Write the standard equation of the circle given a center (-14,7) and a radius of 2
Answers-
A. (x-14)^2 + (y+7)^2 =1
B. (x+14)^2 + (y-7)^2 =8
C. (x-14)^2 + (y+7)^2 =4
D. (x+14)^2 + (y-7)^2 =4

An ordered pair is a refers to the of the x coordinate and the y coordinate of a point. They have two values which is written in a specific order and is quoted by parentheses.

It is used when we need to solve some problems and it also has utilization in the field of statistics.

Ordered pair are also used in coordinate geometry, they are used to portray geometric objects and figures in open space which helps to improve visual perception.

Ordered pairs are used to represent the center, vertices, and length of the sides of a square, circle, rectangle, or polygon with coordinates.

Example:  ( 2 , 4).

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Answer:

x = 5, -5, 3, -3

Step-by-step explanation:

First, substitute u = x^2 into the equation, and we have

u^2 - 34u + 225 = 0

u = x^2

Factor u^2 −34u +225 using the AC method, and we get

( u - 25) ( u - 9) = 0

We know If any individual factor on the left side of the equation is equal to

0, the entire expression will be equal to 0, so

u - 25 = 0

u - 9 = 0

Next, we set u - 25 equal to 0  and solve for u, and we get

u = 25

Then set u - 9 equal to 0 and solve for u, and we get

u = 9

The final solution is all the values that make (u−25)(u−9) = 0  true.

u =25,9

Substitute the real value of u=x^2 back into the solved equation.

x^2 = 25

(x^2)^1 = 9

x^2 = 25

x = 5, -5

Now we solve the second equation

(x^2)^1 = 9

x = 3, -3

So, the answers are: 5, -5, 3, -3

A number line marked with zero, one twelfth, two twelfths, three twelfths, four twelfths, five twelfths, six twelfths, seven twelfths, eight twelfths, ten twelfths, eleven twelfths, and one. From the zero point to the three twelfths mark, a red line is painted.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.

Here,

Multiply one times three, and four by three.

It will equal to three out of twelve or 3/12.

=1/4

A number line marked with zero, one twelfth, two twelfths, three twelfths, four twelfths, five twelfths, six twelfths, seven twelfths, eight twelfths, ten twelfths, eleven twelfths, and one. From the zero point to the three twelfths mark, a red line is painted.

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If he decided that on this way back , he will ride on one of these services then in total 9 ways he can go to the town center and back.

In the given question, there are 3 feeder bus services plying to and from the nearby town center.

Ahmed can ride on one of these services or walk to the town center.

However, he decides that on this way back , he will ride on one of these services.

We have to find in how many ways he can go to the town center and back.

According to the given conditions, we know that there are 3 feeder and we can use these feeder in 3 ways.

So we can write it as;

Number of ways he can go to the town center and back = 3 × 3

Number of ways he can go to the town center and back = 9

Hence, if he decided that on this way back , he will ride on one of these services then in total 9 ways he can go to the town center and back.

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Carly reads at a faster rate than Monica. The number of pages in Monica's novel is greater than the number of pages in Carly's novel.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Carly Equation:

y= - 35x + 220

and, Monica equation:

slope = (90- 240)/ 5-0

slope = -150/5

slope= -30

and, the equation is

y- 240 = -30 x

y= -30x + 240

From comparing both cases Carly start with 220 pages and Monica with 240 pages and Carly will complete in 7 hours whereas Monica will complete in 8 hours.

Hence, Carly reads at a faster rate than Monica.

