Prove that limx→2 2^x=4 using the formal definition of limit​.​

Observing the given figure , It is a balanced balance which signifies both side should be equal, The answer is 2=-8-x and x=-10.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.

There are three ways to solve systems of linear equations :

2=-8-x is the required balanced equation.

-x = 2 + 8

x= -10

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The Venn diagram to illustrate this information is given 24 children got plantain and 18 rice and 21 chose beans.Following relation are given below.

A  Venn diagram is a diagrammatic representation of two or more sets.The Venn diagram shows the relationship among sets using circles and the area they cover concerning each other.Venn diagrams are used to visually depict sets, relationships between sets, and operations on sets.

∪ symbol shows Union of two sets. A complete Venn diagram represents the union of two sets. ∩ shows the Intersection of two sets.Intersection represents something that you want to compare and contrast. Where the two circles intersect we would write traits that the two things have in common.

Now

The number of children who took plantain and beans only are:

Let  beans = a

Rice = b

Plantain = P

So:  a + b = 24 - 9 - 5 = 10

Note that 24 children took plantain.

9 children took only Plantain.

5 took the 3 food items.

So,

b + c = 18 -2 - 5 = 11

a + c = 21 - 3 - 5 = 13

P∩B = a + 5

= 6 + 5 = 11

R ∩ B = C + 5

=7 + 5 = 12

None of the three items of food =  

50 - (3 + 2 + 9 + 6 + 4 + 7 + 5)

= 50 - 36

=14

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Answer:

48 ounces of Mixed Nuts

Step-by-step explanation:

You need to convert pounds to ounces to find the answer to this problem.

1 pound is 16 ounces, so multiply 3 by 16 for your answer,

The required first five terms of the sequence are 2, 10, 50, 250, and 1250.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The first five terms of the sequence, a(n), defined by the recurrence relation a(n+1) = 5a(n) and a(1) = 2, are as follows:

a(1) = 2

a(2) = 5a(1) = 5 × 2 = 10

a(3) = 5a(2) = 5 × 10 = 50

a(4) = 5a(3) = 5 × 50 = 250

a(5) = 5a(4) = 5 × 250 = 1250

Therefore, the first five representations of the sequence are 2, 10, 50, 250, and 1250.

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On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is 500

obtained is 400

so, percentage - 400/500 X 100 = 80%

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Answer: 5:3

Step-by-step explanation:

note: 16 ounces= one pound          
6 ounces = ?

∴6 ounces = pounds

48 cents = pounds

multiplying both sides by 

108 cents = 1 pound in the new price

= $1.08 in the new price 

ratio of old price to new price = 

therefore ratio of old to the new price = 5:3

Answer: four textbooks

Step-by-step explanation:

Due to the fact that element 1 relates to two distinct images, namely 3 and 5. The relationship hence is not a function.

Therefore,

(i) {(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)

Every input has a single output, proving that it is a function.

The elements in the domain of the provided relation are therefore 2,5,8,11,14, and 17.

Here, domain is equal to two and range is one.

(ii) (2,1),(4,2),(6,3),(8,4),(10,5)(12,6),(14,7)

Every input has a single output, proving that it is a function.

Therefore, 2, 4, 6, 8, 10, 12, and 14 make up the domain of the provided relation.

Here, range is 1,2,3,4,5,6,7 and domain is 2,4,6,8,10,12,14.

(iii) (1,3),(1,5),(2,5)

Due to the fact that element 1 relates to two distinct images, namely 3 and 5. The relationship hence is not a function.

The complete question is:

Which of the following relations are functions? Give reasons.

If it is a function determine its domain and range

(i) (2,1),(5,1),(8,1),(11,1),(14,1),(17,1)

(ii) {(2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7)

(iii) {(1,3),(1,5),(2,5)

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The slope of the table shown in the image attached below is equal to: D. 1/3.

Mathematically, the slope of the given table can be calculated by using the following mathematical expression;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided in the table, we have the following data points:

Points on x-axis = (-2, 2).

Points on y-axis = (-4, -2).

