I need help with this please and thank you.

The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.

The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Each element of X receives exactly one element of Y when a function from one set to the other is used.

According to the question,

f (x) = 1/3x - 2

now to find inverse ,

Add 2 to x term  and then divide by 1/3 so, we get,

f⁻¹(x) = (x + 2) / 1/3

f⁻¹(x) = 3(x + 2)

now, compare with f⁻¹(x) = a (x + 2)

a = 3

Calculate the x-intercept by putting f(x) = 0

0 = x + 2

x = -2

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Answer:

zero

Step-by-step explanation:

If a system of equations is graphed as 2 lines, then if the lines intersect, they intersect at one single point, and that point is the solution. There is one solution.

If the lines are parallel and do not intersect, then there is no solution. The number of solutions is zero.

Answer: zero

Answer:

AS a fraction: 1[tex]\frac{11}{20}[/tex]

AS a decimal: 1.55

Step-by-step explanation:

4/5 + 3/4

least common multiple of 5 and 4 is 20. Conver [tex]\frac{4}{5}[/tex] and [tex]\frac{3}{4}[/tex] to fractions with denominator 20.

16/20 + 15/20

since [tex]\frac{16}{20} and \frac{15}{20}[/tex]  have the same denominator, add them by adding their numerators.

[tex]\frac{16 + 15}{20}[/tex]

Add 16 and 15 to get 31.

[tex]\frac{31}{20}[/tex]

[tex]\frac{31}{2^{2}x5 } = 1\frac{11}{20}[/tex]

Hope that helps and have a great day! =) ~sunshine~

Answer:  The formula for finding the area of a triangle is A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).

Plugging in the given coordinates, the area of the triangle is:

A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1))

A = 1/2(-3)(-2)+(-2)(3)+1(-3)

A = -9+6-3

A = 4

Step-by-step explanation:  Step 1: Identify the formula for finding the area of a triangle: A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).

Step 2: Plug the given coordinates into the formula: A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1)).

Step 3: Simplify the equation: A = 1/2(-3)(-2)+(-2)(3)+1(-3).

Step 4: Solve the equation: A = -9+6-3.

Step 5: Find the area of the triangle: A = 4.

5/3 :8/3= 5/3 X3/8 =5/8

Answer:

12

Step-by-step explanation:

10% * 60 = 6

20% * 60 = 12

Answer:

5, 18 and 7 respectively

Step-by-step explanation:

4+9+5=18

18+7=35

Answer:The top box is 11 making the middle boxes 15 20

Step-by-step explanation:

4 11 9

4+11  11+9

15 20

15+20

35

Answer: 1/2

Step-by-step explanation:

Yes, that is correct; If the sky is clear, we are able to see the stars at night.

A star is a celestial body that maintains its shape thanks to its own gravity. Also, a star has the ability to generate its own light, an example of a star is the Sun.

The stars are always there, but during the day, the brightness of the sun makes it impossible for us to see them. However, at night when the sun is no longer visible, the stars become visible to us. This is why we can see the stars in the sky at night when there are no clouds obstructing our view.

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Answer:

this is true

Step-by-step explanation:

The count of the ways in which to chose 4 candies from a store that sells 30 candy bars, obtained by the combination formula, are 27405 ways

A mathematical combination, is the ways in which a number of items can be chosen from a set of items, excluding a reference to the order in which the items are selected.

The number of ways k items can be chosen from n items, can be found by using the following combinations formula;

[tex]\binom{n}{k} = \frac{n!}{k!\cdot (n-k)!}[/tex]

Therefore, the number of ways 4 candies can be chosen from a store that sells 30 candy bars can be found by plugging in k = 4, and n = 30 as follows;

[tex]\binom{30}{4} = \frac{30!}{4!\cdot (30-4)!} = 27405[/tex]

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the size of the stiffness matrix depends on the number of degrees of freedom and the type of elements used in the analysis. It is an important tool in structural mechanics and engineering for analyzing the behavior and performance of structures under different loading conditions.

In structural mechanics and engineering, the stiffness matrix is a mathematical representation of the stiffness of a structure, which relates the forces and displacements of the structure. The size of the stiffness matrix depends on several factors, including the number of degrees of freedom and the type of elements used in the analysis. The number of degrees of freedom (DOF) in the system determines the size of the stiffness matrix. DOF refers to the number of independent displacements or rotations that a structure can undergo in response to external forces. For example, a simple beam structure might have two DOF (vertical displacement and rotation), while a more complex structure such as a truss or frame might have many more DOF. The size of the stiffness matrix also depends on the type of elements used in the analysis. Different types of elements have different degrees of freedom and stiffness properties, which affect the size and shape of the stiffness matrix. For example, a truss element has two DOF and a constant axial stiffness, while a beam element has four or six DOF and variable stiffness properties that depend on its geometry and material properties.

In summary, the size of the stiffness matrix depends on the number of degrees of freedom and the type of elements used in the analysis. It is an important tool in structural mechanics and engineering for analyzing the behavior and performance of structures under different loading conditions.

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The answer is: 1 part sample, 9 parts diluent, 1 part of the first dilution, 9 parts diluent, 1 part of the second dilution, 9 parts diluent

When creating a serial dilution, the starting concentration is typically given as a ratio of sample to diluent. For example, a 1/10 dilution would mean that there is one part of sample and nine parts of diluent.

Now when we create a serial dilution from 1/10 to 1/1000, the first dilution will be 1 part sample and 9 parts diluent. The second dilution will be one part of the first dilution and nine parts diluent. The final dilution will be one part of the second dilution and nine parts diluent.

