Find the solution x-2y=-26 x-y=-2

Answer: Y = -7X-2

Step-by-step explanation:

if there are two co-ordinates (x1,y1) and (x2,y2).

If the line is passing through these co-ordinates

Then Slopw of the line  = (y2-y1)/(x2-x1)

We have one co-ordinate (-1,5) let it be (X1,Y1)

Let second co-ordinate be (X,Y)

Slope = -7 = (Y-5) / (X-(-1))

-7  = (Y-5)/(X+1)

Y-5 = -7 (x+1)

Y-5 = -7x-7

ADDING 5 ON BOTH SIDES OF THE EQUATION

Y-5+5 = -7X-7+5

Y = -7x-2

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})~\hspace{10em} slope = m\implies -7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-5=-7[x-(-1)]\implies y-5=-7(x+1) \\\\\\ y-5=-7x-7\implies y=-7x-2[/tex]

Answer:

The third table is an arithmetic sequence . Its difference is -1.4.

Step-by-step explanation:

In an arithmetic sequence the difference between one term and the next is a constant

8.7 - 1.4 = 7.3

7.3 - 1.4 = 5.9

5.9 - 1.4 = 4.5

4.5 - 1.4 = 3.1

Answer:3rd table

Step-by-step explanation:

Answer:

√11/√11

Step-by-step explanation:

in order to rationalize the denominator we must multiply it with the a radical that simplifies the radical in denominator

in given case radical in denominator is√11, in order to simplify it we need to multiply numerator and denominator by √11.

2√10/3√11 x √11/√11

=2√110/3(11)

=2√110/33!

For this case we must rationalize the denominator of the following expression:

[tex]\frac {2 \sqrt {10}} {3 \sqrt {11}} =[/tex]

To rationalize the denominator, that is, remove the root of the denominator, we must multiply by:

[tex]\frac {\sqrt {11}} {\sqrt {11}}[/tex]

So, we have:

[tex]\frac {2 \sqrt {10}} {3 \sqrt {11}} * \frac {\sqrt {11}} {\sqrt {11}} =\\\frac {2 \sqrt {10} * \sqrt {11}} {3 (\sqrt {11}) ^ 2} =\\\frac {2 \sqrt {110}} {3 * 11} =\\\frac {2 \sqrt {110}} {33}[/tex]

Answer:

Option B

For this case we have:

a)

[tex]\frac {1} {10}[/tex]to convert as a percentage we have:

[tex]\frac {1} {10}[/tex] * 100% = 10%

b)

[tex]\frac {1} {4}[/tex], if we multiply the numerator and denominator by 25 we have:

[tex]\frac {25} {100}[/tex]

c)

Now we must write a fraction that represents 50%.

We have[tex]\frac {1} {2}[/tex]. If we multiply the numerator and denominator by 50 we have:

[tex]\frac {50} {100}[/tex]

Answer:

10%

[tex]\frac {25} {100}\\\frac {1} {2}[/tex]

Answer:

[tex]a=10\%\\\\b=\frac{25}{100}\\\\c=\frac{1}{2}[/tex]

Step-by-step explanation:

To find "a" you can multiply [tex]\frac{10}{100}[/tex] by 100, then this is:

[tex]a=\frac{10}{100}*100\\\\a=10\%[/tex]

To find "b", you can multiply the numerator and the denominator of the fraction [tex]\frac{1}{4}[/tex] by 25, getting:

[tex]b=\frac{1*25}{4*25}\\\\b=\frac{25}{100}[/tex]

To find "c", you can reduce the fraction [tex]\frac{50}{100}[/tex]. Then you get that this is:

[tex]c=\frac{50}{100}\\\\c=\frac{25}{50}\\\\c=\frac{5}{10}\\\\c=\frac{1}{2}[/tex]

Answer:

[tex]P_n=10+90n[/tex]

Step-by-step explanation:

So it said it was linear and gave us two points on that line: (0,10) and (5,460).

y=mx+b is slope-intercept form where b is the y-intercept or the initial amount of beetles and m is the slope (or rate of change in population to number weeks) of the line.  Our variables (x,y) are really (n,P) here.

The slope of the line can be computed using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line }[/tex].

You can also just line up the points vertically and subtract, then put 2nd difference over first difference.

