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WARRIOR [948]
3 years ago
12

You are having a conference call with the CEO of a paper company. You have interpreted the number of trees cut down versus profi

t as the function P(x) = –x^4 + x^3 + 7x^2 − x − 6. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).

Mathematics
1 answer:
Rufina [12.5K]3 years ago
5 0
K, so when x=0, then y=-6
so it goes through the y axis (up and down line) at y=-6

now find the x intercepts, or where y=0
factoring we get P(x)=-1(x+2)(x+1)(x-1)(x-3)
so it goes through the y axis at x=-2, x=-1, x=1, and x=3
put those points
now, the function is 4th degree and the leading coefient is negative, so it starts from bottom left and ends at bottom right
so draw a graph starting from bottom left and going through those points and ending at bottom right
since they are all odd multiplicities, the graph goes through the points to the other side of x axis instead of bouncing off

see graph included (hand drawn)

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A regular octagonal pyramid has a base edge of 3m and a lateral area of 60m^2. Find its slant height.
Olin [163]
Octagon = 8-side polygon

<u>Find area of 1 triangle:</u>
Area of one side triangle = 60 ÷ 8 = 7.5 m²

<u>Given area and length, find height:</u>
Area of each triangle = 7.6 m²
Length of each triangle = 3m

Area = 1/2 x base x height
7.5 = 1/2 x 3 x height
Heigth = 5m

Answer: Slanted Height = 5 m

4 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%20%5Csf%20%5Chuge%7B%20question%20%5Chookleftarrow%7D" id="TexFormula1" title=" \sf \huge
BabaBlast [244]

\underline{\bf{Given \:equation:-}}

\\ \sf{:}\dashrightarrow ax^2+by+c=0

\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.

\sf We\:know,

\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}

\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}

\underline{\large{\bf Identities\:used:-}}

\boxed{\sf (a+b)^2=a^2+2ab+b^2}

\boxed{\sf (√a)^2=a}

\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}

\boxed{\sf \sqrt{\sqrt{a}}=a}

\underline{\bf Final\: Solution:-}

\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}

\bull\sf Apply\: Squares

\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2

\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}

\bull\sf Put\:values

\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}

\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}

\bull\sf Simplify

\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}

\underline{\bf More\: simplification:-}

\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}

\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}

\underline{\Large{\bf Simplified\: Answer:-}}

\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}

5 0
2 years ago
Read 2 more answers
Please solve this question asap
disa [49]

Step-by-step explanation:

y =  \sqrt{4x + 6}

{y}^{2}  = 4x + 6

{y}^{2}  - 6 = 4x

\frac{1}{4} ( {y}^{2}  - 6) = x

Swap x and y

\frac{ {x}^{2} - 6 }{4}  = y

3 0
2 years ago
A new science website has $1824 to buy online ads. If each cost $96, how many ads can the website purchase
a_sh-v [17]

Answer:

19 ads

Step-by-step explanation:

just divide 1824 by 96

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2 years ago
What's the answers to Part A and Part B?​
Westkost [7]

Answer:

there's nothing there

Step-by-step explanation:

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