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Answer:

The linear equation for the line which passes through the points given as (1,5) and (4,11), is written in the point-slope form as y=2x+3.

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (1,5) and (4,11).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 2

Determine the slope of the line.

The points through which the line passes are given as (1,5) and (4,11). Next, the formula for the slope is given as,

[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute 11&5 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$4 \& 1$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,

[tex]$$\begin{aligned}m &=\frac{11-5}{4-1} \\m &=\frac{6}{3} \\m &=2\end{aligned}$$[/tex]

Step 2 of 2

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

[tex]$$y-y_{1}=m\left(x-x_{1}\right)$$[/tex]

Substitute 2 for [tex]$m, 1$[/tex] for [tex]$x_{1}$[/tex], and 5 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows,

[tex]$$\begin{aligned}&y-5=2(x-1) \\&y-5=2 x-2 \\&y=2 x-2+5 \\&y=2 x+3\end{aligned}$$[/tex]

This is the required linear equation.

Answer:

Step-by-step explanation:

[tex] \bf \cfrac{AB}{DE} = \cfrac{BC}{EF} [/tex]

So, ∆ABC ～ ∆DEF by SAS.

The number is 5 if two increased by a number is a dozen. In other words, the correct answer is 5 by solving equations.

Step 1: Write the given information as an equation. "Two increased by a number" can be represented as 2 + x, where x is the unknown number.

Step 2: Translate "Two increased by a number is a dozen" into an equation. The word "a dozen" refers to the number 12.

[tex]2 + x = 12.[/tex]

Step 3: Solve the equation for x. To isolate x, subtract 2 from both sides of the equation:

[tex]2 + x - 2 = 12 - 2.[/tex]

This simplifies to x = 10.

Step 4: Verify the solution. Substitute the value of x back into the original equation:

2 + 10 = 12.

This equation is true, so x = 10 is indeed the solution.

Therefore, the number is 10.

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An equation is formed of two equal expressions. The value of the constant of proportionality is 0.41.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given there exists a proportional relationship between the number of juice bottles bought, j, and the total cost in dollars and cents. Therefore,

c ∝ j

c = kj

As the relation is represented by the equation c=0.41j. Therefore, the value of the constant of proportionality is 0.41.

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Hello,

f(x) = 1/9x + 2 ⇔ y = 1/9x + 2 ⇔ 1/9x = y - 2 ⇔ x = 9(y - 2)

                                                                            x = 9y - 18

⇒ f⁻¹(x) = 9x - 18

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

                         If we have a function, we can find its inverse if we do the

                         following-:

                        [tex]\tiny\bullet[/tex] replace f(x) with y.

                        [tex]\boldsymbol{\sf{y=\displaystyle\frac{1}{9}x+2}}[/tex]

                        [tex]\tiny\bullet[/tex] switch the places of x and y

                        [tex]\boldsymbol{\sf{x=\displaystyle\frac{1}{9}y+2}}}[/tex]

                         [tex]\bullet[/tex] solve for y

                        [tex]\boldsymbol{\sf{x\times9=\frac{1}{9}y\times9+2\times9}}[/tex]

                         [tex]\boldsymbol{\sf{9x=y+18}}[/tex]

                         [tex]\boldsymbol{\sf{-y=-9x+18}}[/tex]

                          [tex]\boldsymbol{\sf{y=9x-18}}}[/tex]

                        [tex]\boldsymbol{\sf{f(x)^{-1}=9x+18}}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

Answer:

18

Step-by-step explanation:

Entire length =105 + 82 =187

subtract 22

subtract 96

subtract 51              result =18

The equation of the parabola in standard form whose vertex is (0, 0) and a focus along the negative part of the x-axis is equal to x² = - 6 · y. (Correct choice: D)

In accordance with the statement, we find that the parabola has its vertex at the origin, therefore it is horizontal and its vertex constant (C) is negative as its focus is in the negative part of the x-axis. Therefore, the equation of the parabola in standard form has the following form:

x² = C · y, for C < 0.     (1)

In consequence, the equation of the parabola in standard form whose vertex is (0, 0) and a focus along the negative part of the x-axis is equal to x² = - 6 · y.

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Answer:

6.2 oz is lower

Step-by-step explanation:

The number line that represents the solution set of the inequality can be seen below.

Here we have the inequality:

15 > n ≥ 3

Then we need to have a open dot at the number 15 on the number line, and then a line that goes to the left until the value 3, where we must have a closed dot (because n = 3 is a solution of the inequality). The number line can be seen below.