Like this:

(5  ,  460)

-(0  ,    10)

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

5       450

So the slope is 450/5=90.

The y-intercept is where the line crosses the y-axis.  A graph crosses the y-axis when it's x value is 0.  Luckily, they give us the y-intercept which is (0,10) so b=10.  Your problem gave us this as well and was just asking for the slope of the line.

Anyways the equation is

y=90x+10

or

y=10+90x

or since we are using P and n:

[tex]P_n=10+90n[/tex]

The explicit formula for the beetle population after n weeks is Pn = 10 + 90n.

To find an explicit formula for the beetle population after n weeks, we need to determine the rate of growth. From the given information, we know that the population increased by 460-10=450 beetles in 5 weeks. Therefore, the rate of growth is 450/5=90 beetles per week.

To find the explicit formula, we can use the formula for a linear growth model: Pn = Po + r*n, where Pn is the population after n weeks, Po is the initial population, r is the rate of growth, and n is the number of weeks.

Substituting the given values, we have: Pn = 10 + 90n.

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Lucy earned a total of $225.50 for the week by combining her regular and holiday earnings.

Lucy's earnings for the week:

Answer:68

Step-by-step explanation:

In an isosceles triangle with angle BCA equal to 44 degrees, the measure of angle CXA is also 44 degrees because the sum of the two bisected base angles is 44 degrees.

In an Isosceles Triangle, the base angles are always equal. Therefore, if m∠BCA (angle BAC) is 44 degrees, then m∠ABC is also 44 degrees.

Because BFAD and CE are bisectors, they split ∠ABC and ∠ACB into two equal angles. So, ∠ABF (or ∠ABX) and ∠ACD (or ∠ACX) are each 22 degrees.

m∠CXA is the sum of ∠ABX and ∠ACX. Therefore, m∠CXA is 22 degrees + 22 degrees = 44 degrees.

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Answer:

The function that shows total sales, including the first hour is

[tex]S(x)=15(x-1)+120[/tex]  or [tex]S(x)=15x+105[/tex]  

Step-by-step explanation:

Let

s(x) -----> function that represent the sales after the first hour

S(x) ----> function that represent the total sales (including the first hour)

x -----> the  number of hours

we know that

The linear equation that represent the total sales is equal to

[tex]S(x)=s(x)+120[/tex] -----> equation A

we have

[tex]s(x)=15(x-1)[/tex] -----> equation B

substitute equation B in equation A

[tex]S(x)=15(x-1)+120[/tex]

[tex]S(x)=15x-15+120[/tex]

[tex]S(x)=15x+105[/tex]  

Therefore

The function that shows total sales, including the first hour is

[tex]S(x)=15(x-1)+120[/tex]  or [tex]S(x)=15x+105[/tex]  

Answer:

Angle D is 70, I believe

Angle D would be supplementary to A

Answer:

[tex]\large\boxed{\dfrac{1}{(m-4)(m-3)}=\dfrac{1}{m^2-7m+12}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\frac{m+3}{m^2-16}}{\frac{m^2-9}{m+4}}=\dfrac{m+3}{m^2-16}\cdot\dfrac{m+4}{m^2-9}=(*)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\m^2-16=m^2=4^2=(m-4)(m+4)\\m^2-9=m^2-3^2=(m-3)(m+3)\\\\(*)=\dfrac{m+3}{(m-4)(m+4)}\cdot\dfrac{m+4}{(m-3)(m+3)}\\\\\text{cancel}\ (m+3)\ \text{and}\ (m+4)\\\\=\dfrac{1}{m-4}\cdot\dfrac{1}{m-3}=\dfrac{1}{(m-4)(m-3)}\\\\\text{use\ FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=\dfrac{1}{(m)(m)+(m)(-3)+(-4)(m)+(-4)(-3)}\\\\=\dfrac{1}{m^2-3m-4m+12}=\dfrac{1}{m^2-7m+12}[/tex]

Answer:

right, isosceles

Step-by-step explanation:

The lines on the two sides means that they are congruent.

Two sides being equal means that the triangle is isosceles.

