George is given two circles, circle and circle X, as shown. If he wants
prove that the two circles are similar, what would be the correct first step in
his proof?

The total amount that will be paid of there's a 15% tip is $57.50.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Let's assume that the cost of the good bought is $50. A 15% tip will give a value of:

= 15% × $50

= $7.50

The total amount to be paid will be:

= $50 + $7.50

= $57.50

Note that an overview was given as the information is incomplete.

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two thirds of a number b which is no more than 12, is b ≤ 18

What is inequality ?

In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.

According to question

two thirds of a number b = (2/3)b

Given two thirds of number b is no more than 12

⇒   (2/3)b ≤ 12

⇒   2b ≤ 12*3

⇒   b ≤ (12*3)/2

⇒   b ≤ 36/2

⇒   b ≤ 18

hence the number b whose 2/3 is no more than 12 is, b ≤ 18

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The maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.

What is a periodic function?

The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.

The maximum value of a periodic function with amplitude 6.5 and minimum value 7 is equal to the sum of the amplitude and the minimum value.

The amplitude of a periodic function is defined as the maximum distance that the function deviates from its centerline. In this case, the amplitude of the function is 6.5.

The minimum value of a function is the lowest value that the function takes on over a given period. In this case, the minimum value of the function is 7.

To find the maximum value of the function, we need to add the amplitude and the minimum value. The maximum value is equal to 6.5 + 7 = 13.5.

Hence, the maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.

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Answer:

-x + 8y = 56

Step-by-step explanation:

.................

a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.

To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.

Applying this rule to the expression 1/58^8, we get:

1/58^8 = 1/(58^8) = 58^-8

Therefore, the correct answer is 58^-8.

It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:

1/58^8 = (1/58)^8 = 58^-8

This simplification shows that the correct answer is still 58^-8.

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The function h(x) = (f.g)(x) would be x² + 10x + 24.

What are composite functions?

A composite function is generally a function that is written inside another function. The composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.

To find h(x) = (f.g)(x), we need to find the composition of the functions f(x) and g(x).

The composition of two functions f(x) and g(x) is denoted by (f.g)(x) and is defined as (f.g)(x) = f(g(x)).

In this case, we have:

h(x) = (f.g)(x) = f(g(x)) = f(x + 5)

Substituting x + 5 for g(x) in the equation for f(x), we get:

h(x) = (f.g)(x) = f(x + 5) = (x + 5)² - 1

Simplifying this expression, we get:

h(x) = (f.g)(x) = x² + 10x + 24

Hence, the function h(x) = (f.g)(x) would be x² + 10x + 24.

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The translation rule that maps the preimage to the image is (x, y) ⇒ (x + 5, y + 1)

From the question, we have the following parameters that can be used in our computation:

Pre-image: L(-4,0), M(-2,0) and N(-3,-3)

Image: L'(1,1), M'(3,1) and N'(2,-2)

The translation rule is calculated as

(x, y) = L' - L

Substitute the known values in the above equation, so, we have the following representation

(x, y) ⇒ (x + 1 + 4, y + 1 - 0)

Evaluate

(x, y) ⇒ (x + 5, y + 1)

Hence, the translation is (x, y) ⇒ (x + 5, y + 1)

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The value of the expression 24 + x ÷ 12 when x = −180 is (b) 9

Expressions are mathematical statements that are represented by variables, coefficients and operators

From the question, we have the following parameters that can be used in our computation:

24 + x ÷ 12

Also, we have the value of the variable to be

x = −180

Substitute the known values in the above equation, so, we have the following representation

24 - 180 ÷ 12

Evaluate the quotient in the above equation

So, we have the following representation

24 - 180 ÷ 12 = 24 - 15

Evaluate the difference in the above equation

So, we have the following representation

24 - 180 ÷ 12 = 9

Hence, the value of the expression is (b) 9

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The equation of line in point-slope form of the line, is y = 5x - 1.

What is point - slope form of the line?

The general form of a linear equation is y - y1 = m(x - x1).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

Given:

The line passes through the points (1, 4) and (2, 9).

