How do you make a truth table?

By adding a duplicate of the identity matrix to the augmented matrix, which was formed, it is possible to find the inverse of a square matrix using row reduction.

If the matrix is capable of being reduced to the identity, the identity matrix will simultaneously change into the inverse matrix. A rectangular array of numbers, arranged in rows and columns, is referred to as a matrix. The dimension, or order, of a matrix, indicates how many rows and columns there are in the array. For example, if a matrix has m rows and n columns, its order is expressed as mxn.

Correct Question :

How do you find the inverse of a 4x4 matrix?

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Answer:

1. FC = 6

2. BC = 10

3. EC = 7

4. BA = 12

5. BC = 7

Step-by-step explanation:

⭐What is the centroid of a triangle?

Using the properties of a centroid, we can determine the lengths the problem is asking us for.

1. If CD = 12, find FC.

So if the median we need to look at is FD,

then CD : FC = 2:1

[tex]\frac{CD}{FC} = \frac{2}{1}\\\\\\\\[/tex] . . . . . . . . write the proportion

[tex]\frac{12}{FC} = \frac{2}{1}[/tex] . . . . . . . . . substitute the known values

[tex]12 = 2FC[/tex] . . . . . .  cross multiply

[tex]FC = 6[/tex] . . . . . . divide both sides by 2 to isolate FC

∴ FC = 6

2. If BG = 15, find BC

So if BG = 15, and BC is the distance from a vertex to the centroid, then BC is 2/3 of BG.

[tex]BC = \frac{2}{2}BG[/tex] . . . . . write equation

[tex]BC = \frac{2}{3}(15)[/tex] . . . . . substitute known values

[tex]BC = \frac{30}{3}[/tex] . . . . . . . . multiply numerators

[tex]BC = 10[/tex] . . . . . .  . . compute

∴ BC = 10

3. If AE = 21, find EC

So if AE is the full median, and EC is the distance from the centroid to the opposite side of a vertex, then EC is 1/3 of AE.

[tex]EC = \frac{1}{3}AE[/tex] . . . . . . . . write equation

[tex]EC = \frac{1}{3}(21)[/tex] . . . . . . . . substitute known values

[tex]EC = \frac{21}{3}[/tex] . . . . . . . . . . . multiply the numerators

[tex]EC = 7[/tex] . . . . . . . . . . . . compute

∴ EC = 7

4. If FA = 6, find BA

If BA is a side length that is bisected by a median, then FA is 1/2 of BA.

[tex]FA = \frac{1}{2}BA[/tex] . . . . . . . make equation

[tex]FA = \frac{1}{2}(6)[/tex] . . . . . . . . substitute known values

[tex]FA = \frac{6}{2}[/tex] . . . . . . . . . . . multiply the numerators

[tex]FA = 3[/tex] . . . . . . . . . . . compute

∴ FA = 3

5. If CG = 3.5, find BC

So if the median we need to look at is BG,

then BC : CG = 2:1

[tex]\frac{BC}{CG} = \frac{2}{1}[/tex] . . . . . . . . . . create the proportion

[tex]\frac{BC}{3.5} = \frac{2}{1}[/tex] . . . . . . . . . . substitute the known values

[tex]BC = 2(3.5)\\[/tex] . . . . . . . . cross multiply

[tex]BC = 7[/tex] . . . . . . . . . . . . . compute

∴ BC = 7

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Answer:

If Samuel drives a compact car, he would need to buy 243.75 gallons of gas per year. If he drives a pickup truck, he would need to buy 250.25 gallons of gas per year. So he would need to buy 6.5 more gallons of gas per year if he drives a pickup truck compared to a compact car.

Step-by-step explanation:

Answer:

  all positive numbers

Step-by-step explanation:

You want to know the domain of the log function.

