Which Function is the inverse of the exponential function y= (3/2)^x ?

The correct inequality that represents the allowable measurements the bar can bend is | x - 4.5 | ≤ 0.1 , So correct option is E.

n mathematics, an inequality is a statement that indicates that two values are not equal. It is a relationship between two expressions that can be compared using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

For example, 5 < 10 is an inequality that indicates that 5 is less than 10. Similarly, x + 3 ≤ 8 is an inequality that indicates that the sum of x and 3 is less than or equal to 8.

Inequalities are used to express relationships between quantities that are not necessarily equal. They can be used to represent constraints, limits, or ranges of values. Inequality statements can be combined with other mathematical expressions, such as equations or inequalities, to create more complex mathematical models.

The correct inequality that represents the allowable measurements the bar can bend is:

| x - 4.5 | ≤ 0.1

This is because the average allowable bend is 4.5 cm with a margin of error of 0.1 cm, which means that the actual allowable bend can range from 4.4 cm to 4.6 cm. The absolute value inequality represents this range of values, with the center of the range being 4.5 cm.

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The expression [tex]\frac{3x^2 + 6x + 3}{x + 1}[/tex] , where x ≠ -1, is equivalent to Option (D) 3x + 3. We can factor the numerator of the expression by first factoring out the greatest common factor of 3.

What is numerator ?

In a fraction, the numerator is the top number that represents the quantity being considered.

Take 3 common from expression:

[tex]3(x^2 + 2x + 1)[/tex]

We can further factor the expression inside the parentheses using the identity [tex](x + 1)^2 = x^2 + 2x + 1[/tex] , giving:

[tex]3(x + 1)^2[/tex]

Therefore, the original expression can be written as:

[tex]\frac{3(x + 1)^2}{x + 1}[/tex]

We can simplify this expression by canceling out the (x + 1) term in the numerator and denominator, leaving us with:

[tex]3(x + 1)[/tex]

So the expression [tex]\frac{3x^2 + 6x + 3}{x + 1}[/tex] , where x ≠ -1, is equivalent to 3(x + 1). This expression represents a straight line with a slope of 3 and a y-intercept of 3.

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The permutation is a bijective function because it is both a one-one and an onto function.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. Here, the components of sets are arranged in a linear or sequential order.

The bijective function is both a one-one function and an onto function.

One-one function means that for every value of the domain, there is only one value of the range. This means that an output value never repeats.

An element x is mapped to each element y by the function f known as the onto function. In other words, there is an x for every y such that:        

                                    f(x) = y

Now we have to prove why permutation is defined as bijective.

The permutation is basically an arrangement of elements.

So for the new arrangement, at one position there is only one element.

So it is one-one.

Also, we are using the given number of elements. we are just changing its positions. So every element in the co-domain is mapped to at least one element in the domain. Also, the co-domain is the range.

So it is onto function.

Therefore the permutation is a bijective function because it is both one-one and onto function.

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Answer:

The correct answer you're looking for is either 85, or 68.07 (rounded)
The correct answer is if x is the hypotenuse or the most extensive length than its 85.
If x is one of the legs then 68.07 (rounded) is the correct answer.

Recommendation:

When trying to solve for a missing length you need to be sure whether it's just a leg or the hypotenuse, usually would be obvious in a picture as the sides attached to the 90º angle are usually legs and the one opposite of it is the hypotenuse.
Anywho below are the two different ways to get the answer.

Disclaimer:

There will be two answers that I will have given and I would suggest looking at the question to see which one it is, I am not only giving one possible answer. (Also very long answer, sorry!)

Note:

If messaged or commented on which numbers go on which side I'll be more than happy to confirm one answer.

Step-by-step explanation:

Figuring out only if X is Hypotenuse:

To solve for a hypotenuse you need to use the equation for the Pythagorean Theorem which states: [tex]a^{2} +b^{2}= c^{2}[/tex].

In this case, 36, and 77 are the two legs that make up this triangle.

