You are treating two of your friends to the movies tonight. Your parent gives you $70.
Tickets are $7 each. At the candy counter, you are buying snacks and drinks for your
friends as they find seats. Snacks are $2 each, and drinks are $2.25. You are trying to
decide what combination of snacks and drinks are possible given the money remaining.
You can only carry 4 drinks on a tray by yourself.
a. Write a system of inequalities for this situation, using x for the number of
snacks and y for bottles of water purchased.
b. Graph the system and find the vertices.
c. Indicate on the graph what combinations of snacks and drinks are possible.
Explain your reasoning in-depth.
d. Does every point within the feasible region represent a valid solution in this
context? Why or why not?
e. Denote one combination that is possible and one that is not. Explain your
reasoning.
f. Prove each of your answers to part (e) algebraically.

Please tell me each one of these answers! Thx

Answer: To find the coordinates of the remaining vertices of square ABCD, we can use the information given about diagonal AC and the properties of a square. Since a square has equal side lengths and right angles, we know that the distance between opposite vertices on a diagonal must be equal to the side length of the square.

Given the coordinates of vertex A and C, we can use the distance formula to find the length of AC:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

AC = sqrt((2 - (-2))^2 + (4 - 1)^2)

AC = sqrt(4 + 9) = sqrt(13)

Now that we know the side length of the square, we can use this information to find the coordinates of the remaining vertices. We know that vertex B has the same y-coordinate as vertex A, but the x-coordinate is 2 units to the left of vertex C. Therefore, the coordinates of vertex B are (-2 + 2sqrt(13), 1).

Similarly, we know that vertex D has the same x-coordinate as vertex A, but the y-coordinate is 4 units down from vertex C. Therefore, the coordinates of vertex D are (-2, 1 + 4sqrt(13))

So, the coordinates of the remaining vertices are (2sqrt(13),1) and (-2, 4sqrt(13)) respectively.

Step-by-step explanation:

Answer:

-6, 19, 29

Step-by-step explanation:

Range = y

Domain = x

The equation is y = 5x + 4

we plug x into the equation:

5 (-2) + 4 = -6

5 (3) + 4 = 19

5 (5) + 4 = 29

The solution is Option C.

The term that must be added to the equation x² - 8x = 9 is 16 and the equation will be ( x - 4 )² = 5²

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

x² - 8x = 9   be equation (1)

( x - a )² = x² + a² - 2ax

So , 2ax = 8x

a = 4

So , the equation will be

( x - 4 )² = x² - 8x + 16

And , adding 16 on both sides of the equation (1) , we get

x² - 8x + 16 = 9 + 16

On simplifying the equation , we get

( x - 4 )² = 25

( x - 4 )² = 5²

Taking square roots on both sides of the equation , we get

x- 4 = 5

Adding 4 on both sides of the equation , we get

x = 9

Therefore , the value of x is 9

Hence , the number to be added to the equation is 16

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Answer: $159.90

Step-by-step explanation:

Assigning a variable: V=Vegetable seeds   F=Flower seeds   T=Top soil

Assigning a value to each variable: V=1.5   F=2.2   T=12.1

The equation:

v(12)+f(15)+t(9)=

1.5(12)+2.2(15)+12.1(9)=

1.5*12=18   2.2*15=33   12.1*9=108.9

18+33+108.9=159.9

Total cost = $159.90

Hope this helps!

The given polynomial does not have x - 3 as its factor.

The factor theorem states that for a polynomial p(x) if there exists a real number a such that p(a) = 0, then (x - a) is one of the factors of p(x).

The remaining factors of the polynomial can be found by dividing it by the same factor.

The polynomial is given as P(x) = 2x¹ − 5x³ - 4x² + 4.

In order to check whether x - 3 is a factor, evaluate P(3) as below,

P(3) = 2 × 3¹ - 5 × 3³ - 4 × 3² + 4

⇒ -161

Since, P(3) ≠ 0, x - 3 is not a factor of P(x).

Hence, the given expression is not a factor of P(x).

