Why do people use the formula: n x (n+1)/2 to find the the sum of the first thirty consecutive whole numbers

The slope of a line parallel to the line whose equation is 5x - 3y = 18 is equal to 5/3.

In Mathematics, the slope-intercept form of an equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Making y the subject of formula, we have the following:

5x - 3y = 18

3y = 5x - 18

y = 5x/3 - 6

In Geometry and Mathematics, two (2) lines are said to be parallel under the following conditions:

m₁ = m₂ ⇒ 5/3 = 5/3

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The value of the functions are,

⇒ f (- 10) = 20201

⇒ f (2) = 17

⇒ f (3) = 143

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 (the independent variable) and another variable (the dependent variable).

Given that;

The value of function is,

⇒ f (x) = 2x⁴ + x² - 10x + 1

Now, We can find all the values as;

At x = - 10;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (- 10) = 2 (- 10)⁴ + (- 10)² - 10 (- 10) + 1

⇒ f (- 10) = 20000 + 100 + 100 + 1

⇒ f (- 10) = 20201

At x = 2;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (2) = 2 (2)⁴ + (2)² - 10 (2) + 1

⇒ f (2) = 32 + 4 - 20 + 1

⇒ f (2) = 17

At x = 3;

⇒ f (x) = 2x⁴ + x² - 10x + 1

⇒ f (3) = 2 (3)⁴ + (3)² - 10 (3) + 1

⇒ f (3) = 162 + 9 - 30 + 1

⇒ f (3) = 143

Thus, The value of the functions are,

⇒ f (- 10) = 20201

⇒ f (2) = 17

⇒ f (3) = 143

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Answer:

Below

Step-by-step explanation:

the difference of 1.02 and 0.98  :

   (1.02 - 0.98)

2 times as much :

2 * ( 1.02-0.98)

Answer:

2(1.02-.98)

Step-by-step explanation:

Answer:

the slope is 24/145

Step-by-step explanation:

slope= rise/run

48/290

24/145

the slope is 24/145

3. The solutions are (3, 8) and (–1, 0).

4. The solutions are (5, 7) and (-2, 0).

5. Data is most appropriate for a linear model.

6. The graph of y = -2x² + 2 is a downward-facing parabola

7. The graph of y = -x² is a downward-facing parabola

8. The graph of y = 2x² is an upward-facing parabola

9. The graph of y = 3x² - 4 is an upward-facing parabola

What is  solutions to the system?

A collection of values for a variable that simultaneously fulfill each equation is the solution to a system of equations.

A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

3. The solutions to the system are (3, 8) and (–1, 0).

To solve the system, we can substitute y = x + 5 from the first equation into the second equation:

x + 5 = x² – x + 2

Rearranging and simplifying, we get:

x² - 2x - 3 = 0

Factoring, we get:

(x - 3)(x + 1) = 0

Therefore, x = 3 or x = -1.

Substituting each value of x into y = x + 5, we get the corresponding y-value:

When x = 3, y = 3 + 5 = 8

When x = -1, y = -1 + 5 = 4

Therefore, the solutions are (3, 8) and (–1, 0).

4. The solutions to the system are (3, 7) and (-4, -2).

To solve the system, we can substitute y = x + 2 from the second equation into the first equation:

x² - 2x - 8 = x + 2

Rearranging and simplifying, we get:

x² - 3x - 10 = 0

Factoring, we get:

(x - 5)(x + 2) = 0

Therefore, x = 5 or x = -2.

Substituting each value of x into y = x + 2, we get the corresponding y-value:

When x = 5, y = 5 + 2 = 7

When x = -2, y = -2 + 2 = 0

Therefore, the solutions are (5, 7) and (-2, 0).

5. The data shown in the graph is most appropriate for a linear model.

6. The graph of y = -2x² + 2 is a downward-facing parabola that opens up and has a y-intercept of (0, 2).

7. The graph of y = -x² is a downward-facing parabola that opens up and passes through the origin (0, 0).

8. The graph of y = 2x² is an upward-facing parabola that opens up and has a y-intercept of (0, 0).

9. The graph of y = 3x² - 4 is an upward-facing parabola that opens up and has a y-intercept of (0, -4).

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The value of x is 11.

