determine 5[g(x)-f(x)]. write your answer in standard form

To find the inverse of a parent function, use the following steps:

1. Switch the x and y variables.

2. Solve the equation for y.

3. Replace y with f-1(x).

4. Simplify the equation.

The inverse of a parent function is a new function that is the "reverse" of the original function. This can be found by switching the x and y variables and solving for y. Once you have switched the variables and solved for y, replace y with f-1(x). This is the notation for the inverse of a function. Simplifying the equation will give you the inverse of the original function. For example, if the function is y = 2x + 1, first switch the variables to x = 2y + 1. Then solve for y to get y = (x - 1)/2. Replace y with f-1(x) to get f-1(x) = (x - 1)/2. Simplifying this equation gives you the inverse of the original function, f-1(x) = (x - 1)/2.

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When you solve an equation for one variable and then substitute the resulting expression in for that variable in the other equation This is known as the  substitution method.

Describe the substitution formula?

In algebra, substitution refers to replacing the variables' (expression's) letters with their corresponding numerical values. The expression's overall value can then be calculated.

What is substitution in math definition?

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As implied by the name, this strategy involves replacing a variable's value from one equation with another.

                            A technique for resolving systems of equations that entails figuring out the answer for one variable before locating the other. When a teacher offers a table containing example sentences and a variety of options for students to choose from using a predetermined pattern, that table is known as a substitution table.

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Using elimination method, the solution of the system of equation 3x + 5y = -2, -x + 2y = 8 is x = -4 and y = 2.

System of equation can be solved using different method such as graphical method, elimination method and substitution method.

Let's solve the system of equation by elimination method.

3x + 5y = -2

-x + 2y = 8

multiply equation(ii) by 3

3x + 5y = -2

-3x + 6y = 24

add the equation

11y = 22

divide both side of the equation by 11

y = 22 / 11

y = 2

Let's find the value of x.

-x = 8 - 2y

-x = 8 - 2(2)

-x = 8 - 4

-x = 4

x = -4

Therefore,

x = -4 and y = 2.

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Answer: We can start by using the proportion method to find the number of girls in the class.

If the ratio of girls to total students is 4:7, that means for every 4 girls, there are 7 students in total. We can set up a proportion:

4/x = 7/21

where x is the number of girls in the class.

To solve for x, we can cross-multiply and get:

4* 21 = 7* x

84 = 7x

Dividing both sides by 7 gives:

x = 12

So there are 12 girls in the class.

Step-by-step explanation:

The fractions which is greater than   [tex]\frac{2}{4}[/tex]  , but denominator of 6 are [tex]\frac{4}{6} ,\frac{5}{6},\frac{6}{6}[/tex] .

What is fraction?

The fraction contains both numerator and the denominator. The top number is known as the numerator, and the bottom number is known as the denominator. The numerator indicated the parts which is taken from whole portion.

Here Amount of Juice in Pedro glass is [tex]\frac{2}{4}[/tex]

So, [tex]\frac{2}{4} = \frac{1}{2}[/tex]

Now, we want fraction which is greater than  [tex]\frac{2}{4}[/tex]  , but denominator of 6.

So ,the fraction having denominator 6 are,

[tex]\frac{1}{6},\frac{2}{6},\frac{3}{6} = \frac{1}{2} , \frac{4}{6} ,\frac{5}{6},\frac{6}{6}[/tex]

Hence the fractions which is greater than   [tex]\frac{2}{4}[/tex]  , but denominator of 6 are [tex]\frac{4}{6} ,\frac{5}{6},\frac{6}{6}[/tex] .

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The square root of minus one √(−1) is the "unit" Imaginary Number. Therefore it doesn't exist.

Now, According to the question:

What is Square Root?

The square root of a number is defined as the value, which gives the number when it is multiplied by itself. The radical symbol √ is used to indicate the square root. For example, √16 = 4. The radical symbol is also called a root symbol or surds. If a number is a perfect square, we can easily find the square root of the number. If the given number is not a perfect square number, the square root can be found using the long division method.

What is the square of (- 1 )=?

The square root of minus one √(−1) is the "unit" Imaginary Number. Therefore it doesn't exist.

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The linear function the model the problem is y = 2x + 5

A linear function is a type of mathematical function that can be represented by a straight line on a graph. It is defined by an equation of the form y = mx + c, where m is the slope of the line and c is the y-intercept (the point where the line crosses the y-axis). Linear functions have certain properties, such as the fact that they have a constant rate of change and that the graph of a linear function is always a straight line.

From the data;

slope (m) = 2

y - intercept = 5

The linear function will be y = 2x + 5

Plotting this on a graph using a graphing calculator, we can easily identify our y - intercepts and slope.

