A Web music store offers two versions of a popular song. The size of the standard version is 2.3 megabytes (MB). The size of the high-quality version is 4.2 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 3427 MB. How many downloads of the standard version were there?

The absolute value |2x+7| simplifies differently depending on values of x. If x > -7/2, |2x+7|=2x+7. If x=-7/2, |2x+7|=0. If x<-7/2, |2x+7|= -(2x+7).

The absolute value |2x + 7| measures the distance of the value 2x + 7 from zero on the number line. To simplify the equation and determine for what values of x the absolute value results are positive, negative or zero, we must consider the following conditions:

In the first case, the inside of the absolute value is positive and thus its value is itself. In the second case, the inside of the absolute value equals to zero and the absolute value of zero is zero. In the third case, the inside of the absolute value is negative and thus its absolute value is the negation of it.

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Answer:

a) ±5

b) ±9

Step-by-step explanation:

In each case, the expression on the left is the square of the expression you're asked to find the value of. Then the value of your expression is the square root of the constant on the right. That square root can be either positive or negative.

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a) a^2 +2ab +b^2 = (a +b)^2 = 25

(a +b) = ±√25 = ±5

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b) a^2 -8ab +16b^2 = (a -4b)^2 = 81

(a -4b) = ±√81 = ±9

Answer:

  17.  37 2/7

  20.  3.4

Step-by-step explanation:

17.  The scale factor of the smaller triangle PQR to the larger triangle LMN is given by the ratio of corresponding sides:

  RP : NL = 18 : 28 = 9 : 14

The perimeter of LMN is the sum of the lengths of its sides:

  16 + 14 + 28 = 58

So, the perimeter of PQR is ...

  (9/14)×58 = 261/7 = 37 2/7 . . . . units

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20. By the same reasoning as above, the sides of triangle RQP are 25/40 = 5/8 of those of triangle MNP. Then ...

  RQ = (5/8)·MN

  5x -2 = (5/8)·24 = 15 . . . . substitute the measures shown

  5x = 17 . . . . . add 2

  x = 17/5 = 3.4 . . . . . . divide by 5

The value of x is 3.4.

the general term for the sequence m, -m, m, -m, . . . is

The correct option is (A).

The given sequence is: m, -m, m, -m, ...

Let's analyze the pattern:

1. For n = 1, the term is m.

2. For n = 2, the term is -m.

3. For n = 3, the term is m.

4. For n = 4, the term is -m.

5. And so on...

From the pattern, we can see that the sign alternates between positive and negative, and the term alternates between m and -m. This suggests that we can use [tex](-1)^(n-1)[/tex] to control the sign alternation and m to control the alternation between m and -m.

Now, let's check the options one by one:

A. [tex]m(-1)^(n-1)[/tex]

  Substituting n = 1, we get[tex]m * (-1)^(1-1) = m * (-1)^0 = m * 1 = m[/tex]

  Substituting n = 2, we get [tex]m * (-1)^(2-1) = m * (-1)^1 = m * -1 = -m[/tex]

  This matches our sequence. So, Option A seems correct.

B.[tex](-m)^n[/tex]

  This doesn't match our sequence because it would give us [tex](-m)^1 = -m,[/tex][tex](-m)^2 = m^2, (-m)^3 = -m^3[/tex], and so on, which doesn't alternate between m and -m.

C.[tex](-1)m^(n + 1)[/tex]

  Substituting n = 1, we get [tex](-1)m^(1 + 1) = (-1)m^2 = -m^2[/tex]

  Substituting n = 2, we get [tex](-1)m^(2 + 1) = (-1)m^3 = -m^3[/tex]

  This doesn't match our sequence because it doesn't alternate between m and -m.

D.[tex](-1)m^(n - 1)[/tex]

  Substituting n = 1, we get [tex](-1)m^(1 - 1) = (-1)m^0 = -1[/tex]

  Substituting n = 2, we get[tex](-1)m^(2 - 1) = (-1)m^1 = -m[/tex]

  This also doesn't match our sequence because it doesn't alternate between m and -m.

So, the correct answer is Option A:[tex]m(-1)^(n-1).[/tex]

Answer:

The new points would be (-7, -1), (-3, -2) and (-8, 1). The angle would not change

Step-by-step explanation:

When you rotate points by 180 degrees, you simply change the sign on the ordered pairs. This will give you the new points.