Thus, the answer is:

1 part sample

9 parts diluent

1 part of the first dilution

9 parts diluent

1 part of the second dilution

9 parts diluent

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____ The given question is incorrect, the correct question is given below:

When creating a serial dilution from 1/10 to 1/1000, the first dilution will be _______ part sample and ______ parts diluent. The second dilution will be one part ____ and nine parts _____. The final dilution will be one part _____ and nine parts diluent.

Choices:

1(one)

9(nine)

1/10 dilution

1/100 dilution

1/1000 dilution

diluent

The inequality form is 4/3<x<11.

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

The given inequality is log₂(3x-4)<log₂(2x+7)

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form: 4/3<x<11

Interval Notation:(4/3,11)

Therefore, the inequality form is 4/3<x<11.

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We can write the inequality as -

{x} < (1/4){8x + 4}

Given is the statement as -

"A number is less than one-fourth the sum of eight times the number and four"

We can write the statement as follows.

Let the number be {x}. Then, we can write the inequality as -

{x} < (1/4){8x + 4}

Therefore, we can write the inequality as -

{x} < (1/4){8x + 4}

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Answer:

Step-by-step explanation:

where is the equation?

Answer:

Step-by-step explanation:

Multiply 4.75 by 2 to find out how much money Maurice gets when finishing 2 chores. $4.75 x 2 = $9.50. So, write $9.50 under 2. For three chores, multiply $4.75 by 3. $4.75 x 3 = $14.25. Write $14.25 under 3.

The total square centimeters of mirrors covering the lateral surfaces is

171.5 cm².

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.

Given:

Perpendicular height = 14.3

So, the Surface area of Prism is

= 5 x 10 x 3 + 1/2 x 5 x 4.3 x 2

= 150 + 21.5

= 171.5

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The sample size for the given data is 17

The sample size is a term used in market research for defining the number of subjects included in a sample size.

Given that, a sample size has an 80% confidence interval, the population standard deviation is s = 120, the margin of error to be approximately 10, We need to find the sample size,

Sample size = (z-score)²×SD×(1-SD) / (confidence interval)²

z-score of 80% confidence interval = 1.28

Sample size = (1.28)²×0.12(1-0.12)/0.10²

= 1.6384×0.12×0.88/0.01

= 17.30

Hence, the sample size for the given data is 17

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The IQR is the best measure of variability, and it equals 4.

Answer:

22.5 minutes

Step-by-step explanation:

Initially, there were 9 students with 30 minutes to clean up the mess. This means they had a total of 9 · 30 = 270 student minutes to clean up the mess.

After the 3 additional students were added, there were a total of 9 + 3 = 12 students on the clean-up crew.

Now, let's assume the time they need to clean up the mess is "t" minutes. Since the number of students and the time are inversely proportional to the amount of work done, we can set up the following equation based on the idea that the amount of work done is the same before and after the addition of the 3 students:

9 · 30 = 12 · t

Solving for "t":

270 = 12t

t = 270 / 12

t = 22.5

So, the principal should give them approximately 22.5 minutes to complete the job with the new crew of 12 students.

Answer:

$50.00 is the amount of interest

There are approximately 1 teaspoon in 5 milliliters. Therefore, in 10 milliliters we have 2 teaspoons approximately.

When converting between milliliters and teaspoons, it's important to know that 1 teaspoon is equal to approximately 5 milliliters. Therefore, to convert 10 milliliters to teaspoons, you would divide 10 by 5, which gives you 2. This means that there are approximately 2 teaspoons in 10 milliliters. It's worth noting that while teaspoons are commonly used in the United States and other countries that use the imperial system of measurement, most countries use the metric system, which uses milliliters as the standard unit of volume. Therefore, it can be helpful to know how to convert between these units of measurement, particularly if you're following a recipe or taking medication that uses a different system than what you're used to.

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The expression (72a³b⁴) / (6a²b) is equivalent to the expression 12ab³.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (72a³b⁴) / (6a²b)

Simplify the expression, then we have

⇒ (72a³b⁴) / (6a²b)

⇒ 12ab³

The expression (72a³b⁴) / (6a²b) is equivalent to the expression 12ab³.

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None of the given polygons appears to be regular.

A regular polygon is a polygon with all sides and angles of equal measure. In other words, a regular polygon is a shape with straight sides that has all angles and sides of equal length.

The simplest example of a regular polygon is a equilateral triangle, which has three sides of equal length and three angles of equal measure. Another example is a square, which has four sides of equal length and four right angles of equal measure.

Figure A is a rhombus, which has opposite sides parallel and all sides equal, but it has two acute angles and two obtuse angles, so it is not regular.

Figure B is a parallelogram, which has opposite sides parallel, but not all sides and angles equal, so it is not regular.

Figure C is a right-angled triangle, which has one right angle, but not all sides and angles equal, so it is not regular.

Figure D is a trapezoid, which has at least one pair of parallel sides, but not all sides and angles equal, so it is not regular.

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Answer:

Obtuse triangle

Step-by-step explanation:

Obtuse triangle has an interior angle measuring more than 90 degrees.

One possible solution is to tutor for 11 hours and clear tables for 5 hours

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

Using the above as a guide, we have the following:

25x + 9y ≥ 270

x + y ≤ 18

Where

x = hours tutoring

y = hours cleaning tables

Next, we plot the graph (see attachment)

One solution from the graph is (11, 5)

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Answer:

2

Step-by-step explanation:

20% = 0.2

What is 20% of 10?

We take

10 times 0.2 = 2

So, 20% of 10 is 2.

Answer: 6 square inches

Step-by-step explanation:

Since the pizza is 16 inches and there is 8 slices divide.

16 inches ÷ 8 slices = 2 inches per slice

Each slice is 2 inches.

Since each slice is 2 inches multiply by 3 slices to get how many square inches she ate.

2 inches per slice x 3 slices = 6 square inches

Therefore she ate 6 square inches of pizza.