What point is the intersection of the equations
y=3x−2 and y=−2x+8

The two-column proof is given below:

Mathematics' earliest branch is geometry, along with arithmetic. The distance, size, shape, and relative position of objects in relation to one another are all aspects of space that are addressed. The term "geometer" refers to a mathematician who specializes in geometry.

Before the 19th century, Euclidean geometry which incorporates the concepts of point, line, plane, distance, angle, surface, and curve as fundamental concepts—was nearly entirely the focus of geometry.

Geometry's use was greatly expanded during the 19th century by a number of discoveries. One of the first of these discoveries is Gauss Theorema Egregium, which roughly states that the Gaussian curvature of a surface is independent of any particular embedding in a Euclidean space.

Statements                                                         Reasons

4.7(2f-0.5)=-6(1.6f-8.3f)                                      Given

4.7(2f-0.5)=-6(-6.7f)                                           Combine like terms

9.4f-2.35= -40.2f                                               Get all the terms to the one  

                                                                           side of an equation

49.6f=23.5                                                           Addition property

f=47/992                                                              Division property                  

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The equations of the asymptotes are y = 2 and x = -1, respectively

The equation of the function is given as

f(x) = 2x² + 7x - 4/x² + 5x + 4

Introduce bracket, to differentiate the numerator and the denominator

So, we have

f(x) = (2x² + 7x - 4)/(x² + 5x + 4)

Next, we plot the graph of the function (see attachment)

The asymptotes are the points on the graph is a line that acts as the limit of another line or curve

From the graph, we have the asymptotes to be

x = -1 and y = 2

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Complete question

What is the equation of the asymptote?

f(x) = 2x² + 7x - 4/x² + 5x + 4

Therefore , the 4 year old children can able to count to 1 to 100 counting by making them learn.

Mathematicians can add numbers using the counting-on technique. When using this method, a learner begins by adding the larger number, then "counts on" with the other addends to get the sum. The student will recognize 4 as the higher number and add three more numbers, such as integers "4... 5, 6, 7," if the number sentence is 4 + 3.

Here,

Children develop and learn on an individual basis, however many

4 year old are able to learn their numbers between 1 and 100 and can count over 10.

They could be prepared to practice counting by fives or other skip counting techniques (5, 10, 15, 20, and so on).

Start working on number recognition with your kid as soon as you can.

Therefore , the 4 year old children can able to count to 1 to 100 counting by making them learn.

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Solving the inequality  [tex]\frac{2x + 4}{2}[/tex] < 6, we get x < 4.

Linear Inequalities are mathematical expressions which consist of a left hand side and a right hand side connected with inequality signs like <, >, ≤, ≥ and ≠.

They are almost like linear equations when we see it, but the '=' sign in linear equations are substituted with inequality signs like those mentioned earlier.

The expression given here is,

[tex]\frac{2x + 4}{2}[/tex] < 6

Multiplying both sides with 2, we get,

2x + 4 < 6 × 2

2x + 4 < 12

Subtracting both sides with 4, we get,

2x + 4 - 4 < 12 - 4

2x < 8

Dividing both sides by 2,

2x / 2 < 8 / 2

x < 4

Hence the inequality [tex]\frac{2x + 4}{2}[/tex] < 6 results in x < 4.

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The factors of [tex]2x^2 + 7x + 15[/tex]  are [tex](2x + 3)[/tex] and [tex](x + 5)[/tex].

To find the factors of  [tex]2x^2 + 7x + 15[/tex] , we can use the factoring method called "splitting the middle term." Here's how it works:

Write the expression as the product of two binomials: [tex](2x^2 + 7x + 15) = (2x^2 + ax + b)(cx + d)[/tex]

Find the factors of the constant term (15) that add up to the coefficient of the middle term (7). The factors of 15 are 1 and 15, 3 and 5, and 5 and 3. The only pair that adds up to 7 are 3 and 5.

Set the coefficients of the two binomials to 3 and 5, respectively. The expression becomes: [tex](2x^2 + 3x + 5)(5x + 3)[/tex]

Rewrite the binomials using the distributive property: [tex](2x^2 + 3x + 5)(5x + 3) = (2x^2 + 5x + 3x + 15) = 2x(x + 5) + 3(x + 5) = (2x + 3)(x + 5)[/tex]

So, the factors of  [tex]2x^2 + 7x + 15[/tex] are [tex](2x + 3)[/tex] and[tex](x + 5)[/tex].

