The estimated population of a certain city over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential.
Number of Years Since Last Census, x
1
2
3
4
Estimated Population, f(x)
49,372
58,207
66,998
75,798


function would best fit the data because as x increases, the y values change
. The
of this function is approximately
.

In order to properly solve a system of linear equations utilizing matrices, you must abide by the below instructions:

First, create a matrix representation of the system of equations.  

Second, generate an augmented matrix by merging the coefficient matrix together with the constant matrix.

Third, apply elementary row operations in order to transform the augmented matrix into either row echelon or reduced row echelon form.

Fourth, use back substitution to accurately determine the variable values.

Ultimately, enter this solution into the original equation in order to obtain the primary variable value.

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

Solving linear equations using matrices involves steps ranging from creating an augmented matrix, performing row operations, back substitution, and then interpreting results

To solve a system of linear equations using matrices, follow these step-by-step instructions:

Step 1: Write the system of linear equations in matrix form.
Represent the coefficients of the variables as a matrix (called the coefficient matrix), and the constants on the right side of the equations as another matrix (called the constant matrix).

Step 2: Create the augmented matrix.
Combine the coefficient matrix and the constant matrix into a single matrix by appending the constant matrix as an additional column. This combined matrix is called the augmented matrix.

Step 3: Perform row operations to achieve row-echelon form.
Use row operations (swapping rows, multiplying a row by a constant, or adding/subtracting rows) to manipulate the augmented matrix into row-echelon form. Row-echelon form has zeroes below the diagonal and non-zero elements on the diagonal.

Step 4: Perform back-substitution.
Starting from the last row of the row-echelon form matrix, solve for the variables using back-substitution. Substitute the values of the variables you find into the previous rows to determine the remaining variable values.

Step 5: Interpret the results.
Once you have solved all the variables, you have found the solution to the system of linear equations. If there are infinitely many solutions or no solutions, this will be indicated by the row-echelon form.

To know more about augmented matrix refer to

https://brainly.com/question/12994814

#SPJ11

The shortest path from vertex A to vertex L in the given diagram is ABDGJLKFI, with a total length of 89.

We can find the length of the shortest path from vertex A to vertex L by calculating the sum of the shortest paths from A to C to F to I to L.

Using Dijkstra's algorithm, we can find the shortest path from A to C, then from C to F, then from F to I, and finally from I to L.

The shortest path from A to C is AB + BC = 3 + 16 = 19. The shortest path from C to F is CF = 25. The shortest path from F to I is FI = 21. The shortest path from I to L is IL = 24.

Therefore, the length of the shortest path from A to L is 19 + 25 + 21 + 24 = 89.

To know more about vertex:

brainly.com/question/14815086

#SPJ1

The calculated length of XY in the right triangle XYZ is 6

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

The right triangle

The value of XY in the right triangle can be calculated using the following sine ratio

sin(30) = XY/XZ

So, we have

sin(30) = XY/12

Cross multiply the equation

So, we have

XY = 12 * sin(30)

Evaluate the products

XY = 6

Hence, the length of XY in the right triangle is 6

Read more about right triangleat

brainly.com/question/2437195

#SPJ1

Answer:

7

Step-by-step explanation:

We can use the fact that the corresponding sides of similar triangles are in proportion to each other.

Let's compare the corresponding sides of the two triangles:

Corresponding sides and ratio

Ratio

Since the triangles are similar, we know that these ratios are equal. That is,

6 / (x-3) = 12 / (x+1)

We can simplify this equation by cross-multiplying:

6(x+1) = 12(x-3)

Expanding and simplifying:

6x + 6 = 12x - 36

42 = 6x

x = 7

Therefore, x has a value of 7.

The age of the radioactive element of half-life 5750 years is 11047.8  years.

Radioactive elements are atoms that are unstable in normal conditions and are converted in another different atoms.

To calculate how old is the bone at the time it was discovered, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for t

Learn more about radioactive element here: https://brainly.com/question/23759636

#SPJ1

Answer:

70.7°

350 feet

Im not too sure about the last one

Answer:

1. f. System of Equations

2. e. No solutions

3. i. One solution

4. h. Like Terms

5. b. Substitution

6. c. Solution

7. a. Elimination

8. d. Infinitely Many Solutions

9. g. Variable

10. j. Coefficients

Step-by-step explanation:

Ur welcome :)

An equation that can be used to determine the angle measure, in degrees, of angle DBC is 67 + n = 90.