The log function ln(x) is defined for all x > 0. A log function with any other base is similarly defined.

  log function domain: all positive numbers

A parent log function has a vertical asymptote at x=0, and an x-intercept at x=1. Its vertical scaling will depend on the base of the logarithm. Like any function, it can be translated and scaled horizontally and vertically.

__

Additional comment

In the field of complex numbers, the log function is defined for any non-zero number. For example, ln(-1) = πi.

The range is all real numbers.

Consequently, this student's quiz results have a median, or "middle," value of 16.

When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.

Here,

the median, or "middle" value in a data set. Your data must be in numerical order in order to calculate the median.

Exam results:

9, 13, 20, 15, 18, 17

Number the rows and columns.

9, 13, 15, 17, 18, 20

Calculate the "middle" value:

9, 13, 15, 17, 18, 20

If there are two middle values, put them together and divide by two.

15 + 17 = 32

32/2 = 16

Consequently, this student's quiz results have a median, or "middle," value of 16.

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Therefore , the solution of the given problem of trigonometry  comes out to be surface x² + y² + z² = p².

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.

Here,

Given:

p = sinθ sin∅

To Locate:

the equation's surface

Solution:

adding p to both sides of the equation

p sinθ sin∅ = p²

p sinθ sin∅ = p²

p sinθ sin∅ =y

x²+y²+z²=y

x² + y² - y+ z² = 0

x²+ (y - 1/2)²+ z² = 1/4

r² =1/4, r= √1/4,

The surface of the sphere having a radius of 1/2 and a center at (0, 1/2, 0) is designated as 1/4.

Sphere-centered coordinates

x = sin p sin

y = sin(p), sin(p),

z = p cos∅

x² + y² + z² = p²

Therefore , the solution of the given problem comes out to be surface

x² + y² + z² = p².

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Therefore , the solution of the given question of triangle  comes out to be the only true option is A.

Any three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.

Here,

Because angles 1 and 2 are close to one another, they are neighboring angles.

A They share a side and are near to each other, making them neighboring angles.

B. The angles are complimentary (add to 90 degrees) False—Angle 2 has a 90 degree angle.

C. They are additional angles. (add to 180) They do not create a straight line, which is untrue.

D. Vertical angles describe them. (Contrary angles) False, they are not created through the intersection of lines.

Therefore , the solution of the given question of triangle  comes out to be the only true option is A.

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The sum of the natural numbers is (a) 25

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

Number type = natural number

Condition = 5 times bigger than their last digit

This means that

Number = 5 * Last digit

Because the number is a natural number, then the number cannot end in 0

This is so because 0 is not a natural number

Solving further, the last digit of the number is at most, 9

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

The number is at most 45 i.e. 5 * 9

Also, it means that it can not have more than 2 digits.

The above highlights in a nutshell is that the number is a multiple of 5 that does not end in 0 and the last digit is 5

Since the last digit is 5, then we have the number to be 25 i.e. 5 * 5

Hence, the number is (a) 25

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Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.

A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:

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Answer:

s = 11.cm

Θ = 2.2.radians

Step-by-step explanation:

0.08/0.2 and 0.2/0.8 are not proportional.

A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.

Given are two numbers, 0.08/0.2 and 0.2/0.8

Checking for if they are proportional or not,

0.08/0.2

Multiplying denominator and numerator by 100,

8/20 = 2/5

And,

0.2/0.8 = 1/4

Since, 0.08/0.2 ≠ 0.2/0.8

Hence, 0.08/0.2 and 0.2/0.8 are not proportional.

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Answer: As for the inequality question you asked,

-2/3, -11/3, and 2.5 are decimal numbers.

-11/3 is smaller than -2/3 because -3.67 is smaller than -0.67

-2/3 is smaller than 2.5 because -0.67 is smaller than 2.5

So the inequality that correctly orders the numbers -2/3, -11/3, and 2.5 is -11/3 < -2/3 < 2.5

It's worth noting that this inequality uses the less than (<) symbol to show the order of the numbers from the smallest to the largest, and it's also worth to remember that this inequality is true only for these specific values, if any of the values were changed it would've resulted in a different inequality.

