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find three consecutive integers such that the sum of twice the second and three times the third is five less than six times the first.

The system of equations have Unique solution.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation is,

⇒ 3x - y = 13

⇒ y + 3 = 9x

Now,

Since, The system of equation is,

⇒ 3x - y = 13

⇒ y + 3 = 9x

It can be written as,

⇒ 3x - y = 13

⇒ 9x - y = 3

Clearly, We have;

⇒ 3/9 = - 1 / - 1

⇒ 1/3 ≠ 1

Thus, It has Unique solution.

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Part A: Calculation of the limit at x = 3In order to find the limit of the function, we can factorize the numerator by factoring out (x-3).  Limit [tex][tex](x 3)\frac{(x^3 - 27)}{ (x-3)} )[/tex]Now, factorize x³ - 27 to get the difference of cubes. The

limit equation becomes,  Limit [tex](x 3) \frac{ (x-3)(x² + 3x + 9)]}{(x-3)}[/tex] Now, we can cancel out the term (x-3) from the numerator and denominator to get the limit equation as

Part B: Limit [tex](x 3) (x^2 + 3x + 9)[/tex]The limit of the function at x = 3 is the value of the function as x approaches 3. By plugging in x = 3 in the equation above, we get, Limit ([tex](x 3) (x^2 + 3x + 9) = (3)^2 + 3(3) + 9[/tex] = 27Part B: Equation of line through f(3) with slope = 27

The slope of the line is 27, and it passes through the point (3, f(3)). The equation of the line can be found using the point-slope form.  [tex]y - f(3) = 27(x - 3)[/tex]

Part C: Simplifying the equation, we get,[tex]y = 27x - 78[/tex] Part C: Graphical representation of the line and the function

The graph of the function f(x) is a parabola opening upward with a vertex at (3, 0). The slope of the line is positive, which means the line will have a positive y-intercept.

The line will intersect the y-axis at (0, -78).Both the graph of the function and the line pass through the point (3, 0). The line is tangent to the graph of the function at that point.

The slope of the line represents the instantaneous rate of change of the function at the point (3, 0). It is the same as the limit we calculated in Part A.

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a least squares linear trend line is just a simple regression line with the years recoded  then it is a true statement

The simple linear regression model is;

y = mx + c

Where,

y = dependent variable

m is the slope

x is the independent variable

c is the y- intercept

The long-term trend only Least-Squares Regression Model also follows the same format except y becomes Yt and x becomes t.

The long-term trend only Least-Squares Regression Model is therefore the same as a simple linear regression only with different variable terms.

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-$650, Spent -$842, Earned +$522 and Earned +$650 are required integers and Spending $650 and earning $650 are opposite transactions but they have the same absolute value.

A number system is defined as a system of writing to express numbers.

Spent $650

Spent $842

Earned $522

Earned $650

Spent -$650, Spent -$842, Earned +$522 and Earned +$650.

Spending $650 and earning $650 are opposite transactions but they have the same absolute value because the absolute value of a number n is written as |n|.

The absolute value of 0 is 0. Two numbers are opposites if they have the same absolute value but different signs. Opposites are the same distance from 0 on a number line, and they are on opposite sides of 0.

Hence, -$650, Spent -$842, Earned +$522 and Earned +$650 are required integers and Spending $650 and earning $650 are opposite transactions but they have the same absolute value.

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Answer:

the width of the flag is 310 ft and the length is 790 ft.

Step-by-step explanation:

Let "w" be the width of the flag and "l" be the length of the flag. We can set up the following equation to represent the problem:

2w + 2l = 2200

We know that the length of the flag is 480 ft greater than the width, so we can set up the following equation to represent this relationship:

l = w + 480

We can substitute the second equation into the first equation to solve for the width of the flag:

2w + 2(w + 480) = 2200

This simplifies to:

4w + 960 = 2200

Subtracting 960 from both sides gives us:

4w = 1240

Dividing both sides by 4 gives us:

w = 310

So the width of the flag is 310 ft.

We can use this value to find the length of the flag by substituting it into the equation l = w + 480:

l = 310 + 480

This simplifies to:

l = 790

So the length of the flag is 790 ft.

Therefore, the width of the flag is 310 ft and the length is 790 ft.

Answer:

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

See the steps below, they should be self-explanatory.

Let me know if anything is unclear.

The system of equations  presented in the graph is written as

Linear function in the slope intercept formula is written in the form

y = mx + c

definition of variable

y = output variable

m = slope

x = input variable

c = y intercept

The dashed line represents inequality without "equal to" hence less than or greater then only. shading above the line is greater than

the line passed through points (0, 2) and (3, 0)

the slope, m is = (2 - 0) / (0 - 3) = -2/3

the y intercept = 2

y > -2x/3 + 2

The solid line means the inequality has equal to hence it either greater than or equal to OR less than or equal to. no shading means it is only equal to

the line passed through points (0, 0) and (2, 2)

the slope, m is = (0 - 2) / (0 - 2) = 1

the y intercept = 0

y = x

The equation of the graph is

y > -2x/3 + 2

y = x

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Answer:

1/ Total percent of discount is 40%

2/ The original price is $520.70

Step-by-step explanation:

1/ We add a 25% discount on every TV store, a 10% discount on purchases, 5% discount for paying cash, so the total is a 40% discount.

