How do you find the center of a dilation of two shapes?

Using the change of base formula log base b of y equals log y over log b x = 4.69743.

To solve 3x + 1 = 15 for x, we can use the change of base formula, which states that log base b of y equals log y over log b. In this case, we can use log base 3 on both sides of the equation to solve for x.

First, we take the log base 3 of both sides of the equation:

log base 3 (15) = log base 3 (3x + 1)

Next, we can use the property of logarithms, which states that log base b (xy) = log base b (x) + log base b (y):

log base 3 (15) = log base 3 (3) + log base 3 (x + 1/3)

We can solve for x by subtracting log base 3 (3) from both sides of the equation:

log base 3 (15) - log base 3 (3) = log base 3 (x + 1/3)

We can then use the change of base formula to solve for x:

log 15/3 = log x + 1/3 over log 3

We can then solve for x by taking the antilog of both sides of the equation:

15/3 = x + 1/3

We can then solve for x by subtracting 1/3 from both sides of the equation:

15/3 - 1/3 = x

Finally, we can solve for x by dividing both sides of the equation by 3:

x = (15/3 - 1/3) / 3

Therefore, x = 4.69743.

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Solving provided question, we can say that the correlation coefficient for data shown will be as [tex]\sqrt{x} =\sqrt{y} = > \sqrt{x^2} = \sqrt{y^2}[/tex]

In statistics, the Pearson's correlation coefficient, often known as Pearson's r, Pearson's product-moment correlation coefficient, bivariate correlation, or simply correlation coefficient, is a metric for the linear correlation between two data sets. A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another variable's value. The values rise or fall jointly for variables with positive correlation. When evaluating the strength and direction of linear relationships between two sets of variables, correlation coefficients are used. If both variables are regularly distributed, use Pearson's correlation coefficient; if not, use Spearman's.

here,

the correlation coefficient for data shown will be as

[tex]\sqrt{x} =\sqrt{y} \\\sqrt{x^2} = \sqrt{y^2}[/tex]

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The ratio of the area of two circles can be found by dividing the area of one circle by the area of the other.

The formula for the area of a circle is A = πr^2, where r is the radius of the circle. To calculate the ratio of the areas of two circles, take the area of one circle and divide it by the area of the other:

Ratio of area of two circles = A1/A2 = (πr1^2)/(πr2^2)

For example, if the radius of one circle is 3 and the radius of the other is 5, then the area of the first circle is 28.27 and the area of the second circle is 78.54. The ratio of the areas of these two circles is then 28.27/78.54, which is 0.36.

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assuming they are the same unit, -1.2 is colder

when a number is negative, the further the number is from zero the less (colder) it is

The graph that represents the solution to the inequality is a number line with closed point at 10 with arrow pointing left

You should be aware that inequality is is a mathematical statement showing that two opposite things are not equal.  The graph is a diagram that illustrates the statement.

The given inequality is 2(b + 2) > 24

Opening the brackets to get

2b+4≥24

2b≥24-4

This implies that 2b≥20

Making b the subject

b≥20/2

b≥10

Therefore, the graph is a number line with closed point at 10 with arrow pointing left

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Answer:

The result can be shown in multiple forms.

Exact Form: m = 49/2  

Decimal Form: m = 24.5

Mixed Number Form: m = 24 1/2 (twenty-four and a half as a fraction)

Step-by-step explanation:

1. Divide each term in 2 m = 49 by 2:

2m/2 = 49/2

2. Simplify the left side.

m = 49/2

The result can be shown in multiple forms.

Exact Form: m = 49/2  

Decimal Form: m = 24.5

Mixed Number Form: m = 24 1/2 (twenty-four and a half as a fraction)

The 49 increased by twice a number m is 49+2m

Given data :

49+2m

Increase means “go up” which is another way to say addition

Twice means “two times” or “doubled”

A number would be a variable since it’s unknown

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Answer:

15

Step-by-step explanation:

Since the sum of all angles in a triangle is 180, we can make an equation

111 + 44 + 2x - 5 = 180

2x - 5 = 25

2x = 30

x = 15

All exponential functions go through the point (0,1) because the value of x when it equals to 0, in the general form of exponential function f(x) = [tex]a^x[/tex], results in [tex]a^0[/tex] = 1, which is why all exponential functions have the point (0,1) on their graph.

