3x + 5y = 5 7x + 5y = 25 what would be x and y for them
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The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

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An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

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Answer:

$195

Step-by-step explanation:

40% represents £130

40% : $130

100% : total

To find total:

($130 / 40) x 100 = $325 is the total

If $130 spent:

$325 - $130 = $195 is the amount left

The height of the tree is the man's height plus x.

\(\tan 26^{\circ}=\frac{x}{16}\\x = 16 \tan 26^{\circ}\)

So, the height of the tree is \(\boxed{(16 \tan 26^{\circ}+1.8) \text{ m}}\)

Answer:

A. 281.25-525a=2.75s

Step-by-step explanation:

The equations that could represent the relationship between the number of students, s, the number of adults, a, and the dollar amount received at the game is 281.25 – 5.25a = 2.75s

The statements about the relationship between the two triangles below that are true include the following:

B. Angle C is congruent to angle S

C. Angle D is congruent to angle T.

E. Triangle DCA is similar to triangle TSR.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the pairs of corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following congruent angles and similar triangles:

∠C ≅ ∠S

∠D ≅ ∠T

ΔDCA ≅ ΔTSR

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Complete Question:

Which statements about the relationship between the two triangles below are true? Check all that apply. Triangle ACD. Angle D is 60 degrees and angle A is 74.9 degrees. Triangle RST. Angle R is 74.9 degrees and angle S is 45.1 degrees.

- Angle C is congruent to angle T

- Angle C is congruent to angle S

- Angle D is congruent to angle T

- Triangle DCA is congruent to triangle TSR

- Triangle DCA is similar to triangle TSR

- Triangle CAD is similar to triangle TSR

- Triangle CAD is congruent to triangle TSR

Answer:

y = 6x + 22

General Formulas and Concepts:

Pre-Alg

Algebra I

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Point (-3, 14)

Point (-1, 16)

Step 2: Find slope m

Step 3: Find y-intercept b

Step 4: Write linear equation

y = 6x + 22

The gender of the manatees could be an important variable when studying manatees. Gender is an a. categorical variable.

An example of a categorical variable is one that divides data into categories. Here, the categorical variable represents a particular gender while studying manatees. Rather than using numerical values, categorical variables are typically expressed by labels or terms like owns or rents. Researchers may more readily identify and analyse data by employing categorical variables. Thus, a categorical variable here is gender.

Variables that typically fall into separate categories or groups are known as categorical variables, and they cannot be quantified on a continuous scale. Gender is a categorical variable in study of manatees because it may be categorised into distinct groups, such as male or female, without the need of quantitative measures.

Complete Question:

Gender of the manatees could be an important variable when studying manatees. what type of variable is gender?

a. Categorical

B. Quantitative

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9514 1404 393

Answer:

  x < -2  or  3 < x

Step-by-step explanation:

6x -4 > 14

  6x > 18 . . . . add 4

  x > 3 . . . . . . divide by 6

3x +10 < 4

  3x < -6 . . . . subtract 10

  x < -2 . . . . . divide by 3

The solution is the union of disjoint sets:

  x < -2  or  x > 3

Answer:

The required option are

Length = 4 and width = x+5

Length = 2 and width = 2x+10

Step-by-step explanation:

Area of the rectangle = Length × width

Given

Area = 4x+20

Factoring out the common terms

Area = 4x + 4(5)

Area = 4(x+5)

Length = 4 and width = x+5

This can also be written as

Area = 2(2x+10)

Length = 2 and width =2x+10

6√5 - 4√3-

i took the test but sorry if its wrong

Answer:

614400°

Step-by-step explanation:

Answer:

1) Yes

2) 2.07 hours/day

Step-by-step explanation:

1)

2.2 + 4 + 2 1/4 + 0 + 1.9 =

= 6.2 + 2.25 + 1.9

= 10.35

She danced a total of 10.35 hours, so she did meet her goal.

2)

10.35/5 = 2.07

She danced an average of 2.07 hours per day.

Answer:

why does it say right twice? ...

Answer: 120

Step-by-step explanation:

100 + 20 = 120. that's it

Step-by-step explanation:

Simple

Total no of marbles = 6 + 4 + 8 = 18

Probability of red marble = 6 / 18 = 1/ 3

Answer:

No

Step-by-step explanation:

one-half is bigger than one-quarter of the same square

Number of Excavation                                  Height of Soils(inches)

0                                                                       3 ins

1                                                                        5 ins

5                                                                       13 ins

10                                                                      23 ins

A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.

A math word problem is a question that is phrased as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."

In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

It is already noted that when Levi starts digging the hole is already 3 inches dip with soil

In each excavation he digs 2 inches of soil each

So, when number of Excavation is :

Zero :  the inches of soil is 3 inches

One : the inches of soil is 3+2 = 5 inches

Five : the inches of soil is 3+2*5 = 13 inches

Ten :the inches of soil is 3 + 2*10 = 23 inches

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The answers of the questions that you have asked is given below on the basis of mathematics.