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Answer:

x > 6

Step-by-step explanation:

3 + 4x > 27

Subtract 3 from both sides:

4x > 24

Divide both sides by 4:

[x > 6]

Rounded to the nearest inch, we get 434 inches cubed.

To determine the radius of the sphere before you can determine its volume. You can calculate the diameter by taking the diameter of 29.5 inches and dividing it by pi.

Let the equation be

[tex]$\begin{gathered}C=\pi \times D \\\frac{29.5}{3.14}=\frac{1475}{157}=9.3949044585987261\end{gathered}$$[/tex]

Then divide the diameter by 2 to get the radius.

[tex]$\frac{\left(\frac{29.5}{3.14}\right)}{2}=\frac{1475}{314}=4.6974522292993631$$[/tex]

So we get a radius of about 4.70.

Then we Utilize the formula for the volume of a sphere which exists

[tex]$V=\frac{4}{3} \times \pi \times r^3$$[/tex]

Substituting in R for 4.69, we get

[tex]$\frac{4}{3} \times 3.14 \times\left(\frac{1475}{314}\right)^3=433.96579644880793$$[/tex]

Rounded to the nearest inch, we get 434 inches cubed.

Therefore, the correct answer is 434 inches cubed.

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If we round to the next inch, we get 434 inches cubed. The three-dimensional equivalent of the two-dimensional circle, a ball is spherical and has a sphere-like shape.

Suppose the equation is  [tex]C = \pi \times D[/tex]

[tex]\frac{29.5}{3.14} =\frac{1475}{314} = 9.3949044522293[/tex]

Next, multiply the radius by two to obtain the diameter.

[tex]\frac{\frac{29.5}{3.14}}{2} =\frac{1475}{314} = 4.6974522293[/tex]

Consequently, we determine that the radius is around 4.70. Next, we use the formula for the volume of a sphere that is known.

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

When we replace 4.69 with R, we obtain , We get 434 inches cubed when we round to the nearest inch.

Basketballs typically have a surface size of 277.6 square inches. Calculate the basketball's circumference. Use the alumrof aera ecafrus formula, which is the reverse of the surface area formula. A basketball has a circumference of roughly 4.7 inches. The circumference of a basketball can be used to determine its volume. Basketballs used in the official NBA have a 29.5-inch circumference and a 434-cubic-inch capacity.

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The inequalities whose symbol will be reversed are -4.5c > 9 and -21/5 ≤ -5/2d

A relationship between two expressions or values that are not equal to each other is called inequality.

Given are given some inequality,

We know that, when anytime you are multiplying or dividing an inequality by a negative, you must reverse the inequality symbol

-4.5c > 9 will have its inequality symbol reversed

-21/5 ≤ -5/2d will have its inequality symbol reversed

Hence, the correct options are -4.5c > 9 and -21/5 ≤ -5/2d

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After 222.5 days, only 0.25 mg amount of the original 3.00 mg sample of Iron-59 will remain due to its 44.5 day half-life.

1. Calculate the number of half-lives in 222.5 days: 222.5 days / 44.5 days = 5 half-lives

2. Calculate the amount of Iron-59 left after 5 half-lives: 3.00 mg x (1/2)^5 = 0.25 mg

Iron-59 has a half-life of 44.5 days. A half-life is the time it takes for half of a given amount to decay. After a single half-life, half of the original amount will have decayed. After two half-lives, three-fourths of the original amount will have decayed, and so on.

In this case, we are given a 3.00 mg sample of Iron-59 that we need to determine how much of it will remain after 222.5 days. To do this, we first need to calculate the number of half-lives in 222.5 days. We can do this by dividing 222.5 days by 44.5 days, which gives us 5 half-lives.

Next, we need to calculate the amount of Iron-59 left after 5 half-lives. We can do this by taking the original amount (3.00 mg) and multiplying it by (1/2)^5, which gives us 0.25 mg. Therefore, after 222.5 days, only 0.25 mg of the original 3.00 mg sample of Iron-59 will remain.

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Answer:

$4 (a)

Step-by-step explanation:

First remove the prices of the total we are given so the $10 and the $5 from the total price which is $27.

This leaves us with 12 dollars. That is how much Nico spend in the 3 packages of strawberries.

Now we want the price of each so divide $12 by 3 packages which gives us $4 per package.

Answer:

Each package of strawberries is $4.00 each.

Step-by-step explanation:

Well, Nico spends a total of $27.00 at the grocery store. If he already spent $10.00 on pizza and $5.00 on granola. That adds up to $15.00 already spent. He has $12.00 left. Correct? If he buys 3 packages of strawberries, thats 12/3. 12 divided by 3 is 4. So Nico spent $4.00 on each package of strawberries.