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The following results for the algebraic equation according to algebra properties are listed below:

In this problem we find an algebraic equation that must be expanded and simplified by means of algebra properties. Now we proceed to present the complete procedure. First, write the complete expression:

(x² + y²)² + 2 · x² · y² - y⁴ = x² · (x² + 4 · y²)

Second, expand the perfect square binomial:

x⁴ + 2 · x² · y² + y⁴ + 2 · x² · y² - y⁴ = x² · (x² + 4 · y²)

Third, use distributive property and add similar terms:

x⁴ + 4 · x² · y² = x² · (x² + 4 · y²)

Fourth, use distributive property once again:

x² · (x² + 4 · y²) = x² · (x² + 4 · y²)

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When the length of one side and the angle of one corner of a right-angled triangle are provided as 16 and 69°, respectively, trigonometric ratios are used to compute the value of b as 35.38.

The values of all trigonometric functions depending on the side ratio of a right-angled triangle are known as trigonometric ratios. The ratios of a right-angled triangle's sides to any acute angle are the angle's trigonometric ratios.

given

one side = 16

angle = 69°

one angle = 90° as right angle triangle

another angle = 69°+ 90° + x = 180°

= 155° + x = 180°

x = 25°

a / sin69° = 16 / sin25°

a = 35. 38

When the length of one side and the angle of one corner of a right-angled triangle are provided as 16 and 69°, respectively, trigonometric ratios are used to compute the value of b as 35.38.

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Total number of prime numbers which are twin are infinite and its general form is given ( 6n - 1 , 6n + 1 ) apart from ( 3, 5 ) where 'n' represents the natural number.

As given in the question,

Prime numbers are those numbers which have only two factors one and the number itself.

Prime numbers which are twins are defined as when the difference between two prime number is equal to 2.

Example of twin prime numbers are as follow :

( 3, 5 ) , ( 5, 7 ) , ( 11 , 13 ) , ( 17 , 19 ) , ( 29 , 31 ), ( 41, 43 ) ,...........,(6n - 1 , 6n + 1 )

where 'n' represents the natural number.

5 is the only prime number which exist in two pairs of twin prime numbers.

Apart from ( 3,5 ) all the twin prime numbers divided by 12.

Therefore, there are infinite prime numbers which are representing as a twin prime numbers.

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Answer:12/9

Step-by-step explanation:

subtract 9 from 21 and 21 will give you 12 silver coins which will be 12 silver coins to 9 gold coins

The bakery used 76.55 % of the flour by the end of the day.

How to calculate Percentage?

The percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

To find the percent of flour used by the bakery, we need to divide the amount of flour used by the total amount of flour and then multiply by 100 to convert the decimal to a percentage.

We can use the formula:

percent used = (the amount used / total amount) x 100

In this case:

percent used = (111 / 145) x 100 = 76.55 %

Hence, The bakery used 76.55 % of the flour by the end of the day.

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The expression that that represents the cost of the dinner plus tip is d(23/100+1)

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3

The cost of the dinner = d

the cost of the tip is 23% of the cost of the dinner = 23/100 × d = 23d/100

Therefore the total cost of the dinner and the tip = 23d/100 + d

by bringing d out

The total cost of dinner and tip = d (23/100+1)

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Answer:

2+2%2%5+51%895%+8+81%9+61%+5%+8+%15+%

Answer:

(- 8, - 6 )

Step-by-step explanation:

y = 2x + 10 → (1)

y = x + 2 → (2)

substitute y = 2x + 10 into (2)

2x + 10 = x + 2 ( subtract x from both sides )

x + 10 = 2 ( subtract 10 from both sides )

x = - 8

substitute x = - 8 into either of the 2 equations and evaluate for y

substituting into (2)

y = - 8 + 2 = - 6

solution is (- 8, - 6 )

The equation of the line in standard form is 2x + 4y = 18.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

The equation of a line in standard form is,

Ax + By = C, where A, B and C are integers.

The equation given is,

(2/3)x + (4/3)y = 6

We need the coefficients to be integers.

Multiply throughout the equation by 3.

2x + 4y = 18, which is the standard form.

Hence 2x + 4y = 18 is the standard form.

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A monomial is an algebraic expression that consists of only one term. Examples of monomials include 4x², a + 6, and a + b + c + d.

