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The total of all S5 terms, the first five terms, and the two different types of mathematical advancement equal 105.5.

An arithmetic progression whenever there is a steady difference amongst terms that follows to each other in a series. For instance, following new number 5, 7, 9, 11, 13, and 15 is an example of an exponential function with a limitation of two. A progress with a set tolerance among any two consecutive numbers generally referred to as a "arithmetic progression" (A.P.). Two types of mathematical progress are possible: series in arithmetic with a finite length A finite mathematical progression is a progression with a finite number of terms. The soon, late, allowance, and quantity of terms may all be calculated using the entries in the series.

given

The geometric sequence 8,12,18,27,81/2's 

first five partial sums, S1,S2,S3,S4, and S5, must be found in order.

S1=8

S2=8+12=20

S3=8+12+18=38

S4=8+12+18+27=65

S5=8+12+18+27+81/2=105.5 as a result.

The total of all S5 terms, the first five terms, and the two different types of mathematical advancement equal 105.5.

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The solution is,  the distance between the points (3, 8, 2)and (3,8,2) is 0.

The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 3 dimensional plane, the distance between points (X1, Y1, Z1) and (X2, Y2, Z2) is given by:

d=√(x2−x1)2+(y2−y1)2+(z2−z1)2

here, we have,

the given points are,

(3, 8, 2)and (3,8,2)

so, distance = √(x2−x1)2+(y2−y1)2+(z2−z1)2

solving we get,

d= 0

as the points are same.

Hence, The solution is,  the distance between the points (3, 8, 2)and (3,8,2) is 0.

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After divide, the solution of the expression is,

⇒ x (x + 2y) / 5

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ (x² - 4y²) ÷ (5x - 10y) / x

Now, We an simplify as;

⇒ (x² - 4y²) ÷ (5x - 10y) / x

⇒ (x² - (2y)²) ÷ (5x - 10y) / x

⇒ (x - 2y) (x + 2y) ÷ 5(x - 2y) / x

⇒ (x - 2y) (x + 2y) × x/ 5 (x - 2y)

⇒ x (x + 2y) / 5

Thus, The solution of the expression is,

⇒ x (x + 2y) / 5

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According to the Pythagorean theorem [tex]c^{2} = a^{2} + b^{2},[/tex] Option D is accurate since[tex](2x-10)^{2} + x^{2} = (3x)^{2}.[/tex]

The Pythagorean Theorem, also known as the Equation, is the fundamental Cartesian geometry relationship between a right triangle's three sides.

The Pythagorean Theorem states that the sum of the squares that thus span the angles of a right triangle is equal to the number that crosses the right triangle's rectangular prism opposite any right angle. Sometimes it is expressed using the general geometric notation [tex]a^{2} + b^{2} = c^{2}[/tex]

Given,

according to the diagram

in right triangle

[tex](base )^{2} + (perpendicular) ^{2} = (hypotenuse)^{2}[/tex]

[tex](2x-10 )^{2} + x^{2} = (3x)^{2}[/tex]

According to the Pythagorean theorem [tex]c^{2} = a^{2} + b^{2}[/tex],

Option D is accurate since [tex](2x-10)^{2} + x^{2} = (3x)^{2}.[/tex]

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A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

First, we need to solve for a common denominator.

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

To get the common denominator between [tex]\frac{18}{7}[/tex] and [tex]\frac{5}{6}[/tex], we multiply their denominators.

Now, we know the fractions would look like this:

To solve for the numerators, we can use these equations:

Now, the fractions look like this:

Adding them together:

Now, we can convert this into a mixed number.

Now that we have this, we can subtract that from 6 to get the missing value.

Therefore, the third fraction is [tex]2\frac{25}{42}[/tex].

Answer:

10.8 units or [tex]2\sqrt{29}[/tex] units

Step-by-step explanation:

The line drawn connecting two points on a graph is known as a line segment.

The formula used to calculate the length of a line segment is derived from the Pythagorean Theorem

Length of a line segment: [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} -y_{1})^{2}}[/tex]

                                         = [tex]\sqrt{[2-(-2)]^{2} + (2-12)^{2} }[/tex]

                                         = [tex]\sqrt{(2+2)^{2} +(-10)^{2} }[/tex]

                                         = [tex]\sqrt{4^{2} + 100}[/tex]

                                         = [tex]\sqrt{16 +100}[/tex]

                                         = [tex]\sqrt{116}[/tex]

                                         = [tex]\sqrt{4}[/tex]×[tex]\sqrt{29}[/tex]

                                        = [tex]2\sqrt{29}[/tex] units

       Diagonal distance = 10.8 units (Rounded to 3 significant figures)

The solution of the inequality will be x ≥ -1/4.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that inequality is one-fourth time the absolute value of the quantity x plus 1 end quantity.

