Danielle's basic cell phone rate each month is $29.95. Add to that $5.95 for voice mail and $2.95 for text messaging. This past month Danielle spent an additional C dollars on long distance. Her total bill was $77.70. How much did Danielle spend on long distance?

Final answer:

The 55th derivative of y = cos(3x) is recognized by repeating the derivative patterns of cosine functions and is found to be -27cos(3x).

Explanation:

The 55th derivative of y = cos(3x) can be found by recognizing that the derivatives of sine and cosine functions repeat every four steps. Considering the pattern cos(x) -> -sin(x) -> -cos(x) -> sin(x) -> cos(x), and that the derivative of cos(3x) is -3sin(3x), we can determine that the pattern repeats every four derivatives with a factor of 3n, where n is the number of times the derivative is taken.

The 55th derivative will be the same as the third derivative in the cycle, but with an iteration count of 55/4, which leaves a remainder of 3, so the 55th derivative will be -27cos(3x).

it pumps 8 gallons a minute so it is 8x ( 8 gallons times x minutes)

you then need to subtract that amount from 1200

 lets say it pumped for 10 minutes,  8 *10 = -80

1200 - 80 =1120

 now the answers you have to choose from are kind of tricky because they don't give you the easiet one

 so using the numbers above

 the formula would be

1120 = -80+1200 =

y =-8x +1200

Final answer:

The equation y = 1200 - 8x models the amount of water in the tank as it is being pumped out.

Explanation:

The equation that models the amount of water in the tank y after x minutes is:

y = 1200 - 8x

This equation represents the initial 1200 gallons of water in the tank decreasing by 8 gallons per minute as it is being pumped out over time.

The midpoint of the range of frequencies given is:

midpoint =  (82.4 + 659.2) / 2 = 370.8 Hertz

Then the difference from midpoint to the other end is:
370.8 - 83.4 = 288.4 Hertz

Therefore the inequality formula is
|f - 370.8| <= 288.4

The answer to the first question is "b. one," according to Euclid's First Postulate. The answer to the second question is "c. infinitely many," according to Euclid's Second Postulate. These principles form the foundation of Euclidean geometry.

In Euclidean geometry, there are fundamental postulates and theorems that govern the behavior of lines and angles in triangles. Let's address your questions:

1. How many lines can be drawn through point A perpendicular to segment BC?

Answer: There can be only one line drawn through point A that is perpendicular to segment BC. This follows from Euclid's First Postulate, which states that a straight line can be drawn between any two points. In this case, the straight line from point A to any point on segment BC is unique and perpendicular.

2. How many lines can be drawn through point C perpendicular to segment AB?

Answer: Infinitely many lines can be drawn through point C that are perpendicular to segment AB. This is based on Euclid's Second Postulate, which states that a straight line can be extended infinitely in both directions. So, you can draw as many lines as you like, all of which are perpendicular to segment AB, and they will extend infinitely in both directions.

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Answer: a=-3b

                  2

Step-by-step explanation:

get all letters on the same side so:

7a-5a (because when you cross the = you do the opposite)=-b+2b

2a=b

you are solving for a so: 2a/2=b/2

so the 2 cancel out and you have a=1/2b

29/1

Improper fractions have a greater numerator.

29 > 1

Answer:

Gina=35, Sara=33

Step-by-step explanation:

Gina's number is 2 more than Sara's.

Lets start by saying cookies as the number.

Sum = 2 numbers add together. The answer to the equation. Lik 5+5=10. 10 is the sum.

You only know that Gina has 2 more cookies than Sara.

If Sara has 3 cookies then Gina has 5 cookies. Whats the Sum? 8.

So, you figure out an random big number but, smaller than 68.

Lets do 68 to try now.  So you do 68/2 = 34. You remember that Gina has 2 more than Sara. So, 35 cookies for Gina. So, you can guess that Sara has 33 cookies.

The unit rate of 324 calories in a 3-ounce serving is

108 calories per 1 ounce.

Given,

There are 324 calories in 3 ounce

We need to find the unit rate which means how many calories in one ounce.

We have,

In 3 ounces there are 324 calories.

We can write it as,

3 ounce = 324 calories

Dividing both sides by 3,

We get,

1 ounce = 324 / 3

1 ounce = 108

So,

In 1 ounce we have 108 calories.

This is our unit rate.

Thus the unit rate of 324 calories in a 3-ounce serving is 108 calories per 1 ounce.

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Step 1

Find the slope of the given line

we have

[tex]3x+4y=15[/tex]

Isolate the variable y

Subtract [tex]3x[/tex] both sides

[tex]3x+4y-3x=15-3x[/tex]

[tex]4y=-3x+15[/tex]

Divide by [tex]4[/tex] both sides

[tex]y=-\frac{3}{4}x+ \frac{15}{4}[/tex]

the slope of the given line is

[tex]m=-\frac{3}{4}[/tex]

Step 2

Find the equation of the line that passes through  the point [tex](8,-2)[/tex] and is parallel to the given line

we know that

if two lines are parallel, then their slopes are equal

The equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{3}{4}[/tex]

[tex](x1,y1)=(8,-2)[/tex]

substitute in the equation

[tex]y+2=-\frac{3}{4}(x-8)[/tex]

[tex]y=-\frac{3}{4}x+6-2[/tex]

[tex]y=-\frac{3}{4}x+4[/tex]  or  [tex]3x+4y=16[/tex]

therefore

the answer is

[tex]y=-\frac{3}{4}x+4[/tex]

or

[tex]3x+4y=16[/tex]

Answer:

3x+4y=16

Clarifying because other explanation was confusing

Just took review

Step-by-step explanation:

1.50x+0.80y≤20 is inequality represents how many hot dogs and how much water you can buy

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given,

a hot dog costs $1.50 each and water costs $0.80 each.

Let  x be the amount of hot dog

y be the amount of water

As hot dog costs $1.50 each, 1.50x

water costs $0.80 each, so 0.80y

You want to buy food and water for yourself and your friends but do not want to spend more than $20

1.50x+0.80y≤20

Hence, 1.50x+0.80y≤20 is inequality represents how many hot dogs and how much water you can buy

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To find the value of x and BC, set up the equation CB + BD = CD and solve for x. The value of x is 3 and BC is 3.

To find the value of x and BC, we can set up the equation CB + BD = CD and solve for x.

Substituting the given values CB = 4x - 9, BD = 3x + 5, and CD = 17, we get (4x - 9) + (3x + 5) = 17.

Combining like terms, we have 7x - 4 = 17. Solving for x, we find x = 3. Plugging this value back into CB = 4x - 9, we get BC = 4(3) - 9 = 12 - 9 = 3.

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