A computer and printer cost a total of $954. The cost of the computer is two times the cost of the printer. Find the cost of each item.

The equation of the circle graphed above is equal to (x - 1)² + (y - 6)² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

By critically observing the graph of this circle, we have the following parameters:

Radius, r = 3 units.

Center, (h, k) = (1, 6).

Substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 1)² + (y - 6)² = 3²

(x - 1)² + (y - 6)² = 9.

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a) The equation of  perpendicular line is y=2x+1

b) The equation of  parallel  line is y = -2x+6

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

a) An equation perpendicular to y= (-1/2)x+4 through the point (-2, -3):

m= -1/2

Slope of perpendicular line is -1/m  = -1/( -1/2) = 2

(x,y) = (-2, -3)

Slope intercept form:

y=mx+b

Substitute x,y and m values to find b

-3= 2(-2) + b

=> -3 = -4 + b

=> b= -3+4 = 1

So the equation of  perpendicular line is y=2x+1

b)  An equation through the point  (1,4)  parallel to  y = -2x + 1

Parallel lines will have same slope , m= -2

(x,y) =  (1,4)

Slope intercept form:

y=mx+b

Substitute x,y and m values to find b

4=-2(1)+b

=> 4 = -2 + b

=> b=4+2 = 6

So the equation of  parallel  line is y = -2x+6

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When the water cooler is completely full, there are approximately 143.52 gallons of water in it.

To calculate the number of gallons of water in the water cooler when it is completely full, we can use the formula for the volume of a cylinder, which is:

Volume = π * (radius)^2 * height

where radius is half of the diameter, and π is the constant pi.

In this case, the diameter of the water cooler is 3.5 feet, so the radius is 1.75 feet. The height of the water cooler is 2 feet. Plugging these values into the formula, we get:

Volume = 3.14 * (1.75)^2 * 2 = 19.18 cubic feet

To convert this volume to gallons, we can multiply it by the conversion factor of 7.48 gallons per cubic foot:

Volume in gallons = 19.18 * 7.48 = 143.52 gallons

In summary, to calculate the number of gallons of water in a cylindrical water cooler, we can use the formula for the volume of a cylinder and then convert the resulting volume from cubic feet to gallons using a conversion factor.

In this case, we needed to use the diameter and height of the water cooler, along with the constant pi and the conversion factor of gallons per cubic foot, to calculate the number of gallons of water in the water cooler when it is completely full.

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The value of x is 80 degrees.

The correct answer is an option (A)

Consider the following figure.

Let us assume that the upper triangle be ABC and the lower triangle be NMC.

We can observe that both the triangles are isosceles triangles, because in both the triangles two sides are congruent.

Consider triangle ABC.

As the triangle is isosceles triangle, from the definition of  isosceles triangle ∠A = ∠B

So, ∠A = 65°

We know that the sum of all the angles of triangle is 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠C = 180° - (65° + 65°)

⇒ ∠C = 180° - 130°

⇒ ∠C = 50°

We can observe that ∠ACB and ∠MCN are opposite angles.

So,  ∠MCN = 50°

Also, triangle MNC is also an isosceles triangle.

so, ∠C = ∠N

⇒∠N = 50°

We know that the sum of all the angles of triangle is 180°

⇒ ∠M + ∠N + ∠C = 180°

⇒ ∠M = 180° - (50° + 50°)

⇒ ∠M = 180° - 100°

⇒ ∠M = 80°

Therefore,  x = 80°

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[tex] \: [/tex]

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[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

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Answer:

[tex] \sf \: n = - 3[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of n.

The equation is,

→ 2 - 2n = 3n + 17

Then the value of n will be,

→ 2 - 2n = 3n + 17

→ 2 - 17 = 3n + 2n

→ -15 = 5n

→ 5n = -15

→ n = -15 ÷ 5

→ [ n = -3 ]

Hence, the value of n is -3.

Answer:1024 grid squares

Step-by-step explanation:

Let's call the side length of the original piece of graph paper "x".

Since, side length of the cut out square is then (x-2) because the cut out square has to have an integer number of grid squares, and each side of the square would take up 2 grid squares on the graph paper.

