has the same probability of being selected.

There are 10 samples.

This means that the probability of each sample being selected is:

1/10 = 0.1

10% probability that each sample of size 3 is selected

6 0

3 years ago