Which shows an equation for this situation?

The cost per slice of pizza is proportional to the number of slices as shown in the graph. What do the points ( 0, 0 ) and ( 1,

Semmy [17]

Answer:

The points represent the price per slice

Step-by-step explanation:

If the cost per slice of pizza is proportional to the number of slices, as shown in the graph, that means the points on the graph represent the price per slice.

Therefore, point (0,0) means that 0 slices of pizza cost $0, and point (1, 2) means that 1 slice of pizza costs $2.

7 0

3 years ago

On a typical long distance call you talk for 30 minutes. On a typical local call you talk for 10 minutes. Your phone company off

klio [65]

The number of long distance calls to be made can be obtained by linear programming

To minimize the phone bill, the number of long distance call to be made is none

Reason:

Maximum number of number of long distance calls = 15

Maximum number of local calls = 30

Number of minutes of calls to make each month = 240 minutes

Duration of each long distance call = 30 minutes

Duration of each local call = 10 minutes

Cost of long distance call = $0.08

Cost of local call = $0.03

Solution:

Let X, represent the number of long distance calls, and let Y represent the number local calls

The objective function is given as follows;

P = 0.08·(30)·X + 0.03·(10)·Y

P = 2.4·X + 0.3·Y

The constraints are;

X ≥ 0

Y ≥ 0

X ≤ 15

Y ≤ 30

30·X + 10·Y ≥ 240

Solving we have;

Y ≥ 24 - 3·X

The above inequality can be plotted with MS Excel

From the objective function, P = 2.4·X + 0.3·Y, the coefficient of the long

distance calls, X is larger than the coefficient of the local calls Y, therefore,

making the minimum possible number of long distance calls of 0, and 24

local calls will give a cost;

P = 2.4 × 0 + 0.3 × 24 = 7.2

Therefore, to minimize the phone bill, the number of long distance calls to

be made is zero long distance calls

Learn more about linear optimization here:

brainly.com/question/21491539

5 0

3 years ago

Solve the equation. 5/6 x-4 = -2

lora16 [44]

Answer:

2 2/5

Step-by-step explanation:

5/6 x-4 = -2

Add 4 to each side

5/6 x-4+4 = -2+4

5/6 x = 2

Multiply by 6/5 to isolate x

6/5 *5/6 x = 6/5 *2

x = 12/5

Changing this from an improper fraction

5 goes into 12 2 times with 2 left over

x = 2 2/5

7 0

3 years ago

Simplify the complex numbers using de Moivre's Theorem and match them with their solutions.

alexandr1967 [171]

For the numbers in $a+bi$ form, convert to polar form:

$1+i=\sqrt2\dfrac{1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)$

By DeMoivre's theorem,

$(1+i)^5=(\sqrt2)^5\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=4\sqrt2\dfrac{-1-i}{\sqrt2}=-4-4i$

$-1+i=\sqrt2\dfrac{-1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4}\right)$

$\implies(-1+i)^6=(\sqrt2)^6\left(\cos\dfrac{18\pi}4+i\sin\dfrac{18\pi}4\right)=8i$

$\sqrt3+i=2\dfrac{\sqrt3+i}2=2\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)$

$\implies2(\sqrt3+i)^{10}=2^{11}\left(\cos\dfrac{10\pi}6+i\sin\dfrac{10\pi}6\right)=2^{11}\dfrac{1-i\sqrt3}2=2^{10}(1-i\sqrt3)$

For the numbers already in polar form, DeMoivre's theorem can be applied directly:

$2\left(\cos20^\circ+i\sin20^\circ\right)^3=2\left(\cos60^\circ+i\sin60^\circ\right)=2\dfrac{1+i\sqrt3}2=1+i\sqrt3$

$2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)^4=2(\cos\pi+i\sin\pi)=-2$

At second glance, I think the 2s in the last two numbers should also be getting raised to the 3rd and 4th powers:

$\left(2(\cos20^\circ+i\sin20^\circ)\right)^3=8\left(\cos60^\circ+i\sin60^\circ\right)=4+4\sqrt3$

$\left(2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)\right)^4=16(\cos\pi+i\sin\pi)=-16$

4 0

3 years ago

What is the mean? 9.12.34.6.8.9.

NISA [10]

Answer:

13

Step-by-step explanation:

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

4 0

3 years ago

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