Solve the real-world situation by using the substitution method.

One smartphone plan costs $30 per month for talk and messaging and $8 per gigabyte of data used each month. A second smartphone plan costs $60 per month for talk and messaging and $3 per gigabyte of data used each month. Let c represent the total cost in dollars and d represent the amount of data used in gigabytes. The system of equations lbrace c = 30 + 8d c = 60 + 3d can be used to represent this situation.

How many gigabytes would have to be used for the plans to cost the same? What would that cost be?

Both plans would cost $_____
if _____ gigabytes of data are used.

Answer:

164m (to 3 s.f.)

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

Option B

Step-by-step explanation:

to calculate this, you need to plug in 1 as I, then 2 as I and then 3 as k, and add the three solutions up

8 + 2 + 0.5 = 10.5

wich is the same as 21/2

8 hours + 3 hours = 11 hours

12 minutes + 15 minutes = 27 minutes

Answer : 11 hours 27 minutes

Answer:

One helpful technique I used to stay focused is to buy a pack of m&ms or mini  candies and every time I complete a problem I eat one candy or m&m. Also, try making a goal for yourself for example "my goal is to complete 100 problems in an hour"

Step-by-step explanation:

I hope this helps

message me with any more questions u have

Answer:

First, let's look at some polynomials of even degree (specifically, quadratics in the first row of pictures, and quartics in the second row) with positive and negative leading coefficients:❤

Answer:

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.

give thanks for more! your welcome!

Step-by-step explanation:

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

Answer:

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

(r - 3)(r + 1) = 0

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

The total cost would be found by Multiplying the price per gallon by number of gallons bought

total cost (C) = $2.75g

Answer:

500

Step-by-step explanation:

because the function is t and thats 1.40 and if you divided 1.40 by 6000 its unknown

Answer:

Its 9.

Step-by-step explanation:

First you do the math inside the parenthesis (13), then your gonna multiply 7 by the numbers you got in the parenthesis (7*13), finally subtract 82 from 7*13 and you get your answer, 9.

( 10+3)-82= -69

13- 82 =69

The exact values for the primary trigonometric ratios related to the terminal arm point (- 5, - 7) are sin θ = - 7√74 / 74 and cos θ = - 5√74 / 74.

In this problem we find the coordinates of a point (x, y), that represents the terminal arm of an angle, that is, the horizontal and vertical distances of that point with respect to the origin. The sine and the cosine are the primary trigonometric ratios, whose formulas are described below:

Sine

sin θ = y / √(x² + y²)

Cosine

cos θ = x / √(x² + y²)

If we know that x = - 5, - 7, then the primary trigonometric ratios are determined below:

sin θ = - 7 / √[(- 5)² + (- 7)²]

sin θ = - 7√74 / 74

cos θ = - 5 / √[(- 5)² + (- 7)²]

cos θ = - 5√74 / 74

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Answer:

58

Step-by-step explanation:

1980+630 then divide by 45

Step-by-step explanation:

Area of parallelogram = base × height or say b×h

Given: h=8 inches

Area=120 sq.inches

⇒120=8×b

⇒120/8=b

⇒120/8=b = 15

Answer = 15 inches b

Answer:

The Answer is A

Step-by-step explanation:

Just Did the Assignment

Answer:

If you have 3 and a half tablespoons of sugar, you can estimate that there is a 21.875% void in between your jelly beans. 16 TBSP = 1 Cup, 1 Cup divided by 16 TBSP = .0625, 3.5 TBSP of sugar x .0625 = .21875, So we know our jar is 547.9637625 cubic inches.

Step-by-step explanation:

Answer:

X can be any number greater than -2 and less than or equal to 1/4.

Step-by-step explanation:

To solve for x in the inequality 3x + 1 ≤ 2 - x < 18 + 7x, we will first isolate the variable x on one side of the inequality.

