A company models its net income, in thousands of dollars, with the function f(x) = 9x² – 54x – 144, where x is the number of units of its product sold. How many units of its product does the company need to sell in order for the net income to equal $0?

Answer:

15

Step-by-step explanation:

Just substitute the x for 5
In this case:

Original function: f(x) = [tex]x^{2}[/tex] - 2x

Substitute function: f(5) = [tex](5)^{2}[/tex] - 2(5)

Now solve for the substitute function

[tex](5)^{2}[/tex] - 2(5)

25 - 10

15

Therefore, f(5) is equal to 15

The length of the support wire on the pole is 27 feet

The given parameters are:

The length (L) of the support wire is then calculated using the following cosine function

cos(x) = b/L

This gives

cos(68) = 10/L

Make L the subject

L = 10/cos(68)

Evaluate

L = 27

Hence, the length of the support wire is 27 feet

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[tex]~~~~~~\cos 45^{\circ} = \dfrac{\text{Base}}{\text{Hypotenuse}}\\ \\\implies \dfrac 1{\sqrt 2} = \dfrac{x}{22}\\\\\implies x = \dfrac{22}{\sqrt 2}\\\\\implies x = \dfrac{22\sqrt 2}{2}\\\\\implies x = 11\sqrt 2\\[/tex]

[tex]\text{L.H.S}\\\\=(\tan q + \sec q)^2\\\\\\=\left(\dfrac{\sin q}{ \cos q} + \dfrac 1{ \cos q} \right)^2\\\\\\=\left( \dfrac{1+ \sin q}{\cos q}\right)^2\\\\\\=\dfrac{(1+ \sin q)^2}{\cos^2 q}\\\\\\=\dfrac{(1+ \sin q)^2}{1-\sin^2 q}\\\\\\=\dfrac{(1 + \sin q)(1 + \sin q)}{(1+ \sin q)(1 - \sin q)}\\\\\\=\dfrac{1+ \sin q}{1- \sin q}\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

Answer:

x - 2

Step-by-step explanation:

x^3 + 3x^2 - 4x - 12 simplifies to (x + 2)(x - 2)(x + 3)

x^2 + 5x + 6 simplifies to (x + 2)(x + 3)

(x + 2)(x - 2)(x + 3)

 (x + 2)(x + 3)

The (x + 2) and (x + 3) cancel

x - 2

Kayden Kohl

9th Grade Student

(Algebra 2)

Answer:

11

Step-by-step explanation:

10/15=6/x-2

then solve for x

x=11

The equation of the line of the best fit on the scatter plot is y = 150x  + 598

From the line in the scatter plot, we have the following points

(x,y) = (3,1048) and (6,1498)

The equation is then calculated using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1} *(x - x_1) + y_2[/tex]

The equation becomes

[tex]y = \frac{1498 -1048}{6 - 3} *(x - 3) + 1048[/tex]

Evaluate

y = 150 *(x - 3) + 1048

Expand the bracket

y = 150x - 450 + 1048

Evaluate the sum

y = 150x  + 598

Hence, the equation of the line of the best fit is y = 150x  + 598

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The correct option is option B :    -4 ≤ x ≤ 1

Increasing and decreasing functions are functions whose graphs go upwards and downwards respectively as we move towards the right-hand side of the x-axis. Increasing and decreasing functions are also called non-decreasing and non-increasing functions.

Here, from graph

as we can observe from x = -4 graph starts increases upto x = 1 and after that graph becomes constant.

Thus, between x belongs -4 to 1 the graph is increasing.

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Answer:

see below

Step-by-step explanation:

I would use the sine function for the info given

 in a right triangle    sine = opp leg / hypotenuse

        so  sin 57 =  10.8/x  

           then x =  10.8 / sin 57 = 12.87

Answer:

<

Step-by-step explanation:

5.62x10^4=56200, 4.7x10^5=470000, so it is <.

Answer:

the answer is 8200

Step-by-step explanation:

8200+8200=16400

The expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.

It is defined as the combination of constants and variables with mathematical operators.

We have:

Sheryl makes $7 per a pair of earrings, e, and $13 per necklace, n, she sells.

Let's suppose the total income of Sherly is T:

Then,

T = 7e + 13n

Here e is the number of earrings she sells and n is the number of necklace she sells.

T is the total income and the expression T = 7e + 13n represents the total income of Sherly.

Thus, the expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.

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Answer:

square rooted numbers like the square root of 2 are irrational because when calculated they don't equal a whole number.

Step-by-step explanation:

3+5√3 = 11.66   // not whole - irrational

√2 =  1.4 // not whole - irrational

√25 = 5 // whole - rational

Answer:

C. 8/17

Step-by-step explanation:

Given:

Hypotenuse = 17

BC = 8

Cos (B) = leg adjacent to ∠B / hypotenuse

= BC/BA

Substitute

Cos (B) = 8/17

Hence option C is correct

For both problems, we can use the section formula.