A square is a two dimensional shape which consist of four sides and four angles, where each angle is 90 degrees.

Given is a square PQRS.

PR and QS are diagonals of the square.

Square has the property that the diagonals bisect the interior angles.

So, ∠Q will be bisected by diagonal QS.

So, ∠PQS = ∠SQR = (6x - 21)°

∠Q is the interior angle of a square, thus it is 90°.

∠Q = ∠PQS + ∠SQR

90 = 6x - 21 + 6x - 21

90 = 12x - 42

12x = 90 + 42

12x = 132

x = 11

Hence the value of x is 11.

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Reason:

The graph starts off very steep at x = 0. As x increases, the steepness goes down. Meaning the tangent lines become more shallow as you move to the right.

This tells us that the person learning the new task learns a lot at first. Then as time wears on, they learn less and less, until leveling off at some plateau.

If your teacher has covered derivatives, then you'll find the derivative of y = 1-e^(-0.28x) is dy/dx = 0.28e^(-0.28x)

Graph this derivative function using something like GeoGebra. Notice how the derivative curve is always decreasing. Therefore, x = 0 is when the derivative is largest, which points to the original function having the steepest increase (aka largest instantaneous rate of change).

See the graph below.

Therefore , the solution of the given problem of unitary method comes out to be  66.05, 66.33, 66.96, 66.83, 66.70, 66.03, 66.12, 65.64 for the closing values provided.

By utilizing what is explicitly learned thus far, taking variable of this global accessibility, and incorporating all crucial elements from previous expression research that utilized a particular approach, the goal can be achieved. It will be possible to get in touch with the entity again if the expected claim outcome actually happens; otherwise, both crucial processes will surely miss the statement.

Here,

We must take the average of the most recent three closing prices and repeat the procedure for the remaining prices in order to determine the 3-day SMA (Simple Moving Average).

Here's a step-by-step procedure:

=> Day 1: (66.21 + 65.90 + 67.05) / 3 = 66.05

=>  Day 2: (65.90 + 67.05 + 67.03) / 3 = 66.33

=>  Day 3: (67.05 + 67.03 + 66.80) / 3 = 66.96

=> Day 4: (67.03 + 66.80 + 66.65) / 3 = 66.83

=>  Day 5: (66.80 + 66.65 + 66.65) / 3 = 66.70

=>  Day 6: (66.65 + 66.65 + 65.80) / 3 = 66.03

=>  Day 7: (66.65 + 65.80 + 65.92) / 3 = 66.12

=>  Day 8: (65.80 + 65.92 + 65.21) / 3 = 65.64

The 3-day SMA is therefore 66.05, 66.33, 66.96, 66.83, 66.70, 66.03, 66.12, 65.64 for the closing values provided.

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(x+4), (3x-1) are the required factors in the given trinomial solution.

The solution provided below has been developed in a clear step by step manner.

Step: 1

Given polynomial is 3x²2² +11x-4

=3x(x+4)-1(x+4)

=(x+4)(3x-1)

Explanation: Please refer to solution in this step.

Step: 2

(x+4), (3x-1) are the required factors

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.

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These figures have curved surfaces, not flat faces. A cylinder is similar to a prism, but its two bases are circles, not polygons. Also, the sides of a cylinder are curved, not flat. A cone has one circular base and a vertex that is not on the base.

When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.

Answer:

Percent rate of change per unit, t ≈ 10.99%

Step-by-step explanation:

The percent rate of change per unit, t, for a function is equal to the derivative of the function with respect to t, divided by the function value at t.

For the given function g(t) = 200(1.12)^t, the derivative with respect to t is:

g'(t) = ln(1.12) * 200(1.12)^t

The function value at t is:

g(t) = 200(1.12)^t

Therefore, the percent rate of change per unit, t, is:

g'(t) / g(t) = [ln(1.12) * 200(1.12)^t] / [200(1.12)^t] = ln(1.12) ≈ 0.1099

Multiplying by 100 to express the answer as a percentage, rounded to the nearest tenth of a percent, we get:

Percent rate of change per unit, t ≈ 10.99%

The area of triangle MNL is approximately 10.44 cm².