3x + 1 ≤ 2 - x

Adding x to both sides, we get:

4x + 1 ≤ 2

Subtracting 1 from both sides, we get:

4x ≤ 1

Dividing both sides by 4, we get:

x ≤ 1/4

Next, we solve the second inequality:

2 - x < 18 + 7x

Adding x to both sides, we get:

2 < 18 + 8x

Subtracting 18 from both sides, we get:

-16 < 8x

Dividing both sides by 8, we get:

-2 < x

Therefore, the solution to the inequality 3x + 1 ≤ 2 - x < 18 + 7x is:

-2 < x ≤ 1/4

This means that x can be any number greater than -2 and less than or equal to 1/4.

The motivations for producers and consumers in the black market are largely driven by financial incentives and a desire to avoid legal consequences.

The black market refers to the illegal trade of goods and services that are not permitted by law, such as drugs, counterfeit items, and stolen goods. Producers and consumers in the black market are motivated by a variety of factors, including:

High profits, Producers in the black market can earn higher profits than they would in legal markets due to the lack of regulation and taxes.

Escaping legal consequences: Producers and consumers may participate in the black market to avoid legal consequences, such as fines or imprisonment, for engaging in illegal activities.

Limited availability, Some goods and services are only available on the black market due to legal restrictions or limited supply.

Low prices, Consumers in the black market can often purchase goods and services at lower prices than in legal markets due to the lack of taxes and regulations.

Desire for anonymity, The black market can provide anonymity for both producers and consumers, allowing them to engage in illegal activities without fear of detection or retribution.

However, participating in the black market also comes with significant risks, including the possibility of arrest, fines, and even violence.

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The intersection of sets M and F contains the elements "c" and "d".

To find the intersection of sets M and F, we need to identify the elements that are common to both sets.

M = {a, b, c, d}

F = {c, d, e, f}

The intersection of M

and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.

Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".

Therefore, the intersection of M and F can be expressed as:

M ∩ F = {c, d}

So, the intersection of sets M and F contains the elements "c" and "d".

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The result of the given terms is -2/5 as per the given question from complex numbers.

There is a multiplicative inverse for every nonzero complex number. As a result, complex numbers are a field with real numbers as a subfield. The complex numbers also form a two-dimensional real vector space with 1, I as the standard basis.

Because of this standard basis, the complex numbers form a Cartesian plane known as the complex plane. This allows for a geometric interpretation of complex numbers and operations, as well as the expression of geometric features and constructions in terms of complex numbers. Real numbers, for example, constitute the real line, which corresponds to the complex plane's horizontal axis.

=(((3/5)+(1/5)i)+((4/5)-(2/5)i) -((9/5)-(1/5)i))

=((3/5)+(4/5)-(9/5))-i((1/5)+i((1/5)-(2/5)+(1/5))

=(-2/5)+i(0)

= -2/5

Therefore, the result of the given terms is -2/5

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Answer:

8 hours

Step-by-step explanation:

Answer:

11/12

Step-by-step explanation:

Answer:

11/12

Step-by-step explanation:

Answer:

The probability of drawing increases from drawing a black card from the bag.

Step-by-step explanation:

If 5 were dropped from red it would leave red with 21 cards and if 1 was dropped from black cards it would leave 25 cards in black cards. It does change the probability of drawing a red card it is more likely now to draw a black card than a red card because there are more black cards than red.

Hope this helps <3

Answer:

17

Step-by-step explanation:

14, 12, 12, 18 , 22 , 20, 17

Put the numbers in order from smallest to largest

12, 12, 14,17, 18 , 20 , 22

The median is the middle number

12, 12, 14,     17,      18 , 20 , 22

The middle number is 17

If the court of the length of the most comprehensive side of a triangle is equivalent to the sum of the squares of the additional two sides, then the triangle is good.

What is meant by Pythagorean theorem?

That exists, in ΔABC, if c2=a2+b2 then ∠C is a right triangle, ΔPQR living at the right angle.

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Answer:

Distributive property says that:

(A + B)*C = A*C + B*C

Now let's try to use it in our expression:

3 + 5*c*(2 + 6*c)

Here we can take the two terms inside the parentheses as A and B, and the term that multiplies them as C, then distributing we get:

3 + (5*c)*2 + (5*c)*(6*c)

Now remember that the multiplications are associative and commutative, then we can write this as:

3 + (2*5)*c + (5*6)*(c*c)

3 + 10*c + 30*c^2

And we can't simplify it anymore.