In the given example, (a) 4x² is a monomial because it consists of only one term, 4x². (b) a + 6 is also a monomial because it consists of only one term, a + 6. (c) a + 6 + c is not a monomial because it consists of more than one term, namely a + 6 and c. (d) a + b + c + d is also not a monomial because it consists of more than one term, namely a, b, c, and d.

To calculate the value of a monomial, we must first determine its degree. The degree of a monomial is the sum of the exponents of its variables. For example, the degree of 4x² is 2 because it consists of only one variable, x, with an exponent of 2.

Once the degree of a monomial is determined, its value can be calculated by substituting the values of its variables. For example, if x = 3, then 4x² = 4(3)² = 36.

In summary, a monomial is an algebraic expression that consists of only one term. Its degree is the sum of the exponents of its variables. To calculate its value, substitute the values of its variables into the expression.

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To change the base of an exponential function, we can use the formula:

log_b(a) = log_c(a) / log_c(b).

To change the base of an exponential function, you can use the property that logarithms with different bases are related by the following equation:

log_b(a) = log_e(a) / log_e(b)

Where log_b(a) is the logarithm of a to the base b and log_c(a) is the logarithm of a to the base e.

For example: To change log_3(7) to log_e(x)/log_e(y), we can use the property that logarithms with different bases are related by the following equation:

logb(a) = logc(a) / logc(b)

So log_3(7) = log_e(7) / log_e(3)

To find x and y we can use the logarithm properties and the definition of logarithm:

log_e(x) = log_e(7)

x = 7

log_e(y) = log_e(3)

y = 3

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The perimeter of a soccer field is 304 meters. The field is 96 meters long. So, its wide becomes: 56 m

The length of a two-dimensional shape's perimeter is referred to as its perimeter. The total length of all the sides of the thing is also a definition for it. The perimeter of the form is equal to the algebraic sum of each side's length. For the various geometric forms, there are formulae accessible. The radius of a shape's edge is known as the perimeter. Discover how to calculate a shape's perimeter by multiplying its side lengths.

Given that,

The perimeter of a soccer field is 304 m

length of the field is 96 m

wide = ?

As we know,

perimeter = 2 (length + width)

or, 304 = 2 (96 + width)

or, 304 = 192 + 2 width

or, width = 112 /2

or, width = 56 m

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Answer: a₁ = 5, a₂ = 6, a₃ = 13 are the only ones I could figure out, I apologize.

Step-by-step explanation: I hope this helps a little!

It is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm because the sum of two sides are greater than third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 25 and 5

25 + 5 > 24

30 > 24

Now we add 25 and 24

25 + 24 > 5

49 > 5

Now we add 5 and 24

5 + 24 > 25

29 > 25

It is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm because the sum of two sides are greater than third sides.

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AA: y=40x+2

BB: y=34x+3

We know that the bank charges $2.25 per month plus $0.10 per bill paid using the service. Let x be the number of bills paid using the service.

The total cost of the service is:

Cost = 2.25 + 0.10x

We also know that the charges are always between $3.50 and $5.00. So we can write this as an inequality:

3.50 <= Cost <= 5.00

To find the number of bills, we can substitute the expression for cost into the inequality:

3.50 <= 2.25 + 0.10x <= 5.00

We can solve this inequality by isolating x on one side:

0.10x >= 1.25

x >= 12.5

So the number of bills paid using the service is greater than or equal to 12.5.

She could pay exactly 12 bills, 13 bills, 14 bills and so on.

The solution is x >= 12.5

Let's call the number of bills paid per month as "x"

We know that the total cost is:

$2.25 (fixed monthly fee) + $0.10x (cost per bill paid)

We also know that the total cost is between $3.50 and $5.00

Therefore, $3.50 <= $2.25 + $0.10x <= $5.00

To solve for x, we can first isolate x by subtracting $2.25 from both sides of the inequality:

$1.25 <= $0.10x <= $2.50

Now we can divide both sides of the inequality by $0.10 to get:

12.5 <= x <= 25

It means that the number of bills paid per month using the service is between 12 and 25 bills, Debbie can pay at least 12 bills and at most 25 bills.