The box in the corner means that the angle is equal to 90 degrees

A ninety degree angles means the triangle is a right triangle

Answer:

x=-3

Step-by-step explanation:

f(x) = -2(x + 3)^2 – 5

This quadratic is in the form

f(x) = a(x - h)^2 + k

f(x) = -2(x -  -3)^2 + - 5

Where (h,k) is the vertex

(-3,-5)

We know the axis of symmetry is along the vertex

x=h is the axis of symmetry

x=-3

The axis of symmetry of the function f(x) = -2 (x + 3)² - 5 is x = -3.

Line of symmetry of a figure or a shape is the line which divides the figure or shape in to equal and symmetrical parts.

This line is also called as axis of symmetry.

It is sometimes also called as mirror line since the line divides in to parts which looks like mirror images.

The given equation,

f(x) = -2 (x + 3)² - 5

f(x) = -2x² - 12x - 18 - 5

f(x) = -2x² - 12x - 23

For a quadratic function of the form, f(x) = ax² + bx + c, the axis of symmetry is,

x = -b/2a

Here,

x = 12 / (2 × -2) = -12/4 = -3

Hence the axis of symmetry is x = -3.

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Answer:

[tex]A.\\\\x+y\leq200\\\\4x+3y\leq750[/tex]

Step-by-step explanation:

x - number of adults

y - number of campers

The room for 200 people: x + y ≤ 200

Each adult costs $4, and each camper costs $3: 4x and 3y

A maximum budget of $750: 4x + 3y ≤ 750

The correct option for the given scenario is option A, which includes two inequalities: one for the capacity constraint (x + y ≤ 200) and one for the budget constraint (4x + 3y ≤ 750), where x is the number of adults and y is the number of campers.

The correct system of inequalities to represent the scenario where x is the number of adults and y is the number of campers, with a room capacity for 200 people and a maximum budget of $750, is:

This corresponds to option A, where the first inequality represents the capacity constraint and the second inequality represents the budget constraint.

Answer:

(x-5)(x-5)

Step-by-step explanation:

Ok... This ones actually pretty simple.

So all you have to do is find 2 numbers that add up to -10, and multiply to 25. You will quickly realize that the only 2 numbers that do that are -5 and -5. Then, all you have to do is write the now factored equation. (x-5)(x-5)

There are 2 ways to check your work. The first is to FOIL (first, inside, outside, last). This should get you back to your original equation

The second way to do it is to plug it into a graphing program. If you graph your factored equation and your original equation, they should be the same!

I hope this helps!

If you have any other questions just feel free to ask me.

For this case we must factor the following expression:

[tex]x ^ 2-10x + 25[/tex]

For this, we must find two numbers that when multiplied give 25 and when added to -10.

These numbers are -5 and -5:

[tex]-5-5 = -10\\-5 * -5 = 25[/tex]

Then, the factorization is given by:

[tex](x-5) (x-5)\\(x-5) ^ 2 [/tex]

Answer:

[tex](x-5) ^ 2 [/tex]

Answer:

[tex]\large\boxed{\bigg(4\times10^8\bigg)^2=1.6\times10^{17}}[/tex]

Step-by-step explanation:

[tex]\text{The sicientific notation:}\ a\times10^k,\ \text{where}\ 1\leq a<10\ \text{and}\ k\in\mathbb{Z}.\\\\\bigg(4\times10^8\bigg)^2\qquad\text{use}\ (ab)^n=a^nb^n\\\\=4^2\times\left(10^8\right)^2\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=16\times10^{16}\ -\ \text{this is not a scientific notation yet}\ a=16>10\\\\=1.6\times10\times10^{16}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\=1.6\times10^{17}[/tex]

Answer:

1.6 x 1017

Step-by-step explanation:

Answer:

y-1=0

Step-by-step explanation:

I'm going to write into y=mx+b form first.

m is the slope and b is the y-intercept.

First step is to find the slope.

To find the slope given two points you can use m=(y2-y1)/(x2-x1).

Instead, I like to line up the points and subtract vertically.  Then put 2nd difference on top of 1st difference.

Let's do that:

 (-2,1)

- (2,1)

--------

 -4, 0

The slope is 0/-4=0.  That means the line is horizontal and is of the form y=a number.

If you look at the points, you see the y-coordinate doesn't change.  The y-coordinate is always 1.  So the equation for the line is y=1.