We have to find the equation of line in point - slope form.

First to find the slope from the given points.

Since,

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Here, [tex](x_1, y_1) = (1, 4), (x_2, y_2) = (2, 9)[/tex]

So, [tex]m = \frac{9-4}{2-1} = 5[/tex]

Now consider, the point slope form of the line

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex]m = 5, (x_1, y_1) = (1, 4)[/tex]

⇒

[tex]y - 4=5(x-1)\\y-4=5x-5\\y=5x-5+4\\y=5x-1[/tex]

Hence, the equation of line in point-slope form of the line, is y = 5x - 1.

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The volume of the tunnel is 225.476cm³

We should know that the volume of an object entails the quantity of things it can hold at a particular time.

The volume of the tunnel = Volume of semi circle + volume of the rectangle

This is given by

V=3/4[tex]\frac{4}{3} \pi r^{3}[/tex] + lbh

volume of the tunnel = 4/3*3.142*(5/2)³ + 4*5*8

Simplifying the expression

(65.476 + 160)cm³

Volume = 225.476cm³

Given that the car exhaust  at 10m³

226cm = 2.26m

Note that 60 seconds = 1 Minute

Therefore 10*2.26=22.6m

=22.6/60 = 3 hours,  46 mins and 2 seconds.

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The LCM of the given pairs are 10, 15,12,30,6,24,20,18, and 63 respectively.

The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers.

There are 9 pairs, so let's name them using the letters A to I.

The LCM of the first pair A (2, 5) is 10.

The LCM of the pair B (3, 15) is 1*3*5 = 15.

The LCM of the pair C (6, 12) is 3*2*1*2 = 12.

The LCM of the pair D (3, 15) is 2*3*1*5 = 30.

The LCM of the pair E (2, 3) is 1*3*2 = 6.

The LCM of the pair F (8, 24) is 2*2*2*1*3 = 24.

The LCM of the pair G (4, 10) is 2*2*5 = 20.

The LCM of the pair H (6, 9) is 3*2*3 = 18.

The LCM of the pair I (7, 9) is 7*9 = 63.

Hence, 10,15,12,30,6,24,20,18,63 are the LCM of the given pairs.

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An item is regularly priced at, 1.98$ is discounted from the regular price.

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

Given that,

First, change the percentage into decimal:

Let us assume,

Sale of regular price = 1%

1% = 1/100 = 0.01

Assume, item regular price is = 2$

Multiply 2 with 0.01:

2 * 0.01 = 0.02

Note that this number 0.02 (0.01 of 2) is the amount off from the original price (2). Subtract 2 from 0.02

2 - 0.02 = 1.98

Therefore,

An item is regularly priced at, 1.98$ is discounted from the regular price.

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4.

find slope;

3 - 0/-2 -(-3) = 3/1 = 3

y = 3x + b

0 = (3)(-3) + b

0 = -9 + b

b = 9

y = 3x + 9

a) Using a base 2, the exponential function can be written as follows:

A(t) = 100(2)^(-t/235)

b) The amount of substance remaining after 1000 years is given as follows: 5.2 grams.

The exponential function for this problem is defined as follows:

A(t) = 100(0.5)^(t/235).

Which gives the amount of a substance after t years, considering a half life of 235 years.

The base can be changed to 2 as follows:

A(t) = 100(2)^(-t/235).

As exchanging the sign of the exponent, the numerator and the denominator of the base are exchanged, and 0.5 = 1/2.

The amount of the substance after 1000 years is calculated as follows:

A(1000) = 100 x (0.5)^(1000/235) = 5.2 grams.

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68,887 is the sum of the sequence (7+21+63...) to the 9th term.

That is, the sequence (as far as we are given) has a common ratio r=3, between successive terms. The initial term  a= 7 and we are interested in the sum to N = 9 terms.

and the sum of the 9th term is

[a^n = a( 1 - r^N)/1 - r ]

=[7 ( 1 - 3^9 )/ 1 - 3 ]

=7 ( 1 - 19683) / -2

= - 137,774 / -2

= 68,887

9th term = 68,887

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The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches

The quantity of surface contained within a semicircle's perimeter is known to as its area.

