find the logarithmic function [tex]f(x)=\log _(_a_)(x-h)[/tex] that describes each graph.

Answer:

A. (x - 3)² + (y + 2)² = 16

Step-by-step explanation:

The formula for a circle plotted on the Cartesian coordinate system is:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

where [tex](a,b)[/tex] is the center of the circle, and [tex]r[/tex] is the length of the circle's radius.

Since the center of the circle in this problem is (3, -2), we know that the left side of the equation should be:

[tex](x - 3)^2 + (y - (-2))^2[/tex]

which can be simplified to:

[tex](x - 3)^2 + (y + 2)^2[/tex]

The radius of the circle is given as 4, so we know that the right side of the equation is:

[tex]4^2[/tex], which is the same as [tex]16[/tex].

Finally, to answer this question, we can put the two sides of the equation together to get:

[tex](x - 3)^2 + (y + 2)^2 = 16[/tex]

To write 1 more than a number, we use the mathematical operation of addition and the notation 1 + Number = N+1.

To write 1 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 1 and we are asked to find the number that is 1 more than it. To do this, we can use the mathematical notation: 1 + Number = N+1.

This notation means that we are adding 1 to a number, which results in N+1. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+1.

Another way to write 1 more than a number is to use the phrase "1 plus a number". This phrase indicates that we are adding 1 to a number to get N+1.

Therefore, In short, to write 1 more than a number, we use the mathematical operation of addition and the notation 1 + Number = N+1. This means that we are adding 1 to a number, resulting in N+1. It can also be written as "1 plus N", indicating the same operation.

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Answer:

The closest estimate to the total cost of Mr. Johnson's turkey (before taxes) is $54.67.

Step-by-step explanation:

You can calculate this by multiplying the weight of the turkey (18 3/4 pounds) by the price per pound ($2.95).

(18 3/4) * ($2.95) = 54.67

Answer:

[tex]-x^{2}[/tex] -4x + 21

Step-by-step explanation:

-(x-3)(x+7)

(-x + 3) ( x + 7)

[tex]-x^{2}[/tex] - 7x + 3x + 21

[tex]-x^{2}[/tex] -4x + 21

Answer:

255 is the highest decimal value a byte can represent.

Step-by-step explanation:

The value of (10x - 2y) + (-3y) - (2x-2y) is 8x-3y (option A)

In math, to subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less. The minuend, subtrahend, and difference are parts of a subtraction problem.

For example, if 5 mangoes were taken from a basket filled with 20 mangoes, the number of mangoes left in the basket is calculated by subtracting 5 from 20 i.e 20-5 = 15 mangoes.

(10x-2y) + (- 3y) - (2x-2y)

10x +2y -3y-2x +2y

collect like terms

10x -2x+2y-3y-2y

8x-3y

= 8x - 3y

Therefore the value of Subtracting (2x - 2y) from the sum of (10x - 2y) and (-3y) is 8x+3y

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A formed angle has been created between the two sides. Two of the sides of XYZ are the same length if XY = YZ. It will be an isosceles triangle as a consequence.

An isosceles triangle in geometry is a triangle with two equal-length sides. There are two ways to describe it: either as having precisely two sides of equal length or at least two sides of equal length, with the equilateral triangle being an exception to the second definition. The two sides have come to an agreement.The base of the triangle is the third side of an isosceles triangle, which is not equal to the other two sides.

The two angles are exactly aligned with the equal sides.

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Fraction value for 1/4 plus 1/4 is 1/2.

The same denominator and different numerators are considered equivalent fractions in mathematics. For instance, since 2/4 and 3/6 both equal 1, they can both be considered similar fractions. A fraction is a portion of a whole. Equivalent fractions depict identical sections of the total.

It is possible to determine the equivalent fraction of any fraction by multiplying the numerator and denominator by the same integer. Equivalent fractions are those that represent the same value despite having different visual characteristics. For instance, if you cut a piece of cake in half and eat one of the pieces, you will have eaten half of the cake.

= 1/4+1/4

= 2/4

= 1/2

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Correct Question:

What is 1/4 plus 1/4 as a fraction?.