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The measure of angle ABD of the described Isosceles triangles is; 115°

The parameters are;

Triangle ΔACD is Isosceles triangle

Triangle ΔBCD is Isosceles triangle

m∠BAC = 20°

m∠BDC = 25°

Whereby ΔBCD and ΔACD have their vertex in the same direction, we can have;

AD ≅ AC Given sides legs of triangle ACD

BD ≅  BC Given sides legs of triangle BCD

BA ≅ BA  Reflexive property

Therefore, we can say that;

ΔDAB ≅ ΔCAB  by SSS congruency rule

By the CPCTC (Congruent Parts of Congruent Triangles are Congruent), we can say that;

m∠BAC ≅ m∠BAD

Thus;

m∠BAC ≅ m∠BAD = 20°

Therefore;

m∠BAC + m∠BAD = 20° + 20°

m∠BAC + m∠BAD  = 40°

Thus, m∠DAC = 40°  by the Angle addition postulate

m∠ADC = m∠ACD = (180 - m∠DAC)/2

= (180 - 40)/2 = 70° This is because they are base angles of an isosceles triangle

∴ m∠ADC = m∠ACD = 70°

Similarly;

m∠BDC = 25° = m∠BCD Base angles of isosceles triangle ΔBCD

m∠BCD + m∠DBC + m∠BCD = 180° Sum of the interior angles of a triangle theorem

m∠DBC = 180° - (m∠BCD +  m∠BCD)

= 180° - (25° +  25°)

= 130°

m∠DBC = 130°

m∠ABD ≅ m∠ABC by CPCTC

m∠ABD = m∠ABC

Therefore;

m∠DBC + m∠ABD + m∠ABC = 360° Sum of angles at a point

m∠DBC + 2 × m∠ABD = 360°

130° + (2 × m∠ABD) = 360°

2 × m∠ABD = 360° - 130°

2 × m∠ABD = 230°

m∠ABD = 230°/2

m∠ABD = 115°

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The cost of a pack of gum is equal to $2.1.

In order to determine the cost of a pack of gum, we would assign variables to the cost of a pack of gum and cost of a candy bar respectively, and then translate the given word problem into an algebraic equation as follows:

Since Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80, a linear equation which models this situation is;

4c + 2g = 9.80    ......equation 1.

Additionally, two packs of gum cost the same as three candy bars:

2g = 3c     ......equation 2.

c = 2g/3     ......equation 3.

Substituting equation 3 into equation 1, we have:

4(2g/3) + 2g = 9.80

8g/3 + 2g = 9.80

14g/3 = 9.80

14g = 29.4

Cost of a pack of gum, g = 29.4/14

Cost of a pack of gum, g = $2.1

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Complete Question:

Brock bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80. Two packs of gum cost the same as three candy bars. Let g represent the cost of a pack of gum and c represent the cost of a candy bar. What is the cost of a pack of gum?

In the parallelogram HIJK, the measure of angle J and K are 45 degrees and 135 degrees respectively.

You should know that a parallelogram is a quadrilateral whose opposite sides are parallel.  The given parameters for the solution are

m<H = 45 degrees

Having said this, the m<K will be:

Produce the line H to P

This implies that <JKP is = 45 degrees ........... corresponding angles

It there means that  <HKJ = 180-45 = 135 degrees

Also; <JKP = <IJK   ................ corresponding angles

Therefore m<J is 45 degrees.

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The correct question:

In parallelogram HIJK, the measure of angle H is 45∘.

Find the measure of angle J. Explain how you know.

Find the measure of angle K. Explain how you know.

The ratios in their simplest forms are 13:9 and 13:12 respectively and the two ratios are not proportional

You should understand that two ratios are proportional if their cross-product give the same result.

The cross product of two ratios entails multiplying the numerator of the first by the denominator of the second and the numerator of the second by the denominator of the first

a. Rewrite the ratio 26: 18 in simplest form.

This is expressed as follow = 26/2  : 18/2

= 13:9

b. Rewrite the ratio 39 : 36 in simplest form.

= 39/3 : 36/3

= 13 : 12

The corss product of the two ratios is

13/9 ≠13/12

this is because 156≠108

Conclusively, they are not proportional

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The number of times of Puerto Rico is 5/6

No earthquake released 10³ of Colombia

From the question, we have the following parameters that can be used in our computation:

The table of values

On the table of values, we have

Colombia = 6.0M

Puerto Rico = 5.0M

This means that

Number of times = Puerto Rico/Colombia

Substitute the known values in the above equation, so, we have the following representation

Number of times = 5/6

Here, we have

Colombia = 6.0M

So, we have

Earthquake = Colombia * 10³

This gives

Earthquake = 6 * 10³

From the table of values, we have no entries with the readings 6 * 10³

Hence, no earthquake released 10³ of Colombia

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The way that they could calculate the point that is equidistant from all three gates is; By joining the entry point of all three friends to form a triangle and then finding the centroid of this triangle , they can calculate the required point.

The circumcenter of a triangle is defined as the locus of point equidistant from the three vertices of a triangle.

From the image attached showing the location of the three gates, the first step to take is to join all the three entry points of the friends in order to form a triangle.