The formula for the Area of a half circle with a Radius (r) is given by  

            Area of Half circle = πr²/2

The formula for the perimeter of a half circle with a radius (r) is given by

           Perimeter of Half circle = πr

Here we have

A picture of a Rectangle with a half circle

Dimensions of Rectangle = 16 in × 12 in

=> Area of rectangle = 16 in × 12 in = 192 in²

=> Perimeter of rectangle shape = 12 + 16 + 12 = 40 inches

[ Here we only take one side of the rectangle since one of the sides is connected with a Half circle ]

The radius of half circle = 8 inch

=> Area of Half circle = π(8)² = (3.14)(64)/2 = 100.96 in²

=> Perimeter of Half circle = πr =(3.14)(8) = 25.12 in

Area of the composite shape

= Ractangle's Area + Half circle's Area

= 192 in² + 100.96 in²

= 292.96 in²

The perimeter of the composite shape

= Ractangle perimeter + Half circle perimeter

= 40 inches + 25.12 inches

= 65.12 inches

Therefore,

The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches

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Total coats should the store plan to sell this winter is 952.

Last winter, a store sold 408 coats in 3 months. This winter, the store plans to sell coats for 4 months.

What is sell?

Determine the total cost of all the purchased units. To find the cost price, divide the total cost by the quantity of units purchased. To get the final price, use the formula for selling price (SP), which is: SP = CP + Profit Margin. The cost of the commodity will then be increased by the margin to determine the proper pricing. Retail math describes the mathematical techniques or formulae utilised in the sales industry. It is earning money or receiving change in the most basic sense. Business owners, retailers, managers, and sales representatives all utilise retail math in their daily work.

3month = 408 coats

1 month = 408/3 =136 coats

Then, 4 months = 136*4 = 544 coats

Total coats should the store plan to sell this winter = 544+408 = 952.

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The measure of ∠A is 29.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Given that,

m∠A = (2x−13)° and m∠B = (2x+ 7)° and ∠A and ∠B are complementary angles.

Therefore

m∠A + m∠B = 90°

(2x−13)° + (2x+ 7)° = 90°

4x + 6 =90

Subtract 6 from both sides:

4x = 84

Divide both sides by 4:

x = 21

Putting x = 21 in m∠A = (2x−13)°:

m∠A = (2 × 21−13)°

m∠A = 29°

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It will take 5 minutes before the stadium is half empty

Given that:

Over 92,000 fans pack the stadium to watch the Tigers play

The fans leave at a rate of 10% per minute

The number of fans that leave per minute will be:

10% of  92,000 = 10/100 × 92, 000 = 9,200

The stadium will be fully empty  in:

time = 92,000/9,200 = 10 minutes

The stadium will be half empty  in:

time = 10 minutes / 2 = 5 minutes

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The point difference between Huskies and Bobcats are 3 x + 4.

Given data :

Difference = Huskies - Bobcats

Hence,

( 5x - 3 ) - ( 2x - 7 )

= 5x - 3 - 2x + 7

= 3x + 4

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The required value of x for the given proportion is 45.31

What is proportion?

Proportion is a mathematical relationship or ratio between two or more values. It is used to compare the size, quantity, or degree of two or more objects or measurements. Proportion can be expressed as a fraction, decimal, or percentage. It is often used in geometry, algebra, and calculus to determine the size of a shape or to solve an equation. Proportion is also used in statistics to compare data sets. In everyday life, proportion is used to make sure that items are in good balance with each other. For instance, proportions are used when baking a cake or making a recipe to ensure that the ingredients are properly combined.

Given, the proportion

x : 15 = 29 : 9.6

or, x = [tex]\frac{29}{9.6}[/tex] × 15

or, x = 45.31

Hence, the required value of x for the given proportion is 45.31

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A) The integers that make the equation false are {2, 54, 86}

B) We found that by solving the linear equation.