2/ Now, let's find the original price

100% - 40% = 60%

We know that the 60% he has to pay is $371.93, so we have to find the 40% discount.

40% = 0.4

Take 371.93 times 0.4 = $148.77

Then we add both numbers together

148.77 + 371.93 = $520.70

The equations of the asymptotes of the hyperbola is 6y = -7x,

There are two asymptotes on each hyperbola. A hyperbola with a horizontal transverse axis and centre at (h, k) contains one asymptote with equation y = k + (x - h) and the other with equation y = k - (x - h). A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels towards as it approaches infinity. The two vertices, the two focus points, and the centre are all on the same horizontal line and equally spaced from one another. This is a horizontal hyperbola because of this. Our graph of the hyperbola follows the lines of the asymptotes.

Given,

Equations of hyperbola,

(y+4)². (x-6)²

——— - ———. =. 1

36. 49

a² = 36

a = 6

b² = 49

b = 7

Asymptotes of the hyperbola:

y = ±b/a × x

y = 7/6x

6y = 7x

y = -7/6 x

6y = -7x

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Answer:

8x2−8y2+6x−6y

Step-by-step explanation:

x2 means x squared

We need to use the concept of Percentile Rank. The Percentile Rank for score 71 is   33.33   and the score of Viktor is   84.

According to the pupils in the particular norm group, a student's performance is shown by their percentile rank. Let's try to put the percentile rank in a tidy mathematical equation now that you are clearer on what it actually is. A collection of values A = x1, x2, x3,..., xn with N values will be used in our attempt to calculate the percentile rank of the data point xm. In this scenario:

PR = L / N × 100 where:

PR stands for percentile rank and has a range of 0 to 100;

L is the quantity of values in set A that are less than or equal to the value of your data, xm; and

The entire collection of values in A has a total of N values.

Given some of the test scores. Arrange the test Scores in ascending order.

A={58,64,66,70,71,75,77,80,84,85,87,90,93,95,96}

N=15

Now find out the values in the set which are less than or equal to 71.

L=5

Apply, PR=L/N ×100

⇒PR=5/15 × 100

PR=33.33 is the Percentile Rank of score 71.

Viktor is in 60th percentile, so find out L.

⇒60=L/15 ×100

⇒L=60×15/100

L=9.

So 84 is Viktor Score.

We need to use the concept of Percentile Rank. The Percentile Rank for score 71 is   33.33   and the score of Viktor is   84.

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Answer:

dont get it

Step-by-step explanation:

Answer:

x = 2

y = 6

Step-by-step explanation:

5x-4=y

We add 4 and subtract y from both sides

5x - y = 4

Now we have 2 equation

5x - y = 4

-2x + 2y = 8

Let's find the x first! We time the first equation by 2

10x - 2y = 8

-2x + 2y = 8

Now add both equations

8x = 16

x = 2

Now let find the y by put 2 back in the x

-2(2)+2y=8

-4 + 2y = 8

2y = 12

y = 6

a)

Step-by-step explanation:

we only need to look at the point, where y = 0.

that is clearly at x = 3.

which function gives y = 0 as result, when x = 3 ?

only a)

y =

[tex] \sqrt[3]{3 - 3} [/tex]

the cubic root of 0 is 0.

as 3 is not equal to the cubic root of 3, b), c) and e) are out.

and d) is

[tex]y = \sqrt[3]{3 + 3} [/tex]

the cubic root of 6 is NOT 0.

so, only a) is the only right answer.

Answer:

i think ur answer is c

Step-by-step explanation:

Answer:

Step-by-step explanation:

take your fingers, raise 2 of them now raise 2 more how many do you see? 4.

According to the information given, the equation that represents the situation is 6c - 1200 = 240.

What is a quadratic equation?

Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

The total costs are:

 $240 in taxes and trips.

 6 nights at the hotel, each night with a cost of c, hence 6c

Then:

T = 6c + 240

The budget is of $1200, hence, since the total cost is equals to the budget:

T = 1200

6c + 240 = 1200

Rearranging:

6c - 1200 = 240

Hence, according to the information given, the equation that represents the situation is 6c - 1200 = 240.

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Answer: 2560

Step-by-step explanation:

m= -8

n=4

p= -12

4(7mp+3p)+4n= 4((7 x -8 x -12)) +4(4)= 2560

Answer:

the team played a total of 14 games

Step-by-step explanation:

To find the number of games the team played, you can divide the total number of points they scored by the mean number of points they scored per game. In this case, you would divide 924 by 66 to get:

[tex]924 / 66 = < < 924/66=14 > > 14 games[/tex]

So, the team played a total of 14 games.