All exponential functions go through the point (0,1) because of the properties of exponential functions. The general form of an exponential function is f(x) = [tex]a^x[/tex], where a is a positive constant. When x = 0, the function evaluates to [tex]a^0[/tex] = 1, which is why all exponential functions have the point (0,1) on their graph.

Another way to understand this is that the exponential function is defined as the function that describes how a quantity grows or decays at a fixed percentage rate over time. The function f(x) = [tex]a^x[/tex], where a is a constant greater than 0 and less than 1, describes the decay of a quantity over time. For example, if the interest rate is 10%, the value of a = 0.1 and the function f(x) = [tex]0.1^x[/tex]. When x = 0, the function evaluates to [tex]0.1^0[/tex] = 1, which means that the initial value of the quantity is 1.

It's important to note that the point (0,1) is called the y-intercept, and it is a special point in the graph of exponential functions, and it's always present in the graph of exponential functions.

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The complete Question is:

Why do all exponential functions go through point(0,1)?

While reflecting about the line y=x, option (c) [tex]r_{y=x}(x,y) = (y,x)[/tex] is correct and while reflecting about the line y= -x, option (b) [tex]r_{y=-x}(x,y) = (-y,-x)[/tex] is correct.

The x-coordinate and y-coordinate are reversed when a point is reflected over the line y = x. The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x (the signs are changed). The line y = x is the point of reflection of the point (x,y) across (y, x).

Firstly, the rule for reflecting a point about the line y=x is:

[tex]r_{y=x}(x,y) = (y,x)[/tex]

While reflecting about the line y=x, we get the reflected points by swapping the coordinates.

So, Option 3 is correct.

Now, the rule for reflecting a point about the line y= -x is:

[tex]r_{y=-x}(x,y) = (-y,-x)[/tex]

While reflecting about the line y= -x, we get the reflected points by multiplying '-1'  with the swapped coordinates.

So, Option 2 is correct.

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Answer:

No, z =9 isn't a solution to 3z+8=25

Step-by-step explanation:

Let's see if it is...

[tex]\sf 3z+8=25[/tex]

Subtract 8 from both sides:-

[tex]\sf 3z+8-8=25-8[/tex]

[tex]\sf 3z=17[/tex]

Divide both sides by 3:-

[tex]\sf \cfrac{3z}{3}=\cfrac{17}{3}[/tex]

[tex]\sf z=\cfrac{17}{3}\;\; or \;\; z=5.6666....[/tex]

Therefore, no z = 9 isn't a solution to 3z+8=25.

____________________

Hope this's what you're looking for!

Have a great day!

Answer:

y = 9

Step-by-step explanation:

[tex]\frac{2}{6}[/tex] = [tex]\frac{y}{27}[/tex] ( cross- multiply )

6y = 2 × 27 = 54 ( divide both sides by 6 )

y = 9

Answer:

Step-by-step explanation: From the question 2/6 = y/ 27

Cross multiply

It becomes 2 * 27 = 6 * y

54 = 6y

Make y the subject

y = 54/ 6

y = 9

A polynomial f(x) has a factor (x-a) if and only if f(a) = 0, according to the factor theorem. It's one of the techniques for factoring a polynomial.

Since, the response above already covered the theorem's formulation.

Here, we shall demonstrate the factor theorem formula, which allows us to factor the polynomial.

When the polynomial f(x) is divided by (x-c), f(c) equals 0.

Remainder Theorem demonstrates that f(x)=(x-c)q(x)+f (c)

where the quotient polynomial is q(x) and the target polynomial is f(x).

Because f(c) = 0, f(x) = (x-c)q(x)+f (c)

(x-c)q(x)+0 f(x) = (x-c)q (x)

Therefore, the polynomial f's factor (x-c) exists (x).

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Answer:

0.29 miles per minute.

Step-by-step explanation:

Please let me know if this helped!!!

Answer:

x = 3

Step-by-step explanation:

6x = 18

Divided both sides by 6

x = 3

Let's check

6(3) = 18

18 = 18

So, x = 3 is the correct answer.

Answer:

x = 3

Step-by-step explanation:

1) 6x = 18

2) Divide by 6.

