What is the next number in this pattern? 1, 2, 4, 5, 8, 9, 13, 14, ... A) 15 B) 18 C) 19 D) 20

Answer:

Your answer is 39.8

You basically add all the numbers and divide by how many numbers there are.

4√5 and 12√5 are like radicals as they have the same radicand.

An expression that has a root, typically a square or cube root, is referred to as a radical.

Radicals with the same root number and radicand are like radicals. (expression under the root).

Radicand is the one whose root you are finding.

Given: 4√5 + 12√5 +4

To identify the like radicals.

As we know, like radicals are those having the same radicand.

In the given expression,  4√5 and 12√5 are like as they have the same expression under the root.

Therefore, 4√5 and 12√5 are like radicals.

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The tax due for a single taxpayer by virtue of the tax rate for single filers; 22% as required in the task content is; 14,459.5.

It follows from the task content that the taxable income of the single taxpayer as discussed in the task content is; 65,725.

Since, the tax rate which is alloted to such individual single filers is; 22%.

It simply follows that the tax due on the individual can be determined as follows;

Tax due = 22% of 65, 725

= (22/100) × 65,725

= 14,459.5

Ultimately, the tax due for a single taxpayer by virtue of the tax rate for single filers; 22% as required in the task content is; 14,459.5.

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Answer:

The inequality that describes the problem for the given equation that is 12 + x ≤ 21 is x = 9.

Step-by-step explanation:

It is given that a shuttle bus to Willow Creek Mall has enough seats for 21 people to ride. Right now, there are 12 people on the bus.

It is further provided that,  let x represent how many more people can ride on the bus and we need to find which inequality describes the problem for the given equation that is 12 + x ≤ 21.

Now,

based on the above-mentioned conditions it can be formulated that;

=> 12 + x = 21

After rearranging the terms;

=> x = 21 - 12

=> x = 9

Therefore, the inequality that describes the problem for the given equation that is 12 + x ≤ 21 is x = 9.

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So, the correct equation is equivalent to the x + 9 = ±5. The third option is correct.

What is the quadratic equation?

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation. The general form of the quadratic equation is ax² + bx + c.

Given

(x + 9)² = 25 is a quadratic equation.

How to find the equation results from taking the square root of both sides?

(x + 9)² = 25 is a quadratic equation.

Taking square root on both sides.

(x + 9) = √25

(x + 9) = ±5

So, the equation is equivalent to the x + 9 = ±5.

Thus, the third option is correct.

In the given function if csc = 13/5 then:

So,

cscθ = 13/5 ⇒ 1/sinθ = 13/5

When both sides are flipped:

Tangent is found by knowing that 13 is the hypotenuse because it is the longest side, and 5 is "opposite," so 12 is "adjacent."

And because cosine is adjacent/ hypotenuse, the equation is:

Secθ is the inverse of cos theta, so it is as follows:

So, (B) sin= 5/13 and (D) tan=5/12 are correct.

Therefore, in the given function if csc = 13/5 then:

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The function e(x) = 8/3x - 8 is a linear function and the zeros of the function is x = 3

The function is given as

e(x) = 8/3x - 8

Set the function to 0

So, we have

8/3x - 8 = 0

Add 8 to both sides of the equations

So, we have

8/3x = 8

Divide both sides of the equation by 8

So, we have

1/3x= 1

Multiply both sides of the equation by 3

So, we have

x = 3

Hence, the zeros of the function is x = 3

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Answer:

11 3/8.

Step-by-step explanation:

3 1/2 * 3 1/4

= 7/2 * 13/4

= 91/8

= 11 3/8.

[tex]\begin{array}{ccll} miles&gallons\\ \cline{1-2} 350 & 20\\ 875& g \end{array} \implies \cfrac{350}{875}~~=~~\cfrac{20}{g} \\\\\\ \cfrac{2}{5}=\cfrac{20}{g}\implies 2g=100\implies g=\cfrac{100}{2}\implies g=50[/tex]

The result of simplifying each number 16¹.⁵ using the exponent rules is 2⁽²⁰⁾

To solve this exercise we have to resolve algebraic operations following the exponent rules.

16¹.⁵

Base= 16=  2⁴

The base number 16 is the same as: 2⁴, then we get:

(2⁴)¹.⁵

Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

4⁽⁴*¹*⁵⁾

4⁽⁴*⁵⁾

2⁽²⁰⁾

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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The result of simplifying the expression  y⁵/₇ / y³/₁₄  using the exponent rules is [tex]\sqrt{}[/tex](y)

To solve this exercise we have to resolve algebraic operations following the exponent rules.