The locus of point P such that PA²+PB² = 16 is [tex]x^{2} +y^{2} + 4x - 4y + 5 =0[/tex]

A locus is the collection of all points that satisfy a condition, typically forming a curve or surface. For instance, the set of points in three-space that are equally spaced out from a given point is a sphere, and the locus of points in the plane that are equally spaced apart from a given point is a circle.

Given that A and B are two fixed points on a plane locus of P such that PA²+PB² =16

Let point P be (x,y) then [tex]{(x-0)^{2} +(y-1)^{2} }+{(x-(-4))^{2}+(y-3)^{2} } = 16[/tex]

is the Locus of the given point P

On simplyfying we  get

[tex]{x^{2}+(y-1)^{2} } +{(x+4)^{2}+(y-3)^{2} } = 16[/tex]

[tex]2x^{2} +2y^{2} +8x-8y+10=0\\x^{2} +y^{2} + 4x - 4y + 5 =0[/tex]

This is the Locus of point P where PA²+PB²  = 16.

The locus of point P such that PA²+PB² = 16 is [tex]x^{2} +y^{2} + 4x - 4y + 5 =0[/tex]

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The frequency distribution table starting with score 26 will be illustrated as:

Class interval Number of data.

26 - 31. 2

32 - 37. 4

38 - 43. 0

44 - 49. 1

Based on the information illustrated, let's assume that the numbers that we have include 27, 26, 45, 32, 35, 37, 36.

It should be noted that frequency distribution are portrayed as frequency table me chart. It shows the actual number or observations.

In this case, the class width is 26 - 31, 32 - 37, etc. The frequency distribution is illustrated above.

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There are 5x6=30 one-to-one functions from a set containing 5 elements to a set containing 6 elements.

A one-to-one (or injective) function is a type of mathematical function that maps each element of one set to one, and only one, element of another set. In other words, a one-to-one function is a function that has a unique output for each input. To calculate the number of one-to-one functions from a set containing 5 elements to a set containing 6 elements, we can use the formula f(x)=y, where x is the number of elements in the original set and y is the number of elements in the target set. In this case, x = 5 and y = 6, so f(x) = 6. Since each element in the original set must be mapped to a unique element in the target set, the total number of one-to-one functions is equal to the product of x and y, or 5 x 6 = 30.

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Answer:

8x2

Step-by-step explanation:

Answer:

A. Corresponding Angles

Step-by-step explanation:

They are both the same angle, and on the same side

Answer:

A. Corresponding angles

Step-by-step explanation:

Corresponding angles hold the same relative position as another angle somewhere else in the triangle. They have the same degree too. So answer is A

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +4}{2}~~~ ,~~~ \cfrac{ y +1}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~3)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +4}{2}=1\implies x+4=2\implies \boxed{x=-2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +1}{2}=3\implies y+1=6\implies \boxed{y=5}[/tex]

By solving a system of equations we can find the two numbers:

y = 5 + √15

x = 5 - √15

We can define the two numbers as x and y, and we know that:

x*y = -10

x  + y = 10

So we have a little system of equations here.

We can isolate x on the second equation to get:

x = 10 - y

And now replace it on the first equation to get:

(10 - y)*y = -10

10y - y^2 = 10

Then we have a quadratic equation:

y^2 - 10y + 10 = 0

The solutions are given by:

[tex]y = \frac{10 \pm \sqrt{(-10)^2 - 4*10*1} }{2} \\\\y = \frac{10 \pm \sqrt{60} }{2}\\\\y = 5 \pm \sqrt{15}[/tex]

So the two numbers are:

y = 5 + √15

x = 5 - √15

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Answer:

A

Step-by-step explanation:

To solve this problem, we need to first find out how much interest the account earns each year. If the account earns 2.5% simple interest per year, and it starts with an initial balance of $260, then the interest earned each year is 0.025 * $260 = $6.50.

Over 5 years, the account will earn a total of 5 * $6.50 = $<<5*6.5=32.50>>32.50 in interest.

To find the total amount of money in the account at the end of the 5 years, we need to add the interest earned to the initial balance of the account. The total amount of money in the account will be $260 + $32.50 = $<<260+32.5=292.50>>292.50.

Therefore, the total amount of money in the account at the end of the 5 years is $292.50.

Answer:

A)  $292.50

Step-by-step explanation:

Simple Interest Formula

A = P(1 + rt)

where:

Given:

Substitute the given values into the formula and solve for A:

⇒ A = 260(1 + 0.025 · 5)

⇒ A = 260(1 + 0.125)

⇒ A = 260(1.125)

⇒ A = 292.50

Therefore, the total amount of money in her savings account at the end of 5 years is $292.50.