What is the sine rule?

The sine rule, also known as the law of sines, is a formula used in trigonometry to find the lengths of the sides and the measure of the angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words:

[tex]a/sin A = b/sin B = c/sin C[/tex]

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides. The sine rule can be used to find the length of a side of a triangle or the measure of an angle if the other two sides and the included angle are known, or if two sides and the angle opposite one of them are known.

To find the area of triangle MNL, we need to first calculate the length of side NL using the sine rule:

sin(38°) / NL = sin(90°) / 4.8

NL = sin(38°) / sin(90°) * 4.8

NL = sin(38°) * 4.8

NL ≈ 2.9 cm

Now we can find the area of the triangle using the formula:

[tex]Area = (1/2) * base * height[/tex]

[tex]Area = (1/2) * 7.2 * 2.9[/tex]

Area ≈ 10.44 cm²

Therefore, the area of triangle MNL is approximately 10.44 cm².

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The highest temperature on record belongs to California's Death Valley which, in 1913, reached a temperature of 134 degrees Fahrenheit, or 56.7 degrees Celsius, Al Jazeera reports.

The highest temperature in India is found in this city, situated at a height of 178 metres in Rajasthan, the country's biggest state. There, 50 degrees Celsius has been recorded as the greatest temperature to date. Extreme weather may be found in the city both in the summer and the winter.

However, according to the India Meteorological Department, the highest temperature ever recorded in India was 51°C (123.8°F) in the town of Phalodi, Rajasthan on May 19, 2016. It's important to note that temperatures can vary greatly depending on the location and time of year.

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Answer:

Moving the decimal 3 places to the left.

Step-by-step explanation:

Take the number 3000 and divide it by 1000 in your calculator.  You will get the answer 3.  Although we do not write it, the decimal in the number 3000 is at the end of the number (after the last zero).  When we divide by 1000, we move the decimal 3 places to the let.  The decimal in the number 3 is at the end or to the right of the 3, we just do not write the decimal.

Helping in the name of Jesus.

Lim initially had $5145, and he withdrew an additional $1040 from his bank account, so he had a total of:

$5145 + $1040 = $6185

Lim divided this total amount equally among his 5 sons, so each son would receive:

$6185 ÷ 5 = $1237

Therefore, each son would receive $1237.

The bug population whose growth shows geometric sequence ,on Week 26 the value is approximately 9,461.01.

What is a geometric sequence, and how can we use it to predict the growth of a population?

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio. Mathematically, a geometric sequence can be expressed as:

[tex]a, ar, ar^2, ar^3, ...[/tex]

where a is the first term, r is the common ratio, and each subsequent term is obtained by multiplying the previous term by r.

Calculation of  the bug population on week 26 -

To solve this problem, we can use the formula for a geometric sequence:

[tex]a_n = a_1 \times r^{n-1}[/tex]

Where:

[tex]a_n[/tex] = the nth term in the sequence

[tex]a_1[/tex] = the first term in the sequence

r = the common ratio between terms

n = the term number

We are given that the bug population follows a geometric sequence, with a first term of 500 and a second term of 600. To find the common ratio, we can divide the second term by the first term:

[tex]r = 600 / 500 = 1.2[/tex]

Now we can use the formula to find the population on Week 26:

[tex]a_{26} = 500 \times 1.2^{(26-1)}[/tex]

[tex]a_{26} = 500 \times 1.2^{25}[/tex]

Evaluate this expression to get:

[tex]a_{26}[/tex] ≈ [tex]9,461.01[/tex]

Therefore, the bug population on Week 26 is approximately 9,461.01.