[(y)⁵/₇] / [(y)³/₁₄]

Using the quotient that indicates that: the exponent result will be the subtraction of these exponents, we have:

(y)⁵/₇ ⁻ ³/₁₄

(y) ⁽¹⁰⁻³⁾/¹⁴

(y) ⁽⁷/¹⁴)

(y) ¹/²

As we have a fractional exponent, you must convert the exponent to root:

[tex]\sqrt{}[/tex](y)

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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The factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4

The given parameters are

f(x) = x^3 + 5x^2 - 16x - 80

x = -4 is a root

To set up the synthetic division, we start by writing out the coefficient of each term

So, we have

-4 |  1    5    -16    -80

Bring down the first coefficient

-4 |  1    5    -16    -80

      1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)

      1

Add

-4 |  1    5    -16    -80

           (-4)

      1     1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1

Add

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1     -20

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20

Add

So, we have

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20    0

This means that,

Quotient = x^2 + x - 20

Remainder = 0

Expand x^2 + x - 20

x^2 + x - 20 =x^2 + 5x - 4x - 20

Factorize

x^2 + x - 20 = (x + 5)(x - 4)

Recall that the initial root is

x = -4

Rewrite as

x + 4 = 0

So, we have the complete factor to be

f(x) = (x + 4)(x + 5)(x - 4)

Set to 0

(x + 4)(x + 5)(x - 4) = 0

Solve for x

x = -4,  = -5 and x = 4

Hence, the factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4

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Answer:lm

Step-by-step explanation:

The median rating assigned by the agents is  mathematically given as

X=4.35

This is further explained below.

Generally,4.35 is the middle rating that the agents have given the product.

In light of the fact that an airline requested that its agents rate the level of convenience offered by 114 flights departing from one of its hub locations on a scale ranging from 1 to 7, the following graph has to be evaluated in order to discover what the median rating that the agents gave was:

X=(8 x 1 + 11 x 2 + 19 x 3 + 17 x 4 + 23 x 5 + 25 x 6 + 11 x 7) / 114

X=(8 + 22 + 57 + 68 + 115 + 150 + 77) / 114

X=497/114

X=4.35

In conclusion, 4.35 is the median rating that the agents have given the product.

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Answer:

Step-by-step explanation:

55

The equation of the straight line is  y = 7/4 x .

A straight line is an endless, one-dimensional shape with no breadth. It is made up of two connected points on either side of a point that are connected indefinitely. A straight line has no curvature. It could be horizontal, vertical, or inclined.

A straight line's equation is of the form y = mx + c, where m denotes the slope and c the y-intercept.

The concept of a line is strongly tied to how the geometry is described given the range of geometries in contemporary mathematics.

For instance, in analytic geometry, a line in the plane is typically defined as the set of points whose coordinates fulfil a particular linear equation, but in a more abstract setting, such as incidence geometry,

The given points for the line is given by (0, 0) and (4, 7)

Now let us calculate the slope of the line:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting the values we get the slope of the line is

m =  7/4

Now we will use the equation :

y-y₁=m(x-x₁)

y-0 = 7/4(x-0)

or, y = 7/4 x

Therefore the equation of the required line is y = 7/4 x

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The slope of the line with equation - 6y = 2x + 7 is - 1/3.

The slope of a line is the rise-to-run ratio or the rise divided by the run. It gives information about a line's slope in the coordinate plane.

The general equation of a straight line is y = mx +c where m is the slope of the line.

Now,

Consider the equation of the line,

- 6y = 2x + 7

Dividing each side of the equation by 6.

( - 6y/ 6 ) = ( 2x / 6 ) + ( 7/6 )

- y = x/ 3 + 7/ 6

Multiplying each side of the equation by - 1,

- y × - 1 = x/ 3 × -1 + 7/ 6 × - 1

y = - x/3 - 7/6

y = - (1/3) × (x) - 7/6

Now comparing the equation with the general equation y = mx + c.

We get, the slope of the line as:

m = - 1/3

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Answer:

2x^2-x-6 (A.)

Step-by-step explanation:

Hope this helps buddy!

Total number of muffins you would have to sell to make at least $ 250.00 in sales is 100 muffins.

The sales amount can be find by the total sales. That is , if there are n products to sell and selling amount is x rs. then we can easily find the total sales by multiplying them and by this total sales we can easily find the number of items sold per units and vice versa.

In the question given,

amount (A) = $ 250.00

Now take any of two values from table ,

Choose any two points and calculate the slope:

slope = [tex]\frac{50 - 20}{20 - 8}[/tex] =  2.5

thus, y = 2.5x

we can also write this as,

A = 2.5 m , where m is number of muffins

Therefore, m = 250 / 2.5 = 100

Hence, Total number of muffins to sell are 100 .

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The complete question is:

In a bake sale, you recorded the number of muffins sold and the amount of sales in a table as shown.

a. What is a function that relates the sales and the number of muffins?

b. How many muffins would you have to sell to make at least $ 250.00 in sales?