1) [tex]Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}[/tex]

2) [tex]P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}[/tex]

3x - 5 = -26​

step 1:

subtract +5 on each side because you have to do the inverse operation

step 2:

3x= -21

step 3:

now divide 3 on each side

the answer is -7

Hope this helped!

TheOneAndOnlyLara~

Answer:

x=-7.

Step-by-step explanation:

Hi student! Let me help you out.

_________________

First, add 5 to both sides.

[tex]\sf 3x=-26+5[/tex]. Upon simplifying, we obtain this.

[tex]\sf 3x=-21[/tex].

                                           ↪

Now divide both sides, by 3.

[tex]\sf x=-7[/tex]

[tex]\therefore,\sf the \quad value \quad of \quad x \quad is \quad -7[/tex]. Which is our final answer.

⇨Hope that this helped! have a great day ahead! ⇦

Best Wishes!

[tex]\star\bigstar\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}[/tex]

◆◆-Greetings!-◈◈

__________________________

Answer:

y = (2x/9) + 1

Step-by-step explanation:

Solving for y we get 3(-2y+x) = 5(-3y+x)+9

Expand the above we get -6y+3x=5(-3y+x)+9

which is -6y+3x = -15y+5x+9

then 9y = 2x+9

which y = (2x/9) + 1

The polynomial equation is P(x) = (x + 1)(x + 1)(x + 1)(x - 4)

The given parameters are:

A polynomial equation is represented as:

P(x) = (x- Root)

So, we have:

P(x) = (x - (-1))(x - (-1))(x - (-1))(x - 4)

Open the inner brackets

P(x) = (x + 1)(x + 1)(x + 1)(x - 4)

Hence, the polynomial equation is P(x) = (x + 1)(x + 1)(x + 1)(x - 4)

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Answer:The data set that is represented in the histogram is {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} Definition of a histogram An histogram is a graph that organises numerical data. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval. the frequency is usually on the vertical axis while the class interval is usually on the horizontal axis.Explaining the graphLooking at the histogram, the age group of 5 - 10 have 3 children in the carpool. the age group of 11 - 13 have 7 children in the carpool. the age group of 14 - 18 have 4 children in the carpool. This means that there are 14 children in the carpool. The correct option should have 14 ages that range between 5 and 18. Here are the options of this question: A. {3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4} B. {5, 10, 4, 11, 12, 13, 12, 13, 12, 11, 14, 14, 19, 18} C. {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} D. {3, 5, 10, 11, 13, 7, 18, 14, 4}

Step-by-step explanation:

The correct situation for the given condition are as follows:

C) Both proposed placements will light the same sized area.

F) Dylan's proposed placement will light exactly half of the yard.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e.,  A = 1/2 × b × h.

The area of a triangle =  (base x height) / 2

and,

both lights illuminate the same base and height = (60 x 38) / 2

                                                                                 =  1,140 sq ft

Both Dylan's and Nikki's proposed placement will lit exactly half of the yard.

The yard's total area = 60 x 38 = 2,280 sq ft,

which is twice the area lit by the lights.

Thus, The correct situation for the given condition are as follows:

C) Both proposed placements will light the same sized area.

F) Dylan's proposed placement will light exactly half of the yard.

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Answer:

-17, -10, -6, -5, 3, 8 only change is between 3 and 8

Using the assumed values, the volume of the cone is [tex]V = \frac {250}3\pi[/tex]

The volume of a cone is calculated using:

[tex]V = \frac 13\pi r^2h[/tex]

The parameters are not given.

So, we use the following assumed values

Radius, r = 5

Height, h =10

Using the assumed values, we have:

[tex]V = \frac 13\pi * 5^2 * 10[/tex]

Evaluate the product

[tex]V = \frac {250}3\pi[/tex]

Hence, using the assumed values, the volume of the cone is [tex]V = \frac {250}3\pi[/tex]

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Answer: C (490/3

Step-by-step explanation:

The function's behavior at vertical asymptote x = 2 is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]

The attached graph represents the missing information in the question.

From the attached graph, we have the following highlights:

This means that the limit of f(x) approaches negative infinity and positive infinity at this value of x

Hence, the function's behavior is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]

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Answer: See the screenshot below.

Explanation:

We'll be using these trig functions

The inverse of those help us find the angle. Notation like arcsine is the same as inverse sine denoted as [tex]\sin^{-1}[/tex] on many calculators.

The decimal results are approximate.

In the proof given, BC║AD and CD║BA because: B. slopes of opposite sides are equal.

If two lines are parallel, they will have the same slope value,.

Slope = rise/run.

Slope of BC = rise/run = -2/5

Slope of AD = -2/5

Slope of BA = rise/run = -6/1 = -6

Slope of BA = rise/run = -6/1 = -6

Therefore, we can conclude that BC║AD and CD║BA because: B. slopes of opposite sides are equal.

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