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Here are the possible outcomes of randomly drawing two marbles from the bag:

O, G

O, B

G, O

G, B

B, O

B, G

There are six possible outcomes in total, each with an equal chance of occurring. Therefore, the theoretical probability of drawing an orange marble and a green marble from the bag is 1/6 or approximately 0.167.

Since the center of the circle lies on the y-axis, the x-coordinate of the center must be 0.

Also, since the diameter of the circle is 12 units, the radius is half of that, or 6 units.

Using the standard form of the equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius, we can substitute the values we know and simplify the equations to see which ones match.

The equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are:

   x^2 + (y - 6)^2 = 36 (center is at (0, 6))

   x^2 + (y + 6)^2 = 36 (center is at (0, -6))

Therefore, the two options that represent the circles with the given properties are:

x^2 + (y - 6)^2 = 36 and x^2 + (y + 6)^2 = 36.

To model with mathematics is to test ideas using math and computer programs to simulate an object or action.

In order to understand a real-life problem, modelling entails developing a set of mathematical equations that accurately reflects a situation.

The model frequently needs to be modified because it does not adequately capture the situation.

By knowing how the system functions, which variables are significant in the system, and how they relate to one another, one can utilise a mathematical model to better understand a real-life situation. Moreover, models can be used to forecast and predict what a system will do in the future or for various parameter values. Finally, a model can be used to estimate variables that are challenging to precisely evaluate.

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Answer:

8, 39, 250, 1031

Step-by-step explanation:

(Needing a bit more context but if its sequences then:)

Answer:

£33.93

Step-by-step explanation:

A 13% discount means that the new price will be 87% of the original, as 100 - 13 = 87.

This can be calculated by converting the percentage into a decimal, then multiplying by the decimal:

87 / 100 = 0.87

39 * 0.87 = 33.93

For the equation 75x+30y=1500,  x is (100 - 2y) / 5 and y is (100 - 5x) / 2.

An equation is a mathematical statement that uses symbols and numbers to express a relationship between two or more variables. It states that two expressions are equal to each other.

We can solve for x and y in the equation 75x + 30y = 1500 by using algebraic manipulation.

First, we can simplify the equation by dividing both sides by the greatest common factor of 75 and 30, which is 15:

(75x + 30y) / 15 = 1500 / 15

Simplifying the left side gives:

5x + 2y = 100

Next, we can isolate one of the variables. Let's isolate y by subtracting 5x from both sides:

5x + 2y - 5x = 100 - 5x

Simplifying the left side gives:

2y = 100 - 5x

by dividing both sides by 2:

y = (100 - 5x) / 2

This is the equation for y in terms of x. We can use this equation to solve for y given a value of x, or we can substitute it back into the original equation to solve for x in terms of y.

Let's solve for x in terms of y by isolating x in the equation 5x + 2y = 100:

5x = 100 - 2y

Dividing both sides by 5 gives:

x = (100 - 2y) / 5

This is the equation for x in terms of y. We can use this equation to solve for x given a value of y, or we can substitute it back into the original equation to solve for y in terms of x.

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The closest option to the cone area is 923.2 m². 

A cone is a shape formed from a series of line segments or lines that connect a common point, called a vertex or vertex, to all points on the base of a circle that do not contain vertices. The distance from the apex of the cone to the base is called the height of the cone.

To solve this problem, we need to find the surface of the cone. Formula for the surface area of cone:

A = [tex]\pi[/tex]r² + [tex]\pi[/tex]rℓ

where r is the radius of the base, ℓ is the height of the depression, and π is a constant of approximately 3.14159.

First, we find the radius of the base. Since the bottom line of the cone is listed as 18 feet and we know the radius is 14 feet, we can use the Pythagorean theorem to find the height of the cone.

h² = ℓ² - r²

h² = 19.3² - 14²

h ≈ 11.48 feet

Now we can compute the surface.

A = [tex]\pi[/tex](14)² + [tex]\pi[/tex](14)(19.3)

A ≈ 923.2 square feet

So the closest option to the cone area is 923.2 m². 

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Answer:

the solution to the equation 2x + 18 = 42 is x = 12.