The second step to take now, will be to find the centroid of the triangle, such that all three friends must start moving in the direction of the midpoint of the opposite side.

Finally, following that procedure, the point equidistant from all the three gates can be calculated.

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The area of rectangle in the simplest Form is: [tex]= 45[/tex]

What is the area of a rectangle?

The area of a rectangle of length (L) and width (W) is given by the multiplication of the dimensions, as follows:

Area of rectangle = Length (L) * Width (W)

Given:

Area of rectangle =[tex]\sqrt{15*9*5*3}[/tex]

                              ⇒[tex]\sqrt{3*5*3*3*5*3}[/tex]

                              ⇒3*5*3

                              ⇒45

Therefore, the area of rectangle in the simplest Form is: 45

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Answer:

yes?

Step-by-step explanation:

Answer:

Step-by-step explanation:

So 3 minus 7. 3 – 7 = -4 *just trust me on that one ;) So the difference of 3 and 7 is -4.

Based on the given set of real numbers, a list of all the rational numbers in the set include the following: B. √4, -2/3, 1, 9/8, √(9/4), 2.4. Therefore, the correct answer option is: B. square root of 4 comma space short dash 2 over 3 comma space 1 comma space 9 over 8 comma space square root of 9 over 4 end root comma space 2.4 with bar on top.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the square root of 11.

In this scenario, the rational numbers include all of the following:

However, -√2 and √10 would not be classified as rational numbers because they cannot be obtained when an integer is divided by another integer.

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Answer:

A)  f(x) = tan(2x - π)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.3cm}\underline{Standard form of a tangent function}\\\\$f(x)=A \tan(B(x+C))+D$\\\\where:\\\\\phantom{ww}$\bullet$ $A=$ vertical stretch\\ \\\phantom{ww}$\bullet$ $\dfrac{\pi}{|B|}=$ period\\\\\phantom{ww}$\bullet$ $C=$ horizontal shift (positive is to the left)\\\\\phantom{ww}$\bullet$ $D=$ vertical shift\\\end{minipage}}[/tex]

The parent tangent function is:

[tex]f(x)=\tan(x)[/tex]

The period of the parent tangent function is π.

A tangent function is discontinuous when cos(x) = 0, so it has vertical asymptotes whenever cos(x) = 0.

Therefore, the parent tangent function has vertical asymptotes at:

[tex]x=\dfrac{\pi}{2}+\pi n[/tex]

and so its domain is:

[tex]\left\{ x \in \mathbb{R} \;| \;x \neq \dfrac{\pi}{2}+\pi n\right\}[/tex]

If the domain of the given tangent function is:

[tex]\left\{ x \in \mathbb{R} \;| \;x \neq \dfrac{\pi}{4}+\dfrac{\pi}{2}n\right\}[/tex]

then its vertical asymptotes are when:

[tex]x =\dfrac{\pi}{4}+\dfrac{\pi}{2}n[/tex]

Therefore, its period is π/2.

[tex]\implies \dfrac{\pi}{|B|}=\dfrac{\pi}{2}[/tex]

[tex]\implies B=2[/tex]

And it has been horizontally shifted by π/2:

[tex]\implies f(x)=\tan\left(2\left(x-\dfrac{\pi}{2}\right)\right)[/tex]

[tex]\implies f(x)=\tan\left(2x-\pi\right)[/tex]

Function g(x)

[tex]g(x)=\tan(x- \pi)[/tex]

Function h(x)

[tex]h(x)=\tan \left(x-\dfrac{\pi}{2}\right)[/tex]

Function j(x)

[tex]j(x)=\tan \left(\dfrac{x}{2}- \pi \right)[/tex]

The radius of the hemisphere with volume 3839cm³ is 11.9cm

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.The volume of the hemisphere is derived by Archimedes. The volume of a hemisphere = (2/3)πr3 cubic units.

The volume of a hemisphere is given as ⅔πr³

Where r is the radius

V = ⅔×3.14r³

3839 = 2/3× 3.14r³

r³ = (3839× 3)/3.14×2

r³ = 11517/6.28

r³ = 1833.9

r = cube root of 1833.9

r = 11.9cm

Therefore the radius of the hemisphere is 11.9cm

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The given function table is found not to be a function.

A function is defined as a relation in which each possible input value leads to exactly one output value. That means that “the output is a function of the input.” Meanwhile, the input values make up the domain, and the output values make up the range.

Now, the coordinates from the given function table are as follows;

(2, 3)

(3, 3)

(4, 3)

(5, 3)

(6, 3)

This shows that all the range values are the same for different x-values and as such it doesn't fit the definition of a function as stated above.