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Answer: an=2(-2)ⁿ⁻¹    a₉=512     a₆=-64

Step-by-step explanation:

Since we have an alternating minus sign in this sequence, therefore the first multiplier of the following sequence will be (-1)ⁿ.

And since the first term of the following sequence is positive, the first multiplier of the following sequence is (-1)ⁿ⁻¹.

The second multiplier of the following sequence is 2ⁿ because the sequence has the form: 2, 4, 8, 16, ..., 2ⁿ .

[tex]Thus,\ a_n=(-1)^{n-1}(2^n)\\\\ a_n=2(-2)^{n-1}\ \ \ (1)[/tex]

Find the 9th and 6th terms of the sequence by formula (1):

a₉=2(-2)⁹⁻¹

а₉=2(-2)⁸

a₉=2(256)

a₉=512

a₆=2(-2)⁶⁻¹

а₆=2(-2)⁵

a₆=2(-32)

a₆=-64

The sum of the interior angle of a regular nonagon will be 1,260°.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The interior angle of the polygon is given as,

Interior angle = 180° - 360° / n

And the sum of the interior angle is given as,

Sum of the interior angle = n x (Interior angle)

The number of sides of the regular nonagon is 9. Then the interior angle is given as,

Interior angle = 180° - 360° / 9

Interior angle = 180° - 40°

Interior angle = 140°

Then the sum of the interior angle of a regular nonagon will be given as,

Sum of the interior angle = 9 x 140°

Sum of the interior angle = 1,260°

The sum of the interior angle of a regular nonagon will be 1,260°.

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Answer:

The graph of given function is shown below.

Step-by-step explanation:

The absolute parent function is g(x)=|x|. The graph of parent function is a V-shape d and vertex of the function is origin.

The given function is

             .... (1)

The vertex from of an absolute function is

         .... (2)

where, a is a constant and (h,k) is vertex of the function.

From (1) and (2) we get

The value of a is -1. The value of a is negative it means the graph of parent function reflect across x-axis.

The vertex of the function is (0,-2). It means the graph of parent function shifts 2 units down.

Inspect the graph to see if any vertical line drawn would intersect the curve more than once.

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

f(x)=log(2x)

g(x)=log1/10(x-3)  the base of log is 1/10

Domain is x>3

Range is all real numbers

g(x) is decrease on the interval x>3

asymtote is x=3

x intercept is x=4

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The percentage of money Indrani receives is 43.75%.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given,  Indrani and Jagad share some money in the ratio,

Indrani : Jagad = 7 : 9.

We know the percentage of money for both a and b in the form of a : b can be obtained as, [a/(a + b)]×100.

Therefore, the percentage of money Indrani gets is,

= [7/(7 + 9)]×100.

= (7/16)×100.

= 43.75%.

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Answer:

43.75%

Step-by-step explanation:

Overall, you required 12 to 14 gallons, or 45 to 53 liters, of paint to paint the exterior of your 2000 square foot home.

It might be challenging to calculate or estimate the precise amount of paint that you will need when painting your home. When calculating how much paint you will need, there are many factors to take into account. Every paint has a varied coverage, which determines how many square feet may be painted with each gallon of paint.

According to a rule of thumb and general recommendations, you will require 10 to 12 gallons, or 38 to 45 litres, of exterior paint for a G+0/1 storey house with a 2000 square foot area, as well as 2 gallons of paint for exterior trim for approximately two coats, which includes painting for sliding, overhangs, and soffits, as well as exterior trim for painting the gutters, fascia, and window trims. Overall, you required 12 to 14 gallons, or 45 to 53 liters, of paint to paint the exterior of your 2000 square foot home.

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Answer:

A. M1+ M2 + M3

Step-by-step explanation:

M1 is the money supply that makes it easy to convert assets/items into currency.

M2 is the deposits and money market funds.

Add M1, M2, and M3 to calculate the entire money supply of all the money in the economy.

Answer:

A. M1+ M2 + M3

M3 consists of all currency notes held by the public, all demand deposits with the bank, deposits of all the banks with the RBI and the net Time Deposits of all the banks in the country. So M3 = M1 + time deposits of banks.