The given inequality can be solved as below:-

4x ≥ −1

4x ≥ −1

x ≥ -1 / 4

Therefore, the value of x for the inequality is - 1 / 4.

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Answer:

The answer Is B)  x ≤ −17 or x ≥ 15

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

51÷6= 51/6 = 8 3/6 = 8 1/2  = 8.5

6

The total time Elise spent riding Maximum Velocity on her last visit to Adventure Island can be expressed as: 145d seconds.

In mathematics, an expression is a combination of numbers, symbols, and/or variables that can be evaluated to produce a value. Expressions can also include functions, such as sin(x) or log(y), as well as operators like multiplication (*), division (/), and exponentiation (^). Expressions can be used to represent mathematical formulas, equations, and relationships in a concise and symbolic way, making them easier to work with and manipulate using mathematical tools and techniques.

Here,

If we know the value of d, we can calculate the total time Elise spent riding Maximum Velocity by simply multiplying the ride time by the number of rides.

For example, if Elise rode Maximum Velocity 3 times, the total time she spent on the ride would be:

145 seconds/ride x 3 rides = 435 seconds

So, using the expression from the previous answer, we can substitute the value of d to get the actual calculation:

Total time = 145d seconds

For instance, if Elise rode Maximum Velocity 5 times during her last visit, the total time spent on the ride would be:

Total time = 145 x 5 = 725 seconds

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Answer:

(1) 17 (2) +3 every new term (5+3) or 8+3) or 5+x*3

we can use this as to find 2nd number (1) as its first one to be found 5+3(1) 5+3=8

(3) 5+9*3=5+27 , 32

(4) 5+9*3 ,

we can test this out by counting

starter: 5

1 -> 8

2-> 11

3-> 14

4 -> 17

5 -> 20

6 -> 23

7 -> 26

8 -> 29

9 -> 32 (realisticly it is still the 10th but it's the 9th after the 1st.)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's call the height of the building "h", and the height of the antenna "a". From the given information, we have:

Angle of elevation to the top of the building = 7°

Angle of elevation to the top of the antenna = 7° + 5° = 12°

We can use tangent to find the height of the building and the height of the antenna. The tangent of an angle is equal to the height divided by the distance, so we have:

tan(7°) = h / 319

And

tan(12°) = (a + h) / 319

We can use the first equation to solve for h:

h = 319 * tan(7°)

And use the second equation to solve for a:

a = 319 * tan(12°) - h

Now that we have expressions for h and a, we can use the tangent function to find the values for h and a. We can use a calculator or look up the values in a table of tangent values.

Rounding the height of the antenna to the nearest 10th of a foot, we find:

a = 319 * tan(12°) - h = approximately 69.9 feet.

The solution to the logarithmic equation is; x = 81/4

We want to solve the logarithmic equation;

log₃x + log₃4 - 2log3 = 2

From property of logarithms, we know that;

logₐ4 = log 4/log a

Similarly we know that;

log a + log b = log (ab)

log a - log b = log (a/b)

Thus;

log₃x + log₃4 - 2log₃3 = 2 is;

(log₃4x) - 2log₃3 = 2

(log₃4x) - log₃3² = 2

log₃(4x/3² ) = 2

3² = 4x/9

4x = 9 * 9

4x = 81

x = 81/4

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increase=(30/100)*50

=15

so,

value after increase

=50+15

=65

Since 1 unit on the map represents 1 block, Carmen walks 22 blocks after school.

To find the total distance Carmen walks, we need to find the distance between each of the four locations: school, park, hobby shop, and home.

The distance between two points (x1, y1) and (x2, y2) in a plane can be calculated using the Pythagorean theorem:

d = √((x2 - x1)² + (y2 - y1)²)

First, let's find the distance between the school and the park:

d = √((-5 - (-5))² + (4 - (-3))²) = √((0)² + (7)²) = √(49) = 7

Next, let's find the distance between the park and the hobby shop:

d = √((3 - (-5))² + (-3 - (-3))²) = √((8)² + (0)²) = √(64) = 8

Then, let's find the distance between the hobby shop and home:

d = √((3 - 3)² + (-3 - 4)²) = √((0)² + (7)²) = √(49) = 7

Finally, the total distance Carmen walks after school is the sum of the distances between the four locations:

d = 7 + 8 + 7 = 22

Since 1 unit on the map represents 1 block, Carmen walks 22 blocks after school.

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Based on the information in the graph, it can be inferred that the perimeter of the room is 44 feet.

To find the perimeter of the room in the graph we must apply the following formula:

According to the above, if each of the sides is 11 feet long we have two alternatives

In both operations the result would be 44.

Based on the above, the perimeter of the room would be 44 feet.

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Step 1: Solve the equation V(t) = 4 for t. To solve the equation V(t) = 4 for t, divide both sides of the equation by 11, which gives us t = 4/11.

