5x + 10x – 54 = 66<br> Solve please hurry

The length of a rectangular park is four timesfour times its width. The park is surrounded by a 33-foot-wide path. Let x denote

tiny-mole [99]

Answer:

A(x) = 4x^2 + 330x + 4356

Step-by-step explanation:

width of park: x

length of park: 4x

width + path width = x + 66

length + path width = 4x + 66

area = (x + 66)(4x + 66)

area = 4x^2 + 66x + 264x + 4356

area = 4x^2 + 330x + 4356

A(x) = 4x^2 + 330x + 4356

7 0

3 years ago

A library building is in the shape of a rectangle. Its floor has a length of (3x + 5) meters and a width of (5x − 1) meters. The

AleksAgata [21]

The problem says that the expression (3x + 5)(5x − 1) <span>represents the area of the floor of the building in square meters. Therefore, to solve this problem you have to follow the proccedure shown below.

1. First, to simplify the expression (3x + 5)(5x − 1) you must apply the distributive property. Then, you obtain:

15x</span>²-3x+25x-5

2. Then, you have:

15x²+22x-5

3. As you can see, the correct answer is the last option: 15x²+22x-5

7 0

3 years ago

Determine whether the variable is qualitative or quantitative.

Oduvanchick [21]

Answer:

Qualitative variable

A. The variable is qualitative because it is an attribute characteristic.

<h2>What are Quantitative and Qualitative variables?</h2>

A qualitative variable is one in which the "true" or naturally occurring levels or categories taken by that variable are not described as numbers but rather by verbal groupings.

Example: levels or categories of hair color (black, brown, blond)

A quantitative variable on the other hand are those in which the natural levels take on certain quantities (e.g. price, travel time)

That is, quantitative variables are measured in some numerical unit (eg. pesos, minutes, inches, etc.)

<h2>How is hair color a qualitative variable?</h2>

Because hair color is a categorical variable, it is a qualitative variable too. This is because hair color can be put into different categories depending on the color of someone or something's hair. Someone could have blond, brown, or black hair; they might even have red hair. It's all different and are attributed characteristic, they are all put into different categories, but can only be measured statistically while remaining constant (with different amounts).

<h2>What is a numerical variable and what is a categorical variable?</h2>

A categorical variable is a category or type. For example, hair color is a categorical value or hometown is a categorical variable. Species, treatment type, and gender are all categorical variables.

A numerical variable is a variable where the measurement or number has a numerical meaning. For example, total rainfall measured in inches is a numerical value, heart rate is a numerical value, number of cheeseburgers consumed in an hour is a numerical value.

<em>A categorical variable can be expressed as a number for the purpose of statistics, but these numbers do not have the same meaning as a numerical value. </em>For example, if I am studying the effects of three different medications on an illness, I may name the three different medicines, medicine 1, medicine 2, and medicine 3. However, medicine three is not greater, or stronger, or faster than medicine one. These numbers are not meaningful.

Learn more about qualitative and quantitative variables:

#SPJ2

7 0

2 years ago

You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). O

Neko [114]

Answer:

a)q(p)=-15p+ +300

b)R(p)=-15p²+300p

c)C(p)=-30p+1600

d.1)P(p)=-15p²+330p-1600

d.2)p=$11

Step-by-step explanation:

(a).Before getting started, we are going to consider the cartesian plane, where x-axis corresponds to the cover charge and y-axis corresponds to number of guests per night . There, we will locate the following coordinates according to the previous information:

(9,165) (10,150).

Remember that the slope-intercept form of the linear equation is y=mx+b where m is the slope and b is te intercept.

The slope can be calculated by the next formula:

$m=\frac{y2-y1}{x2-x1}$

In this case we will assign (9,165) as the first coordinate and (10,150) as the second one. The order does not matter. At the end we get the same value for m.

Therefore:

$m=\frac{150-165}{10-9} = -15$

Now, we have the slope and two poitns. According to this, and taking into account that point-slope form of the equation of a line is y-y1=m(x-x1), find a linear demand equation.

Any of two coordintates can be selected. In this case we will select the second one.

y-150=-15(x-10) equation 1

Solve equation 1 for y

y=-15x+150+150

y=-15x+300

Above we had defined x as cover charge (p) and y as number of guests (q). Thus, rewrite equation 1.

q(p)=-15p+ +300.

it equation shows the number of guests per night as a function of the cover charge,

(b). The nightly revenue can be calculated multplying the price of the cover charge by the number of guests. So, we just have to multiply the equation 1 by p.

p*q(p)=p*(-15p +300)

R(p)=-15p²+300p equation 2

(c) To get the cost function of the nightclub we just have to multiply the cost of the two non-alcoholic drinks by the number of the guests ( equation 1) and add to it nightly overheads.

C(p)=2*(-15p+300)+1000

C(p)= -30p+600+1000

C(p)=-30p+1600 equation 3

(d) In order to find the profit in terms of the cover charge we will subtract nightly costs ( equation 3) from nightly revenue (equation 2)

P(p)=R(p)-C(p)

P(p)=-15p²+300p - (-30p+1600)

P(p)=-15p²+300p+30p-1600

P(p)=-15p²+330p-1600

To determine that the entrance fee we should charge for a maximum profit we are going to use the first derivative test (y'(x)=0) in order to find an extremum point.

Compute the first derivative of P(p)

P'(p)=-30p+330=0

30p=330

p=330/30

p= $11

The entrance fee that we should charge for a maximum profit is p=$11 per guest.

5 0

3 years ago

How do you solve inequalites

zhenek [66]

<span>Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own.But these things will change direction of the inequality: ...<span>Don't multiply or divide by a variable (unless you know it is always positive or always negative)</span></span>

7 0

3 years ago

5x + 10x – 54 = 66 Solve please hurry