The triangles SAT and SAO are congruent by the Side-Angle-Side (SAS) congruence theorem.

The Side-Angle-Side congruence theorem states that if any of the two sides on a triangle are the same, along with the angle between them, then the two triangles are congruent.

For the triangles SAT and SAO in this problem, we have that:

The common angle are between the common sides, hence the SAS congruence theorem was used to determine the congruence of the two triangles.

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The curve's y-intercept is 4, and its slope is 2.

To depict the curve, we will make use of the idea of slope and intercept in linear equations.

A line's slope and y-intercept are represented by the equation y = mx + c, where m represents the slope and c represents the y-intercept.

When y = 2x - 4 is put into comparison with the generic form, we get

The curve has a slope of 2 and a y-intercept of -4.

Picking two points on the line y = 2x – 4 will make it easier for us to plot the graph.

Since the supplied line's y-intercept is 4, the line y = 2x - 4 must pass through (0, -4).

Put y = 0

0 = 2x - 4

x = 2

Line passes through (2,0).

Draw a line passing through (0,4) and (2,0) and we get the graph.

Correct question :

How do you graph y = 2x - 4 on a graph?

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A linear equation in two variables is an equation that can be written in the form of:

ax + by = c,

where a, b, and c are constants, and x and y are variables.

Linear equations in two variables are also called a system of linear equations in two variables. In this type of equation, the variables are related linearly, meaning that the highest power of the variables is 1. This is in contrast to non-linear equations, which have variables with powers greater than 1.

For example,

2x + 3y = 6 is a linear equation in two variables.

4x - 6y = 10 is also a linear equation in two variables.

A system of linear equations in two variables can have one unique solution, infinitely many solutions, or no solution. The solution of the system can be found by different methods such as graphing, substitution, elimination, matrix method, and numerical methods, as mentioned in the previous answers.

Linear equations in two variables are used to model many real-world situations such as in finance, physics, economics, and many more. The study of linear equations in two variables is a fundamental part of algebra and is a stepping stone to more advanced mathematical concepts.

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The equation of the line in slope intercept form is  y = 4x + 5.

The equation of line can be represented in slope intercept form as follows:

y = mx + b

where

A line passes through the points (0, 5) and (1,9).  The slope of the line can be found as follows;

m = slope = 9 - 5 / 1 - 0

m = 4 / 1

m = 4

Hence, let' find the y-intercept of the equation using (0, 5).

y = 4x + b

5 = 4(0) + b

b = 5

Therefore, the equation of the line is y = 4x + 5.

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Answer:

C

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = G (10, 1 ) and (x₂, y₂ ) = H (3, 5 ) , then

midpoint = ( [tex]\frac{10+3}{2}[/tex] , [tex]\frac{1+5}{2}[/tex] ) = ( [tex]\frac{13}{2}[/tex] , [tex]\frac{6}{2}[/tex] ) = ( [tex]\frac{13}{2}[/tex] , 3 )

By using the formula, Quantity = Percent × Whole, 20 is 50% percent of 40.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the percentage which 20 is of a whole number (40), we would apply the following mathematical expression (formula);

Quantity = percent × whole number

Substituting the given parameters into the percentage and quantity formula, we have the following;

20 = percent × 40

Percent = 20/40

Percent = 0.5

Next, we would multiply the resulting decimal value by 100 as follows;

Percentage = 0.5 × 100

Percentage = 50%.

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Answer:

$46

Step-by-step explanation:

We already have our first value of 34.5 and the second value of 75. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1

34.5 = 75% × Y

STEP 2

[tex]34.5 = \frac{75}{100} *Y[/tex]

Multiplying both sides by 100 and dividing both sides of the equation by 75 we will arrive at:

STEP 3

[tex]Y = 34.5 *\frac{100}{75}[/tex]

STEP 4

Y = 34.5 × 100 ÷ 75

STEP 5

Y=46

Answer:

The original price is 46

Step-by-step explanation:

The x be the original price of the item.

