Write the augmented matrix for the following system of equations.
- 3x + 2y = 7
5 – 2x = 7y

The argument is not valid.

The argument form is: p ∧ ∼ q → r, p ∨ q, q → p, therefore r. We can use the truth table to determine whether this argument is valid or invalid. Here is the annotated truth table:


 
   p
   q
   ∼q
   p ∧ ∼q
   p ∨ q
   p ∧ ∼q → r
   q → p
   r
 
 
   T
   T
   F
   F
   T
   T
   T
   T
 
 
   T
   F
   T
   T
   T
   T
   T
   T
 
 
   F
   T
   F
   F
   T
   T
   F
   F
 
 
   F
   F
   T
   F
   F
   T
   T
   F
 

From the truth table, we can see that the conclusion r is not always true, even when all the premises are true. For example, in the third row of the table, all the premises are true, but the conclusion is false. This means that the argument is invalid. The truth table supports this conclusion because it shows that there are cases where the premises are true but the conclusion is false. Therefore, the argument is not valid.

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\( \sf \: 1. \bigg[ \frac{4 + ( - 5)}{ - 2 - 3} \bigg]\bigg[ \frac{14 + ( - 21)}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{4 + ( - 5)}{ - 2 - 3} \bigg]\bigg[ \frac{14 + ( - 21)}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{4 - 5}{ - 2 - 3} \bigg]\bigg[ \frac{14 - 21}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{ - 1}{ - 5} \bigg]\bigg[ \frac{ - 7}{ - 6} \bigg] \\ \)

\( \sf \longrightarrow \: \frac{1}{ 5} \times \frac{ 7}{ 6} \\ \)

\( \sf \longrightarrow \: \frac{7}{30} \\ \)

C) 7/30 ✅

________________________________

\( \sf \: 2. \bigg[ \frac{7+ ( - 6)}{ - 4 - 9} \bigg]\bigg[ \frac{20 + ( - 45)}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{7 + ( - 6)}{ - 4 - 9} \bigg]\bigg[ \frac{20 + ( - 45)}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{7 - 6}{ - 4 - 9} \bigg]\bigg[ \frac{20 - 45}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{1}{ - 4 - 9} \bigg]\bigg[ \frac{ - 25}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{1}{ - 13} \bigg]\bigg[ \frac{ -25}{ 6} \bigg] \\ \)

\( \sf \longrightarrow \: \frac{ - 25}{ - 78} \\ \)

\( \sf \longrightarrow \: \frac{ 25}{ 78} \\ \)

A] 25 / 78 ✅

________________________________

\( \sf \: 3. \bigg[ \frac{4+ ( - 5)}{ - 2 - 4} \bigg]\bigg[ \frac{18 + ( - 36)}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4+ ( - 5)}{ - 2 - 4} \bigg]\bigg[ \frac{18 + ( - 36)}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4 - 5}{ - 2 - 4} \bigg]\bigg[ \frac{18 - 36}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{-1}{ - 6} \bigg]\bigg[ \frac{18 - 36}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{-1}{ - 6} \bigg]\bigg[ \frac{-18}{ 4} \bigg] \\ \)

\( \sf \longrightarrow \frac{18}{ - 24} \\ \)

\( \sf \longrightarrow -\frac{6}{ 8} \\ \)

\( \sf \longrightarrow -\frac{3}{ 4} \\ \)

C] -3/4 ✅

________________________________

\( \sf \: 4. \bigg[ \frac{7+ ( - 3)}{ - 6 - 2} \bigg]\bigg[ \frac{18 + ( - 6)}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{7+ ( - 3)}{ - 6 - 2} \bigg]\bigg[ \frac{18 + ( - 6)}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{7- 3}{ - 6 - 2} \bigg]\bigg[ \frac{18 - 6}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4}{ - 6 - 2} \bigg]\bigg[ \frac{12}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4}{ - 8} \bigg]\bigg[ \frac{12}{ -1} \bigg] \\ \)

\( \sf \longrightarrow \frac{48}{ 8} \\ \)

\( \sf \longrightarrow \frac{6}{ 1} \\ \)

\( \sf \longrightarrow 6 \\ \)

D] 6 ✅

________________________________

\( \sf \: 5. \bigg[ \frac{8+ ( - 2)}{ - 5- 6} \bigg]\bigg[ \frac{40 + ( - 48)}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{8+ ( - 2)}{ - 5- 6} \bigg]\bigg[ \frac{40 + ( - 48)}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{8 - 2}{ - 5- 6} \bigg]\bigg[ \frac{40 - 48}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{6}{ - 5- 6} \bigg]\bigg[ \frac{-8}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{6}{ - 11} \bigg]\bigg[ \frac{-8}{ 1} \bigg] \\ \)

\( \sf \longrightarrow \frac{-48}{ - 11} \\ \)

\( \sf \longrightarrow \frac{48}{ 11} \\ \)

B] 48/11 ✅

________________________________

Answer:

Step-by-step explanation:

To find the inverse of a matrix, we need to put it in the reduced row echelon form (RREF) using elementary row operations. We can augment the given matrix with an identity matrix of the same size, and then apply the row operations to both matrices simultaneously until the left-hand side becomes an identity matrix. The right-hand side will then be the inverse of the original matrix.