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The height of the triangular pyramid will be 154 cm.

A pyramid with a triangle base is referred to as a triangular pyramid. Vertices are essentially corners in geometry. Both regular and irregular triangular-based pyramids contain four vertices.

Pyramids with triangular bases have six edges, three of which run along the base and three of which rise above the base.

The volume of the triangular pyramid will be,

Volume = 1/2 x Base x h

11120 = 1/2 x ( 17 x 17 /2 ) x h

h = ( 11120 x 2 x 2 ) / ( 17 x 17 )

h = 44480 / 289

h = 154 cm

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X xcm 6cm 8cm is equal to 10cm if the area of the trapezium underneath is 40%2cm2.

Provide A B C D. trapezium the length of the sides excluding the base is 10,

[tex]$$\therefore \mathrm{AD}=\mathrm{DC}=\mathrm{CB}=10 \mathrm{~cm} \text {. }$$[/tex]

Draw a parallel DP & CQ on AB.

Let [tex]$\mathrm{AP}=x \mathrm{~cm}$[/tex]

In symmetry

[tex]$$\mathrm{QB}=x \mathrm{~cm}$$[/tex]

Consider area A of the trapezium. A B C D

[tex]$$\begin{aligned}& \left.A=\frac{1}{2} \text { (Sum of parallel sides }\right) \times(\text { Height }) \\& A=\frac{1}{2}(D C+A B) \times \text { DP } \quad \ldots(1)\end{aligned}$$[/tex]

Therefore, DPCQ creates a rectangle because DP & CQ are perpendicular to A B and C D were parallel to A B.

[tex]$$\therefore \mathrm{PQ}=\mathrm{DC}=10 \mathrm{~cm}$$[/tex]

Thus,

[tex]$$\begin{aligned}A B & =A P+P Q+Q B \\& =x+10+x \\& =2 x+10\end{aligned}$$[/tex]

Use the equation A r e a = h 2 (a + b) to determine a trapezium's area. The distance between a and b, which are two parallel sides, is denoted by the letter h. To put it another way, add the two parallel sides together, divide by 2, and then multiply this number by the separation between the parallel sides. The surface of a shape's surface is measured by its area. The length and width of a rectangle or square must be multiplied to determine their respective areas. A has a perimeter of x by y.

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The value for x is 10; the perimeter is 56 inches; a possible area the area is 7 square feet (option c); and a possible perimeter is 25 m (option a).

To find the correct value for x, let's replace the possible values and verify if the total is >11.

2x + 9

(2 x 0) + 9 = 0 + 9 = 9

(2 x -5) + 9 = -10 + 9 = 1

(2 x 10) + 9 =20 + 9 = 29

(2 x -8) + 9 = -16 + 9 = 7

Based on this, the correct value for x is 10

The perimeter of an octagon can be calculated using this formula:

8 x lengh of one side

8 x 7 inches =  56 inches

The area of a shape is calculated by multiplying side x side. Due to this, areas are always expressed using square meters, square feet, square kilometers, etc. Based on this principle, a possible area is 7 square feet (option c).

The perimeter is found by adding the lengh of all the sides in a shape. Due to this, it is expected a perimeter is expressed in meters, kilometers, centimeters, etc. Based on this a possible perimeter is 25 m (option a).

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The number of solutions that exist for the system of equations graphed as shown is B . One .

To find the number of solutions that exist in a system of graphs, you need to look at the number of points of intersection that there are.

The number of points of intersection shows the number of solutions. If there is one point of intersection, then there is one solution.

The system of equations graphed, has one point of intersection so there is only one solution .

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Answer: k = 5/3

Step-by-step explanation:

    To solve, we will isolate the variable, k, by using inverse operations.

   Given:

2/5k + 1/6 = 3/10k + 1/3

   Subtract 1/6 from both sides of the equation:

2/5k = 3/10k + 1/6

   Subtract 3/10k from both sides of the equation:

1/10k = 1/6

   Divide both sides of the equation by (1/10), which is the same as multiplying both sides by 10:

k = 5/3

Answer:

k=5/3

Step-by-step explanation:

2/5k+1/6=3/10k+1/3

Move the 3/10k to the left side with subtraction

1/10k+1/6=1/3

Move the 1/6 to the right with subtraction

1/10k=1/6

Divide the 1/10 from each side

Getting K=5/3

The correct answer is B.We can find by complex number by using complex form.

Complex numbers are the numbers that are expressed in the form of a+ib where a and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example 2+3i is a complex number where 2 is a real number (Re) and 3i is an imaginary number (Im).

