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

Answer:

A.  x ≥ 21[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

81 - 1[tex]\frac{1}{5}[/tex] x ≤ 55

-1[tex]\frac{1}{5}[/tex] x ≤ 55-81

-[tex]\frac{6}{5 }[/tex] x ≤ -26

x ≥ -26(-[tex]\frac{5}{6}[/tex])       **flip the inequality when you divide by a negative number

x ≥ 21[tex]\frac{2}{3}[/tex]

0.36d³ - 4.31d² - 2.5d - 2 = 0 is the function and the graph of the function is given below -

function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable).

y = x² is an illustration of this. Any input for x yields a single output for y. Because x represents the input value, one can state that y is a function of x.

To determine the number of days after the game's release that was played by the same number of students for the two functions S^1(d) and S^2(d).

Here, the functions each model the number of students S.

played an online video game d days.

We need to set the two functions equal to each other and solve for d.

S^1(d) = S^2(d)

or,  0.45d³ - 3d² + 4.75d + 16  = 0.09d³ - 1.31d² + 7.25d + 18

Subtracting 0.09d³ - 1.31d² + 7.25d + 18 from both sides we get:

or, 0.36d³ - 4.31d² - 2.5d - 2 = 0

So, the graph becomes:

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Answer:

It is 6.4*10^-2.

this is your answer

The pound of cement used based on the information will be C. 2 pounds.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.

The pound of cement used will be:

Gravel = 1 2/3 × 3

= 5 pounds

Cement used will be:

= 2/5 × 5.

= 2 pounds.

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Answer:

27

Step-by-step explanation:

To find 45% of 60, you can multiply 60 by 0.45

60 x 0.45 = 27
45% of 60 is 27.

1.  you are asked to find how many weeks it would take Alex to work 51 hours.

2. Alex  works  [tex]3\frac{1}{7}[/tex] weeks.

3. It makes sense in fractional from.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.

Alex works 3 hours a day and 4 days a week.

Alex works in a week = ( 3×4) hour = 12 hour

Alex  works = 51 hours = 48 hours + 3 hours = (48/12) weeks + 1 day

= 3 weeks and 1 day.

= [tex]3\frac{1}{7}[/tex] weeks.

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Answer:

The set A is defined as the set containing the elements c, d, e, f, and g.

The set B is defined as the set of odd numbers greater than 5 and less than 13. This set includes the elements 7, 9, and 11.

Step-by-step explanation:

By drawing the line x + y = 2, one of the solution to the given system of equations is (0, 2).

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²  

Where:

From the information provided, we have the following system of equations:

x² + y² = 9             ......equation 1.

x + y = 2              .............equation 2.

Next, we would use an online graphing calculator to plot the given system of equations and then highlight (read) the point of intersection, which is the ordered pair (0, 2).

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There are 3,024 different ways 1,214 can be shown.

Basically A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.

Given 1,214

since there are 4 places in the digit,

so 4 values less than 10 can be solved by

9, 8, 7, and 6

so by permutation to find ⁹P₄ = 9!/(9 - 4)!

= (9 x 8 x 7 x 6 x5!)/5!

⁹P₄  = 3,024

Hence there are 3,024 different ways.

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Answer:14 a

Step-by-step explanation:

The explanation is that it is E

Answer:

  $202.30

Step-by-step explanation:

You want to know the value of a 20% tip on a bill of $1011.50.

The tip amount can be found by multiplying the bill amount by the tip percentage:

  20% · $1011.50 = $202.30

Lucas tipped the server $202.30.

__

Additional comment

You know that 10% of the amount can be found by moving the decimal point one place: $101.15.

20% of the amount will be double this value: $202.30. You can do this math mentally.

Answer:

I hope this helps. Let me know if you have any doubts. Have a nice day!!

============================================================

Explanation:

We'll need to find the slope of the line through the two given points.

[tex](x_1,y_1) = (-3,17) \text{ and } (x_2,y_2) = (2,-3)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-3 - 17}{2 - (-3)}\\\\m = \frac{-3 - 17}{2 + 3}\\\\m = \frac{-20}{5}\\\\m = -4\\\\[/tex]

The slope is -4.

Think of -4 as -4/1. The reciprocal is -1/4, and it flips in sign to +1/4 or simply 1/4.

The original slope -4 leads to the perpendicular slope 1/4. The two slopes multiply to -1. This is true of any perpendicular lines where neither is vertical nor horizontal.

------------------------

In short, the answer equation will involve a slope of 1/4. This points us directly to choices A and E as two answers so far.

Something like choice B is not an answer since it has slope 4. Choice C is ruled out because 4x+y = -8 solves to y = -4x-8. It has a slope of -4.

Choice D on the other hand has x-4y = 2 solve to y = (1/4)x - 1/2, and this has a slope of 1/4 that we want. This means choice D is another answer.

Choice F and choice G are ruled out because they involve slopes of 4 and -4 respectively.