Here are the steps:

[ 5 3 | 1 0 ]

[13 8 | 0 1 ]

R1/5 -> R1:

[ 1 3/5 | 1/5 0 ]

[13 8 | 0 1 ]

R2-13R1 -> R2:

[ 1 3/5 | 1/5 0 ]

[ 0 1/5 | -13 1 ]

R1-(3/5)R2 -> R1:

[ 1 0 | 26/5 -3/5 ]

[ 0 1 | -13 1/5 ]

So, the inverse matrix is:

[ 26/5 -3/5 ]

[-13 1/5 ]

The measure of central tendency that is referred to as the most frequently occurring value in a set is called the mode. The mode represents the value or values that occur with the highest frequency in the data set. Unlike the mean and median, which are based on numerical calculations, the mode is simply the value that appears most often.

The mode is a measure of central tendency in statistics that refers to the most frequently occurring value in a set of data. It is defined as the value or values that appear with the highest frequency in the dataset. Unlike the mean and median, which are calculated based on numerical computations, the mode is simply the value that occurs most often.

To find the mode of a dataset, you would need to look at the frequency distribution of the data. The frequency distribution tells us how many times each value appears in the dataset. The mode represents the value with the highest frequency in the dataset.

For example, consider the following dataset: 2, 3, 5, 5, 5, 7, 8, 8, 9. In this dataset, the value 5 appears three times, which is more than any other value. Therefore, the mode of this dataset is 5.

The mode is a useful measure of central tendency because it can help us identify values that are more common in the dataset compared to others. However, it may not always be a good representation of the "typical" value in the dataset if there are multiple modes or if the mode is influenced by outliers.

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Answer:

x = 22/15

Step-by-step explanation:

2.5(6x-4)=10+(1.5+0.5)

Combine like terms

2.5(6x-4)=10+(2)

2.5(6x-4)=12

Divide each side by 2.5

6x-4 = 4.8

Add 4 to each side

6x = 8.8

Divide by 6

6x/6 = 8.8/6

x = 88/60

x = 22/15

An expansion where image size increased is formed when scale factor k is greater than 1

The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.

The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image.

The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted. Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size.

when the scale factor K is greater than 1 , The image will enlarged

Hence, An expansion will be occur.

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Answer:

The answer is 1 9/19

Step-by-step explanation:

Answer:

This question can be solved using direct and inverse variation. Direct variation can be solved using unitary method that is common sense like if you buy 10 chocolates for 100 rupees how many rupees would you pay for 20 - this is simple as if 10 chocolates is 100 then 20 would be 200. HOWEVER,  Inverse Variation is when one value increase the other value decreases and they are proportional. They have a formula called x1/x2 = y2/y1.

In this problem we can use this formula, x1/x2 = 15/42 and y2/y1 = 30/x

so hence 15/42 = 30/x

= 15x = 30*42

x= 1260/15

 = 84

Therefore 84 is the answer.

Answer:46

Step-by-step explanation:

Answer:

49,889,327.04

Step-by-step explanation:

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In order to show these triangles congruent , we must identify the vertical angles

SAS criterion stands for Side-Angle-Side criterion. Under this criterion, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

As in the given figure there are two triangles( ΔABC and ΔCDE)

And it is given that the side AC=CE & BC=CD

as we can see that the sides AB and DE are parallel.

So, the ∠ACB and ∠DCE will be equal (vertically opposite angle)

And we can also say that;

∠ABC = ∠CDE & ∠BAC = ∠CED (alternate interior angle)

so, the triangles ΔABC and ΔCDE are congruent through SAS congruency criteria

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Answer:

R: (-3, -4)

S: (-3, -1)

T: (1, -4)

Step-by-step explanation:

You would subtract 1 from all the initial x values, and 5 from all the initial y values

Answer:

x=32

Step-by-step explanation:

you have to solve by taking the interior angle of polygon

The center of mass is 1. 6cm

The formula for determining the center of mass is expressed as;

Center of mass, xcm = \(\frac{m1x1 + m2x2}{m1 + m2}\)

Where;

Now, let's substitute the values

Center of mass = \(\frac{4(1) + 6(2)}{4 + 6}\)

Center of mass = \(\frac{4 + 12}{10}\)

Center of mass = \(\frac{16}{10}\)

Center of mass = 1. 6 cm

Thus, the center of mass is 1. 6cm

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51% of the sodas served at Emilia's Diner last night were regular.

A percentage is a relative value that represents one hundredth of a whole. One percent (symbolised 1%) is one hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.