Also, spinning the points will not change the angle between them. Therefore it stays the same.

Answer:

Message instructor about this question

Step-by-step explanation:

The question does not provide the appropriate information for a suitable answer. The equation tells you height above sea level, but the question asks when the height above ground level will be zero. No information is given as to where ground level is in relation to sea level.

The best choice is "Message instructor about this question." Ask the instructor where ground level is in relation to sea level.

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In any event, the equation can be made somewhat simpler by factoring -16 ouf of it. Then you get ...

h(t) = -16(t^2 -7t -18) = -16(t -9)(t +2)

For h(t) = 0, solutions are ...

0 = -16(t -9)(t +2)

A product will be zero only when at least one of the factors is zero.

t = 9 or -2 . . . . . values that make the factors zero

The rocket comes back to sea level 9 seconds after launch.

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If the rocket is launched from ground level (288 ft), then we want to find t when ...

h(t) = 288 = -16t^2 +112t +288

Subtracting 288 and factoring out -16, we get ...

0 = -16(t^2 -7t) = -16t(t -7)

Solutions are ...

t = 0 or t = 7

It is no surprise that the rocket is at ground level at t=0, since we have assumed that is where it is launched from. The other solution, t=7, tells us the rocket returns to gruond level 7 seconds after launch.

_____

Possible solutions are ...

9 seconds if "ground level" means "sea level."

7 seconds if "ground level" means "launch height."

... something else if "ground level" is not one of these

Answer: 18 gallons.

Step-by-step explanation:

Let's call the total gallons that the container can hold x.

Then, based on the information given in the problem, you can write the following expression:

[tex]\frac{4}{9}x+4=\frac{2}{3}x[/tex]

Now, you must solve for x, as you can see below. Therefore, you obtain the following result:

[tex]\frac{4}{9}x+4=\frac{2}{3}x\\\\4=\frac{2}{3}x-\frac{4}{9}x\\\\4=\frac{2}{9}x\\\\4*9=2x\\\\36=2x\\\\x=18\ gallons[/tex]

To solve the container problem, we set up a proportion based on the given fill levels and found that the total capacity of the container is 18 gallons.

To solve how many gallons the container can hold, we need to set up a proportion based on the information given. The container was initially 4/9 full, and after adding 4 gallons of water, it became 2/3 full. We can use this ratio to find the total capacity of the container.

Therefore, the container's total capacity is 18 gallons.

Answer:

15 rentals

Step-by-step explanation:

You can (and may be expected to) set up an equation that equates the total cost at one store to the total cost at the other store. When you work through the solution of this equation, you find that the "break even" number of rentals is the ratio of the difference in fixed cost (setup fee) to the difference in per-use cost (rental charge).

Here, that ratio is ...

(15.00 -7.50)/(2.25 -1.75) = 7.50/0.50 = 15

15 rentals will make the total costs the same.

so after 15 movie sales they will be equal

Answer:

1/4 of the pan

Step-by-step explanation:

1/3 of 3/4 = 1/4

Answer:

Correct Answer 7/10

Step-by-step explanation:

Explanation:

The first determinant is that of the matrix of coefficients:

[tex]|A|=\left|\begin{array}{cc}5&2\\-3&-5\end{array}\right|=(5)(-5)-(-3)(2)=-19[/tex]

The second determinant is the same as the above but with the constants substituted for the x-coefficients.

[tex]|A_x|=\left|\begin{array}{cc}14&2\\3&-5\end{array}\right|=(14)(-5)-(3)(2) =-76[/tex]

The third determinant is the same as the first but with the constants substituted for the y-coefficients.

[tex]|A_y|=\left|\begin{array}{cc}5&14\\-3&3\end{array}\right|=(5)(3)-(-3)(14)=57[/tex]

_____

The solution to the system of equations is then ...

[tex]x=\dfrac{|A_x|}{|A|}=\dfrac{-76}{-19} =4\\\\y=\dfrac{|A_y|}{|A|}=\dfrac{57}{-19} =-3[/tex]

7 inches best 7 x 2 = 14 / 2 = 7 inches

The new price is $15.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Original Price: $20.

