4^(3x)= 16^(x-2)

Solve for x.

Answer: To find the inverse of a function f(x), we need to switch the x and y variables and then solve for y.

So, the inverse function f^-1(x) of f(x) = 2x - 3 is:

f^-1(x) = (x+3)/2

This is the inverse of the function, and it can be denoted by f^-1(x) = (x+3)/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

85

The triangle formed by sides 24, 25 and 5 cm is not a right angled triangle.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Let us consider the triangle is a right angle triangle

so,  

24 and 5 will be the base and heights

[tex]\sqrt{24\x^{2} + 5\x^{2} } = 24.51\\[/tex]

so 25 is not equal 24.51 cm

so the triangle formed by sides 24, 25 and 5 cm is not a right angled triangle.

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During exercise, there was a substantial link between heart rate, coronary flow, and cardiac oxygen consumption. As heart rate increases, so does oxygen consumption, which seems to reach a maximum at very fast heart rates.

Your pulse and heart rate both serve as indicators of how your heart is working. Your heart rate is the number of times it beats in a minute. Your arteries widen as a result of the number of times your heart beats every minute.

In healthy people, heart rate, workload, and oxygen consumption are all linearly connected up to a certain point. The heart's reaction to physical exercise or stress is considered to be controlled by the sympathetic nervous system.

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Longitudes: The vertical lines running north-south, join the two poles. They are called the meridians of longitude. They are spaced farthest apart at the equator and converge at a point at each pole.

Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

What is the uses of latitude?

Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.

The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.

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Answer:

C

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

the first term a₁ from the table below n = 1, a₂ below n = 2 and so on

here a₁ = 100 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-50}{100}[/tex] = - [tex]\frac{1}{2}[/tex] , then

[tex]a_{n}[/tex] = 100 [tex](-\frac{1}{2}) ^{n-1}[/tex]

Answer:

Step-by-step explanation: By using linear inequation, it can be calculated that-

After 50 hours,  Plan B be more profitable than Plan A for the painter

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤

A one degree inequation is known as linear inequation.

Here, a linear inequation needs to be solved

Let after t hours,  Plan B be more profitable than Plan A for the painter

For plan A

A painter Charges $500 plus $45 per hour

Cost after t hours = $(500 + 45t)

For plan B

A painter Charges  $55 per hour

Cost after t hours = $55t

By the problem,

55t > 500 + 45t

55t - 45t > 500

10t > 500

t >

t > 50

After 50 hours,  Plan B be more profitable than Plan A for the painter

The end points of the diameter of a circle then we can easily find out the center point of the circle using the midpoint formula given by: Midpoint=(x1+x22,y1+y22).

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The lengths in the scale drawing are smaller than the corresponding lengths in the original figure.

When the scale factor is less than 1, the image of a shape will be reduced in size compared to the original shape. This means that all dimensions of the shape will be scaled down by the same factor. For example, if a shape is scaled down by a factor of 0.5, its length, width, and height will all be half the size of the original shape. Additionally, the area and volume of the image shape will be scaled down by the square and cube of the scale factor respectively.

In other words, when the scale factor is between 0 and 1 it will be a reduction and if it's greater than 1 it will be an enlargement.

As can be seen from the question, the scale factor is less than one as it is 1 / 3. This means that the lengths on the scale drawing would be smaller than the lengths on the original drawing.

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As per the unitary method, the number of toys ha had at first is 48.

Here we have given that  Hanif had some number of toy.

Here we also know that after selling 18 of them to the customer, then he till had 30 toy in hand.

Now, we have to find how many toy did Hanif have at first.

Let us consider that x is the number of toy he had at first.

Here we know that the following value are given,

number of toys left = 30

number of toys sold = 18

Then the total number of toys at first is calculated as,

=> x = number of toys left + number of toys sold

Apply the values on the equation, then we get

=> x = 30 + 18

=> x = 48.

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Colin will have a total amount of $ 675.90 with Colin.

The interest charged on a loan or deposit is known as compound interest. It is the idea that we used the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. 