Step-by-step explanation:

The farmer should expect to harvest 17,500 pounds of spinach from the field.

What is a function?

A function is a mathematical relation between a set of inputs (called the domain) and a set of possible outputs (called the range). The inputs are usually denoted by variables and the outputs are usually denoted by the value of a function. A function assigns exactly one output to each input.

In the given problem, g(z) = 400z - z^2 is a function that describes the area of a field in square feet, where z represents the width of the field in feet.

Given that the width of the field is 50 feet, we can substitute this value into the function to find the area of the field:

g(50) = 400(50) - 50^2 = 20,000 - 2,500 = 17,500 square feet

We know that the farmer will plant spinach in this field and expect to harvest 1 pound of spinach per square foot. Therefore, the total number of pounds of spinach the farmer should expect to harvest from the field is:

1 pound/square foot * 17,500 square feet = 17,500 pounds

Hence, the farmer should expect to harvest 17,500 pounds of spinach from the field.

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The farmer should expect to harvest 17,500 pounds of spinach from the field.

What is a function?

A function is a mathematical relation between a set of inputs (called the domain) and a set of possible outputs (called the range). The inputs are usually denoted by variables and the outputs are usually denoted by the value of a function. A function assigns exactly one output to each input.

In the given problem, g(z) = 400z - z^2 is a function that describes the area of a field in square feet, where z represents the width of the field in feet.

Given that the width of the field is 50 feet, we can substitute this value into the function to find the area of the field:

g(50) = 400(50) - 50^2 = 20,000 - 2,500 = 17,500 square feet

We know that the farmer will plant spinach in this field and expect to harvest 1 pound of spinach per square foot. Therefore, the total number of pounds of spinach the farmer should expect to harvest from the field is:

1 pound/square foot * 17,500 square feet = 17,500 pounds

Hence, the farmer should expect to harvest 17,500 pounds of spinach from the field.

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The score interval that is within one standard deviation of the mean is

(70 , 80).

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.

Some of the properties of the standard deviation are:

1. It cannot be negative

2. It is only employed to calculate the spread or dispersion around a data set's mean

3. It displays the degree of deviation  from the mean value

4. The larger the spread, the more standard deviation, with data of about the same mean.

Given,

 The mean of the test μ = 75

The standard deviation σ = 5

We are asked to find the scores within one standard deviation of the mean.

This means that the scores should be in the interval ( μ - σ , μ + σ )

μ - σ = 75 - 5 =70

μ + σ = 75 + 5 = 80

Therefore the scores should be in the interval = ( 70,80), which is within one standard deviation of the mean.

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The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.

What is iteration ?

iteration can be defined as the repeating itself to perform a particular task.

Given

X2 is when n=1

X2 = X1+1 = X1 ^ 3 - 5/10

because X1 = -1

so X2  = -1-5/10 = -6/10 = -0.6

X3 is when n=2

X3 = X2+1

= X2 ^ 3 -5/10

because X2 = -3/5

so X3 could be

X3 = (-0.6*-0.6*-0.6) - 5 / 10

X3 = -0.041600

Hence, The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.

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The answer of Coin word problem is Sarah has 425 quarters.

There are often two different equation types in coin word problems. The total number of coins is described by one equation, while the total amount of money is described by the other equation. However, let's choose some variables that will represent the problem's unknown values before we begin creating our equations.

Word Problems, also known as story problems, can be found in both daily life and the Common Core State Standards for every school level,  

Let q  be the number of quarters and d  be the number  of dimes

Then we are doing as :

q  +  d    =  600  →   d = 600  - q    (1)

0.25q + 0.10d  = 123.75      (2)

Sub (1)  into (2)  for d

0.25q + 0.10 ( 600 - q)   = 123.75    

simplify,

0.25q + 60  -0.10q  =  123.75

0.15q + 60 = 123.75    (subtract 60 from both sides)

0.15q  =  63.75     ( divide both sides by  0.15)

q = 425

Therefore, she has  425 quarters

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The x-intercept in a quadratic formula is where the graph of the function crosses the x-axis.