(10 × 4) + (11 × 4)

(10 × 4) + 44 or 40 + (11 × 4)

Answer: y= -3x -1

you should calculate the gradient of the line using the points shown in the question (-1, 2) and (1, -4)

Gradient formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex] (next you should substitute the values from

                                                  the points)

                                [tex]m= \frac{2-(-4)}{-1-1} \\m=-3[/tex]  

The length of w is 251.8 cm, to the nearest 10th of a centimeter.

Length is a measure of one dimension of a physical object or space. It is typically taken to mean the longest dimension of an object, though it can also refer to the overall size of a two-dimensional object or shape, such as a rectangle. Length is generally measured in units such as meters, feet, or inches. Length is an important concept in many fields, such as geometry, physics, engineering, and architecture. It is also used to calculate distances between two points in space.

The formula to calculate the length of w is as follows: w=√(x2 +V2-2xVcosm/V). Substituting the given values, we get w=√(2602 + 802-2(260)(80)cos80°). Simplifying this expression, we get w=251.8 cm. So, the length of w is 251.8 cm, to the nearest 10th of a centimeter.

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Answer: you didn’t even say please

explanation: why don’t you ask your mother you make me sad

The number indicated on the number line is -0.896

what is number line ?

The visual representation of numbers on a straight line is called a number line. On an endless line that extends on both sides, either horizontally or vertically, this line is used to compare numbers that are spaced at equal intervals. The numbers on a horizontal number line grow as we approach towards the right side and drop as we move towards the left.

Each spacing = 0.0005

Exact middle between -0.895 and -0.896 is -0.8955

But, there is a slight more distance

So, it is -0.8956

Rounded to 3 decimal places -0.896 ( Because 6 at last is > 5, add 1 to 5)

The number indicated on the number line is -0.896

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The output values of the function are (a) 7, (b) -6 and (d) 10

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

(4,7),

(−3,8),

(11,14),

(12,−6),

(1,10)

The domain is the set of the x values

So, we have the following representation

x = {4, -3, 11, 12, 1}

Remove repeated entries

x = {4, -3, 11, 12, 1}

The range is the set of the output values

So, we have

Range = {7, 8, 14, -6, 10}

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Yes, a parabola can be represented as a function in the form of y = ax^2 + bx + c, where a, b, and c are constants. It is a quadratic function, and it is a type of a conic section.

Parabolas are commonly used in mathematics, particularly in the fields of algebra, calculus, and physics. They are used to model a wide range of phenomena, such as the trajectory of a projectile, the shape of a parabolic antenna, and the path of light through a lens. Parabolas also have many applications in engineering, such as the design of parabolic mirrors and the optimization of parabolic troughs for solar energy collection. They are also used to find the vertex of a parabola and the focus point.

The difficulty of working with parabolas depends on the specific context and the mathematical skills of the person using them. Understanding the basic properties of parabolas and how to graph them is a fundamental concept in algebra and is typically taught in high school. Solving problems involving parabolas can range from relatively simple, such as finding the vertex or axis of symmetry, to more advanced, such as optimization or intersection with other functions.

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The second graph with numbers till 50 is not the accurate representation of the quiz grades.. The solution is obtained by using the concept of frequency plot.

What is frequency plot?

A frequency plot is a graphic data analysis approach for condensing information about a variable's distribution. The response variable is split into intervals of the same size (or bins). For every bin, the response variable's frequency is determined.

The vertical axis represents frequencies or relative frequencies, and the horizontal axis represents the response variable in the frequency plot (i.e., the mid-point of each interval).

The first graph accurately represents the quiz grades as the graph ranges from 0 to 100 and the markings on it are made from 10 to 70.

The second graph is not the accurate representation of the quiz grades because the graph is ranging from 0 to 50 but the quiz grades are ranging from 10 to 70.

The third graph accurately represents the quiz grades as the graph ranges from 0 to 90 and the markings on it are made appropriately.

The fourth graph also accurately represents the quiz grades as the graph ranges from 0 to 80 and the markings on it are made accurately.

Hence, the second graph with numbers till 50 is not the accurate representation of the quiz grades.

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The statement that is true about J and K is that the expected values of J and K will be equal, and the variability of J will be greater than the variability of K. (Option E)

The sample size of J is 40 and sample size of K is 100. According to the central limit theorem if there is a population with mean μ and standard deviation σ and sufficiently large random samples is taken from the population with replacement, then the distribution of the sample means will be approximately normally distributed. Based on the theorem, both J and K will have the same expected value or mean.

As the standard deviation is inversely proportional to the same size, as the sample size increases, the standard deviation and related variability decreases. Hence, the variability of J will be greater than variability of K.

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a. Is there a real number x such that x^2 = -1?

b. Does there exist x such that x^2 = -1?

A variable in mathematics is an alphabet or phrase that stands for an unknown amount, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are utilized. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.