The measure of n is equal to 23 degrees.

In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).

By substituting the given parameters into the complementary angle formula, the sum of the angles is given by the following mathematical equation;

∠ABD + ∠DBC = 90

∠ABD + n = 90

67 + n = 90.

n = 90 - 67

n = 23°

Read more on complementary angle here: brainly.com/question/17952433

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

-166/, -0.82,

Step-by-step explanation:

The above fraction, decimal are all evaluated answer for (11/16−(3/4)2)×1

The answer in exponent form is 147x^29.

A scientific notation is a method of expressing very large numbers in the form of exponent.

In the given question, we have;

(7x^9)^2*3x^11

applying the law of indices,

(7x^9)^2*3x^11 = (7^2)*x^(9*2)*3x^11

                        = 49x^18*3x^11

                        = (49*3)*x^(18+11)

                        = 147x^29

Thus, the expression can be simplified as: 147x^29.

Learn more about scientific notation at

#SPJ1

You must measure 24 male students to estimate the mean height within one inch with 93% confidence.

Since we want to estimate the mean height within one inch, the margin of error (E) is 1 inch:

E = Z * (Standard deviation / √Sample size)

Now, we can rearrange the formula to solve for the Sample size (n):

1 = 1.81 * (2.7 / √n)

Solving for n:

n = (1.81 * 2.7 / 1)²

n ≈ (4.887)²

n ≈ 23.88

Since we cannot have a fraction of a person, we round up to the nearest whole number:

n ≈ 24

So, you must measure 24 male students to estimate the mean height within one inch with 93% confidence.

Read more on Sample size here: https://brainly.com/question/30224379

#SPJ1

Answer:

C Exponential

Step-by-step explanation:

3x^2 -- its using an exponent

Answer:

Four units left and one unit up

Step-by-step explanation:

Since we're subtracting from x, the figure is going to go toward the left side of the coordinate plane, and since we're adding to y, the figure is going to go up.

The length of the square with a diagonal of 32 cm is 22.6 cm.

A square is a plane shape with all sides and angles equal.

To calculate the length of the square from its diagonal, we use Pythagoras formula

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for l

Learn more about square here: https://brainly.com/question/27307830

#SPJ1

The wrestler's weight at the first match will be 152.1 pounds. The solution has been obtained by using the substitution method.

What is the substitution method?

The substitution method is a strategy used in algebra to solve simultaneous linear equations. In this process, as the name suggests, the value of one variable from one equation is swapped in the second equation.

We are given that the given situation can be modeled by the equation

y = −1.1x + 162.

Now, we need to find weight at the first match which is 9 weeks away.

So, we get that x = 9.

By substituting this value in the equation, we get

⇒ y = -1.1 (9) + 162

⇒ y = -9.9 + 162

⇒ y = 152.1

Hence, the wrestler's weight at the first match will be 152.1 pounds.

Learn more about substitution method from the given link

https://brainly.com/question/30339603

#SPJ1

Mr. Moketsi could help students in their learning of properties of 2D shapes through hands-on activities and discovery, as suggested by the constructivist perspective.

Mr. Moketsi initiates the class by inquiring about their comprehension of 2D shapes and their properties, provoking conversation amongst students as they share their thoughts with their peers and their teacher.

He subsequently introduces an assortment of manipulatives, such as pattern blocks, geoboards, and tangrams to encourage experimentation and inquiry into these geometric figures, while posing thought-provoking questions throughout the lesson to help learners make connections between different shapes with a focus on discovering their unique attributes.

Mr. Moketsi encourages reflection, questioning how this newfound knowledge may be applied in reality, stimulating critical thinking abilities during classroom interaction with surfaces representing planes containing lengths and widths.

Find out more on the constructivism approach at https://brainly.com/question/28170990

#SPJ1

a. To build the airport at the same distance from the center of each town, they should locate the intersection of the perpendicular bisectors of the segments connecting each pair of towns.

b. To build the airport equidistant from each road, locate the intersection of the angle bisectors at each town

The precise location of the airport will be the point where these perpendicular bisectors intersect. This point will be equidistant from the center of each town.

b. To build the airport equidistant from each road, locate the intersection of the angle bisectors at each town. This point is the precise airport location. Equidistant from all connecting roads.