We would insert these two numbers to replace a and b for when solving the equation.

Now you have [tex]36^{2}+ 77^{2}= c^{2}[/tex].

You then do the exponent operations for the terms that we know the values of and also add them up together to get this equation:
1296 + 5929 = 7725 or [tex]c^{2}[/tex].

After that, we'll make sure to add the terms on the first side and keep [tex]c^{2}[/tex] on the other and to also square root them giving this equation: [tex]\sqrt{7725} = \sqrt{c^{2}[/tex].

With that, your answer is 85 = X


Figuring out only if X is a Leg:

Figuring out only if X is Hypotenuse:
To solve for a leg you need to use the equation for the Pythagorean Theorem which states: [tex]c^{2}- b^{2}= a^{2}[/tex]

In this case, 36, is one of the two legs that make up this triangle while 77 is the Hypotenuse.

We would insert these two numbers to replace b and c when solving the equation.

Now you have [tex]72^{2} -36^{2} =a^{2}[/tex]

You then do the exponent operations for the terms that we know the values of and also add them up together to get this equation:
5929 - 1296 = 4633 or [tex]a^{2}[/tex]

After that, we'll make sure to subtract the terms on the first side and keep [tex]a^{2}[/tex] them on the other and also to square root them giving this equation:  
[tex]\sqrt{4633} =\sqrt{a^{2} }[/tex]

With that, your answer is 68.07 (rounded) = X

I hope this was helpful!

Answer: 40

Step-by-step explanation: Because jasmine is enlarging the drawing, we can divide 60 and 3.75 to get how much she is enlarging. 60 divided by 3.75 is 16 meaning she is enlarging by 16. So now we multiply 16 times 2.5 to find the top and we get 40.

The inverse of the function will be f⁻¹(y) = y + 1.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.

The given function is y = x - 1.

To find the inverse of this function, we need to solve for x in terms of y.

y = x - 1

Adding 1 to both sides, we get:

y + 1 = x

Therefore, the inverse function is:

x = y + 1

f⁻¹(y) = y + 1

Note that the inverse function represents the reflection of the original function across the line y = x.

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The workers listed in order from least to greatest fraction of a shift worked are Lisa (1/4) < Jose (1/3) < Trent (2/3).

A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided. In a simple fraction, both are integers. A fraction can be found in either the numerator or the denominator of a complex fraction.

Trent worked eight of the twelve hours, or roughly two-thirds of the shift.

By dividing the number of hours Jose worked by the total number of hours in the shift, we can turn the number of hours Jose worked into a fraction:

Jose worked (12 - 8)/12 = 4/12 = 1/3 of the shift.

Lisa worked of the shift:

Lisa worked (12 - 8 - 1)/12

= 3/12

= 1/4 of the shift.

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The final answer is 1/10, which is a reduced fraction in lowest terms.

What is the fraction?

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity by another.

To perform the operation described, we first need to multiply the two fractions together using cross multiplication:

(3/5) x (1/6) = (3 x 1) / (5 x 6) = 3/30

The resulting fraction 3/30 is an improper fraction, meaning that the numerator is larger than the denominator. To convert this to a mixed fraction, we need to divide the numerator by the denominator, and express the remainder as a fraction. In this case:

3/30 = 1/10

Hence, the final answer is 1/10, which is a reduced fraction in lowest terms.

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(a) Vertical angles: [tex]$\angle 5$[/tex] and [tex]$\angle 2$[/tex]

(b) Supplementary angles: [tex]$\angle 3$[/tex] and [tex]$\angle 4$[/tex] (or [tex]$\angle 1$[/tex] and [tex]$\angle 2$[/tex], since they are also a pair of supplementary angles)

A figure created by two lines meeting at the same place is called an angle. The lines that make up the angle are known as its sides, and the point is known as the vertex. Angles are expressed in degrees, ranging from 0 to 360. Angles that are perpendicular to one another when two straight lines connect are known as vertical angles. Angles 1 and 3 in the image below measure 90°, while angles 2 and 4 also measure 90°. Vertical angles have the same measure.