According to the mathematical operation, the variable is a quantity that can change or is not fixed. Typically, in algebra, we use the terms "x" and "y" to express an unknown integer. However, this is not unique, and we are free to employ any alphabet.

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When selecting true claims, you might opt for those that were first made in the narrative and are not adamant declarations. All things considered, the evidence strongly suggests that the 1930s were the beginning of the Great Depression.

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Answer:c

Step-by-step explanation:

Answer: The length of AC to one decimal place in the trapezium is 18.1 cm

Step-by-step explanation: Using Pythagoras theorem, we can find the length AC

Pythagoras theorem

c² = a² + b²

Therefore, draw a line from the point B to the line AD and call it line BX.

BX ║ CD

Therefore,

16² - 7² = BX²

256  - 49 = BX²

BX² = 207

BX = √207

BX = 14.3874945699

BX = 14.4 cm

Therefore,

11² + 14.4² = AC²

121 + 207.36 = AC²

AC = √328.36

AC = 18.120706388

AC = 18.1 cm

Hoped This Helped!

A triangle has 3 angles. The measure of the angles in triangle ABC is ∠ABC, ∠BCA and ∠BAC.

According to the angle sum property of a triangle, the sum of all three angles of a triangle is equal to 180°. That is

∠ABC + ∠BCA + ∠BAC.

In an acute triangle, all three angles are acute, meaning they are less than 90 degrees.

In a right triangle, one of the angles is always 90 degrees, which is the angle formed by the two legs of the triangle. The other two angles are acute, meaning they are less than 90 degrees.

In an obtuse triangle, one of the angles is greater than 90 degrees, which is the obtuse angle. The other two angles are acute, meaning they are less than 90 degrees.

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The diameter of the sphere tank is 27.2 ft.  

Every point on the surface of the sphere is equally spaced from its center, making it a three-dimensional round solid object.

The capacity of a sphere is defined as its volume or the area that the sphere occupies. Cubic units are used to measure a sphere's volume.

The formula for the Volume of a sphere is given by

Here we have

A spherical water tank holds 10,500 ft³ of water.  

Here capacity of the sphere = Volume of the sphere  

As we know the volume of the sphere = 4/3 πr³  

=> 4/3 πr³ = 10500

=> πr³ = 10500(3/4)

=> (22/7)r³ = 7875

=> 22r³ = 7875(7)    

=>  r³ = 55125/22  

=>  r³ = 2505

=> r = 13.6  (Approx)  

As we know diameter = 2 × Radius

=> Diameter of sphere = 2(13.6) = 27.2 ft

Therefore,

The diameter of the sphere tank is 27.2 ft.  

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Answer:

106 bucks

Step-by-step explanation:

Answer:

x = - 1/6c + 1/6k

Step-by-step explanation:

...........

The word problem is "In a restaurant, the constant fee for a table is $ 16 and every food item costs $ 8 if a family wants to spend only $ 75 how many items they can order?"

and the inequality 8x + 16 ≤ 75.  

Inequality simply means that two things aren't equal. One of the items might be lower too, greater than, or equivalent to the other things.

Signs that can be used in Inequalities are

≠  means not equal  

<  means less than

>  means greater than

≤  means less than or equal

≥  means greater than or equal

Here we need to create a word problem that can lead to Writing an inequality in the form of Ax + B ≤ C.

The word problem can be written as follows

In a restaurant, the constant fee for a table is $ 16 and every food item costs $ 8 if a family wants to spend only $ 75 how many items they can order?

And the problem can be solved as follows

Let the family order x items

Then the amount can be spent by the family = 8x + 16

As we said the family wants to spend only $ 75

=> 8x + 16 must be less than $ 75

The inequality that can be represented is 8x + 16 ≤ 75  

Therefore,

The word problem is "In a restaurant, the constant fee for a table is $ 16 and every food item costs $ 8 if a family wants to spend only $ 75 how many items they can order?"

and the inequality 8x + 16 ≤ 75.  

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Answer:

432 cubic inches

Step-by-step explanation:

The volume of the rectangular prism is 6 * 12 * 3 * 2 = 432 cubic inches.

Answer:

770.97692cm^2

Step-by-step explanation:

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c 2 Solving for A

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=15·12+20·12+13·12+1

2·﹣154+2·(15·20)2+2·(15·13)2﹣204+2·(20·13)2﹣134≈770.97692

Answer:

1008 cm²

Step-by-step explanation:

The surface area of the triangular prism is made up of:

Area of rectangle 1 = 20 × 15 = 300 cm²

Area of rectangle 2 = 20 × 13 = 260 cm²

Area of rectangle 3 = 20 × (5 + 9) = 280 cm²

Area of one triangular base = 1/2 × (5 + 9) × 12 = 84 cm²

Therefore,

SA of the triangular prism = 300 + 260 + 280 + 84 + 84 = 1008 cm²