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Answer:

I didnt know but i worked it out and searched it up and i got this

Step-by-step explanation:

(2a+4c-5b+2a+5b-4c)

Answer:

w = 12

l = 18

Step-by-step explanation:

Hello!

Recall the perimeter of a rectangle is twice the sum of the length and the width of the rectangle.

Let w be the width. The length is 6 less than twice the width. That means, l is 2w - 6.

Plug it into the formula and solve, given that P is 60.

The width is 12 inches. We can plug in 12 for 2w - 6 to find the length.

The length is 18 inches.

The width is 12 inches, and the length is 18 inches.

The interquartile range of the data set is 21.

Given that the heart rate of 10 adults is measured and the results are 83, 87, 90, 92, 93, 100, 104, 111, 115, 121.

The interquartile range shows the extent of the middle half of the distribution. Quartiles segment any distribution, ordered from low to high, into four equal parts. The interquartile range (IQR) contains the second and third interquartile ranges, the central half of the dataset.

The value of quartile 1 is Q₁=90

The value of quartile 3 is Q₃=111

So, the interquartile range is

IQR=Q₃-Q₁

IQR=111-90

IQR=21

Hence, the interquartile range of the data set 83, 87, 90, 92, 93, 100, 104, 111, 115, 121 is 21.

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The solution to the equations 2/x+3/y=9/xy; and 4/x+9/y=21/xy are x = 1, and y = 3.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The complete question is:

Solve for x and y:

2/x+3/y=9/xy; and 4/x+9/y=21/xy   x ≠ 0, y ≠ 0

We have two equations:

2/x+3/y=9/xy;

4/x+9/y=21/xy

Solving substitution method:

[tex]\rm \dfrac{4}{\dfrac{9-2y}{3}}+\dfrac{9}{y}=\dfrac{21}{\dfrac{9-2y}{3}y}[/tex]

y = 3

x = 1

Thus, the solution to the equations 2/x+3/y=9/xy; and 4/x+9/y=21/xy are x = 1, and y = 3.

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The least possible value of the expression is 2020

The expression is given as:

[tex](x + 4)(x + 5) + \frac{10^6}{x(x + 9)}[/tex]

Next, we plot the expression on a graph (see attachment)

From the attached graph, the minimum value of the expression is 2020 under the domain of x > 0

Hence, the least possible value of the expression is 2020

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The original price of each tickets is; $60 per ticket

We are told that $215 is what it costs after the discount. Thus, we add the amount taken off, back on to get;

$215 + $25 = $240

Now, since he wants to buy 4 tickets, then we divide the amount above by 4 to get the cost of each individual ticket.

Original Cost of each individual ticket = 240/4 = $60

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A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The length of GF is 254 units.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Since a centroid of a triangle divides the median into a ratio of 2:1. Therefore, the ratio of AG: DG is,

AG / DG = 2/1

(19x+14)/(9x+20) = 2/1

19x + 14 = 18x + 40

19x - 18x = 40 - 14

x = 26

Assuming the triangle is an equilateral triangle, therefore, the length of GF will be,

GF = DG = 9x+20

GF = DG = 9(26) + 20

GF = 254 units

Hence, the length of GF is 254 units.

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Answer:  26 units

Step-by-step explanation:   Trust Me!!!  

The answer is correct on Edge. I just got it right!

In the beginning, they have 50 and 180 cows respectively.

The two farmers bought  a total of 230 cows .

A year later the first farmer had 10% more cows than in the beginning.

Therefore,

let

x = number of cow he has initially.

A year later the percentage increase = 0.1x

whereas the second had 20% increase. Therefore,

let

y = number of cow he has initially.

A year later percentage increase = 0.2y

Hence,

x + y = 230

1.1x + 1.2y = 263

1.1x + 1.1y = 253

1.1x + 1.2y = 263

0.2y = 10

y = 10 / 0.2

y = 50

x = 230 - 50

x = 180

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If the distance is 45 miles and speed of both cyclist is 14 and 16 miles per hour then they will take time of 1.5 hour to meet.

Given First cyclist is riding at 14 miles per hour and second at 16 miles per hour. The distance is 45 miles.

We know that speed is the distance covered by an object in a particular period of time.

Speed=distance/time.

It is expressed as kilometers per hour or miles per hour, etc.

If both riders are riding towards each other then the speed will be 16+14 =30 miles per hour.

Distance=45 miles.

Time =distance/speed

=45/30

=1.5

Hence if first cyclist is riding at 14 miles per hour and second is riding at 14 miles per hour and the distance is 45 miles then they will meet after 1.5 hours.

