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77julia77 [94]
2 years ago
9

Cineplex operates two movie theaters in a city. The profits from one theater can be represented by the expression t3 – +2 + 2t –

100, where
tis the number of tickets sold. The profits from the second theater can be represented by the expression t2 – 2t – 300.
Which statements are true about the expression representing Cineplex's total profits in that city?
The total profit expression is a polynomial
The total profit expression has a constant term
The total profit expression is quadratic
The total profit expression is a binomial.
The total profit expression has four terms.
Mathematics
1 answer:
ira [324]2 years ago
8 0

Answer:

The total profit expression is a polynomial.

The total profit expression has a constant term.

The total profit expression is a binomial.

Step-by-step explanation:

I just answered this and got them right

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For the equation ae^ct=d, solve for the variable t in terms of a,c, and d. Express your answer in terms of the natural logarithm
saveliy_v [14]

We have been given an equation ae^{ct}=d. We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

\frac{ae^{ct}}{a}=\frac{d}{a}

e^{ct}=\frac{d}{a}

Now we will take natural log on both sides.

\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})

Using natural log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})

We know that \text{ln}(e)=1, so we will get:

ct\cdot 1=\text{ln}(\frac{d}{a})

ct=\text{ln}(\frac{d}{a})

Now we will divide both sides by c as:

\frac{ct}{c}=\frac{\text{ln}(\frac{d}{a})}{c}

t=\frac{\text{ln}(\frac{d}{a})}{c}

Therefore, our solution would be t=\frac{\text{ln}(\frac{d}{a})}{c}.

5 0
2 years ago
As part of a new advertising campaign, a beverage company wants to increase the dimensions of their cans by a multiple of 1.11.
Elis [28]

Answer:

124.67cm³

Step-by-step explanation:

==>Given:

Dimensions of current can:

Height (h) = 12cm

Diameter = 6cm (radius = 3cm)

Volume of current can (V1) = 339.12 cm³

Dimensions of future cans to be increased multiple of 1.11:

height = 12cm × 1.11 = 13.32 cm

radius = 3cm × 1.11 = 3.33 cm

Volume of future can (V2) = πr²h = 3.14*3.33²*13.32

= 3.14*11.0889*13.32 = 463.791025

V2 ≈ 463.79 cm³

==>Find how much more would new cans hold = Volume of new can - volume of current can

= 463.79 cm³ - 339.12 cm³

= 124.67cm³

5 0
2 years ago
In Quadrilateral ABCD , AB ∥ CD, and m∠2=35°.
Marianna [84]
Angle 2 and 5 are alternate interior angle and they are congruent. That means that m <5= 35°.
4 0
2 years ago
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Find the gradient of the line segment between the points (2,3) and (-3,8).
fiasKO [112]

Answer:

m = -1

Step-by-step explanation:

Given

Points (2,3) and (-3,8)

Required

Determine the gradient

Gradient (m) is calculated by dividing the change in y values by the change in x values.

i.e.

m = \frac{y_2 - y_1}{x_2 - x_1}

Where:

(x_1,y_1) = (2,3)

(x_2,y_2) = (-3,8)

m = \frac{y_2 - y_1}{x_2 - x_1} becomes

m = \frac{8 - 3}{-3 -2}

m = \frac{5}{-5}

m = -1

<em>Hence, the gradient is -1</em>

7 0
2 years ago
Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x – 2)2 + 3?
Andrei [34K]

Answer:

A. right 2, up 3

Step-by-step explanation:

We have that,

The function f(x) = x^2 is transformed to g(x) =(x- 2)^2+3.

We see that,

The function f(x) is translated 2 units to the right and 3 units upwards to obtain the function g(x).

So, the correct transformation is 'right 2, up 3'.

Hence, option A is correct.

5 0
2 years ago
Read 2 more answers
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