If we subtract 1 on both sides we get y-1=0.

So general form is Ax+By+C=0 which is why I decide to move the one on the other side of the equation.  

If I had noticed earlier that the y-coordinates were the same I would have stopped and say y=whatever y-coordinate I seen. However, I really didn't take notice of that until after I found the slope.

Answer:

1)A'(8,-10), B'(10,-8), C'(2,-4)

2)A''(8,-4), B''(10,-6), C''(2,-10)

Step-by-step explanation:

Given:

Points A(8,8) B(10,6) C(2,2)

reflection over y=-1

Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 9,7 and 3

after reflections, the perpendicular distance will be 18,14,6 and the points will be at

A'(8,-10), B'(10,-8), C'(2,-4)

Now

Points A(8,-10), B(10,-8), C(2,-4)

reflection over y=−7

Perpendicular distance between points y-coordinates of points (A, B and C) and y=-7 are 3,1 and 3

after reflections, the perpendicular distance will be 6,2,6 and the points will be at

A''(8,-4), B''(10,-6), C''(2,-10) !

Answer : The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.

Answer:

The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.

Step-by-step explanation:

An equation is shown below:

4(x − 3) − 5(x + 1) = 3

This equation shows, the equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.

The distributive property is when you multiply the sum in the equation and multiply each number or addend in the equation.

Answer:

The length in the draw is 10 cm

Step-by-step explanation:

step 1

Find the scale plan

Divide the width in the draw by the width in the real

so

[tex]\frac{4}{8}=\frac{1}{2}\frac{cm}{m}[/tex]

That means----> 1 cm in the draw is equal to 2 m in the real

step 2

Find the length in the draw

using proportion

[tex]\frac{1}{2}\frac{cm}{m}=\frac{x}{20}\frac{cm}{m}\\ \\x=20/2\\ \\x=10\ cm[/tex]

Answer:

See below in bold.

Step-by-step explanation:

52, 19, 44, 49, 37, 46, 52, 36, 54, 13, 14, 17, 34, 16, 51

The mean =  35.6

The absolute differences from the mean =

16.4, 16.6, 8.4, 13.4, 1.4, 10.4, 16.4, 0.4, 18.4, 22.6, 21.6, 18.6, 1.6, 19.6, 15.4

The squares of these differences =  

268.96, 275.56, 70.56, 179.56, 1.96, 108.16, 268.96, 0.16, 338.56, 510.76, 466.56, 345.96, 2.56, 384.16, 237.16.

The Sum of these squares = 3459.6

Sample Variance  3459.6 / 14 = 247.11 and

Population  Variance = 3459.6 / 15  = 230.64

Sample standard deviation =  √247.11 = 15.72

Population Standard deviation = √230.64 =  15.19.

Sample standard deviation =  √247.11 = 15.72

Population Standard deviation = √230.64 =  15.19.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

Given

52, 19, 44, 49, 37, 46, 52, 36, 54, 13, 14, 17, 34, 16, 51

The mean =  35.6

The absolute differences from the mean =

16.4, 16.6, 8.4, 13.4, 1.4, 10.4, 16.4, 0.4, 18.4, 22.6, 21.6, 18.6, 1.6, 19.6, 15.4

The squares of these differences =  

268.96, 275.56, 70.56, 179.56, 1.96, 108.16, 268.96, 0.16, 338.56, 510.76, 466.56, 345.96, 2.56, 384.16, 237.16.

The Sum of these squares = 3459.6

Sample Variance  3459.6 / 14 = 247.11 and

Population  Variance = 3459.6 / 15  = 230.64

Sample standard deviation =  √247.11 = 15.72

Population Standard deviation = √230.64 =  15.19.

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Answer:

The amount of salads sold that day were 93.

