The curve = 2 + + has a minimum point (3, 4). Using the squared completion method, find the value of p and the value of q.

<img src="https://tex.z-dn.net/?f=12x%20%5E%7B2%7D%20%20%2B%204x%20%2B%2020" id="TexFormula1" title="12x ^{2} + 4x + 20" alt="1

Nesterboy [21]

<h3>Answer: </h3>

The GCF is 4

The polynomial factors to $4(3x^2+x+5)$

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Further explanation:

Ignore the x terms

We're looking for the GCF of 12, 4 and 20

Factor each to their prime factorization. It might help to do a factor tree, but this is optional.

12 = 2*2*3
4 = 2*2
20 = 2*2*5

Each factorization involves "2*2", which means 2*2 = 4 is the GCF here.

We can then factor like so

$12x^2 + 4x + 20\\\\4*3x^2 + 4*x + 4*5\\\\4(3x^2 + x + 5)$

The distributive property pulls out that common 4. We can verify this by distributing the 4 back in, so we get the original expression back again.

The polynomial inside the parenthesis cannot be factored further. Proof of this can be found by looking at the roots and noticing that they aren't rational numbers (use the quadratic formula).

4 0

2 years ago

A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

so

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

8 0

2 years ago

Brandon had $500. He spent 47% of his money on a tablet computer. How much did his computer cost?

Kobotan [32]

47% of 500 is 235 dollars

8 0

3 years ago

Read 2 more answers

Which ordered pair would form a proportional relationship with the point graphed below?

nevsk [136]

Answer:

(90,60)

Step-by-step explanation:

if you look closely through the linear graph, the line crosses through (90,60) and not the other given pairs.

proportional relationships are plots that also match in the same graphing format (keep in mind when you have trouble next time)

5 0

3 years ago

Read 2 more answers

What term refers to common, non-rechargeable batteries?

kiruha [24]

Answer:

Lithium

Explanation:

Lithium batteries features primary cell construction.They are single-use or non rechargeable batteries

6 0

1 year ago

The curve = 2 + + has a minimum point (3, 4). Using the squared completion method, find the value of p and the value of q.​

The curve = 2 + + has a minimum point (3, 4). Using the squared completion method, find the value of p and the value of q.