Discount Rate: 25%.

The discount amount,

= 25% of 20

= 5

The price,

= 20 - 5 = $15

Therefore, $15 is the new price.

To learn more about the percentage;

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Answer:

See below.

Step-by-step explanation:

15 - -5

= 15 - 1(-5)

= 15 + 5

= 20.

Answer:

15--5

add the negatives so its positive.

15+5=20

Step-by-step explanation:

Your answer is (C) !

The correct equation to find the amount of time they spent swimming laps is:

[tex]c. \( \frac{1}{2} \times 1 \frac{1}{2} \)[/tex]

To find the amount of time Paul and Krystal spent swimming laps, we need to determine what half of 1 1/2 hours is. This can be calculated by multiplying 1 1/2 by 1/2.

Let's look at the options:

a. [tex]\( 1 \frac{1}{2} - \frac{1}{2} \):[/tex] This would subtract 1/2 hour from 1 1/2 hours, which is not what we need.

b. [tex]\( 1 \frac{1}{2} \div \frac{1}{2} \):[/tex]This would divide 1 1/2 hours by 1/2, which is not what we need.

c. [tex]\( \frac{1}{2} \times 1 \frac{1}{2} \):[/tex]This is the correct operation, as it multiplies 1 1/2 hours by 1/2 to find half of the time.

d.[tex]\( \frac{1}{2} + 1 \frac{1}{2} \):[/tex] This would add 1/2 hour to 1 1/2 hours, which is not what we need.

So, the correct equation to find the amount of time they spent swimming laps is:

[tex]c. \( \frac{1}{2} \times 1 \frac{1}{2} \)[/tex]

Let's calculate it:

[tex]\[\frac{1}{2} \times 1 \frac{1}{2} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \text{ hours}\][/tex]

Therefore, Paul and Krystal spent [tex]\( \frac{3}{4} \)[/tex] hours (or 45 minutes) swimming laps.

Answer:

they became "roamin' numerals"

Step-by-step explanation:

Answer:

The least number of pizza make deal 1 better than deal 2 is 4

The cost of deal 1 is $53.99 and the cost of deal 2 is $60

The cost per pizza of deal 1 is $5.399

The better deal is deal 1

Step-by-step explanation:

* Deal 1 becomes better if it costs less than deal 2

- Assume that the number of pizza are n

* Deal 1:

∵ The cost of one large pizza = $8.99 for first 1 and = $5 for each

   additional one

∵ They ordered n large pizza

∴ The cost = 8.99 + 5(n - 1)

- Multiply the bracket by 5

∴ The cost = 8.99 + 5n - 5

- Add like terms

∴ The cost = 3.99 + 5n

∴ The cost of deal 1 = 3.99 + 5n

* Deal 2:

∵ The cost of any large pizza is $6

∵ They ordered n large pizza

∴ The cost = 6 × n = 6n

∴ The cost of deal 2 = 6n

- We need Deal 1 better than deal 2

- Then, put the cost of deal 1 < the cost of deal 2

∵ 3.99 + 5n < 6n

- Subtract 5n from both sides

∴ 3.99 < n

∴ n > 3.99

∴ n = 4

* The least number of pizza make deal 1 better than deal 2 is 4

∵ n = 10

∴ The cost of deal 1 = 3.99 + 5(10) = 53.99

∴ The cost of deal 2 = 6(10) = 60

* The cost of deal 1 is $53.99 and the cost of deal 2 is $60

∵ The cost per one pizza = total cost ÷ the number of pizza

∴ The cost per pizza of deal 1 = 53.99 ÷ 10 = 5.399

* The cost per pizza of deal 1 is $5.399

∵ The unit price of deal 1 is $5.399

∵ The unit price of deal 2 is $6

∵ $5.399 < $6

∴ The unit rate of deal 1 is less than the unit price of deal 2

* The better deal is deal 1

Deal #1 becomes a better deal at 4 pizzas. The cost of 10 pizzas for Deal #1 is $43.99, and for Deal #2 is $60.00. The cost per pizza in Deal #1 is $8.99 for the first pizza and $5 for each additional pizza. Deal #1 is the better deal when ordering 4 or more pizzas because the cost per pizza decreases as more pizzas are added to the order.