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Answer:

a1

Step-by-step explanation:

Just add the numerators if both fractions to get: a + 1 = a1

Answer:

a+1

Step-by-step explanation:

Well if you have the same denominator, which in this case you do, it's equal to b, you can simply add the numerators. This gives you the expression [tex]\frac{a+1}{b}[/tex] so the numerator is a+1

Your question presented was: [tex]\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )-\frac{1}{3} (\frac{1}{2} -\frac{2}{3}x)[/tex]

Okay, lets distribute this problem and break it into two parts. We will distribute 2/5 and -1/3 to the numbers in parenthesis. This is the distributive property.

Step 1.
[tex]\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )[/tex] when distributed is [tex]\frac{2}{15} x - \frac{30}{40}[/tex]

Please note that -1/3 can be rewritten as + -1/3. So you must distribute the negative.

Step 2.
[tex]\frac{-1}{5} + \frac{2}{9} x[/tex]
So..lets put the 2 parts of the equation together

[tex]\frac{2}{15} x - \frac{30}{40}[/tex] + [tex]\frac{-1}{5} + \frac{2}{9} x[/tex] can be simplified by getting the common denominator.

You can only add like terms, so those fractions with x can only be combined with x.
Step 3.
Lets reformat while we're at it
[tex]\frac{6}{45} x + \frac{10}{45} x -\frac{30}{40} -\frac{8}{40}[/tex]

We got 45 because the LCM (Lowest Common Multiple) of 15 and 9 was 45. We multiplied both sides of the fraction by 3 for 2/15x and we multiplied by 5 on both parts of the fraction for 2/9x.

Now we combine.
Step 4.
[tex]\frac{16}{45}x-\frac{38}{40}[/tex]. We can still simplify!
Step 5.
-38/40 can be simplified by a common factor, 2! So our final answer is
[tex]\frac{16}{45}x-\frac{19}{20}[/tex]

I hope this helps you, heart if it helps.

Answer:

Step-by-step explanation:

1). 7x - 2y = 5 , A = 7 , B = 2 , C = 5

2). 4x - y = 1 , A = 4 , B = - 1 , C = 1

3). 5x - 2y = 3 , A = 5 , B = - 2 , C = 3

4). 4x - 3y = 3 , A = 4 , B = - 3 , C = 3

5). 2x + y = 15 , A = 2 , B = 1 , C = 15

The transformed function is:

[tex]g(x) = ( (x + 1)/3 - 2)^2 + 2*( (x + 1)/3 - 2)[/tex]

The parent function is:

[tex]f(x) = x^2 + 2x[/tex]

Here the axis of symmetry is at:

[tex]x = -2/2*1 = -1[/tex]

So first we need to apply a horizontal compression by a factor of 3 with respect to the line x = -1.

Here we can, for the moment, define a new variable that is zero when x = -1, let's define:

z = x + 1.

x = z - 1

Writing our function in terms of z, we get:

[tex]f(z) = (z - 1)^2 + 2*(z - 1)[/tex]

Now we can apply a compression by a factor of 3 around the origin. Then we have:

[tex]f(z/3) = (z/3 - 1)^2 + 2*(z/3 - 1)[/tex]

Returning to the original variable, we have:

[tex]f((x+1)/3) = ( (x + 1)/3 - 1)^2 + 2*( (x + 1)/3 - 1)[/tex]

Now we want to shift it one unit to the right, then we have:

g(x) = f( (x + 1)/3 - 1)

Replacing the actual function we get:

[tex]g(x) = f((x+1)/3 - 1) = ( (x + 1)/3 - 1 - 1)^2 + 2*( (x + 1)/3 - 1 - 1)\\\\g(x) = ( (x + 1)/3 - 2)^2 + 2*( (x + 1)/3 - 2)[/tex]

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Step-by-step explanation:

3y-13>-9

3y-13<-1

3y>4

3y<12

12>3y>4

y=2,3,4

Answer:

[tex]\left[ \dfrac{4}{3},4 \right][/tex]

Step-by-step explanation:

Inequality 1

[tex]3y-13\geq -9[/tex]

Add 13 to both sides:

[tex]\implies 3y-13+13\geq -9+13[/tex]

[tex]\implies 3y\geq 4[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3y}{3}\geq \dfrac{4}{3}[/tex]

[tex]\implies y \geq \dfrac{4}{3}[/tex]

Therefore, y is equal to or bigger than 4/3.

Inequality 2

[tex]3y-13\leq -1[/tex]

Add 13 to both sides:

[tex]\implies 3y-13+13\leq -1+13[/tex]

[tex]\implies 3y\leq 12[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3y}{3}\leq \dfrac{12}{3}[/tex]

[tex]\implies y\leq 4[/tex]

Therefore, y is equal to or smaller than 4.