They could find the intersection of the medians of the triangle formed by the three towns. The airport is located at the centroid of a triangle, equidistant from 3 towns at the intersection of medians.

Read more about precise location here:

https://brainly.com/question/1838815

#SPJ1

The contradicting statement is

B. I and III

The contradictory statement is that of I and III since the sum of angles in a triangle is always 180 degrees.

Given that

I. triangle ABC is a right triangle. say angle C = 90 degrees and

angle B = 103 degrees,

So the sum of the angles in the triangle would be:

= angle B + m angle C

= 103 + 91

= 194

This is against the law of angles of a triangle

Learn more about angles in a triangle at

https://brainly.com/question/25215131

#SPJ1

Answer:

Step-by-step explanation:

House

B) Down Payment: $151,800

C) $607,200

D) $819,720

E) $1,426,920

F) $47,564

Car:

B) $2,902.50

C) $16,447.50

D) $3,700.6875 = $3,700.69

E) $20,148.1875 = $20,148.19

F) $335.803125 = $335.80

DONE !!! :)

The amount of medication should they receive per dose is,

⇒ 363.6 mg

Given that;

A patient weighs 160 pounds and needs medication with dosage instructions of 15 mg/kg/day.

And, It is to be given in 3 doses each day.

Hence, We get;

1 pounds = 1/2.2 kg

160 pounds = 160 x 1/2.2 kg

                  = 72.72 kg

Since, It is to be given in 3 doses each day.

Hence, The amount of medication should they receive per dose is,

⇒ 72.72 x 15 / 3

⇒ 363.6 mg

Thus, The amount of medication should they receive per dose is,

⇒ 363.6 mg

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ1

The remaining ribbon will be 14 feet.

Olga decorates blankets with ribbon she has 12 yards of ribbon

and, she uses 22 feet of the ribbon to decorates blankets

Now, we have to find the she decorates the blankets how many feet of ribbon will remain?

Firstly, Convert the yard into feet

We know that:

There are 3 feet in 1 yard

So, 36 feet in 12 yards

Now, The remaining ribbon will be the original amount less the amount used.

=> 36 - 12 = 14 feet

Learn more about Yards at:

https://brainly.com/question/14516546

#SPJ1

A linear function would be the best fit for the given data because as x increase the y-values change linearly.

Rounded to the .5 the slope of the function is approximately 32.5

A linear relation means that any increase of 1 unit in the independent variable (x) has always the same impact in the other variable (y).

In this particular case, the increases in the y-value are:

56 - 24 = 32

88 - 56 = 32

122 - 88 = 34

The mean of that, rounded to .5, is (32 + 32 + 34)/3 = 32.5

So the change is almost the same one, then this seems to be a linear relation.

Learn more about linear relations at:

https://brainly.com/question/13828699

#SPJ1

Answer:

The two numbers are 494 and 504

Step-by-step explanation:

Let x = one of the numbers

Let y = the other number

x + y = 998

x - y = 10   or x = y + 10

Substitute y + 10 for x in the first equation and solve for y

x + y = 998

y + 10 + y = 998  Subtract 10 from both sides

y + y = 988  Combine like terms

2y = 988  Divide both sides by 2

y = 494

One of the numbers is 494.

x = y + 10  Substitute 494 for y

x = 494 + 10

x = 504

The other number is 504.

Check:

x + y = 998

504 + 494 = 998

998 = 998 checks

x - y = 10

504 - 494 = 10

10 = 10 checks

Helping in the name of Jesus.

Based on the image, we can infer that the router cannot cover the kitchen area.

To calculate if the router covers the living room and kitchen area, we must identify the area that the router can cover. In this case, the router covers an area of 850 square feet. However, we must take into account that this area is counted around the router.

From the above, we can infer that the router has signal coverage of 14 meters around it, so it would only cover the living room area.

Learn more about routers in: https://brainly.com/question/29869351

#SPJ1

The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

Read more about Midpoint of Line segment at: https://brainly.com/question/896396

#SPJ1