Step-by-step explanation:

The absolute value of a number is the non-negative distance between the number and zero on a number line, regardless of sign.

This means that the absolute value of a negative number is always positive. Therefore, if a and b both are negative numbers, their absolute values will be positive numbers. If a is greater than b, then the absolute value of a must be greater than the absolute value of b. This can be expressed mathematically as follows:

|a| > |b|

This equation states that the absolute value of a is greater than the absolute value of b. In other words, the distance between a and zero is greater than the distance between b and zero on a number line.

To illustrate this, let’s take an example of two negative numbers, a=-3 and b=-5. The absolute values of these two numbers are 3 and 5 respectively. Since 3 is greater than 5, the absolute value of a is greater than the absolute value of b. This holds true regardless of the sign of the numbers, as long as a is greater than b.

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Answer:

Step-by-step explanation:

The y-intercept of g(x) is 3 * 2 = 6.

To find the x-intercepts of g(x), we need to find the values of x that make g(x) equal to 0. Since g(x) = 2f(2x + 3), this means we need to find the values of x that make f(2x + 3) equal to 0. Therefore, we can find the x-intercepts of g(x) by solving the equation f(2x + 3) = 0 for x.

Since the x-intercepts of f(x) are at 2 and -4, this means that the equation f(x) = 0 has solutions at x = 2 and x = -4. Substituting these values into the equation f(2x + 3) = 0, we get:

f(2(2) + 3) = 0

f(4 + 3) = 0

f(7) = 0

and

f(2(-4) + 3) = 0

f(-8 + 3) = 0

f(-5) = 0

Therefore, the x-intercepts of g(x) are at x = 7/2 and x = -5/2. These are the only intercepts of g(x) that we can determine for certain.

TRUE: The ratio of 6 and 8 is equivalent to 3/4.

Remember that the ratio is the same when you multiply both sides of a fraction by a number.

= 3/4

= 3*2 / 4*2

= 6/8

= 6:8

Thus, the ratio of 6 and 8 is equivalent to 3/4.

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Is 6:8 equals 3/4 ? Is it true or false and why?

Answer:

B • r = s - 2

Step-by-step explanation:

Rachel will always be two year younger than Sean. if we substitute the letters with their ages...

[rachel's age] 2 = [ sean's age] 4 - 2

2 = 4 - 2

it can't be A

2 = 4 (two does not equals four)

it can't be C

2 = 4 + 2 (the correct answer is 6, Rachel is not 6 years old)

it can't be D

4 = 2 - 2 (the correct answer is 0. Rachel's not 0 years old as well.

[ also s is the subject in this case. but we are looking for r ]

Answer: B

Step-by-step explanation:

The graph of f(x) = [tex]x^{5}-8x^{4}-16x^{3}[/tex] has the following end behavior : as x decreases, x5 increases; as x increases, x5 decreases; and the graph crosses the x-axis at x = 0 instead of at x = 4.

Given, f(x) =  [tex]x^{5}-8x^{4}-16x^{3}[/tex]

                   f(x) =  [tex]x^{5}-8x^{4}-16x^{3}[/tex]

                         = [tex]x^{3}[/tex](x - 4)(x - 4) = 0

                    [tex]x^{3}[/tex] = 0

                     x = 0

                   x - 4 = 0

                        x = 4

         Thus, x = 0 and x = 4 are the roots.

As a result, the graph will touch the x-axis but not the repeated root of x = 4, indicating that the graph has a repeated root.

Correct question :

What is the end behavior of the graph of f(x)= [tex]x^{5}-8x^{4}-16x^{3}[/tex]   ?

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The time t at which the population is 500 is 45 hours.

The equation gives the rate of change of the population at time t:

dP/dt = kP

where P is the population at time t and k is the constant of proportionality.

We can use this equation to find the value of k by substituting the known values of P and t at time t=24 hours:

dP/dt = kP

1000 = k*300

k = 1000/300

k = 10/3

Now that we know the value of k, we can use the equation to find the time t at which the population is 500:

dP/dt = kP

500 = (10/3)P

P = 500*3/10

P = 150

Since the population at time t=0 hours is 300, the population has decreased by 150 over the 24 hours, so t = -150/(-10/3) = 45 hours.