The number of grid squares in the cut out square is then (x-2)^2.

The number of grid squares left on the graph paper is 124, so we have:

x^2 - (x-2)^2 = 124

Expanding the right side:

x^2 - x^2 + 4x - 4 = 124

Simplifying:

4x = 128

therefore:

x = 32

therefore original graph paper contains 32 grids i.e 32^2 = 1024

Answer:

  any of {128, 133, 140, 160, 224, 320, 380, 700, 1024}

  1024 if the original grid was square

Step-by-step explanation:

You want to know how many grid squares are on a piece of graph paper if a square number of grid squares can be cut from it to leave 124 grid squares.

If the graph is square to begin with, a square of x² can be removed from its size (x+a)² to leave 124 squares. That is ...

  (x +a)² -x² = 124

  (a)(2x+a) = 124

The factor pairs of 124 are ...

  124 = 1·124 = 2·62 = 4·31

Of these, only 2 and 62 differ by an even number, so we have a=2 and x=30.

The graph paper could be 32 units square originally, having 1024 grid squares.

There is nothing in the problem statement that requires the original graph paper be square. If it is not necessarily square, there are 13 possible shapes it could be. Those have 9 different possibilities for numbers of grid squares.

The graph paper could have originally had this number of grid squares:

__

Additional comment

You may notice that removing a 24×24 square from a graph that is 25×28 leaves no border on one side.

These values were found using a search script.

<95141404393>

Answer:

Tony and his cousin will each have 42 points in 3 turns.

Step-by-step explanation:

10 x 3 = 30

30 + 12 = 42

14 x 3 = 42

The factors of the cubic function f(x) = 64x³ + 27 are (4x + 3) and (16x² − 12x + 9). The correct answer would be options (A), and (D).

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original.

The cubic function is given in the question, as follows:

f(x) = 64x³ + 27

The above expression can be rewritten as:

f(x) = (4x)³ + (3)³

Compare the sum of cubic formula a³ + b³ = (a + b)(a² - ab + b²) and we get

f(x) = (4x + 3)(16x² − 12x + 9)

Thus, the factors of the cubic function are (4x + 3) and (16x² − 12x + 9).

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The function for the Pakistani Rupee (y) in terms of UAE Dirhams (x) can be represented as, y = 71.59 x.

A function is defined as a relation from a set A to a set B for which an element in set A maps to one and only one image in set B.

Usually the set A consists of the independent variable and set B consists of dependent variable.

We have to find a function relating the conversion of Pakistani rupees and UAE dirhams.

Let y denotes Pakistani Rupees and x denotes the UAE dirhams.

We know that,

1 UAE dirham = 71.59 Pakistani Rupees

So,

2 dirhams = 2 × 71.59 = 143.18 rupees

In this way,

x dirhams = 71.59 x rupees

So, we can write this as,

y = 71.59 x

Hence the required function is y = 71.59 x.

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To solve the equation cos²x + sin x = 1, we can use the trigonometric identity cos²x = 1 - sin²x. By substituting this identity into the equation, we get:

1 - sin²x + sin x = 1

Combining like terms, we get:

1 - sin²x = 0

Solving for sin x, we get:

sin x = 1

However, the sine function has a range of [-1, 1], so the only solution in the interval [0, 2π] is sin x = 1, which corresponds to x = π/2. So the solution to the equation cos²x + sin x = 1 in the interval [0, 2π] is x = π/2.

Answer: 37 points

Step-by-step explanation:

0 |-1| , 1.3 , 2, |2.7|

Step-by-step explanation:

it's right because |-1| is an absolute value and the absolute value is 1

Answer:

0,  |- 1| , 1.3,  2,  |2.7|

Step-by-step explanation:

The absolute value of any number, x,  denoted by |x| is the positive of that number

So | 2.7 | = 2.7

| - 1 | =  1

Therefore the order of the absolute values is
0,  1, 1.3, 2, 2.7 which is the same as 0,  |- 1| , 1.3,  2,  |2.7|

Answer:

-4

Step-by-step explanation:

Answer:

f(0) = 4

Step-by-step explanation:

[tex]f(x) = {2x}^{2} + 4[/tex]