The formula for compound interest is given by

Here we have

Colin invests $600 at a rate of 1.5% per year compound interest for 8 years

Here principal amount, p = $ 600

Rate of interest, r = 1.5% =

Number of compounds per year = 1

Time period, t = 8

By the Compound interest formula A = P (1 + r/n)^nt

A = 600( 1 + 0.015/1)⁽¹⁾⁽⁸⁾  

A = 600(1.015)⁸

A = $675.90  

Therefore,

Colin will have a total amount of $ 675.90.

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The function c(x) represents the price of the jeans after the coupon code is applied will be c(x) = 2x - 5.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

Katherine receives an email with a coupon code for $5 off of a pair of jeans from her favorite store.

Let 'x' be the cost of jeans. Then the cost of pair of jeans will be given as,

⇒ 2x

The function c(x) represents the price of the jeans after the coupon code is applied and will be given as,

c(x) = 2x - 5

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The degree of a polynomial is the highest power of the variable in the equation. In this case, the equation 2x² 5x³ 7 has the highest power of x being 3, so the degree of the polynomial is 5.

Step 1: Identify the highest power of the variable (x).

Step 2: Count the number of terms in the equation.

Step 3: The degree of the polynomial is the highest power of the variable plus the number of terms minus one.

Step 4: In this case, the highest power of x is 3 and the number of terms is 3, so the degree of the polynomial is 3 + 3 - 1 = 5.

The degree of the polynomial 2x² 5x³ 7 is 5. This can be calculated by taking the highest power of the variable (x) and adding it to the number of terms in the equation (3), and then subtracting 1.

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The hypothetical value of the sum of the geometric series is 1

The first term that we have in this progression is given as 1/2. Next we have to find the common ratio that lies between the values.

The sum of the infinite geometric series can be gotten by

a / (1 -r)

where a is the first term in the series = 1/2

r is the common ratio of the progression = 1/2

we would have to input the values. such that we would have:

1/2 / (1- 1/2)

(1/2) / (1/2)

= 1

The sum of the series is 1.

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Our point A(x,y) rotates 270 degrees anticlockwise around the origin to become A' (y,-x). This implies that we reverse x and y and turn x negative.

A figure can be rotated 90 degrees anticlockwise by rotating it 270 degrees clockwise. It would now be (x, y) = (-y, x)

A translation in geometry is a type of transformation that shifts a geometric figure in a specific direction without altering its size or orientation. The figures are congruent before and after the transformation because it is a type of rigid transformation.

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Answer: y= 120

Step-by-step explanation: y= 180 -2x30

=180-60

=120

Answer:

[tex]a_{73}=367[/tex]

Step-by-step explanation:

[tex]a_n=a_1+(n-1)d\\a_{73}=7+(73-1)(5)\\a_{73}=7+(72)(5)\\a_{73}=7+360\\a_{73}=367[/tex]

We can start by using the following equation to determine the number of yards of red fabric r she will need for each costume:

1 + r = y (y represents the total number of yards of fabric for each costume)

We know that the total number of yards for all the costumes is 8 and there are 5 costumes, so we can use this information to set up another equation:

5y = 8 (y represents the total number of yards of fabric for each costume)

Now we can substitute the first equation into the second equation to get:

5(1 + r) = 8

Expanding the left side of the equation:

5 + 5r = 8

Subtracting 5 from both sides:

5r = 3

Dividing both sides by 5:

r = 3/5

So, Mrs. Byers will need 3/5 yards of red fabric for each costume.

To find the m<MKL given that MK bisects <JKL proves that; m<MKL is 38^o.

A straight line that splits a measure of an angle into two equal parts is termed as an angle bisector. So that the measure of the two parts are the same.

Given in the question that MK bisects <MKL, then;

m<JKL = m<JKM + m<MKL     (definition of an angle bisector)

So that;

m<JKM = m<MKL

(3a + 20) = (2a + 26)

3a + 20 = 2a + 26

collect like terms

3a - 2a = -20 + 26

a = 6

Thus,

m<MKL = (2a + 26)

            = 2(6) + 26

            = 12 + 26

            = 38

m<MKL = 38^o

To find the m<MKL given that MK bisects <JKL proves that; m<MKL is 38^o.