Every real number is a complex number when the imaginary part is zero. But remember that every complex number is not a real number. For example we can write 5 as 5+0×(i). Hence Every Real Number is a Complex Number.

Now

A complex number is of the form a+ b(i)

 =8/3 +[tex]\sqrt{-7/3}[/tex]

 =8/3 +[tex]\sqrt{7/3}[/tex] [tex]\sqrt{-1}[/tex]

=8/3+[tex]\sqrt{7/3}[/tex] (i)

The second option is a complex number because it can be rewritten in the form

a + b(i).

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The new equations are:

a) g(x) = (1/2x)^(1/3)-3

b) j(x) = 2((x+4)^(1/3))

c) h(x) = (8x-24)^(1/3)

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The new equations are:

a) g(x) = (1/2x)^(1/3)-3

b) j(x) = 2((x+4)^(1/3))

c) h(x) = (8x-24)^(1/3)

A transformation function is a mathematical function used to transform a set of data points from one coordinate system to another. The transformation function takes the form of an equation that expresses a relation between two variables. It is commonly used in sciences such as physics and engineering to convert data from one coordinate system to another.

For example, if one measure the position of an object in Cartesian coordinates (x,y), the transformation function allows one to express the position of the same object in polar coordinates (r,θ). This can be written as: r = sqrt(x2 + y2); θ = arctan(y/x)

To write a new equation from a transformation function, one must first determine the desired coordinate system. Then, one can use the transformation function to find the relation between the two variables in the given coordinate system. For example, if one wants to express the position of an object in Cartesian coordinates from polar coordinates, the equation would take the form: x = r*cos(θ) ;    y = r*sin(θ)

This equation expresses the relation between the two variables in Cartesian coordinates. Then, one can use this equation to determine the position of any object in Cartesian coordinates given its position in polar coordinates.

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Answer:

x = -11.2

Step-by-step explanation:

hope it helps

Answer:

  Here, we use an underscore preceding the repeating digit(s).

  1/3 = 0.3_3

  1/6 = 0.16_6

  1/7 = 0.142857_142857

  1/9 = 0.1_1

Step-by-step explanation:

You want the four largest unit fractions that are repeating decimals, and their decimal equivalents.

The decimal equivalent of a fraction will repeat if the denominator of that fraction has factors other than 2 and 5.

A fraction with a given numerator will be larger if its denominator is smaller.

The fractions of interest will have denominators that are the smallest integers greater than 1 that have factors other than 2 and 5. Consider the integers:

  2 . . . . factor is 2

  3 . . . . suitable denominator

  4 = 2² . . . . factors are 2

  5 . . . . factor is 5

  6 = 2·3 . . . . suitable denominator

  7 . . . . suitable denominator

  8 = 2³ . . . . factors are 2

  9 = 3² . . . . suitable denominator

Using an overline to signify the repeating digits, the fractions of interest are ...

  [tex]\dfrac{1}{3}=0.\overline{3}\\\\\text{ }\dfrac{1}{6}=0.1\overline{6}\\\\\dfrac{1}{7}=0.\overline{142857}\\\\\text{ }\dfrac{1}{9}=0.\overline{1}[/tex]

__

Additional comment

The number of repeating digits may be as many as one less than the denominator. This is the case for 1/7, which has 6 repeating digits. 1/17 is another example, with 16 repeating digits.

The four unit fraction that has its numerator as 1 and a repeating decimal is

A repeating decimal are also called recurring decimal, is a time of decimal number with only digits that repeat after the decimal at regular intervals.

In mathematics, a repeating decimal is written in short form with an overline on the number that repeats

In the problem, the repeating fraction requires to have a unit numerator and the greatest. from knowledge of fractions, the ones with lesser numerators are the greatest.

The greatest is 1/3 = 0. 333.....

others are

1/6 = 0.166.....

1/7 = 0.142957142957.......

1/9 = 0.111111.........

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The ordered pair of the equation of line is given by

A ( 6 , 6 ) , B ( 0 , 2 ) , C ( -2 , -6 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , let the first point be A ( 6 , 6 )

Let the second point be B ( 0 , 2 )

The slope of the line m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2 - 6 ) / ( 0 - 6 )

Slope m = -4 / -6

Slope m = 2/3

And , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 6 = 2/3 ( x - 6 )

On simplifying the equation , we get

y - 6 = ( 2/3 )x - 4

Adding 6 on both sides of the equation , we get

y = ( 2/3 )x + 2

Therefore, the value of A is y = ( 2/3 )x + 2

Hence , the equation of line is y = ( 2/3 )x + 2

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Answer:fsjcc

Step-by-step explanation:

8473274+5487643=593fdj

]