Therefore, the solution to the inequalities in interval notation is:

[tex]\left[ \dfrac{4}{3},4 \right][/tex]

The trinomial represented by the algebraic tiles is x^2  + 4x + 3

On the horizontal axis, we have:

1 row under the big square.

This represents x + 1

On the vertical axis, we have:

3 columns beside the big square.

This represents x + 3

So, we have:

(x + 1) * (x + 3)

Expand

(x + 1) * (x + 3) = x^2  + x + 3x + 3

Evaluate

(x + 1) * (x + 3) = x^2  + 4x + 3

Hence, the trinomial represented by the algebraic tiles is x^2  + 4x + 3

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After 6 years, the difference between owning the house and renting is $12,000.

The first step is to determine the total cost of renting the house for six years.

Total cost of renting the house = rent per month x number of years x number of months in a year

1500 x 12 x 6 = $108,000

Difference = cost of owning - cost of renting

$120,000 - $108,000  = $12,000

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The coordinates of the circumcenter of triangle having coordinates of (0,0),(4,0),(4,-3) are (1,-17/6).

Given The coordinates of triangle are (0,0),(4,0),(4,-3).

Let the triangle be ABC.

Let the coordinates of the circumcenter be D(x, y).

We know that the length of circumcenter from the corner points are equal to each other.

In this way AD=BD=DC

AD=[tex]\sqrt{(x-0)^{2} +(y-0)^{2} }[/tex]

=[tex]\sqrt{x^{2} +y^{2} }[/tex]

DC=[tex]\sqrt{(4-x)^{2} +(-3-y)^{2} }[/tex]

BD=[tex]\sqrt{(4-x)^{2} +(0-y)^{2} }[/tex]

=[tex]\sqrt{(4-x)^{2} +y^{2} }[/tex]

AD=DC

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

Squaring both sides we get

[tex]x^{2} +y^{2}=16+x^{2} -8x+9+3y+3y+y^{2}[/tex]

8x-6y=25--------------------1

DC=BD

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

8x+6y=-9---------------------2

Solve equation 1 and 2

Add both equations

8x-6y+8x+6y=25-9

16x=16

x=1

put the value of x in 1

8x-6y=25

8*1-6y=25

-6y=25-8

y=-17/6

Hence the coordinates of circumcenter is (1,-17/6).

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Answer:

729

Step-by-step explanation:

I have not done this in some time so the terms may be a bit unconventional, but they work. The key to this is multiplying by -3.

1*(-3) = -3

-3*(-3) = 9

And so on.

1, -3, 9, -27, 81, -243, 729

The value of the given expression is 1/16

Given the exponential function below as shown;

(1/2)^4

This means the product of 1/2 in 4 places. This can be expressed as;

(1/2)^4 = 1/2 * 1/2 * 1/2 *1/2

(1/2)^4 = 1/4 * 1/4

(1/2)^4 =1/16

Hence the value of the given expression is 1/16

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Answer:

Mercury - 0.39 and 0.242

Venus - 0.72 and 0.616

Earth - 1 and 1

Mars - 1.52 and 1.88

Uranus - 19.18 and 84.00

Neptune - 30.06 and 165.00

The distance between Mercury, Venus, Earth, Mars, Uranus, and Neptune from the sun is 0.39, 0.72, 1, 1.52, 19.18, and 30.06 respectively.

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

The distance between each planet from the sun will be given as

Mercury - 0.39 and 0.242

Venus - 0.72 and 0.616

Earth - 1 and 1

Mars - 1.52 and 1.88

Uranus - 19.18 and 84.00

Neptune - 30.06 and 165.00

Hence, the distance between Mercury, Venus, Earth, Mars, Uranus, and Neptune from the sun is 0.39, 0.72, 1, 1.52, 19.18, and 30.06 respectively.

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Answer:

Simplifying

x2 + 6x + 13 = 20

Reorder the terms:

13 + 6x + x2 = 20

Solving

13 + 6x + x2 = 20

Solving for variable 'x'.

Reorder the terms:

13 + -20 + 6x + x2 = 20 + -20

Combine like terms: 13 + -20 = -7

-7 + 6x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0

-7 + 6x + x2 = 0

Factor a trinomial.

(-7 + -1x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying

1 + -1x = 0

Solving

1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0

0 + -1x = 0 + -1

-1x = 0 + -1

Combine like terms: 0 + -1 = -1

-1x = -1

Divide each side by '-1'.

x = 1

Simplifying

x = 1

Solution

x = {-7, 1}

Step-by-step explanation:

hope this helps if not let me know have a blessed day