To determine at what number of pizzas Deal #1 becomes a better deal than Deal #2, we need to compare the total cost of pizzas under each deal.

For Deal #1, the cost structure is as follows:

The first pizza costs $8.99.

Each additional large pizza on the same order costs $5.

For Deal #2, the cost is a flat rate of $6.00 per large pizza.

Let's first find out at what point the total cost of pizzas under Deal #1 equals the total cost under Deal #2. We'll denote the number of additional pizzas (after the first one) as 'n'.

The total cost for Deal #1 can be expressed as:

[tex]\[ C_1 = 8.99 + 5n \][/tex]

The total cost for Deal #2 is:

[tex]\[ C_2 = 6(n + 1) \][/tex]

We set [tex]\( C_1 \) equal to \( C_2 \)[/tex]  to find the break-even point:

[tex]\[ 8.99 + 5n = 6(n + 1) \][/tex]

[tex]\[ 8.99 + 5n = 6n + 6 \][/tex]

[tex]\[ 8.99 - 6 = 6n - 5n \][/tex]

[tex]\[ 2.99 = n \][/tex]

Now let's calculate the cost of 10 pizzas for each deal:

For Deal #1:

[tex]\[ C_{10} = 8.99 + 5(10 - 1) \][/tex]

[tex]\[ C_{10} = 8.99 + 5 \times 9 \][/tex]

[tex]\[ C_{10} = 8.99 + 45 \][/tex]

[tex]\[ C_{10} = \$43.99 \][/tex]

For Deal #2:

[tex]\[ C_{20} = 6 \times 10 \][/tex]

[tex]\[ C_{20} = \$60.00 \][/tex]

The cost per pizza in Deal #1 is $8.99 for the first pizza and $5 for each additional pizza. As the number of pizzas increases, the average cost per pizza decreases.

Answer:

10. 5556 discs per month

11. 3.33 hours; 0.196%

Step-by-step explanation:

I find "appropriate technology" for questions like these to be a graphing calculator.

10. Put the given function definitions into the formula for profit and look for the peak of the profit curve. It is found at x ≈ 5556.

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11. The peak of the graph is found at t=3.333. The value of A(t) there is about 0.1962.

_____

If these are part of a calculus course, you can find the maximum values by differentiating the P(x) or A(t) functions and setting the derivative to zero. You get a linear equation in each case, so finding the independent variable value is not difficult:

10. 5 -.0009x = 0

11. (.16 -.048t)e^(-.3t) = 0

Trigonometry

[tex]Sine\frac{Opposite}{Hypotenuse} Cos\frac{Adjacent}{Hypotenuse} Tan\frac{Adjacent}{Opposite} \\S\frac{O}{H} C\frac{A}{H} T\frac{A}{O}[/tex]

Depending on which angle you use, decides which formula you use.

We'll use the top right angle.

9 is the adjacent.

x is the opposite.

So you need to use

[tex]Tan\frac{Adjacent}{Opposite} \\Tan45\frac{9}{x} \\x = \frac{9}{Tan45} \\x = 9[/tex]

If you solve y, you can check this is correct by doing pythagoras' theorem.

[tex]Cos\frac{Adjacent}{Hypotenuse} \\Cos45\frac{9}{y} \\y = \frac{9}{cos45} \\y = 9\sqrt{2}[/tex]

[tex]\sqrt{9^{2}+9^{2} } = 9\sqrt{2}[/tex]

Answer:   [tex]\bold{\dfrac{41}{80}}[/tex]

Step-by-step explanation:

[tex]\dfrac{puppies}{total}+\dfrac{kittens}{total}+\dfrac{unicorns}{total}\\\\\\=\dfrac{15}{80}+\dfrac{16}{80}+\dfrac{10}{80}\\\\\\=\large\boxed{\dfrac{41}{80}}[/tex]

Answer:

False. He is not correct.