Step-by-step explanation:

Information to note:

Salad = $6.50

Drinks = $2.00

Total amount sold = 209

Total amount of money gained = $836.50

Set the system of equation. Let salad = s, and drinks = d

s + d = 209

6.50s + 2d = 836.50

Isolate the variable s in the first equation. Note the equal sign, what you do to one side, you do to the other. Subtract d from both sides:

s + d = 209

s + d (-d) = 209 (-d)

s = 209 - d

Plug in the new expression for s into the second equation:

s = 209 - d

6.50s + 2d = 836.50

6.50(209 - d) + 2d = 836.50

Simplify. Isolate the variable, d. First, distribute 6.50 to all terms within the parenthesis:

6.50(209 - d) = 1358.5 - 6.50d

1358.5 - 6.50d + 2d = 836.50

Simplify. Combine like terms:

1358.5 + (-6.50d + 2d) = 836.50

1358.5 - 4.50d = 836.50

Isolate the variable, d. Note the equal sign, what you do to one side, you do to the other.

Subtract 1358.5 from both sides:

1358.5 (-1358.5) - 4.50d = 836.50 (-1358.5)

-4.50d = 836.50 - 1358.50

-4.50d = -522

Isolate the variable, d. Divide -4.50 from both sides:

(-4.50d)/-4.50 = (-522)/-4.50

d = -522/-4.50

d = 116

The amount of drinks sold were 116.

Plug in 116 for d in one of the equations:

s + d = 209

s + (116) = 209

Isolate the variable, s. Subtract 116 from both sides:

s + 116 (-116) = 209 (-116)

s = 209 - 116

s = 93

The amount of salads sold that day were 93.

~

Answer:

3 and 9

if f(x)=x^2+13 and g(x)=12x-14

Step-by-step explanation:

So when we are looking for the intersection of two functions, we are trying to figure out when they are the same.  When you think same, you should think equal (=).

So we want to find when f(x)=g(x) for x.

f(x)=g(x)

[tex]x^2+13=12x-14[/tex]

Let's get everything to one side.

Subtracting 12x and adding 14 to both sides.

[tex]x^2+13+14-12x=0[/tex]

I'm going to reorder the left hand side and also simplify the 13+14 part:

[tex]x^2-12x+27=0[/tex]

Now since the coefficent of x^2 is just 1 our job is to find two numbers that multiply to be 27 and add up to be -12.

Those numbers are -3 and -9 since -3(-9)=27 and -3+(-9)=-12.

So the factored form of our equation is

[tex](x-3)(x-9)=0[/tex]

Since the product is 0, then at least one of the factors must be 0.

So we want to solve both x-3=0 and x-9=0.

x-3=0 can be solved by adding 3 on both sides. This gives us x=3.

x-9=9 can be solved by adding 9 on both sides. This gives us x=9.

The intersection of f and g happens at x=3 or x=9.

Answer:

x = 9 and x = 3

Step-by-step explanation:

Given

f(x) = x² + 13 and g(x) = 12x - 14

To find the points of intersection equate the 2 functions, that is

f(x) = g(x)

x² + 13 = 12x - 14 ← subtract 12x - 14 from both sides

x² - 12x + 27 = 0 ← in standard form

Consider the factors of the constant term ( + 27) which sum to give the coefficient of the x- term ( - 12)

The factors are - 3 and - 9, since

- 3 × - 9 = + 27 and - 3 - 9 = - 12, hence

(x - 3)(x - 9) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 9 = 0 ⇒ x = 9

The functions intersect at x = 3 and x = 9

Answer:

90

Step-by-step explanation:

90 is where the middle line is

please mark brainliest :)

Answer:

90.

Step-by-step explanation:

The median is the point near the middle of the box.  It is 90.

Answer:

36cm

Step-by-step explanation:

If the current banner is a reduction of 1/6, then you have to expand it by the reciprocal. 6/1 *6 =36.

Answer:

36 cm.

Step-by-step explanation:

It is given that A button with a diameter of 6 cm is made from a circular banner. The scale factor of the reduction was 1/6 .

Let [tex]d[/tex] be the diameter of the original banner.

The scale factor of the reduction was 1/6 . It means,

[tex]\text{New diameter}=\frac{1}{6}\times \text{Original diameter}[/tex]

[tex]6=\frac{1}{6}\times d[/tex]

Multiply both sides by 6.

[tex]36=d[/tex]

Hence, the diameter of the original banner is 36 cm.

Answer:

Should be 1st number, 3rd number, 2nd number

Step-by-step explanation:

Mixed fraction has a 3 in it, which means its over 100%. 6/20 is 30%, and the other one is negative.