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Answer:5x to the -4 power

Over

1x to the -9 power

Step-by-step explanation:thankssss

Yes, it is possible to form a triangle with sides of 3.5cm, 4.5cm, and 7.5cm. This is because these triangle's sides adhere to the triangle inequality theorem.

The triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is because in order to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side, otherwise it would be impossible to connect the three sides and form a closed shape.

In this case,

3.5 cm + 4.5 cm = 8 cm > 7.5 cm

3.5 cm + 7.5 cm = 11 cm > 4.5 cm

4.5 cm + 7.5 cm = 12 cm > 3.5 cm

So it is possible to form a triangle with these side lengths.

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Answer:

it will the the same shape you esrased but two more squares to the left

points (-3,1)(-5,1)(-4.5,3)(-6,5)

The number 8 is not a prime number because it is divisible by the numbers other than itself such as two and four.

A prime number is that number which can only be divided either by its own or by 1.

Let us understand this by an example, assume that we are provided with the numbers 2, 4, 6 and 3.

Now let us remember the basic tables of 2 and 3 which are in an order 2, 4, 6, 8... and 3, 6, 9, 12....

Now we cannot that the number 3 and 2 are only repeated in their tables only.

But the number 4 and 6 have appeared in the table of 2 and 3 along with their own tables.

So what we can understand from here is that the numbers 2 and 3 are the prime numbers because they are not divisible by any other number then themselves but the number 4 and 6 are not prime numbers because they are divisible by the numbers other than themselves.

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Answer:

See below

Step-by-step explanation:

The purple is the pre-image.  The orange is the image.  The green is showing that the pre-image and the image are the same difference by the y axis.

The points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

The points on the graph of f(x) = log9x can be calculated by substituting the given values of x in the equation. For example,

f(-1/81) = log9(-1/81) = log9(-1) - log9(81) = undefined

f(20) = log9(20) = log9(2*2*2*5) = log9(2) + log9(2) + log9(2) + log9(5) = 1 + 1 + 1 + 1.5 = 4.5

f(11/9) = log9(11/9) = log9(11) - log9(9) = 1.041393 - 0.954210 = 0.087183

f(-13) = log9(-13) = log9(-1) - log9(13) = undefined

f(2439) = log9(2439) = log9(3*13*37) = log9(3) + log9(13) + log9(37) = 0.477121 + 1.11394 + 1.579789 = 3.168910

f(181) = log9(181) = log9(3*3*7*7) = log9(3) + log9(3) + log9(7) + log9(7) = 0.477121 + 0.477121 + 0.84509 + 0.84509 = 2.55231

f(2) = log9(2) = log9(2) = 1

Hence, the points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

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The number of tiles that are white if there are 12 tiles in total will be 9.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario. It is important to note that an equation is the mathematical statement.

In this case, there are 3 times as many white tiles as there are shaded.

The number of tiles that are white if there are 12 tiles in total will be:

3x + x = 12

4x = 12

Divide

x = 3

Shaded tiles = 3

White tiles = 3x

= 3 × 3

= 9

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Answer:

23.5 it is hard to see the little dashes

Step-by-step explanation:

Answer:

I believe its A, correct me if i'm wrong.

Step-by-step explanation:

A hypothesis test involves a comparison between research results from a sample and a hypothesis about a population.

Thus, option (A) is correct.

In hypothesis testing, a researcher starts with a null hypothesis, which represents the assumption of no difference or no effect in the population.

The researcher collects data from a sample and performs statistical analysis to determine whether the evidence supports or rejects the null hypothesis in favor of an alternative hypothesis.

The research results obtained from the sample are compared to the hypothesis about the population to determine whether there is enough evidence to reject the null hypothesis and accept the alternative hypothesis.

Thus, option (A) is correct

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You need to buy 3.625 yards of fabric to have enough for your project.

To find out how many yards of fabric you need to buy, you can subtract the amount of fabric you already have from the total amount of fabric needed for the project.

Total amount of fabric needed - Fabric you already have = Fabric you need to buy

6.5 yards - 2.875 yards = 3.625 yards

so we can say that:

You need to buy 3.625 yards of fabric to have enough for your project.

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