Lucy ate eight more than three times as many pretzels as Matt Lucy ate 56 pretzels how many pretzels did Matt eat

Which table shows a constant rate of change of –3? A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6.

Andrew [12]

Answer:

c

Step-by-step explanation:

6 0

2 years ago

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After learning the midpoint construction Sally realizes that she could determine one fourth the length of a segment how could sh

Viefleur [7K]

The midpoint of two points is the point which divides the line segment joining the two points into two equal parts.

Suppose, we have a line segment AB with a point C, between point A and point B such that the distance AC is equal to the distance CB, then we say that point C is the midpoint of line AB.

Suppose, we have another point D between point A and point C, such that the distance AD is equal to the distance DC, then we say that point D is the midpoint of AC.

Notice that point D is a fourth of line segment AB.

Thus, AD is <span>one fourth the length of segment AB.

Therefore, one fourth the length of a segment can be obtained by evaluating the midpoint of the midpoint of the line segment.
</span>

7 0

2 years ago

What is the geometric mean of 3 and 147

Makovka662 [10]

multiply the two numbers together, then take the square root

3* 147

441

sqrt(441)

21

The geometric mean is 21

3 0

2 years ago

Which equation represents a proportional relationship with a constant of proportionality of 14? y = x + 14 y = 14x 14y = x y = x

Ivanshal [37]

For $y$ and $x$ to be the variables.

Equation that represents a proportional relationship with a constant or proportionality of 14 is : $y = 14x$

Here, $y$ and $x$ are proportional to each other with a constant of proportionality of 14

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2 years ago

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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

2 years ago