Therefore, the time t at which the population is 500 is 45 hours.

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dP/dt = kP

We can use this equation to find the value of k by substituting the known values of P and t at time t=24 hours:

dP/dt = kP

1000 = k*300

k = 1000/300

k = 10/3

dP/dt = kP

500 = (10/3)P

P = 500*3/10

P = 150

Since the population at time t=0 hours is 300, the population has decreased by 150 over the 24 hours, so t = -150/(-10/3) = 45 hours.

Therefore, the time t at which the population is 500 is 45 hours.

Answer: 3/6 or 1/2

Step-by-step explanation:

In a 6-sided die, there are 3 odd numbers 1,3 and 5. So. P(odd) is 3/6 or 1/2.

The slope-intercept form of a straight line of equation 5x + 2y = 10 is y = (-5/2)x + 5.

The slope-intercept form of a line is:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

To put the equation 5x + 2y = 10 in slope-intercept form, we need to solve for y. We can do this by rearranging the terms and isolating y:

2y = -5x + 10

y = (-5/2)x + (10/2)

Thus, the slope-intercept form of the equation 5x + 2y = 10 is:

y = (-5/2)x + 5

This means that the slope of the line is (-5/2) and the y-intercept is (0,5).

--The question is incomplete, answering to the question below--

"What is the slope-intercept form of 5x + 2y = 10?"

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Answer: 27

Step-by-step explanation:

two base ten blocks then 7

The true statement about the interval is that:

The given interval is -7 ≤ x < -4, the numbers in the interval are

-7, -6, -5,

The numbers are all negative and the number starts from -7 but did not get to -4

since the interval starts from -7 which is a lesser number than -6 and a lesser when compared with -5 we say the interval is increasing

In negative numbers, the larger the number the lesser it has value and and lesser the number the closer it is to zero and the higher the number

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A unique array value is a value that appears only once among all the other values in the given array. Hence the name unique.

An array is a set of items, images, or numbers arranged in rows and columns. Arrays are practical illustrations of multiplication ideas.

Arrays are needed in cases where you need  to store and manipulate large amounts of data efficiently.

Some of the benefits of using arrays include:

1. Arrays allow you to store a large number of items in a single data structure, which makes it easier to work with large datasets.

2. Arrays allow you to access and modify the items in the array quickly, using the index of the item.

A data structure called an array is used to hold a number of elements together. Each item in an array is recognized by its index, or place within the array. A value that only appears once in an array is considered to be unique array value. Think about the following array, for instance:

[1, 2, 3, 4, 5, 6]

Because each value only occurs once in this array, each value is distinct.

Contrarily, think about the following array:

[1, 2, 3, 3, 4, 5]

Since it appears twice in this array, the number 3 is not unique. Since they only exist once, each of the other values is distinct.

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The weight of container will be 20 kg

Let x be the number of car toys packed into container. Toy cars weigh 3 kilogram apiece and are shipped in a container that weighs 5 kilograms when empty, then the total weight of container with toy cars is

x.3 + 5 = 3x + 5

The number of toy trucks is also x. Toy trucks, which weigh 2 kilograms apiece, are shipped in a container weighing 10 kilograms, then the total weight of container with toy trucks is

x.2 + 10 = 2x +10

When packed with toys and ready for shipment, both kinds of containers have the same weight. Thus,

3x + 5 = 2x + 10

x = 15

The weight of container = x + 5

= 15 + 5

= 20 kg

Hence, the weight of container will be 20 kg

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The basic approach to solve this problem is to first sort array and then traverse through all the the elements and check for missing value and repeating value.

Approach:

c++ implementation

#include <bits/stdc++.h>

using namespace std;

void printTwoElements(int arr[], int size)

{

   int i;

   cout << "The repeating element is ";

   for (i = 0; i < size; i++) {

       if (arr[abs(arr[i]) - 1] > 0)

           arr[abs(arr[i]) - 1] = -arr[abs(arr[i]) - 1];

       else

           cout << abs(arr[i]) << "\n";

   }

   cout << "and the missing element is ";

   for (i = 0; i < size; i++) {

       if (arr[i] > 0)

           cout << (i + 1);

   }

}

int main()

{

   int arr[] = { 8, 3, 4, 5, 5, 6, 1 };

   int n = sizeof(arr) / sizeof(arr[0]);

   printTwoElements(arr, n);

}

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The mean absolute deviation of a set of data is the mean distance (or the average distance) between each data element and the mean of the data elements.