The discount is 25%

x - .25x = 34.50

.75x = 34.50

Divide each side by .75

x = 34.50/.75

x = 46

The original price is 46

The symmetry of a quadratic function is a vertical line that is x = − b/2a.

Quadratic function is defined as the function of the form f(x) = ax² + bx + c, where a, b and c are real numbers with a = 0 and it has the domain of a quadratic function is (−∞,∞).

Here we have given that we need to find the symmetry of a quadratic function.

As we all know that When a quadratic function is graphed in the coordinate plane, then the resulting parabola and corresponding axis of symmetry are vertical.

Here we have also know that in order to find the symmetry we have to  replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.

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The prime factorization of 36 is (2 2 3 3) while that of 49 is (7 7), respectively. As can be seen, the prime numbers 36 and 49 have no common prime factors, making them co-prime.

Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number. As an illustration, the prime number 2 contains two factors, 2 and 1.

The prime numbers that divide a positive integer exactly are said to be its prime factors. Integer factorization, often known as prime factorization, is the process of locating these integers. According to the basic theorem of mathematics, each positive integer has a distinct prime factorization.

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Answer:

1.5053412e+25

Step-by-step explanation:

use a calculator dude

The probability of selecting a 2 and then a number divisible by 4 will be C. 1/24.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur

The probability of selecting 2 is 1/6.

The probability of selecting a number divisible by 4 will be 1/4.

The probability of selecting a 2 and then a number divisible by 4 will be:

= 1/6 × 1/4

= 1/24

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Protein of [tex]125 g[/tex] Yoghurt A is [tex]6,5 g[/tex]

Protein of [tex]150 g[/tex] Yoghurt B is [tex]4,0 g[/tex]

How many grams of protein are provided by [tex]100 g[/tex] of yoghurt A?

First, find the ratio of the weight of the yogurt A

[tex]125 g : 100 g[/tex]

125 and 100 have the same factor is 25. then divide both numbers by 25 to simplify it.

[tex]\frac{125}{25}:\frac{100}{25} =5:4[/tex]

Find grams of protein are provided by [tex]100 g[/tex] of yoghurt A use comparison [tex]5:4[/tex]

[tex]\frac{4}{5}(4)=\frac{16}{5}=3,2 g[/tex]

[tex]3,2g[/tex] of protein are provided by [tex]100 g[/tex] of yoghurt A.

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The area on the map in square centimetres is 64 cm².

The scale of the plan is 1:20, meaning that for every 1 unit of measurement on the plan, the corresponding measurement on the actual boat is 20 units.

If the actual area of the base of the boat is 0.64 m², then the area on the map will be:

(0.64 m²) * (1/20)² = 0.0064 m²

To convert this to square centimetres, we multiply by 10,000 (since 1 m² = 10,000 cm²):

0.0064 m² * 10,000 = 64 cm²

Therefore, the area on the map in square centimetres is 64 cm².

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Answer:

16 cm²

Step-by-step explanation:

The scale of the map indicates the ratio of the linear dimensions of the map to the actual ones. Then the area of the map will correlate with the actual one, as with a scale square:

S map = S actual * (1:20)²

S map = 0.64 m² * 1/400

S map = 0.0016 m²

But we know that 1 meter contains 100 cm, so 1 m² = 10,000 cm². Then:

0.0016 m² * 10000 = 16 cm²

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According to the solving  the average of this new list of numbers is 60.

The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

The sum of the original list's four numbers, whose average is 90, is as follows:

4 × 85 = 232

Since 80 is the fourth number inside the original list, the first three numbers in the original list add up to:

232 − 105 = 127

The total of these updated first 3 numbers is also: if the first 3 numbers inside the new list are the same as those in the old list:

127

The total of the first four numbers with in new list, if the fourth number is 96, is:

127 + 115 = 242

As a result, the new list of four numbers' average is:

242 ÷ 4 = 60

According to the solving  the average of this new list of numbers is 60.

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The rule of parallel lines: they never intersect each other.

We know that two lines are parallel to each other if they lie in the same plane and never intersect each other.