Supplementary angles make up the second set of angles in the figure. Supplementary angles are two angles that sum up to 180°. Angles 1 and 4 and 2 and 3 form extra angle pairs in the illustration below. Angles 1 and 4 are individually 90 degrees, while angles 2 and 3 are also 90 degrees. As a result, the two angle pairs displayed in the illustration are additional angles.

(a) Vertical angles: [tex]$\angle 1$[/tex] and [tex]$\angle 3$[/tex]

(b) Supplementary angles: [tex]$\angle 3$[/tex] and [tex]$\angle 4$[/tex] (or [tex]$\angle 1$[/tex] and [tex]$\angle 2$[/tex], since they are also a pair of supplementary angles)

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Therefore , the solution of the given problem of trigonometry comes out to be csc θ - csc(90° - θ) is equal to -√(13) / 6.

Mathematics and cubic splines relationships It is believed that astrophysics was created with in third century BC, when the various fields were merged. Many geometric equations can be solved or the results of computations involving them can be determined using precise mathematical methods. Trigonometry is the analysis of the six basic trigonometric formulas. They are known by a variety of titles and acronyms, including sine, dispersion, angle, angle, etc (csc).

Here,

=> h² = 2² + 3²

=> h² = 4 + 9

=> h² = 13

=> h = √(13)

Using the specification of csc, we can now determine the value of csc:

csc θ = hypotenuse / opposite

csc θ = sqrt(13) / 3

csc(θ) - csc(90° - θ) must be calculated using the identity:

csc(90° - θ) = sec θ

As a result, we have:

csc θ - csc(90° - θ) = csc θ - sec θ

= (hypotenuse / opposite) - (hypotenuse / adjacent)

= (√(13) / 3) - (√(13) / 2)

= √(13) / 6 * (2 - 3)

= -√(13) / 6

Therefore, in its simplest radical version, csc θ - csc(90° - θ) is equal to -√(13) / 6.

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Answer:

D or B

Step-by-step explanation:

from my perspective, that doesn't look like a or b, and it looks like it's 90 degrees. But it could also be "We need more information to solve this problem, due to it all being x. i hope I'm correct, sorry if I'm not, and Goodluck!!!!!

Answer: The length of one fairy fly is 1.39×10−4 meter. To find the total length of two fairy flies placed end to end, we need to add their lengths.

1 fairy fly = 1.39×10−4 meter

2 fairy flies = 2 × 1.39×10−4 meter (adding the lengths of two fairy flies)

= 2.78×10−4 meter

Therefore, the total length of two fairy flies placed end to end is 2.78×10−4 meter.

Step-by-step explanation:

The probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as 0.5.

The probability of an event is a number that indicates how likely the event is to occur.

It is expressed as a number in the range from 0 and 1 or it can be expressed using percentage notation, in the range from 0% to 100%

Given is that the probability of a randomely selected fertilized egg will take 21 days to hatch is 0.028.

We can write the probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as -

P{E} = {0.028 + (1 - 0.028)}/2

P{E} =  1/2

P{E} = 0.5

Therefore, the probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as 0.5.

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The ordered pair is not the solution of the given equation. The solution has been obtained by using the substitution method.

One method for resolving equation systems is the substitution method. Use one equation to find an expression for one of the variables in terms of the other variable in order to apply the substitution procedure. Then, in the second equation, replace that variable with that expression.

We are given an equation as 7 = y - 5x.

The ordered pair is given as (4, 28).

On substituting this in the equation, we get

⇒7 = 28 - 5(4)

⇒7 = 28 - 20

⇒7 ≠ 8

Hence, the ordered pair is not the solution of the given equation.

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We proved that ΔPQR congruent to ΔSTR and  ΔJKL is congruent to ΔNKM using the given conditions.

What are congruent traingles?