- When x = 0, then f(x) = f(0)

[tex]f(0) = 2(0) {}^{2} + 4 \\ f(0) = 4[/tex]

Answer:5/8

Step-by-step explanation: you put the numbers in a fraction the smallest goes on top and the more enormous number at the bottom you simply by finding the most significant standard number between the 2 numbers which is in this case 6 divide it by that and that is how you get your answer

The function that best models the number of game systems sold  is

y = 30.5(0.7)ˣ

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Consider the equation :

y = 30.5(0.7)ˣ

Plug in x=0,

y= 30.5(0.7)⁰ = 30.5 *1 = 30.5

The point is (0,30.5)

Similarly, when we plug in x=1 and x=2, we get y=21.35 and y=14.95 respectively

The other 2 points in (x, y) form are (1,21.35) and (2, 14.95)

These points are matching with the points on the graph

So, the function that best models the number of game systems sold  is

y = 30.5(0.7)ˣ

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Un-simplified rate of dollars-gallons = 22.5/9  $ and and gallons to dollars 9/22.5 $ .  and simplified rate of dollars-gallons = 22.5/9  $ = 2.5 and and gallons to dollars 9/22.5  = 0.4 .

Here first we have to calculate the rate of gallons of gas as per gallons so for that we will find the rate of 1 gallons for that we will divide the  22.4$ to 9 gallons so ans is 22.5$/9 is the rate for 1 gallons

and 2nd we have to calculate the amount of gas as per $ like we have to calculate the the amount if we spend 1 $  so for that we will divide 9 gallons / 22.5$ = 9/22.5

And here in 1st part we  are not calculate the ans in decimal as we have to calculate this on un-simplified  ans .

and in 2nd part we calculate it .

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Some of the similarities between sales tax and hotel tax include the following:

B) Both must be paid in advance when you make a hotel reservation.

C) Both are based on a percentage of the original cost.

Taxation can be defined as the involuntary fees that are levied on individuals or business firms by the government of a particular country, so as to generate revenues that can be used to fund public projects, institutions and activities.

The types of tax.

In Economics, there are different types of tax that are levied on individuals or business firms by the government and these include the following:

Hotel tax

Sales tax

Property tax

Income tax

we can reasonably infer and logically deduce that both sales tax and hotel tax must be paid in advance when making a hotel reservation in the United States of America.

Hence, Some of the similarities between sales tax and hotel tax include the following:

B) Both must be paid in advance when you make a hotel reservation.

C) Both are based on a percentage of the original cost.

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The complete question is given below:

What are some similarities between sales tax and hotel tax? Select all that apply. Multiple select question. cross out A) Both are an additional amount one must pay. cross out B) Both must be paid in advance when you make a hotel reservation. cross out C) Both are based on a percentage of the original cost. cross out D) Both the sales tax and the hotel tax are equal when you stay in a hotel. cross out E) Both represent a guest fee that hotels charge their customers.

The weighted mean cost of a haircut for Malachi is $15.67, divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.

We must compute the total cost of all haircuts and divide it by the total number of haircuts in order to determine the weighted mean price of a haircut for Malachi. The expense of each haircut must be weighed according to the frequency with which it occurred, though, because they varied in price.

To begin, let's figure out how much each haircut will cost overall:

2 haircuts at $12.00 each = $24.00

3 haircuts at $15.00 each = $45.00

1 haircut at $25.00 = $25.00

Total cost = $24.00 + $45.00 + $25.00 = $94.00

Next, We must determine the total number of cuts:

2 haircuts + 3 haircuts + 1 haircut = 6 haircuts

Finally, The weighted mean cost of a haircut can be determined by dividing the total cost by the total number of haircuts:

The weighted mean cost of a haircut = Total cost / Total number of haircuts

= $94.00 / 6 haircuts

= $15.67 per haircut (rounded to the nearest cent)

Therefore, Malachi's weighted mean haircut expense is $ 15.67 , divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.

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Sullivan received half as many candy as Carter did, or half as many candies as Sullivan received.

" Amount is defined as the representation of total quantity of given object."