Parallel lines are always equidistant from each other.

Also, the parallel lines are coplanar.

Mathematically, the parallel lines are represented by the symbol, ‘||‘.

If two lines l₁ and l₂ are parallel to each other then they are represented as l₁ || l₂.

Two lines parallel to a third line are parallel

As we know, the slopes of parallel lines are equal.

Let us assume that m₁ be the slope of line l₁ and m₂ be the slope of line l₂.

If line l₁ and l₂ are parallel to each other then m₁ = m₂

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The ratio of the side of a right-angled triangle opposite to a specified angle to the hypotenuse; when expressed as a real number between 0 and 1, it defines the sine of the angle.

Whenever the ratio is found by using the opposite side and the hypotenuse, we call it sine ratio.

We then say that sine 45 degrees is equal to 0.707. In short, we can use the symbol sin instead of sine and write sin (45 degrees) = 0.707

In general, sine of angle A =   length of leg opposite angle A / hypotenuse

sin(A) =   opposite/hypotenuse

In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

The ratio of the side of a right-angled triangle opposite to a specified angle to the hypotenuse; when expressed as a real number between 0 and 1, it defines the sine of the angle.

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The total time that Tony bakes the casserole is calculated by adding the two times together.

The first time the casserole bakes for 25 5/12 minutes and the second time it bakes for 2 3/6 minutes. The two times can be written in fractions as 25 5/12 + 2 3/6. To add fractions with different denominators, the denominators must first be made equal.To accurately calculate the total amount of time the casserole bakes, the fractions must be converted to their equivalent value in the same unit. 5/12 minutes is equal to 10/24 minutes and 2 3/6 minutes is equal to 8/6 minutes. To add the two fractions, 10/24 and 8/6, they must be converted to have the same denominator. The least common denominator is 24, so 10/24 is equal to 5/12, and 8/6 is equal to 16/24.  To make the denominators equal, the common denominator of 12 must be used. 25 5/12 can be rewritten as 225/12 and 2 3/6 can be rewritten as 15/12. 225/12 + 15/12 = 240/12. The fraction 240/12 can be reduced to 20/1. Therefore, the total time that Tony bakes the casserole is 20 minutes. The formula used to calculate this time is (25 5/12) + (2 3/6) = (225/12) + (15/12) = (240/12) = (20/1).

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Eric and willow will have the same number of baseball cards (when they initially have 350 and 250 cards respectively ) after 20 weeks.

Given,

Number of baseball cards Eric has =  350

Eric collects 10 cards per week.

Number of baseball cards Willow has = 250

Willow collects 15 cards per week

Let after [tex]x[/tex] weeks both eric and willow have the same number of baseball cards .

According to the question,

                                     [tex]350 + 10x = 250 + 15x\\5x = 100\\x=20[/tex]

Therefore, after 20 weeks both eric and willow have the same number of baseball cards.

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An equation with infinite solutions has both sides equal.

We know that a solution of an equation is a value that satisfies given equation.

As we know the system of equations has infinitely many solutions if the system of lines are coincident, and if they have the same y-intercept.

In some equations, any value for the variable makes the equation true. This means, an equation has infinitely many solutions.

Consider the equation 5x + 13 = 3x + 13 + 2x

5x + 12 = 5x + 12             .....(combine like terms)

13 = 13                           ........(subtrsct 5x from each side)

As we know 13 = 13 is always true.

To check that above equation has an infinite number of solutions, we try substituting some different values for x

For x = 3

5(3) + 13 = 3(3) + 13 + 2(3)

15 + 13 = 9 + 13 + 6

28 = 28

The statement 28 = 28 is always true. So, x = 3 is a solution.

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The number of people in the waiting room is 102.

A fraction is a quantity that is a non-integer. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 2/3.  

The first step is to determine the total number of people in the waiting room. To do this, divide 136 by 2/3.

Number of people in the waiting room = 136 ÷ 2/3

= 136 x 3/2 = 204

Number of people in the waiting room if it is half full = total number of people in the waiting room x 1/2

204 x 1/2 = 102

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