Substituting the given points into the slope formula, we have;

Slope, m = (12 - 8)/(15 - 3)

Slope, m = 4/12

Slope, m = 1/3

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Answer:

To calculate the percent of change for your grade, you will need to know your original grade and your revised grade. If you originally got 5 questions right and you checked your work and ended up with 15 questions right, you can calculate the percent of change as follows:

Subtract your original score from your revised score to find the difference: 15 - 5 = 10

Divide the difference by your original score and multiply by 100 to express the change as a percentage: (10 / 5) x 100 = 200%

This means that your grade increased by 200%.

Step-by-step explanation:

Answer:

$5043

Step-by-step explanation:

To find the value of the investment after 12 years, you can use the following formula:

A = P * (1 + r/n)^(nt)

Where:

A = final amount

P = principal

r = interest rate

n = number of times the interest is compounded per year

t = number of years

Plugging in the values from the problem, we get:

A = 3600 * (1 + 3.5/100)^(1*12)

Solving this equation, we get:

A = $5043.33

So, after 12 years, the investment will be worth $5043.33.

Answer:

2028

Step-by-step explanation:

156 x 13 = 2028

The point shown on the graph is

(4, -5, 6)

An ordered triplet of lines (the axes) that are pair-wise perpendicular and pass through the same point (the origin) make up a Cartesian coordinate system for a three-dimensional space.

Each axis also has an orientation, and the length of all three axes is equal.

In ordered triplet, the order of the axis is (x, y, z)

z is vertical up positive and down negative

y is horizontal right is positive and left is negative

x is the axis pointing to us which is positive pointing away is negative

Using this information, to trace the point shows that the point marked by a dot is  (4, -5, 6).

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The percentage of the exam that she has taken is 75%.

Percentage is a measure of frequency that is used to express the ratio of an amount as a number out of 100. The sign that is used to represent percentage is %.

In order to convert a number to percentage, multiply the number by 100. In order to determine the percent of exams that she has taken, multiply the ratio of exams taken and the total number of exams by 100.

Percent of the exams she has taken = (number of exams taken / total number of exams) x 100

Percent of the exams she has taken = (27 / 36) x 100

Percent of the exams she has taken = 75%

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Answer:

linear function can be found by looking at a linear graph and determining the equation of the line and converting that equation into a function.Step-by-step explanation:

The steps to do this are: Find the y-intercept (this is equal to b in the formula) Find the slope of the line (this is equal to m in the formula)

Answer:

  57

Step-by-step explanation:

You want a positive number that gives a product of 1995 when it is multiplied by each of its digits.

The prime factors of 1995 are 3, 5, 7, 19. The product of 3 and 19 gives 57, so multiplying 57 by 5 and 7 will result in the product 1995.

The original number is 57.

<95141404393>

Area and circumference of the circle are 78.5 m² and 31.4 m respectively.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that, a circle have a radius 5 m

Area of a circle = π × radius²

Circumference = 2π×radius

Area = 3.14 × 5² = 3.14 × 25 = 78.5 m²

Circumference = 3,14 × 2 × 5 = 31.4 m

Hence, area and circumference of the circle are 78.5 m² and 31.4 m respectively.

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equation in slope-intercept form of the line that pae through the point (4, 7) and is parallel to the line represented by y = 2x - 5 is ( y - y1 ) = m( x - x1 ) => y - 7 = 2 (x-8) => 2x - y - 1 = 0

A number that specifies a line's direction and slope is known as the slope or slope of a line in mathematics. A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x).

equation is -

y = 2x - 5

since these are parallel to each other,

slope, m= 2

now the equation is -

( y - y1 ) = m( x - x1 )

y - 7 = 2 (x-8)

2x - y - 1 = 0

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As a result, you are turning the entire trapezium figure 90 degrees clockwise in order to change the trapezoid LMNQ into L′M′NQ′.

In American and Canadian English, a trapezoid is a quadrilateral with at least one set of parallel sides. In British and other versions of English, the word is a trapezium. A trapezoid is always a convex quadrilateral in Euclidean geometry. The parallel sides of the trapezoid are referred to as its bases.