Step-by-step explanation:

To solve for x in the equation 2x + 18 = 42, you can follow these steps:

Subtract 18 from both sides of the equation:

2x + 18 - 18 = 42 - 18

2x = 24

Divide both sides of the equation by 2:

2x/2 = 24/2

x = 12

Therefore, the solution to the equation 2x + 18 = 42 is x = 12.

Answer:

[tex] \sf \: x = 12[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 2x + 18 = 42

Then the value of x will be,

→ 2x + 18 = 42

→ 2x = 42 - 18

→ 2x = 24

→ x = 24 ÷ 2

→ [ x = 12 ]

Hence, the value of x is 12.

The expression that represents Maliq's total points is given as follows:

C. 69x.

The amount of points for each landing is given as follows:

The number of times that Maliq landed on each space is given as follows:

Hence the expression for the total points is given as follows:

21x + 19(2x) + 2(5x) = 21x + 38x + 10x = 69x.

(we multiply the terms and then combine the like terms, as all the terms have the variable x they are like terms).

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Answer:

Step-by-step explanation:

We can simplify the expression using the rules of exponents:

(-27)^(-2/3) = 1/(-27)^(2/3)

Now, we can use the fact that (-a)^(2/3) = (a^(2/3)) to simplify the expression further:

1/(-27)^(2/3) = 1/(3^3)^(2/3) = 1/3^(3*2/3) = 1/3^2 = 1/9

Therefore, x = 1/9.

The mean absolute variation for the group of integers 42, 45, 47, 50, 53, 56, 58, and 65 is therefore roughly 6.5.

What one standard deviation (SD) means. on a normal or bell-shaped distribution of the data. The region of a bell curve starting at position 13 on the y axis is approximately filled by 1 SD = one standard deviation = 68% of a ratings or data values.

Here's how to find the mean absolute deviation of the set of numbers 42, 45, 47, 50, 53, 56, 58, and 65:

Find the mean:

mean = (42 + 45 + 47 + 50 + 53 + 56 + 58 + 65) / 8

mean = 50.375

Find the absolute difference between each number and the mean:

|42 - 50.375| = 8.375

|45 - 50.375| = 5.375

|47 - 50.375| = 3.375

|50 - 50.375| = 0.375

|53 - 50.375| = 2.625

|56 - 50.375| = 5.625

|58 - 50.375| = 7.625

|65 - 50.375| = 14.625

Find the average of these absolute differences:

mean absolute deviation = (8.375 + 5.375 + 3.375 + 0.375 + 2.625 + 5.625 + 7.625 + 14.625) / 8

mean absolute deviation ≈ 6.5

Therefore, the mean absolute deviation of the set of numbers 42, 45, 47, 50, 53, 56, 58, and 65 is approximately 6.5.

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To solve the equation 3/4x + 3 - 2x = -1/4 + 1/2x + 5, we first need to simplify both sides by combining like terms:

3/4x - 2x + 3 = -1/4 + 1/2x + 5

Next, we can simplify the fractions on the right side by finding a common denominator of 4:

3/4x - 2x + 3 = -1/4 + 2/4x + 20/4

Simplifying the right side further, we get:

3/4x - 2x + 3 = 19/4 + 1/2x

Now we can isolate the variable x by moving all the terms containing x to one side of the equation and all the constants to the other side:

3/4x - 2x - 1/2x = 19/4 - 3

Combining like terms:

-5/4x = 5/4

Finally, we can solve for x by multiplying both sides by the reciprocal of -5/4:

x = -1

Therefore, the solution to the equation is x = -1.

The similar triangles are Δ SRQ ~ Δ RPQ  ~ Δ SRP

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given is right triangle PRQ, a perpendicular line is drawn to the side PQ from angle R

we need to tell the similar triangles,

From the figure we have,

Δ SRQ ~ Δ RPQ  ~ Δ SRP

And, according to the definition of similar triangle,

SP / RP = PR / RQ

PQ / RQ = RQ / SQ

Hence, the similar triangles are Δ SRQ ~ Δ RPQ  ~ Δ SRP

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