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form. It is necessary for both triangles to be superimposed on one another.

1) Consider triangles ΔPQR and ΔSTR

PQ ≅ ST     -   Given

QR ≅ TR     - Given

R is the midpoint of PS  - Given

PR ≅ SR  - Since R is the midpoint it cuts line PS equally

ΔPQR  ≅ ΔSTR - Since the corresponding sides of the triangles are equal, they are congruent triangles.

2) Consider triangles ΔJKL and ΔNKM

JL ≅ NM     -   Given

K is the midpoint of JN and LM  - Given

JK ≅ NK  - Since K is the midpoint it cuts line JN equally

LK ≅ MK  - Since K is the midpoint it cuts the line LM  equally

ΔJKL  ≅ ΔNKM - Since the corresponding sides of the triangles are equal, they are congruent triangles.

Therefore we proved that ΔPQR congruent to ΔSTR and  ΔJKL is congruent to ΔNKM using the given conditions.

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Answer:

32 ft

Step-by-step explanation:

pls make me brainleist

The values that make the inequality m + 4 > -6 true are -4, 0, and 5.

The values that make the inequality n - 3n ≤ 8 true are -4, 0, and 5.

The values that make the inequality -5 < 5f true are 0 and 5.

The values that make the inequality 7 ≤ -y + 7 true are -10, -4, 0, and 5.

An inequality for the statement "Hank's height (h) is less than or equal to 6 feet." is h ≤ 6.

An inequality for the statement "A magazine (m) cost more than $3.50" is m > $3.50.

An inequality for the statement "The temperature (t) is at least -5 degrees" is t ≥ -5.

In this exercise, we would evaluate the given inequalities as follows;

-4 + 4 > -6

0 > - 6 (True).

0 + 4 > -6

4 > - 6 (True).

5 + 4 > -6

9 > - 6 (True).

n - 3n ≤ 8

-4 - 3(-4) ≤ 8

8 ≤ 8 (True).

0 - 3(0) ≤ 8

0 ≤ 8 (True).

5 - 3(5) ≤ 8

-10 ≤ 8 (True).

Generally speaking, the phrase "at least" simply means or represents greater than or equal to and it can be denoted by this inequality symbol (≥).

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Answer:

look in the comments and have a good day

Answer:

$1300

Step-by-step explanation:

To find the total account balance, use the simple interest account balance formula.

P(1+rt)

1000(1 + .06 · 5)

1000(1 + .3)

1000(1.3)

$1300

[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=23\pi \end{cases}\implies 23\pi =2\pi r\implies \cfrac{23\pi }{2\pi }=r\implies \cfrac{23}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{23}{2} \end{cases}\implies A=\pi \left( \cfrac{23}{2} \right)^2\implies A=132.25\pi[/tex]

Answer:

Below

Step-by-step explanation:

The wedge shaped area is ABOVE (greater than)  and INCLUDES  y = 5x+2    AND  ABOVE (greater than ) y= -3x-2

See image below:

If the original triangle has an area equal to 729 small dotty triangles. The original triangle has an area of 8 square units.

Let's first find the pattern of the number of small triangles in each row. The first row has 1 small triangle. The second row has 3 small triangles. The third row has 5 small triangles, and the fourth row has 7 small triangles. We can see that the pattern is that each row has 2 more small triangles than the previous row.

To find how many small triangles are in the third row, we add 2 to the number of small triangles in the second row:

3 + 2 = 5

So there are 5 small triangles in the third row.

To find how many small triangles are in the fourth row, we add 2 to the number of small triangles in the third row:

5 + 2 = 7

So there are 7 small triangles in the fourth row.

To find the total number of rows, we can count the number of rows from the top of the triangle to the bottom. Alternatively, we can use the formula for the sum of an arithmetic series to find the number of terms in the sequence. In this case, the first term is 1, the common difference is 2, and the last term is 7. Using the formula:

n = (last term - first term) / common difference + 1

n = (7 - 1) / 2 + 1

n = 4

So there are 4 rows in the triangle.