Answer:

1/2

Step-by-step explanation:

If you want more equivalent fractions, then you can multiply it by different numbers. The same number should be multiplied in numerator as well as denominator. You can divide it with the smallest number possible to get the simplest form

No, Root 3x 5 is not a polynomial, because it does not meet the definition of a polynomial.

A polynomial is a mathematical expression consisting of variables and coefficients, which only uses the operations of addition, subtraction, multiplication, and non-negative integer exponents. In other words, it must be an expression that can be written in the form ax^n + bx^(n-1) + cx^(n-2) + dx^(n-3) + ... + z, where n is an integer, and a, b, c, d, ... and z are real numbers.

Root 3x 5 does not fit this definition, because it contains a square root (√) which is not one of the operations listed. Additionally, it does not fit the form of a polynomial, as it does not contain any coefficients or exponents. The formula for root 3x 5 is simply √3x 5, and the calculation is the square root of 3x 5, or √15, which is equal to 3.75.

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Answer:

(-2, 1)

Step-by-step explanation:

x = -2

-2(-2) + 2y = 6

4 + 2y = 6

2y = 2

y = 1

Answer:

5

Step-by-step explanation:

You should do cross multiplication.

Multiply 3 by 10 and 6 by 'h'

So 3×10=6h

6h=30

h=30÷6=5

The graph with x 3 is called a cubic graph.

A graph is a visual representation of data, usually plotted on a two-dimensional plane. When graphing a function, the x-axis is used to represent the independent variable and the y-axis is used to represent the dependent variable. A graph with x 3 is a graph that shows the relationship between the independent variable, x, and the dependent variable, x3. This type of graph is called a cubic graph, as the graph follows a cubic equation.

The graph with x 3 is called a cubic graph.

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Answer:

Y=-3x+2

Step-by-step explanation:

The basic formula is y=mx+b where m is the slope and b is the y intercept

If you look y is at positive 2. Then you can count from the y intercept to the point, it's down 3 over 1 so it would be -3/1 which is just -3

Answer:

Mean - 84

Median - 77

Mode - 84, 96, 72, 77, 91 (Or no mode)

Range - 12

Step-by-step explanation:

Mean;

Step 1 - Add all the numbers up:

84 + 96 + 72 + 77 + 91

= 420

Step 2 - divide that by 5 (because there are 5 numbers):

420 ÷ 5

= 84

Median;

Step 1 - Put the numbers in order:
84, 72, 77, 91, 96

Step 2 - Find the middle number

84, 72, 77, 91, 96

Mode;

There aren't any repeated numbers so you can put all the numbers or no mode

84, 96, 72, 77, 91

Range;

Step 1 - Subtract the smallest number from the biggest number:

96 - 84

= 12

You're welcome :)

The volume of the storage compartment is 1246 cube ft.

In the given question, we have to find the volume of the storage compartment.

The diagram of the question is given below.

If we see the diagram it forms two recatangle with the lengths given below.

As we know that the volume of the cuboid is

V = LBH

where, L = length, B = breadth, H = Height

Now finding the volume of the cuboid A.

So V(A) = 10*8*15

V(A) = 1200 cube ft

Now finding the volume of the cuboid B.

So V(B) = 2*8*3

V(B) = 48 cube ft

Now the volume of the storage compartment is the sum of the volume of cuboid A and volume of the cuboid B, then we subtract 2 ft because we count the 2 ft of height two times.

The volume of storage compartment = volume of the cuboid A + volume of the cuboid B - 2 ft

The volume of storage compartment = 1200 + 48 - 2

The volume of storage compartment = 1248 - 2

The volume of storage compartment = 1246 cube ft

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