After solving the given inequality the answer is logx+5log₁₀(x-1) ≥ 3.

So,

Given: logx+5 log(x-1) ≥ 3

logx+5 log(x-1) ≥ 3 ⇒ logx+5log₁₀(x-1) ≥ 3

Therefore, after solving the given inequality the answer is

logx+5log₁₀(x-1) ≥ 3.

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The simplified form of the expression which is as described by the word phrase given in the task content is; 83.4.

In order words, when the sum of 5.5 and 4.3 all divided by the quantity 4 end quantity times the quantity 2 minus 6 end quantity squared plus 5 is being simplified, it gives 83.4

According to the task content, it follows that the expression given by the word phrase and required to be simplified is;

{(5.5 + 4.3)/4} × (2-6)² + 5.

Hence, it follows from PEMDAS guidelines that the parentheses be solved first as follows;

{(9.8)/2} × (-4)² + 5

= 4.9 × 16 + 5

Hence, by multiplying first, we have;

= 78.4 + 5

= 83.4.

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The simplified form of the expression which is as described by the word phrase given in the task content is; 83.4.

In order words, when the sum of 5.5 and 4.3 all divided by the quantity 4 end quantity times the quantity 2 minus 6 end quantity squared plus 5 is being simplified, it gives 83.4

What is the simplified form of the word phrase given in the task content?

According to the task content, it follows that the expression given by the word phrase and required to be simplified is;

{(5.5 + 4.3)/4} × (2-6)² + 5.

Hence, it follows from PEMDAS guidelines that the parentheses be solved first as follows;

{(9.8)/2} × (-4)² + 5

= 4.9 × 16 + 5

Hence, by multiplying first, we have;

= 78.4 + 5

= 83.4.

Answer:

f(1) = 1 , f(-2) = -5, f(5) = 9

Step-by-step explanation:

f(x) = 2x-1

then,

f(1) = 2×1-1

= 2-1

= 1

f(-2) = 2×(-2)-1

= -4-1

= -5 ( when sign is both negative the values are added but sign is kept negative)

f(5) = 2×5-1

= 10-1

= 9

the formula by using x=-2 in the other direction.

Reversing equation is what?

The goal of equation solving is to get the variable by itself on one side of the equation and a number on the other side. To isolate the variable, we must turn around the processes that effect it. To achieve this, w, we carry out each operation's inverse on both sides of the equation.

based on the provided statement;

Eliminate the biggest shared variable on both sides of the equation:

3x+2=-4

Unknown terms should be moved to the left side of the equation:

3x=-4-2

Determine the total or difference:

3x=-6

Add the variable's coefficient to both sides of the equation, then subtract it:

x=-6/3

x=-2

Calculate the product or quotient x=-2

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1 yard is added to the field position on average for each running play.

In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. For instance, based on the information provided, the average of the digits 2, 3, 4, 7, and 9 is 5.

Detailed explanation:

A data set's average can be calculated by:

Average = sum of data values/ total number of values

Given: The total number of plays =6

Sum of the change in field position resulting from each play is given by :-

sum =-3+2+(-1)+(-2)+(-3)+(1)

         =-6

Now, the average change in field position per running play is given by :-

Average = sum/total plays

               =-6/6

               =-1

Hence, the average change in field position per running play is -1 yard per play.

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We will have $ 672.97 in the account if no money is added or withdrawn from the account.

Amount deposited in the account = $ 600

Interest rate = 3.9 % annually

Time period = 3 years.

No money is added or withdrawn.

So, we will use the Compound Interest to calculate the amount after 3 years.

We have:

Compound interest formula:

A = P ( 1 + r )ⁿ

Here, P = $ 600

r = 3.9 %

n = 3 years

Substituting the values in the formula, we get that:

Compound interest = $ 600 ( 1 + 0.039 )³

Amount = $ 600 ( 1.039 )³

Amount = $ 600 ( 1.122)

Amount after 3 years = $ 672.97

Therefore, we will have $ 672.97 in the account if no money is added or withdrawn from the account.

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The value of the side length n is 15 units.

According to the question we have been given that ΔABC ≈ ΔQRS

And we know that when two triangles are similar then their corresponding sides are proportional to each other that is

           [tex]\frac{AB}{QR} = \frac{BC}{RS} = \frac{AC}{QS}[/tex]          (1)

Now we need to find the value of n which is the length of RS

To find the value of n we will use the above equation (1), we get

  The values that we have been given are :

   AC = 2 ,  BC = 6  and   QS = 5 , RS = n

We use the proportion,

              [tex]\frac{BC}{RS} = \frac{AC}{QS}[/tex]

                [tex]\frac{6}{n} = \frac{2}{5}\\n = \frac{6}{2} * 5\\n = 15[/tex]

Hence the value of the side length n is 15 units.

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