To calculate the percentage of regular sodas, divide the total number of sodas by the number of regular sodas and multiply the result by 100.

As a result, the percentage of regular sodas is:

(51/100) x 100% = 51%

As a result, 51% of the sodas served last night at Emilia's Diner were regular.

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Answer:

C.5

Step-by-step explanation:

Fiona:

After t trials, she would have:

\(f(t) = 4.127(1.468)^t\)

Karl:

After t trials, he would have:

\(k(t) = 0.897(1.992)^t\)

At what number of trials would Fiona and Karl have the same number of beans?

This is t for which:

\(f(t) = k(t)\)

So

\(4.127(1.468)^t = 0.897(1.992)^t\)

\(0.897(1.992)^t = 4.127(1.468)^t\)

\(\frac{(1.992)^t}{(1.468)^t} = \frac{4.127}{0.897}\)

\((\frac{1.992}{1.468})^t = 4.6\)

\((1.35695)^t = 4.6\)

\(\log{(1.35695)^t} = \log{4.6}\)

\(t\log{1.35695} = \log{4.6}\)

\(t = \frac{\log{4.6}}{\log{1.35695}}\)

\(t = 5\)

So the correct answer is 5 trials, option C.

Answer: 1,4

Step-by-step explanation:

2(5x) = 14

10x = 14

x = 14/10

x = 1.4

Answer:

the value of x in 2 (5 ^ x) = 14 is:

c. 1.21

Step-by-step explanation:

To rank the steps involved in transforming one couple to another couple in a parallel plane, here is the correct order:

Identify the initial couple and the desired final couple.

Determine the translation vector that will move the initial couple to the desired final couple.

Translate the initial couple using the determined translation vector. This will shift the entire couple in the parallel plane.

Verify that the translation has successfully moved the initial couple to the desired final couple.

If necessary, make any additional adjustments or transformations to align the initial and final couples precisely in the parallel plane.

Confirm that the final couple is now in the desired position and orientation relative to the initial couple, maintaining the parallelism of the plane.

By following these steps in order, you can effectively transform one couple to another in a parallel plane.

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The target population is the population of interest that researchers aim to generalize their findings to.

The correct answer is c. sample.

In a research study, the population of interest is often too large or too difficult to access entirely. Therefore, researchers select a representative subset of the population to study, which is called a sample. In this case, patients with inflammatory bowel disease are the population of interest, and those who participate in the study are the sample.

The accessible population refers to the portion of the population that is accessible to the researcher. For example, if a researcher is studying the prevalence of a disease in a certain region, the accessible population would be the individuals living in that region.

An element refers to a single member of the population or sample.

The target population is the population of interest that researchers aim to generalize their findings to.

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Answer:

3/4

Step-by-step explanation:

Get into y=mx+b

Subtract 3x

4y=3x+36

Divide by 4

y=3/4x+9

Parallel= 3/4

Perpendicular= -4/3

Answer:

it is 3,3 or X<3 you can use either one

D is the answer

Step-by-step explanation:

Answer:

The answer is -3 because it passes through (0,0) and (2,-6).

Answer:

6 balloons in each pack

Step-by-step explanation:

54 divided by 9 is 6

Answer:

Step-by-step \(5x-4x =x \\4x^{2} -x^{2}=3x^{2} \\-24+11=-13\\3x^{2} +x-13\)

Answer:

x^5 + 151x -264

Step-by-step explanation:

See the attached page.

Answer: 37 degrees

Hope this helps :)

Step-by-step explanation:

(The box in the corner tells you this is a right angle)

A right angle is 90 degrees

90 - 53 = 37

Answer:

37 degrees

Step-by-step explanation:

Angle a is equivalent to 37 degrees because the picture signifies a right angle; all right angles are equal to 90 degrees. The equation to solve this would be: 53+x=90, you would solve this by subtracting 90-53=x; x=37

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With the help of the figure we can say that triangles are congruent by SAS Rule

What is Congruence of Triangle?

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides are equal and all three of their corresponding angles are equal in size. These triangles can be moved, rotated, flipped, and turned to look exactly the same.

Solution:

By SAS rule, two triangles are said to be congruent if any two sides and the angle included between the sides of one triangle are comparable to the corresponding two sides and the angle included between the sides of the second triangle.

In given figure, sides AB= PQ, BC=QR and angle between AB and BC equal to angle between PQ and QR i.e. ∠B = ∠Q. Hence, Δ ABC ≅ Δ PQR.

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Answer:Arnold earns $87 of interest in 5 years.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

True. Marginal cost refers to the additional cost incurred by producing one more unit of output.

Since the production of one more unit requires the use of additional variable factors of production (such as labor or raw materials), marginal cost always reflects the cost of those variable factors. Fixed costs, on the other hand, do not change with changes in output and are not included in marginal cost calculations. Therefore, marginal cost only reflects the change in cost associated with variable factors of production.

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