Step 2: Interpret the result. The value of t = 4/11 tells us that when the temperature of the water in the cooler is 4/11, the volume of the water is 4.

Therefore, the value of t = 4/11 tells us that when the temperature of the water in the cooler is 4/11, the volume of the water is 4.

Since there are more molecules in larger volumes than smaller ones, the pace of cooling will be slower if the water's volume is increased. Losing the heat energy from all the molecules will therefore take longer.

The question is incomplete and requires further explanation. For the mentioned part, the information is not significant to determine volume of water in the cooler.

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From the given data value of function f ' (- 10) is,

⇒ f ' (- 10) = 0.035

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.

Given that;

Table for the given data is shown.

Now, We have to find the value of f ' (- 10).

Since, - 10 is in between - 11 and - 9.

Hence, The slope given the value of f ' (- 10) as;

⇒ f ' (- 10) = (1.12 - 1.05) / (- 9 - (- 11))

⇒ f ' (- 10) = (0.07/2)

⇒ f ' (- 10) = 0.035

Thus, From the given data value of f ' (- 10) is,

⇒ f ' (- 10) = 0.035

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Step-by-step explanation:

a regular function finds the functional result y to a given x value.

the inverse function finds the original x to a given y value.

g^-1(1) is therefore the x-value, so that g(x) = 1.

so, we look through the value pairs. where do we find y = 1 ? ah, in the pair (9, 1).

x = 9 lead to the functional result y = 1.

therefore, g^-1(1) = 9

h(x) = y = -3x - 14

in other words, h(x) expresses y in terms of x.

h^-1(x) expresses x in terms of y.

so, we want to transform the functional equation, so that it says "x = ...." :

y = -3x - 14

y + 14 = -3x

x = (y + 14)/-3

and to turn it into regular function notation, we rename x to y and y to x :

y = h^-1(x) = (x + 14)/-3 = (-1/3)(x + 14)

(h○h^-1)(x) = x

always.

in that process we find first what original input value for h lead to the value of x. and then we use that as input value for h. and, of course, we have to get x as result.

to check here in our case

(h○h^-1)(-5) = -5

h^-1(-5) = (-5 + 14)/-3 = 9/-3 = -3

h(-3) = -3×-3 - 14 = 9 - 14 = -5

there you have it.

Answer:

Below

Step-by-step explanation:

16.15549442 rounded to the nearest 10th is 16.2

Answer:

16.2

Step-by-step explanation:

Find the number in the tenth place 1 and look one place to the right for the rounding digit 5. Round up if this number is greater than or equal to 5 and round down if it is less than 5

Answer: 11 1/2 cm or 11.5 cm

Step-by-step explanation:

       To see how much taller the woman is than her son, we will subtract the son's height from the woman's height. We can convert these fractions into decimals to make it easier to subtract.

159 1/4 - 147 6/8 = 159.25 - 147.75 = 11.5 = 11 1/2 cm

Answer:

x = 8, y = 15

Step-by-step explanation:

Part (a)

If x and y are inversely proportional, the relationship can be expressed as
[tex]y \propto \dfrac{1}{x}\\\\\rm{(or \;alternatively\;x \propto \dfrac{1}{y})\\\\}\\\\[/tex]

The above relationship [tex]y \propto \dfrac{1}{x}[/tex] can be written as an equation:

[tex]y = \dfrac{k}{x} \codts\cdots(1)[/tex]

where the constant k is known as the constant of proportionality

Part (b)

We know that when x = 12, y = 10

Plugging this into equation (1):

10 = k/12

k/12 = 10

k = 12 x 10

k = 120

So the proportional equation (1) becomes
y = 120/x

We are now given the equation
y = x + 7

Substitute y = 120/x

120/x = x + 7

Subtract 120/x from both sides
0 = x + 7 - 120/x

Multiply by x both sides;
0 = x² + 7x - 120

Or,
x² + 7x - 120 = 0

This is a quadratic equation which we can solve by factoring. There are various techniques. One of them is to find two factors of 120 and see if their sum or difference can be made -7

Factors of 120 are:
[tex]1,\:2,\:3,\:4,\:5,\:6,\:8,\:10,\:12,\:15,\:20,\:24,\:30,\:40,\:60,\:120[/tex]

Take the two factors, a and b that will add or subtract to -7 and multiply to -120

We see that if we choose a = -15 and b = 8

a + b = -7

and

a x b = -120

The solution to the equation is x = 8 or x = -15

Since we are told that both x and y are positive, we can ignore x = -15 and just state that x = 8 is a solution

If x = 8, substitute this in y = x + 7 to get

y = 8 + 7 = 15

This checks with our original proportionality equation:
y = 120/x = 120/8 = 15

Answer
x = 8, y = 15

The equation of the graphed line is expressed as: A. y + 5 = -3/2(x - 4).