The steps for Finding the Mean Absolute Deviation of a Data Set are as follows:

Step 1: Find the mean of the data set.

Step 2: Find the sum of the data values, and divide the sum by the number of data values.

Step 3: Find the absolute value of the difference between each data value and the mean: |data value – mean|.

Step 4: Find the sum of the absolute values of the differences.

Step 5: Divide the sum of the absolute values of the differences by the number of data values.

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"It's pouring if the grass is wet." Our inverse sentence would be, "If it is NOT raining, then it is NOT wet on the grass."

Given,

Inverse Sentence;

Each of the original statements is presupposed to be false in an inverted statement. "If it is not snowing" would be the polar opposite of "If it is snowing." "Then it is not chilly" would be the polar opposite of "then it is cold."

Example of inverse sentence;

Now, we can construct the three other statements using the concepts we established before. If anything, we would say the opposite: "If the grass is wet, it's pouring." "If it is NOT raining, then the grass is NOT wet," would be our inverse claim.

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The price of the two pencils is Rs.100 (expensive) and Rs.60 (cheaper).

Let the price of the expensive pencil be = x

And the price of the cheaper one be = y.

According to the question:

The difference between the price of 2 = 40

Therefore,

x- y =40

Total amount = 1800.

The number of Expensive pencils that can be bought = 1800/x.

The number of Expensive pencils that can be bought = 1800/y.

According to the question,

1800/y -1800/x = 15 (the number of extra pencils)

= (1800x -1800y)/xy = 15

= 1800x -1800y =15xy

= 1800 (x-y) =15xy

Substituting x-y as 40

1800 x 40 =15xy

xy = 4800.

We know that x-y =40

Therefore, x = y+ 40

xy = 4800

(y+40) y = 4800

[tex]y^{2}[/tex] + 40 y = 4800

Using the quadratic equation formula,

y = 52.111 or y = -92.111

Thus, the cost of the cheaper pencil (y)= Rs. 52.111

The cost of the expensive pencil (x) = 52.111 + 40 = Rs 92.111

Therefore the cost of two pencils is =   Rs. 52.111 and Rs 92.111.

The end behavior of the graph of f(x) = x^5 + 8x^4 + 16x^3 is asymptotic: it goes towards positive infinity as x approaches positive infinity, and negative infinity as x approaches negative infinity.

The end behavior of the graph of a polynomial function with degree 5 is determined by the leading term, which in this case is x^5. Since the degree of the leading term is odd and the coefficient is positive, the graph of f(x) = x^5 + 8x^4 + 16x^3 will approach positive infinity as x approaches positive infinity, and negative infinity as x approaches negative infinity. This is known as an asymptotic end behavior. As the x-values get larger and larger, the magnitude of the y-values will also get larger and larger, approaching infinity in either direction. This can be seen by looking at the graph of the function, which will have an "S" shape that curves up and to the right (positive infinity) for large positive x-values, and down and to the left (negative infinity) for large negative x-values.

For x > 0, the end behavior is:

f(x) = x5 + 8x4 + 16x3

lim x→∞ f(x) = lim x→∞ x5 + 8x4 + 16x3

lim x→∞ f(x) = lim x→∞ x5

lim x→∞ f(x) = +∞

For x < 0, the end behavior is:

f(x) = x5 + 8x4 + 16x3

lim x→−∞ f(x) = lim x→−∞ x5 + 8x4 + 16x3

lim x→−∞ f(x) = lim x→−∞ x5

lim x→−∞ f(x) = −∞

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The joint relative frequency of students using mobile devices in traditional classes, is

The joint relative frequency of students that use mobile devices in the setting of a traditional class is :
= Number of students using mobile devices in traditional class / Number of total students accessing courses

Number of students using mobile devices in traditional class =  46 students

Number of total students accessing courses = 200

The  joint relative frequency of students using mobile devices in traditional classes :

= 46 / 200

= 23 %

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