6x = 18

6 6

x = 3

Answer:

$9

Step-by-step explanation:

because we would take the total which is $39 so we divide 39/ 4 1/3 = to 9 so for one crate it is going to be $9 a crate

hope this helps

Finding the coordinates of an object in an image involves using image processing techniques such as object detection and image segmentation.

Object detection involves identifying the presence of an object in an image, while image segmentation involves isolating the object in the image.

Once the object is identified and isolated, its coordinates can be determined by using the position of the object's bounding box or contour.

Bounding box is a rectangular box that surrounds the object, its coordinates can be determined by the position of its top-left corner and bottom-right corner.

Contour is the boundary of the object, its coordinates can be determined by the points that are part of the boundary.

Computer Vision libraries such as OpenCV, Tensorflow or PyTorch can be used to perform object detection and image segmentation. They also provide pre-trained models which can be used for object detection and image segmentation without the need to train a model from scratch.

In conclusion, finding the coordinates of an object in an image requires using image processing techniques such as object detection and image segmentation to identify and isolate the object, and then determining its coordinates by using the position of the object's bounding box or contour.

This process can be aided by using Computer Vision libraries such as OpenCV, Tensorflow or PyTorch.

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Answer:

x<-13 or x>-3

Step-by-step explanation:

solve 9 abs(x + 8)>45 = x<-13 or x>-3

It is possible to construct a triangle whose sides are 1.5 cm 2 cm and 2.5 cm because the sum of two sides are greater than three sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 1.5 cm 2 cm and 2.5 cm.

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

To check this we firstly add the 1.5 and 2

1.5 + 2 > 2.5

3.5 > 2.5

Now we add 2.5 and 2

2.5 + 2 > 1.5

4.5 > 1.5

Now we add 1.5 and 2.5

1.5 + 2.5 > 2

4 > 2

It is possible to construct a triangle whose sides are 1.5 cm 2 cm and 2.5 cm because the sum of two sides are greater than third sides.

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The given statement "The notation "f(x)" (f of x) is another way of representing y-values in a function" is true because it represents the range or output values.

In Mathematics, a function is a mathematical expression which can be used for defining and showing the relationship that exist between two or more variables in a data set.

This ultimately implies that, a function typically indicates the relationship between input values (domain or x-values) and output values (range or y-values) of a data set, including the ways in which the elements in a table are uniquely mapped (paired).

In conclusion, we can reasonably infer and logically deduce that the output values (range or y-values) of a function are plotted on the y-coordinate of a graph and they are primarily denoted by either the notation f(x) or y.

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The solution of the expression for x is y+ 5.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is y = x - 5. The solution of the expression for x will be,

y = x - 5

x = y + 5

Therefore, the solution of the expression for the value of x will be x = y + 5.

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Answer:

JM is the answer

Step-by-step explanation:

i was going to explain but my brain is in shambles right now

Answer:

0.0081

Step-by-step explanation:

n^4

n = 0.3

We just need to put 0.3 in for n and solve

(0.3)^4 = 0.3 x 0.3 x 0.3 x 0.3 =  0.0081

Answer:

x ≈ 50.06°

Step-by-step explanation:

using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{23}{30}[/tex] , then

x = [tex]sin^{-1}[/tex] ( [tex]\frac{23}{30}[/tex] ) ≈ 50.06° ( to 2 decimal places )

The value of f(1) is equal to 7

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here f(x)=8x-2/2x putting x=1 we get

f(1)= 8-2/2

     = 7

Hence f(1) is equal to 7

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Answer:

X = 45, Y = 14√2

Step-by-step explanation:

We are given that the diagram is a square, and is cut in half using the length that is 28. Therefore x = 45

Now for y, we know that we have a 45 45 90 triangle with hypotenuse of 28, and the formula for that is the legs have length of x, and hypotenuse of x√2

y = x

=> 28 = x√2

x = 14√2

=> y = 14√2

Answer:1.75

Step-by-step explanation:

On solving the provided question we cans say that the inequality is 16x+5y320

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

Firm the question, the amount she spends on food every month is 16x and the amount he spends on travel every month is 5y.

Therefore, the total amount she spends every month is 16x+5y.

Since she can't spend more than $320 each month, the inequality is

16x+5y320.

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