------------------------

Summary: The 3 answers are choices A, D and E

Step-by-step explanation:

the slope of a line is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

so for (-3, 17) and (2, -3) we get

x changes by +5 (from -3 to 2).

y changes by -20 (from 17 to -3).

the slope is

-20/+5 = -4/1 = -4

now, a perpendicular slope (90° to the original slope) is putting the slope fraction upside-down and flips the sign :

+1/4 or simply 1/4.

the slope in an equation of the form "y = ..." is always the factor of x.

y + 2 = (1/4)(x - 1)

yes, there are only some constant additions or subtractions to get to a or "y = ..." form, so 1/4 is indeed the factor of x and the slope of this line.

y = 4x + 12

4 <> 1/4, so, no, it is not.

4x + y = -8

y = -4x - 8

-4 <> 1/4, so, no, it is not.

x - 4y = 2

-4y = -x + 2

y = (1/4)x - 2/4

1/4 is indeed 1/4, so, yes, it is.

y = (1/4)x - 15

1/4 is indeed 1/4, so, yes, it is.

y + 3 = 4(x - 2)

similar to the first one, but 4 <> 1/4, so, no, it is not.

y = -4x + 3

-4 <> 1/4, so, no, it is not.

The probability that the next customer will pay cash or a credit card is 56%, since 3 customers paid cash and 53 customers used a credit card out of a total of 81 customers.

Customers are individuals or organizations who purchase goods and services from a business. They play an important role in a company's success as they provide the revenue needed to sustain and grow the business. Customers become loyal to a business when they are provided with quality products, excellent customer service, and competitive prices. Companies that focus on customer satisfaction often develop long-term relationships with their customers, as they understand the importance of customer loyalty. Companies must strive to continually meet the changing needs of their customers in order to remain successful in the long term.

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Answer: 2.25 grams

Step-by-step explanation:

In this problem, we are given the ratio of grams to weight. Since we are trying to find how many grams to give to a person with a specific weight, we can use proportions to solve.

[tex]\frac{150mg}{5kg} =\frac{x}{75kg}[/tex]               [cross multiply]

[tex]11250=5x[/tex]                  [divide both sides by 5]

[tex]x=2250mg[/tex]

We are almost done with the problem. The problem is asking for grams, not mg, so we can use unit conversions to change that.

[tex]\frac{1000mg}{1g}=\frac{2250mg}{y}[/tex]          [cross multiply]

[tex]1000y=2250[/tex]               [divide both sides by 1000]

[tex]y=2.25[/tex]

Therefore, we need to give 2.25 grams.

The amount of syrup she needs is 3/4 cups of syrup. Option A

A fraction can be described as the part of a whole variable, element or number.

The several types of fractions are;

Also, proportion can be defined as a mathematical comparison between two numbers

From the information given, we have that;

6 cups of soap = 1 /4 cup of syrup

Then 18 cups of soap = x cups of syrup

cross multiply, we get;

6x = 18(1/4)

multiply the values

6x = 18/ 4

Divide both sides by the coefficient of x , we get;

x = 18/ 4 × 1/6

x = 3/ 4 cup of syrup

Hence, the value is 3/4

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Answer:

−12r+32−2r 2

Step-by-step explanation:

(−8−r)(2r−4)

Apply the distributive property by multiplying each term of −8−r by each term of 2r−4.

−16r+32−2r

2

+4r

Combine −16r and 4r to get −12r.

Answer:

R-12

Step-by-step explanation:

Open the parenthesis, then solve

-8-r + 2r-4

-r+2r-8-4

r-12

Your answer will be R-12

Answer:

Step-by-step explanation:

You want to solve graphically the system of inequalities expressing that Rashaad has no less than a total of 18 dimes (x) and nickels (y) with a combined value of at most $1.50, of which at least 4 are dimes.

An inequality can be written for each of the constraints:

  x + y ≥ 18 . . . . . . . no less than 18 coins

  0.10x +0.05y ≤ 1.50 . . . . . . at most $1.50 in value

  x ≥ 4 . . . . . . . . . . at least 4 dimes

A graph of these inequalities is attached. The marked points are the vertices of the triangular solution space. Each is a possible solution, along with all of the grid points inside the triangle.

One possible solution is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.

Using graph to solve the system of linear inequality the most likely solutions will be 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50

Systems of linear inequalities are equations with two or more linear inequalities that contain two or more variables. These equations can be used to represent real-world problems and to find the solutions of such problems. The solutions of a system of linear inequalities are all the points that are common to all of the linear inequalities in the system.

In this problem, we have to define our variables and then solve this using graphical method. The point of intersection between the two lines lies the solution to the linear inequality.

Let;

x + y ≥ 18

0.1x + 0.05y ≤ 1.50

x ≥4

Using a graphing calculator to solve this,

The possible solutions is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.

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Answer: To find the expected amount of money the radio caller should win, you can multiply the prize amount by the probability of winning that prize, and add those products for each prize. The expected value is also known as the mean value.