Finally, we can use the formula for the sum of an arithmetic series to find the total number of small triangles in the original triangle. In this case, the first term is 1, the common difference is 2, and the number of terms is 4. Using the formula:

sum = (n / 2) * (first term + last term)

sum = (4 / 2) * (1 + 7)

sum = 4 * 4

sum = 16

So there are 16 small triangles in the original triangle. Since each small triangle has an area of 1/2, the total area of the original triangle is:

area = 16 * (1/2)

area = 8

Therefore, the original triangle has an area of 8 square units.

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Answer:

Step-by-step explanation:

To find the measure of the central angle for the group that likes the student government program in a circle graph, we need to determine what proportion of the total number of students surveyed this group represents. We can do this by adding up the number of students who like the program and the number of students who think it is unnecessary, since these two groups represent the total number of students surveyed. Then we can divide the number of students who like the program by the total number of students surveyed and multiply by 360, which is the total number of degrees in a circle.

Total number of students surveyed = 190 + 135 + 220 = 545

Proportion of students who like the program = 190 / 545 ≈ 0.3486

So the measure of the central angle for the group that likes the program would be:

0.3486 x 360 ≈ 125

Therefore, the measure of the central angle for the group that likes the student government program would be approximately 125 degrees in a circle graph.

Answer:

3hours and 40 mins

Step-by-step explanation:

The value of x is given as follows:

x = 4.8.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

In the context of this problem, the parameters are given as follows:

Applying the Pythagorean Theorem, the value of x is obtained as follows:

x² + 14² = (x + 10)²

x² + 196 = x² + 20x + 100

20x = 96

x = 96/20

x = 4.8.

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The response that would best help the customer recognize the fallacy behind the faulty inference is: D. "What if a child runs out into the street right in front of your car?"

This response uses an example of a potential emergency situation to show that having low tread on tires can be dangerous even if the customer "never drives very fast or far.

" It challenges the customer's assumption that low tread is only a concern for high-speed or long-distance driving and highlights the importance of having sufficient tread depth for unexpected situations.

Therefore the correct option is C.

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One mistake Quinn made was in setting up the equation.

An equation is a mathematical statement that expresses the relationship between two or more quantities, using symbols such as +, -, =, and so on. It can be used to solve problems involving unknowns, such as the number of solutions to an equation or the value of a certain variable. In addition, equations can help to predict future outcomes based on current data.

Quinn set up the equation incorrectly by subtracting 3/2 from both sides instead of subtracting 3/1 from both sides. This caused the equation to become unbalanced, resulting in an incorrect solution. To solve the equation correctly, Quinn should have subtracted 3/1 from both sides to get the correct equation: 2/3 = q.

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she made the mistake of calculating

Step-by-step explanation:

The interpretation the transformation that creates the graph is 1 unit to the left and 4 units to the right.

The link between lines and points is described by a network's mathematical representation, a graph.

Given, that Figure X was transformed to produce Figure Y.

We must ascertain the transformation that is applied in this case.

The process of changing an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. A vertical reflection crosses the x-axis vertically and a horizontal reflection crosses the y-axis horizontally of a graph.

A graph can be horizontally translated by moving the base graph to the left or right in the y-axis direction.

Just a little bit of a tilt to the left and upward is made to the graph.

Figure X undergoes a translation of translation 1 unit left and 4 units up.

Hence translation 1 unit left, and 4 units up is the transformation which accomplish the graph.

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The complete question is:

Figure Y is the result of a transformation on Figure X. Which transformation would accomplish this?

The scale factor of the dilation will be 1/4.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The blue figure is a dilation image of the black figure.

And, The origin is the center of dilation.

Now,

Since, The blue figure is a dilation image of the black figure.

And, The origin is the center of dilation.

Here, The length of black figure = 8 units

And, The length of blue figure = 2 units

So, The scale factor of the dilation = 2/8

                                                         = 1/4

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