An x-intercept is a point on the graph of a function where the y-coordinate is equal to zero. In other words, it's a point on the graph where the function intersects the x-axis. The x-intercepts of a quadratic formula can be found by setting the y-value equal to zero and solving for x.

The quadratic formula is typically in the form of ax^2 + bx + c =0, thus by setting y=0 we get x = -b/2a and x = -b/2a, these are the x-intercepts where the graph of the function will cross the x-axis. The x-intercepts are also known as the roots or zeroes of the function, and are important for understanding the overall shape of the graph.

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To solve many simultaneous linear equations, use the substitution method in algebra.

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another.

The first stage in the substitution approach is to determine any variable's value in terms of the other variable from one equation. If there are two equations, x+y=7 and x-y=8, for instance, we can deduce from the first equation that x=7-y. The substitution approach is applied in this manner as the first stage.

There are three steps in the substitution technique:

Therefore, the answer is x= -2 and y= -8.

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250% (percent) of 5a is 4b.

A percentage is a number or ratio that can be expressed as a fraction of 100.

here, given that,

a is 200% of b

i.e. a=2b

Now, 5a=10b

So, we have,

5a/4b

=10b/4b

=5/2

=250%

Hence, 250% (percent) of 5a is 4b.

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On solving the provided question, we can say that difference of cylinder between the height of the soap 8 cm.

One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.

[volume of cylinder]=pi*r²*h- =  h=[volume of cylinder]/(pi*r²)

Volume=5652 cm³

r=7.5 cm, so,  h= [tex][5652]/(3.14*7.5²) = h=32 cm[/tex]

the height of the soap in the full dispenser is 32 cm

the height when 4,239 cubic centimeters of soap remains in the dispenser is h  [tex]=[4239]/(3.14*7.5²) = h=24 cm[/tex]

the difference is [tex]32-24 = 8 cm[/tex]

the answer is

8 cm

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Answer:

gay

Step-by-step explanation:

gayayayayayayaydyfyfaygaygagya

The volume of Pill Bluetooth Speaker is 39.78 cubic inches.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, Pill Bluetooth Speaker consists two semi sphere and cylinder.

The diameter of the cylinder and semi sphere is 2 inches. the height of the cylinder is a foot.

Radius =2/2 1 inch

We know that, the volume of semi sphere is 2/3 πr³

= 2/3 ×3.14×1³

= 2.1 cubic inches

We know that, 1 foot =12 inches

The volume of cylinder is πr²h

= 3.14×1²×12

= 37.68 cubic inches

Total volume =37.68+2.1

= 39.78 cubic inches

Therefore, the volume of Pill Bluetooth Speaker is 39.78 cubic inches.

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"Your question is incomplete, probably the complete question/missing part is:"

Pill bluethooth Speaker consists two semisphere and cyclinder. The diameter of the cylinder and semisphere is 2 inches. the height of the cylinder is a foot. The According to the Statement please fill in the blanks. please answer the following in inch format and round it to nearest tenth.

a) Volume of the Bluetooth Speaker ______

If Swimming Pool On a certain hot summers day, 498 people used the public swimming pool. The number of children is 325 and the number of adult is 173.

Children = x

Adults = y

x + y = 498  Equation .....1

1.50x + 2.50y = 920  Equation ...2

Multiply (1) by 2.50

2.50x + 2.50y = 1,245  Equation  Equation ....3

1.50x + 2.50y = 920  Equation ...2

Subtract (2) from (3)

1x = 325

x = 325/1

x = 325 (Children)

Substitute x = 325 in (1)

x + y = 498

325 + y = 498

y = 498 - 325

y = 173 (Adult)

Therefore 325 children and 173 adults swam at the pool.