$500 * 1/8 = $62.50

$750 * 1/8 = $93.75

$1,250 * 1/8 = $156.25

$2,500 * 1/8 = $312.50

$5,000 * 1/8 = $625.00

$10,000 * 1/8 = $1250.00

$25,000 * 1/8 = $3,125.00

Total expected value = $62.50 + $93.75 + $156.25 + $312.50 + $625.00 + $1250.00 + $3,125.00 = $5,050.00

So, the expected amount of money the radio caller should win if the caller gets to spin the wheel once is $5,050.

It's worth to mention that the probability for each prize is the same, but the prizes are not the same so each prize win will be different according to the prize amount.

The expected value doesn't assure that the prize will be won, but it's a good approximation of the prize the caller could win.

Step-by-step explanation:

By using concept of angle relationship, we get x equal to 27°.

We compare the position, measurement, and congruence of two or more angles when we talk about angle relationships. For instance, two pairs of vertical angles are created when two lines or line segments intersect.

∠BAF+∠EAF=180°

∠EAF=180° - 138°

∠EAF=42°

Since, ∠EAF and ∠BAC are vertically opposite angle,

Hence,

∠EAF =  ∠BAC =42°

Again,

∠EAD+∠DAC+BAC=180°

4x+30°+42°=180°

4x=180°-72°

4x=108°

x=27

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The following statements are true based on the diagram below

When two or more curves, lines, or edges come together, it is called a vertex (plural: vertices or vertexes) in geometry. As a result of this definition, polygonal and polyhedral corners as well as the intersection of two lines to form an angle are referred to as vertices.

The vertex of an angle is the point at which two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location.

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Answer:

Step-by-step explanation:

y= 265

The rate of change of the equation is 25.

The rate at which one quantity changes in relation to another quantity is known as the rate of change function. Simply put, the rate of change is calculated by dividing the amount of change in one item by the corresponding amount of change in another.

Given that the linear equation is y = 25x + 115. The rate of change of the equation is represented by the slope or gradient of the equation of the line.

Here in the equation y = 25x + 115 the rate of change is 25. Which is equivalent to the slope of the line.

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Answer:

it is undefined

Step-by-step explanation:

Slope of the line x=-24 is undefined. We'll compare the line x = -24, with x = h. So this line is a vertical line that is parallel to the y-axis. We know that the slope of the y-axis is undefined. Since x=-24 and y-axis are parallel, so x=-24 will have the same slope, that is undefined.

Answer:

undefined slope

Step-by-step explanation:

When you have the line x=-24, you have a vertical line, where the x-value is constant, given in the equation, but the y-value varies between negative infinity and positive infinity. If we were to plug two points into the slope formula, we would get: [tex]\frac{y_2-y_1}{-24-(-24)}\to\frac{y_2-y_1}{0}[/tex], because there is no change in x, the x values are the same. Thus it is said that the slope is undefined.

Answer:

Domain: All real numbers

Range: All real numbers greater than or equal to -1

The equation connecting y and x is y = 63/x and the value of y when x =21 is 3

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

Variation = inverse variation

y = 7, x = 9

An inverse variation is represented as

k = xy

Where k is the constant of proportion

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

k = 7 * 9

Evaluate

k = 63

So, we have the following representation

xy = 63

Make y the subject

y = 63/x

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

y = 63/21

Evaluate

y = 3

Hence, the solution is 3

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identification of the expression 4x- 2y + 6 = 2x is

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, a linear expression 4x-2y + 6 = 2x

Coefficient:

Coefficients are the numbers by which the variables in an equation are multiplied

Thus, the Coefficient terms for this equation = 4x, -2y, 2x

Constants:

the constant is the part of the expression that does not vary with the value of x and y.

Thus, constant terms for this equation = 6

variable terms:

These are the terms that vary at the different values of x and y.

Thus, variable terms for this equation = 4x, -2y

Like terms:

Terms that have identical variable parts (same variable(s) and same exponent(s))

thus, Like terms for this expression = 4x, 2x

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6. Larry's total sales during the pay period is $20,000.

7. Tom should leave $3 (approximate)

What is the meaning of total sales?

Total sales revenue usually referred to as gross sales is the sum of the value of the products and services a company provides to its clients over the course of a given reporting period.

Given that Larry earns $840 per pay period, plus a commission of 8% on his sales.

Assume that Larry sale $x during the last pay period.

The total earn is 840 + 8% of x

= 840 + 0.08x

According to the question:

840 + 0.08x = 2,440.00

Subtract 840 from both sides:

0.08x = 2,440 - 840

0.08x = 1600

Divide both sides by 0.08

x = 1600/0.08

x = 20,000

The sales is $20,000.

7. Given that,  Tom's bill at a local restaurant was $19.47. He leaves 15% of the total bill as a tip.

15% of $19.47

= 15/100 × $19.47

= 2.920

≈ 3 (approximate)

Tom should leave $3.

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