Average, also known as mean, is  measure of central tendency in statistic that represents the typical value or central value of  set of numbers. It is calculated by adding up all the values in a set and dividing the sum by the total number of values in the set

3)  Kasha's car gets an average of 25 miles per gallon (135 miles / 5.4 gallons = 25 mpg). For a 300-mile road trip, she would need 12 gallons of gas (300 miles / 25 mpg = 12 gallons). At $2.59 per gallon, filling up her tank would cost her $31.08 (12 gallons x $2.59/gallon = $31.08).

4)  Using the scale of 4 inches = 50 feet, we can set up a proportion to find the height of the model: 4 inches/50 feet = x/120 feet. Cross-multiplying, we get 50x = 4 x 120, which simplifies to 50x = 480. Dividing both sides by 50, we get x = 9.6 feet. Therefore, Dale's model is 9.6 feet tall.

5)  If 1/2 inch on the map represents 75 miles in reality, then 1 inch on the map represents 150 miles (since 2 x 75 = 150). Therefore, 31/4 inches on the map represents 31/4 x 150 = 487.5 miles in reality.

6)  We can use a proportion to find the scale of the model: 8 inches/x = 250 feet/1. Cross-multiplying, we get 8x = 250, which simplifies to x = 31.25. Therefore, the scale of the model is 1:31.25 (or 1/31.25).

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The total number of students at the party after the new boy students joined is: x + n = (x + n).

The original number of students attending the school party was x. Of those x students, y were girls and z were students who liked to dance. After the new boy students joined the party, the total number of students increased to x+n, where n is the number of new boy students who joined. All of the new boy students (n) like to dance.

The new number of students who like to dance can be calculated by adding the original number of students who liked to dance (z) and the number of new boy students who like to dance (n).

Therefore, the total number of students who like to dance after the new boy students joined the party is:

z + n = (x x y) + n

The total number of students at the party (x+n) can be calculated by adding the original number of students (x) and the number of new boy students (n).

Therefore, the total number of students at the party after the new boy students joined is: x + n = (x + n) .

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Answer: $16

Step-by-step explanation:

If both computers work together it will take them 12 minutes to do the same job.

We will be using the given formula :

Time = (W) / (V1 + V2), where W is the amount of work to be done, and V1 and V2 are the efficiencies of two workers.

Let the amount of work to be done be 1 (all the email sent).

The efficiency of the slower computer is 1/30.

The efficiency of the faster computer is 1/20.

When both computers work together, the efficiency of the slower computer and the efficiency of the faster computer are added, so their efficiency is 1/30 + 1/20 = 1/12.

Substituting the values in the formula, we have :

Time = (W) / (V1 + V2)

Time = (1 ) / (1/30 + 1/20)

Time = (1) / 1/12

Time = 12 minutes

Therefore, if both computers work together, it will take them 12 minutes to do the same job.

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Answer:

The equation of the graph is;

y = 4·x

Step-by-step explanation:

The coordinates of two points, (x₁, y₁), and (x₂, y₂) respectively on the straight line graph are;

(-3, 12), and (2, 8)

The slope, m, of the straight line graph is given as follows;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Therefore, by substitution of the values, we have;

\(Slope, \, m =\dfrac{8-(-12)}{2-(-3)} = \dfrac{8 + 12}{2 + 3} =\dfrac{20}{5} = 4\)

The equation of the graph in point slope form is therefore;

(y - 8) = 4×(x - 2)

y = 4·x - 8 + 8 = 4·x

y = 4·x.

The equation that represent the number of floors in building is y = h/12

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

To solve this problem, we have to state the equation using the information of the problem:

Information about the problem:

Writing the equation according to the information gave, we have:

y = h/12

The "y" variable is the dependent variable, it will change according to the height of the building (x).

The "x" variable is the independent variable, because it doesn't depend on any other value, just the height of the building.

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The key approach is to analyze the relationship between the number of solutions to the equation Ax = 0 and the result of Gaussian elimination.

Since the columns of A are linearly dependent, there exist scalars c1, c2, ..., cn (not all zero) such that c1a1 + c2a2 + ... + cnan = 0, where ai represents the columns of A. We can rewrite this equation as a system of linear equations: Ax = 0, where x = [c1, c2, ..., cn]T is a column vector.

The linear dependence of the columns implies that the system Ax = 0 has infinitely many solutions, as we can always find non-trivial combinations of the columns that yield the zero vector.

Now, let's consider applying Gaussian elimination to matrix A. Gaussian elimination transforms the matrix into reduced row echelon form. If the resulting matrix has at least one row of all zeros, it means that there is at least one free variable in the system Ax = 0. This indicates that the system has infinitely many solutions.

Since the system Ax = 0 has infinitely many solutions, and the result of Gaussian elimination with a row of all zeros indicates linear dependence, it follows that the rows of A must also be linearly dependent. Therefore, the linear dependence of the columns implies the linear dependence of the rows.

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Answer:

0.10

Step-by-step explanation:

0.10 = 10/100 or 10%

Multiply 400*0.10 to get 10% of 400.