Given: When (-7,-2) to L, L becomes L' (-2,7)

You will often obtain a rotation of 90 degrees clockwise or 270 degrees counterclockwise around the origin (0,0), as well as a reflection across the x-axis and across the line of symmetry of the image, if you have (x,y) and it becomes (y,-x).

The entire graphic is therefore rotated 90 degrees in a clockwise orientation.

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The translation of the sentence "4 times as large as the product of w and 11" to an expression is 44w

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

“4 times as large as the product of w and 11.”

The number is represented with w

So, the statement remains unchanged as follows

“4 times as large as the product of w and 11.”

4 times as large means 4 *

So, we have the following representation

4 times as large as the product of w and 11 ⇒ 4 * the product of w and 11.

the product of means that we multiply

4 times as large as the product of w and 11 ⇒ 4 * w * 11

Evaluate the products

This gives

4 times as large as the product of w and 11 ⇒ 44w

Hence, the expression is 44w

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On solving the provided question, we can say that - the plotting data will be done by 3 to 24 ; 6 to 61 ; 5 to 56; 1 to 15

A graph that demonstrates the relationship between two or more variables is the most common way to depict a data set using a chart. Both hand-drawn and computer-drawn diagrams are acceptable. Start at the origin and move 2 units to the right before moving 3 units up to draw the coordinates for the point 2,3 on the coordinate plane. Make your points clear. As a result, the pink dot with the letter P on it denotes 2.3. A number line containing each value in your data collection should be first created before making a line chart. Then, on the number line, put an X (or dot) over each value of the data. Put an X over the number for each time a value appears in a record where it does.

so we have to plot data from the given data, we can do by

3 to 24 ; 6 to 61 ; 5 to 56; 1 to 15

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On solving the provided question, we can say that - the percentage value of 12 % of 90 = 10.8

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

12% of 90 = 12/100 X 90

= 0.12 X 90 = 10.8

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

V =355/113 * (5)² * 7  thus correct option is V equals 355 over 113 times 6 squared times 8.

Volume, which is expressed in cubic units, is a unit of measurement for the 3-dimensional space occupied by matter or encircled by a surface. The SI unit of volume = area * height is the cubic metre (m3), which is a derived unit. A "litre" (L) is the name given to the cubic decimeter (dm3).

Here,

The volume of cylinder = πr²h

Given : Diameter = 12 inches

radius = 12/2 = 6 inches

Height = 8 inches

Thus ,

To find the volume  we put the all the above values in the formula:

=> V = πr²h

=> V = 22/7 * 6² * 8

=> V =355/113 * (6)² * 8

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

V =355/113 * (5)² * 7  thus correct option is V equals 355 over 113 times 6 squared times 8.

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Answer:

V equals 355 over 113 times 6 squared times 8.

Step-by-step explanation:

Answer:

r=3

Step-by-step explanation:

use slope formula : y2-y1 / x2-x1

-5-3 / r-5

the numerator is -8 which means the denominator has to be -2 in order to have the slope be 4

so r-5 = -2

3-5 = -2

Answer:

  y = -5x -19

Step-by-step explanation:

You want the equation of the line parallel to y=-5x+3 through point (-3, -4).

The equations of parallel lines differ only in their constant. We can find the new constant by using the values at the given point:

  y = -5x +b

  -4 = -5(-3) +b

  b = -4 -15 = -19 . . . . . . subtract 15

The equation is ...

  y = -5x -19

Answer:

B, C, E

Step-by-step explanation:

Let y = length.

Then, y - 5 = width.

area = length × width

area = y(y - 5)

area = 750

y(y - 5) = 750

y² - 5y = 750

A: y(y + 5) = 750

Since y = length, width must be y - 5, not y + 5, so A does not work.

B: y² - 5y = 750

This is what we got above, so this equation works.

C: 750 - y(y - 5) = 0

750 = y(y - 5)

750 = y² - 5y

This is the same as B and works.

D: y(y - 5) + 750 = 0

y(y - 5) = -750

The area cannot be -750, so this equation does not work.

E: (y + 25)(y - 30) = 0

y = -25 or y = 30

This also works.

Answer: B, C, E

Answer:

1st question :55%

2nd ":122.22%

3rd ":81.82%