According to the question,

Number of candies Sullivan got = s

Number of candies Carter got = 2s

Compare the given amount of data we get,

Number of candies Carter got = 2(Number of candies Sullivan got )

This shows Carter got twice number of candies comparison to Sullivan.

or

Number of candies Sullivan got = 1/2 (Number of candies Carter got)

Sullivan got half number of candies compare to Carter.

Hence, we conclude Carter got twice number of candies in comparison to Sullivan or Sullivan got half number of candies compare to Carter.

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Why is it crucial to ensure that each sample has at least 10 successes and failures when building a confidence interval for the difference between two population proportions. This will allow us to select a sample distribution for p1-p2 that is roughly normal.

A distributor is a business that takes part in the value chain's distribution step. Making a good or service available to the consumer or business user who wants it is the process of distribution. This might be done by the producer or service provider directly or through indirect channels like distributors or intermediaries. Distribution is one of the four elements of the marketing mix, along with the other three being the product, pricing, and promotion. The broad strategic goal and objective of a corporation should guide distribution decisions. The main task of strategic planning is to develop a thorough distribution plan. At the strategic level, there are three basic distribution tactics: mass, selective, and exclusive distribution.

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The mentioned characteristics of quadrilateral are the properties of the Rhombus. So option C is correct.

Given that,

A quadrilateral  TUVW,

UV || WT,  

TU || VW

TV = UW  (Diagonals )

TV ⊥ UW (Diagonals are perpendicular)

Hence, the given characteristics are of the rhombus.

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Answer:

3/8

Step-by-step explanation:

1. If there are three parts green and 5 parts yellow, you can add them to find the total parts

2. 5+3 is 8

3. Then to find the green, which is three, we can divide it

4. 3 green parts/ total which is 8

5. 3/8

Step-by-step explanation:

the answer for -1/4(-8x+12y)

2x-3y

Answer:

2x-3y

Step-by-step explanation:

For this equation we are using distributive property

-1/4(-8x)           -1/4(12y)

     ↓                      ↓

    2x                   -3y

So, 2x-3y is the answer.

The difference between the investment below and one with the same principal at the same rate compounded yearly is $18123.29.

The Payback Period is the most straightforward metric to use when contrasting investment options. Simply defined, this is the minimal amount required for you to recoup your initial investment.

compound interest, which is referred to as

[tex]A = P(1+r/n)^n×t[/tex]

Where

A = amount at the end of t years

r = interest rate.

n = periodic interval

P = principal amount deposited

Considering  investment compounded annually

P = 7000

r = 3% = 3/100 = 0.03

n = 1

t = 17 years

[tex]A = 7000(1 + 0.03/1)^1× 12A = 7000(1.03)^12[/tex]

A = $9980.32

For the second investment,

n = 6

[tex]A = 7000(1 + 0.08/6)^6 × 12A = 7000(1 + 0.0133)^72A = 7000(1.0133)^72A = $18123.29[/tex]

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The measure of m∠A is 27.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

m∠A = (2x + 5) and m∠B = (4x + 19)

∠A and ∠ B are complementary angles.

So,

Solve for x.

(2x + 5) + (4x + 19) = 90

2x + 5 + 4x + 19 = 90

6x + 24 = 90

6x = 90 - 24

6x = 66

x = 11

Now,

m∠A.

= (2x + 5)

= 2 x 11 + 5

= 22 + 5

= 27

Thus,

m∠A = 27

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Answer:

Below

Step-by-step explanation:

Second choice      at x = 0     it is = 6

  and as the exponent (x) gets more negative it gets larger meaning it has a coefficient of < 1     ( it is 3/4)

The graph that best models the situation of the home value increasing every year is Graph A

To find the graph, use the percentage increase to find the value of the house in two different time periods and then check which graph coincides with this prediction.

After 5 years, the value of the house should be:

= 200, 000 x ( 1 + 6 % ) ⁵

= $ 267, 645

After 10 years :

= 200, 000 x ( 1 + 6 % ) ¹⁰

= $ 358, 170

The best graph for the situation is therefore Graph A which starts from $ 200, 000 and passes through the above points.

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Answer:

6.9x10^20

Step-by-step explanation:

688588478685758486759+2345678909876545355=

6.90934158E20