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Answer: 6.280

Step-by-step explanation:

Therefore the expression simplified using only positive exponents is 10h^4v^22.

An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ. For example, 2⁻⁴ = 1 / (2⁴) = 1/16.

A mathematical procedure called multiplication shows how many times a number has been added to itself. The multiplication symbol (x) or (*) are used to denote it. A mathematical process that shows how many equal amounts add up to a given number is called division.

To simplify the expression using only positive exponents, we need to make sure that all the exponents are positive.

We can simplify the expression:

(2h^7v^-3)/(5h^-4v^5)^-5

= (2h^7v^-3)/(1/(5h^-4v^5)^5)

= (2h^7v^-3) * (5h^4v^25)

= 10h^4v^22

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Answer:

∠T = 130°

Step-by-step explanation:

The figure we are given is a quadrilateral, a 4 sided shape.

There are many different types of quadrilaterals, such as a rhombus, rectangle, etc.

How will we know which quadrilateral the given figure is?

We will have to look at the given properties of the figure to find out.

We are given that there are two adjacent pairs of congruent sides.

RS = RU, and ST = UT.

Thus, the given quadrilateral is a kite.

Now that we know that the given figure is a kite, we can utilize a kite's angle properties to find out ∠T.

In a kite, the non-vertex angles (∠S and ∠U) are congruent.

If ∠S = 60°, then ∠U = 60°.

In a kite, the sum of the interior angles is 360°.

Hence:

∠R + ∠S + ∠T + ∠U = 360°

Therefore, we can substitute the angles we know into the equation and solve for ∠T.

∠R + ∠S + ∠T + ∠U = 360°

110 + 60 + ∠T + 60 = 360

110 + 120 + ∠T = 360

230 + ∠T = 360

∴ ∠T = 130°

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The minimum and maximum possible heights of the bowling pin are 14.96875 inches  and 15.03125 inches

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

Absolute deviation = 0.03125 inches

Height = 15 inches

The minimum is calculated as

Minimum = Height - Absolute deviation

Substitute the known values in the above equation, so, we have the following representation

Minimum = 15 - 0.03125 inches

Minimum = 14.96875 inches

The maximum is calculated as

Maximum = Height + Absolute deviation

Substitute the known values in the above equation, so, we have the following representation

Maximum = 15 + 0.03125 inches

Minimum = 15.03125 inches

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The equation that will make a system with infinite solutions is the third option.

y = 2x + 6

A system of linear equations will have infinite solutions only if the two equations represent the same line.

Here we know that one of the linear equations of the system is:

2y - 4x = 12

If we now divide the whole equation by 2, we will get:

(2y - 4x)/2 = 12/2

y - 2x = 6

Now we can move the "2x" term to the right side, then we will get.

y = 2x + 6

So the equations:

y = 2x + 6

2y - 4x = 12

Represent the same line, then that system will have infinite solutions.

Finally, the correct option is the third one.

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Therefore , the solution of the given problem of function comes out to be  f(g(x)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)

Each x value in the domain has one but only one y value range, according to the rule of a function. Definition. If there is only one and only one value of x such that f(x) = y, then the function is one-to-one

Here,

Given : f(x) =X² - 8x+16/2 + 2x

g(x) =(6x)/(x-4)

To find the f(g(x)) :

=> f(g(x)) = f(6x/(x-4))

=>  f(6x/(x-4)) =  (6x/(x-4) )^2 - 8((6x)/(x-4)) +16/2 + 2(6x)/(x-4)

=>  f(6x/(x-4)) = 36[tex]x^{2}[/tex]/ ( [tex]x^{2}[/tex]+ 16 - 8x) - 36[tex]x^{2}[/tex]/(x+4) +8

=> f(6x/(x-4)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)

Therefore , the solution of the given problem of function comes out to be  

f(g(x)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)

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