Answer:

3 32/40, 6/20, - 2/10

Step-by-step explanation:

3 32/40,  -2/10  , 6/20

We want greatest to least

Positive numbers are greater than negative numbers, so the negative number is the smallest

Since there is only one number with a whole number attached and none of the numbers are improper fractions (numerator larger than denominator) it would be the largest

3 32/40, 6/20, - 2/10

Answer:

Step-by-step explanation:

The total of the three exams must be at least 93*3 = 279

The total so far is

98 + 87 + x > 279

185 + x > 279                   Subtract 185 from both sides.

185-185+x > 279-185

x > 94

So I think you should pick 95

If you need a whole number result, you should pick 97

The graph of y=(x-1)^2-3 can be transformed to the graph of y=1/2(x+4)^2 by stretching it vertically and shifting it horizontally to the left.

The graph of y=(x-1)^2-3 transformed to produce the graph of y=1/2(x+4)^2 can be done by manipulating the equation and observing its effect on the graph.

Step 1: Identify the transformation of the parent function y=x^2

Step 2: The transformation y=1/2(x+4)^2 indicates a vertical stretch by a scale factor of 1/2 and a horizontal shift to the left by 4 units.

Therefore, the graph of y=(x-1)^2-3 is transformed to the graph of y=1/2(x+4)^2 by stretching it vertically and shifting it horizontally to the left.

A: The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.

B: The graph is stretched vertically by a factor of One-half, translated left 5 units, and translated up 3 units.

C: The graph is translated left 5 units, compressed horizontally by a factor of One-half, and translated down 3 units.

D: The graph is stretched horizontally by a factor of One-half, translated left 5 units, and translated down 3 units.

Answer:

The graph is stretched horizontally by a factor of 1/2, translated left 5 units and up 3 units.

Step-by-step explanation:

I put both equations into a graphing calculator and compared them. Five units left and 3 up agree with answers A and B. The second equation showed a wider parabolic than the first one, which agrees only with answer C. Therefore, it is my opinion that neither answer is correct. I chose D, but since this is a unit test I can't go in and see if I was correct or not.

Answer:

The correct option is C

Step-by-step explanation:

The expressions are:

=(3x²+5x-8)+(5x²-13x-5)

Open the parenthesis

=3x²+5x-8+5x²-13x-5

Now solve the like terms:

=8x²-8x-13

Thus the correct option is C....

The equation of the line is y = 0.6*x - 1, the graph is in the image at the end.

How to find the linear equation?

A linear equation in the slope-intercept form can be written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is given by:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the points (−5,−4) and (5,2), so the slope is:

a = (2 + 4)/(5 + 5) = 6/10 = 0.6

y = 0.6*x + b

And it passes through (5, 2), then:

2 = 0.6*5 + b

2 - 0.6*5 = b

-1 = b

The equation is:

y = 0.6*x - 1

The graph is in the image below.

Answer:

Part 1) [tex]324\pi\ units^{2}[/tex] ------> [tex]7,776\pi\ units^{3}[/tex]

Part 2) [tex]36\pi\ units^{2}[/tex] ------> [tex]288\pi\ units^{3}[/tex]

Part 3) [tex]81\pi\ units^{2}[/tex] ------> [tex]972\pi\ units^{3}[/tex]

Part 4) [tex]144\pi\ units^{2}[/tex] ------> [tex]2,304\pi\ units^{3}[/tex]

Step-by-step explanation:

we know that

The largest cross sectional area of that sphere is equal to the area of a circle with the same radius of the sphere

Part 1) we have

[tex]A=324\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]324\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=324[/tex]

[tex]r=18\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=18\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (18)^{3}[/tex]

[tex]V=7,776\pi\ units^{3}[/tex]

Part 2) we have

[tex]A=36\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]36\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=36[/tex]

[tex]r=6\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=6\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]

[tex]V=288\pi\ units^{3}[/tex]

Part 3) we have

[tex]A=81\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]81\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=81[/tex]

[tex]r=9\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=9\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (9)^{3}[/tex]

[tex]V=972\pi\ units^{3}[/tex]

Part 4) we have

[tex]A=144\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]144\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=144[/tex]

[tex]r=12\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=12\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (12)^{3}[/tex]

[tex]V=2,304\pi\ units^{3}[/tex]