Here we have the following linear equation:

7m - 11 = 5m + 43

And the set of the possible solutions is S: {2, 27, 54, 86}

The simplest way to see which integer makes the equation false, we just need to replace the values of the possible solution sets and see which ones give a false equation.

Another method is to simplify the equation, and i will do that:

7m - 11 = 5m + 43

7m - 5m = 43 + 11

2m = 54

m = 54/2

m = 27

So the equation has a single solution, m = 27.

Then the integers that make the equation false are {2, 54, 86}

B) We determined the only true solution for the linear equation, and thus, all the other possible integers aren't solutions, thus, make the equation false.

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The value of x for the given function at the value of y = 4 will be 2.536.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the function is y = x² - x. On drawing the graph of the function y = x² - x we get the parabola at the vertex of ( 0.5,-0.25).

When we plot the coordinate y = 4, the value of the coordinate x on the graph will be x = 2.536. The graph of the function is attached with the answer below.

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Answer:

86

Explanation:

3² × (2³ + 4) - 22

9 × (8 + 4) - 22

9 × 12 - 22

108 - 22

86

Answer:

  12 units

Step-by-step explanation:

You want to know the perimeter of rectangle ABCD after it has been dilated by a factor of 1.

The original rectangle ABCD has a perimeter of ...

  P = 2(L +W) = 2(4 +2) = 12

The perimeter of the dilated rectangle is the original perimeter multiplied by the dilation factor:

  P' = 12·1 = 12

The dilated rectangle has a perimeter of 12 units.

__

Additional comment

Dilation by a factor of 1 changes nothing at all. The center of dilation is irrelevant.

2 points of inflection will f(x) = 3x5+2x4 - 5x - 12 have.

What is Inflection points definition?

An inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

If [tex]$f^{\prime \prime}(x) > 0$[/tex]then f(x) concave upwards.

If [tex]$f^{\prime \prime}(x) < 0$[/tex]then f(x) concave downwards.

[tex]$$f^{\prime \prime}(x)=126 x^5+40 x^3$$[/tex]

Show Steps

Find intervals: Concave Downward: [tex]-\infty < x < 0$, Concave Upward: $0 < x < \infty$[/tex]

Plug x=0 into [tex]$3 x^7+2 x^5-5 x-12: \quad-12$[/tex]

(0,-12)

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y ≥ 0 , Zero possible solution.

What is inequality ?

In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.

According to question

a represents the number of tables sold and y represents the number of chairs sold

Using a and y as variables, we get

a + y ≤ 18

100y + 400a ≥ 2900

Simplified,

100(y + 4a) ≥ 2900

y + 4a ≤ 29

Given the minimum number of tables that need to be sold, we evaluate using a = 10

y + 4(10) ≥ 29

y ≥ -11

y represents the number of chairs sold

therefore, y ≥ 0

Since we can't purchase -11  chair, we round up our result giving us y ≥ 0

Now

the store must sell a minimum of 10 tables and tables for $400 each

then

10*400 = $4000

which is more than worth of chairs and tables $2900

hence Zero possible solution.

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Answer:

Tabatha drives 1/6 mile more per minute than Horatio drives

Step-by-step explanation:

The median of the data sets 10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32 is 21.

The Median is the "middle" of a sorted list of numbers. In other words, Median, in statistics, is the middle value of the given list of data when arranged in an order.

Therefore, let's find the median of the data sets.

Firstly, we have to sort the data in ascending order before we can find the median in the data set.

10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32

Hence, the sorted data set is 10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32.

Therefore,

median = 21

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A point estimate (mean) for the average height of all people at the place where you work is 62.26

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

In statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.

Given,

Number of observations =  20

Mean = sum of all observation / number of observations

Mean =  66 +65 +66+ 67+ 62+ 70+ 69+ 68+ 71+ 78+ 61+ 62.5+ 64+ 64.2+ 64.3+ 58+ 60+ 63+ 65+ 66.2 / 20

Mean = 1245.2 / 20 = 62.26

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