The equation that represents a line can be written in point-slope form as y - b = m(x - a), where a point on the line is (a, b) and the slope is m.

Slope (m) = rise/run = -3/2

Substitute a point on the line (a, b) = (4, -5) and m = -3/2 into y - b = m(x - a):

y + 5 = -3/2(x - 4)

The equation is: A. y + 5 = -3/2(x - 4).

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The function rule for "The output is one more than twice the input x ." is y= 2x+ 1.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

given:

"The output is one more than twice the input x ."

let the output by y.

Then, the mathematical expression for the above statement is

= 1+ 2x

Thus, the output is, y= 2x+ 1.

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Answer:

Step-by-step explanation:

3 divided by 42 = 14 so 14 times 5 = 70

Answer: 70

Step-by-step explanation:

Since 42 push-ups can be done in 3 minutes, then you would divide

42 by 3 and get 14.

Once you get that, you would need to Multiply 14 by 5 and get as your final answer, 70

When the value of c is 13 and d = 2, then the value of the expression

0. 5c -2. 7d is 1.1

It is given that the expression for the given value of the variables is

0. 5c -2. 7d

If the value  of c is 13 and the value of d is 2, then the value of expression is

0. 5c -2. 7d

putting the value of 'c' and 'd'

0. 5c -2. 7d = 0.5(13) - 2.7(2)

0. 5c -2. 7d = 6.5 - 5.4

0. 5c -2. 7d = 1.1

so, the value of the expressions for the given value of the variables  i.e., c = 13 and d = 2 is 1.1

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The asymptotes for the function are:

x = 5 and x = -1.

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

There are three types of asymptotes.

1) Horizontal asymptotes

2) Vertical asymptotes

3) Oblique asymptotes

Now,

Horizontal asymptotes.

f(x) = 14 / (x - 5)(x + 1)

f(x) = 14/(x² + x - 5x - 5)

f(x) = 14 / (x² - 4x - 5)

The degree of the numerator is less than the denominator.

So,

Horizontal asymptotes.

y = 0

i.e

The x-axis.

Now,

Vertical asymptotes

f(x) = 14 / (x - 5)(x + 1)

Simplify in its lowest term.

Now,

Set the denominator to zero.

So,

(x - 5) ( x + 1) = 0

x - 5 = 0

x = 5

And,

x + 1 = 0

x = -1

Now,

Since there is a horizontal asymptote there are no oblique asymptotes.

Thus,

The asymptotes for the function are:

x = 5 and x = -1.

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Answer:

Step-by-step explanation:

The ratio of the sides are 1:2 and the ratio of the areas is 1:4

Two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other, this is called similarity.

Since, the side lengths of the triangles are not given, let us consider,

Δ HIJ =

HI = 12, IJ = 14, HJ = 16

And,

Δ EFG =

EF = 24, FG = 28, EG = 32

Therefore, the ratios of the side lengths of Δ HIJ to the corresponding side lengths of Δ EFG are;

HI / EF = 12/24 = 1/2

IJ / FG = 14/28 = 1/2

HJ / EG = 16/32 = 1/2

Since, we get all the ratios equal, therefore, the Δ HIJ is similar to Δ EFG

With a scale factor of 1/2,

The ratio of area is found by squaring the scale factor for length.

Therefore,

ar(Δ HIJ) / ar(Δ EFG) = (1/2)² = 1/4

Hence, the ratio of the sides are 1:2 and the ratio of the areas is 1:4

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Correct answer is: A power model is appropriate because the scatter plot of log angle and log height is roughly linear.

The graphs known as scatter plots show how two variables within a data collection relate to one another. Both a two-dimensional plane and the Cartesian system are used to represent the data points. The Y-axis is used to plot the dependent variable, while the X-axis is used to represent the independent variable or characteristic. Data points are shown on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.

According to Scatter plot, the relation between log(height) and log(launch angle) is linear.

Let, us consider log(height) = m log(launch angle) + b

Height = [tex]10^{(log(launch angle))}[/tex] + b

Height = [tex](launch angle)^{m}[/tex] + 10ᵇ

Height = (10)ᵇ + [tex](launch angle)^{m}[/tex]

Thus, the relation of height and launch angle is in power mode.

Correct answer is: A power model is appropriate because the scatter plot of log angle and log height is roughly linear.

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On the number line if CD = 6 then the point C lied either on -2 or 10.

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, the whole number is a collection of numbers that contains both zero (0) and all counting numbers (1, 2, 3,4,5,6), whereas the natural number is a collection of all counting numbers (1, 2, 3,4, 5, 6).

Given that, CD = 6 and D lies at 4.

Then C would lie either on the left or right side of the point D.

On left the point C would be:

4 - 6 = -2

On right the point C would be at:

4 + 6 = 10

Hence, on the number line if CD = 6 then the point C lied either on -2 or 10.

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