Step-by-step explanation:

To find the percent increase subtract  the old time from the new time then divide that number by the old time. 25-20=5. 5/20=.25. There was a 25% increase in time worked. Evan worked 125% of the original time but only worked 25% more time.

y^2-14y+49

(y-7)(y-7)

Answer:

y^2-14y+49 I hope i can help you out

45.00x +17.99 = 422.99 (Setup Equation)

45.00x = 405 (Subtract 17.99 from both sides)

x = 9 (Divide both sides by 45.00)

Answer:

9

Step-by-step explanation:

First, you write out the equation. We don't know how many tickets Eva bought, so it can be represented by x. Each ticket costs 45 dollars. The amount of tickets times 45 plus the fee will equal 422.99, so the equation will look like this:

45x + 17.99 = 422.99

Subtract 17.99 from both sides:

45x = 405

Divide 45 on both sides:

x = 9

Eva bought 9 tickets

hope this helps :)

Answer:

[tex](-3, \frac{9}{5})[/tex]

Step-by-step explanation:

We have the equation [tex]2x + 5y-3 = 0[/tex].

The ordered pairs of this equation have the form [tex](x_0, y_0)[/tex]

Where x is the independent variable and y is the dependent variabe.

That is, the points belonging to the line [tex]2x + 5y-3 = 0[/tex] have the form [tex](x_0, f (x_0))[/tex]

For [tex]y = f(x)[/tex].

So, we need to find [tex]f(x_0)[/tex] for x_0 = -3.

Then we substitute x = -3 into the equation and clear the value of y.

[tex]2(-3) + 5y -3 = 0[/tex]

[tex]-6 + 5y = 3\\\\5y = 9\\\\y = \frac{9}{5}[/tex].

Then the ordered pair is:

[tex](-3, \frac{9}{5})[/tex]

Answer: -13

j(5)=11

k(5)=24

11-24=-13

A)

recall that there are 180° in π radians.

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ s=10\\ r=5 \end{cases}\implies 10=5\theta \implies \cfrac{10}{5}=\theta \implies \stackrel{\textit{radians}}{2=\theta } \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ x&2 \end{array}\implies \cfrac{180}{x}=\cfrac{\pi }{2}\implies 360=x\pi \\\\\\ \cfrac{360}{\pi }=x\implies 114.59\approx x[/tex]

B)

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ r=5\\ \theta =2 \end{cases}\implies A=\cfrac{(2)(5)^2}{2}\implies A=25[/tex]

Answer:

AC

Step-by-step explanation:

A chord is a line segment connecting two points on a circle.

Basically, it means that a chord is a line that has both endpoints on the edge of the circle.

Answer:

The dimensions ⇒ 3 × 4

Step-by-step explanation:

* Any matrix has two dimensions

- Raw and column

- The dimensions very important in the operations on matrices

- We called the number of raw m and the number of column n

- We must write the number of raw before the number of column

- m × n is the dimensions of the matrix

* Example : If the dimension of a matrix is 2 × 3, that

  means the matrix has 2 raw and 3 column

* Now lets look to our problem

∵  It has 3 raw and 4 column

∴ Its dimensions is 3 × 4

Answer:

Size of matrix = 3 × 4

Step-by-step explanation:

We are given the following matrix and we are to determine its dimensions:

[tex] \left [ \begin {array}{cccc} 1&-3&8&4\\7&5&3&0\\9&6&-2&-1 \end { array } \right ] [/tex]

We know that the dimension of a matrix is written in the form:

rows × columns

Here we have 3 rows and 4 columns. Therefore, the size of this matrix is 3 × 4.

ANSWER

8π ft

EXPLANATION

The circumference of a circle is calculated using the formula C=πd.

Where d=8 is the diameter of the circle.

We substitute d=8 into the formula to obtain,

C=8π ft.

Because we are looking for the exact circumference, we leave the answer in terms of π.

Answer:

The correct answer is,

circumference = 8π feet

Step-by-step explanation:

Formula:-

Circumference of a circle = 2πr

Or circumference = πd

Where 'r' is the radius of circle and 'd' is the diameter of circle

It is given that, diameter of circle is 8 feet

To find the circumference

Here d= 8 feet

Circumference = πd = π * 8 = 8π feet

Answer:

50%

Step-by-step explanation:

you need to figure out what percent ok AK is BG

so we know that AK is 20 units long 10-(-10)=20

and BG is 10 units long 8-(-2)=10

so then you can solve with a proportion

10/20 = x/100

cross multiply that out

20x=1000

divide by 20

x= 50

50%

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation: