PLEASE HELP RIGHT AWAY!!

Answer:

-x(x^2+2x+3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

-x is common to all three terms.  Thus, -x^3-2x^2-3x = -x(x^2 + 2x + 3).

Use the quadratic formula to find the roots (and thus the factors) of

x^2 + 2x + 3:  a = 1; b = 2; c = 3.

Thus, the discriminant is b^2-4ac, or 4 - 4(1)(3), or -8.

Because this discriminant is negative, x^2 + 2x + 3 has two complex, unequal roots.  They are:

      -2 ± i√8                  

x = --------------  or  -1 ± i*2*√2

Thus, the three factors of the given polynomial are:

-x, (x + 1 + 2i√2), and (x + 1 - 2i√2)

            2

Answer:

[tex]y=\frac{-3}{2}x +\frac{5}{2} \\or \\y=\frac{5}{2} -\frac{3}{2} x[/tex]

Step-by-step explanation:

slope-intercept form is: [tex]y= mx+b[/tex]

3x + 2y = 5.

rearrange

[tex]2y=5-3x\\y=\frac{5}{2} -\frac{3x}{2}[/tex]

Answer:

b on ed2020

IG: user_6232003

Step-by-step explanation:

Answer:

A. 26°

Step-by-step explanation:

If ON =OL, then the two triangles are are similar.

The base angles must be equal.

[tex](9x-8)\degree=(7x+8)\degree[/tex]

We group the similar terms to obtain:

[tex]9x-7x=8+8[/tex]

[tex]2x=16[/tex]

Divide through by 2 to get:

x=8

[tex]m\angle OML=90-(7x+8)[/tex]

Substitute x=8

[tex]m\angle OML=90-(7(8)+8)[/tex]

[tex]m\angle OML=90-(56+8)[/tex]

[tex]m\angle OML=26\degree[/tex]

Answer:

The correct answer is option A. 26°

Step-by-step explanation:

From the figure we can see that,

ON = OL

OM ⊥ NL

Therefore m<N = m<L

To find the value of x

m<N = m<L

7x  + 8 = 9x -8

9x - 7x = 8 + 8

2x = 16

x = 8

To find the value of m<OML

x = 8

m<L = 9x - 8

= 9*8 - 8 = 72 - 8 = 64

m<OML = 180 - (<L + <O)

 = 180 - ( 64 + 90)

 = 26°

Therefore the correct answer is option A. 26°

Answer:

D)  [tex]S_{14} = 875[/tex].

Step-by-step explanation:

Given  : If the first term of the series is 30 and the 14th term is 95,

To find : what is the sum of all the terms of the series.

Solution : We have given

First term = 30 .

14 th term = 95.

Sum of all term = [tex]S_{n} =\frac{n(first\ term +\ last\ term)}{2}[/tex].

Here, n = 14.

 [tex]S_{14} =\frac{14(30 +95)}{2}[/tex].

 [tex]S_{14} =\frac{14(125)}{2}[/tex].

 [tex]S_{14} =\frac{1750}{2}[/tex].

 [tex]S_{14} = 875[/tex].

Therefore, D)  [tex]S_{14} = 875[/tex].

Answer:

The sum of all the terms in series is 875.

Step-by-step explanation:

Given : If the first term of the series is 30 and the 14th term is 95,

To find : What is the sum of all the terms of the series?            

Solution :

The first term of the  series is 30 i.e. a=30

The 14th term of series is 95 i.e. [tex]a_{14}=95[/tex]

We know that in arithmetic series the 14th term is defined as

[tex]a_{14}=a+13d[/tex]

Substitute the value of a,

[tex]95=30+13d[/tex]

[tex]95-30=13d[/tex]

[tex]65=13d[/tex]

[tex]d=\frac{65}{13}[/tex]

[tex]d=5[/tex]

The common difference is 5.

The sum of the series is given by,

[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]

[tex]S_{14}=\frac{14}{2}[2(30)+(14-1)5][/tex]

[tex]S_{14}=7[60+(13)5][/tex]

[tex]S_{14}=7[60+65][/tex]

[tex]S_{14}=7[125][/tex]

[tex]S_{14}=875[/tex]

Therefore, The sum of all the terms in series is 875.

To solve this problem, you would have to apply the Pythagorean Theorem: a^2+b^2=c^2

X is the hypotenuse; therefore:

24^2+7^2=x^2

576+49=x^2

625=x^2

To solve this you would have to figure out what the square root of 625 is.

Answer: 25

Step-by-step explanation:

Pythagoreans theory

a2 + b2 = c2

24(square) + 7(square) =c(square)

576 + 49= c square

625=c square

c=√625

c=25

Answer:

Production of  2800  juice boxes is the break even point.

Step-by-step explanation:

Break-even point is the point where profit is zero and number of manufactured goods are all sold

Let number of juice boxes be y

charges of local store for 1 juice box= $0.65

charges of local store for y juice box=$0.65y

Factory cost of y juices boxes= $1400 + $0.15y

Assuming all juice boxes manufactured can be sold, to find the break-even point

charges of local store for y juice box= Factory cost of y juices boxes

$0.65y=$1400 + $0.15y

$0.65y-$0.15y= $1400

$0.50y=$1400

y= 1400/0.5

y=2800

hence production of  2800  juice boxes is the break even point!

ANSWER

[tex]\theta = 0 ,\frac{7\pi}{6} ,\frac{11\pi}{6 } [/tex]

EXPLANATION

We want to solve

[tex] \sin( \theta) + 1 = \cos(2 \theta) [/tex]

on the interval

[tex]0 \leqslant \theta \: < \: 2\pi[/tex]

Use the double angle identity to obtain:

[tex] \sin( \theta) + 1 = 1 - 2\sin ^{2} \theta[/tex]

Simplify to get;

[tex] 2\sin ^{2} \theta + \sin( \theta) + 1 - 1 = 0[/tex]

[tex]2\sin ^{2} \theta + \sin( \theta) = 0[/tex]

Factorize to obtain:

[tex]\sin \theta (2\sin \theta + 1) = 0[/tex]

Either

[tex]\sin \theta = 0[/tex]

This gives us

[tex] \theta = 0[/tex]

on the given interval.

Or

[tex]2\sin \theta + 1= 0[/tex]

[tex]\sin \theta = - \frac{1}{2} [/tex]

This gives us

[tex]\theta = \frac{7\pi}{6} ,\frac{11\pi}{6 } [/tex]

Therefore the solutions within the interval are:

[tex]\theta = 0 ,\frac{7\pi}{6} ,\frac{11\pi}{6 } [/tex]

You could use a ruler, think about how you want the polygon inside of the circle or how you want the circle to surround the polygon. When you use a ruler, make sure your co-ordinates inside of the circle are correct though before drawing the line.

I hope this info helps! :3

To construct a regular polygon inside a circle, divide the circle into "n" equal sectors using "n" radii, where "n" represents the number of sides in the polygon. Connect the center of the circle to each of the marked points on the circumference to create the regular polygon.

Determine the Circle: Start by drawing the given circle with a compass, and label its center as "O."

Select the Number of Sides: Decide on the number of sides for the regular polygon. Let's assume "n" as the number of sides.

Construct Diameter: Draw a diameter of the circle passing through the center "O," using a straightedge.

Construct Central Angle: To create a regular polygon with "n" sides, divide the circle into "n" equal sectors by constructing "n" radii (lines from the center to the circumference) evenly spaced around the circle. Each of these radii forms a central angle of 360°/n.

Find Vertices: On the circumference of the circle, mark "n" points (labeled A₁, A₂, A₃, ..., Aₙ) evenly spaced. These points will serve as the vertices of the regular polygon.

Connect Vertices: Use a straightedge to draw lines connecting the center "O" of the circle to each of the marked points (A₁, A₂, ..., Aₙ).

Construct Regular Polygon: The polygon with vertices A₁, A₂, ..., Aₙ, and center "O" is the regular polygon inscribed inside the circle.

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[tex]-0.7+\frac{2}{8} =[/tex]

[minus, 0, point, 7, plus, 2, divided by, 8, equals]

You can make the denominators the same to combine them, so you can multiply -0.7 by [tex]\frac{8}{8}[/tex]

[tex]-0.7(\frac{8}{8})+\frac{2}{8}[/tex]

[tex]-\frac{5.6}{8}+\frac{2}{8}=-\frac{3.6}{8}= - 0.45[/tex]

Final answer:

The sum of −0.7 and ⅔ is −0.45 when the fraction is simplified to 0.25 and then added to −0.7.

Explanation:

Fractions are used extensively in mathematics, particularly in arithmetic, algebra, geometry, and calculus, as well as in everyday situations such as cooking, measurements, and financial calculations. They provide a convenient way to express quantities that are not whole numbers and to perform operations such as addition, subtraction, multiplication, and division.

The student is asking for the sum of -0.7 and the fraction 2/8. To find the answer, first simplify the fraction 2/8, which can be reduced to 1/4. Now, convert 1/4 into decimal form, which is 0.25. Next, add this decimal to -0.7 to find the sum:

-0.7 + 0.25 = -0.45.

Therefore, the exact decimal for the expression −0.7 + ⅔ is -0.45.

The answer is:

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

To find the resultant expression, we need to apply the distributive property.

It  can be defined by the following way:

[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

Also, we need to remember how to add like terms: The like terms are the terms that share the same variable and exponent, for example:

[tex]x+x+x^{2}=2x+x^{2}[/tex]

We were able to add only the two first terms since they were like terms (they share the same variable and the same exponent)

So , we are given the expression:

[tex](x+y)(x^{2}-xy+y^{2})[/tex]

Then, applying the distributive property, we have:

[tex](x+y)(x^{2}-xy+y^{2})=x*x^{2}-x*xy+x*y^{2}+y*x^{2}-y*xy+y*y^{2}\\\\x*x^{2}-x*xy+x*y^{2}+y*x^{2}-y*xy+y*y^{2}=x^{3}-x^{2}y+xy^{2}+yx^{2}-xy^{2}+y^{3}\\\\x^{3}-x^{2}y+xy^{2}+yx^{2}-xy^{2}+y^{3}=x^{3}+y^{3}[/tex]

Hence, the answer is:

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

Have a nice day!

Answer:

y=50x+100

Step-by-step explanation:

y=mx+b

100 is b because its a flat fee

The slope is 50 because it is dependent on x, the amount of people.

The correct answer is y=150x.For example, if I were to equal 300. Then that would mean two people would have bought the membership. So, X equals two.

Answer:

b=10

Step-by-step explanation:

A=1/2bh

The A and h are already given

100=1/2b(20)

So what times 20 equals 2 times as much as 100? Its 10

100=1/2(10)(20)

100=1/2(200)

100=100

So the answer is b=10

The area of the triangle is 16. 

You can find this by plotting each of the points and drawing the triangle. You can then use the distance formula to determine each side length. The rectangle will be 2 on one side and 4 on the other. When multiplied together, it will give you the above answer

The coordinates of the midpoints for each side are (2.5, 5.5) , (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).

And, yes, the midpoints are the vertices of a rectangle, as its opposite sides are the same in length.

Use the formula for the midpoint of two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are,

[tex][\dfrac{(x_1 + x_2)}{2} , \dfrac{(y_1 + y_2)}{2} ][/tex]

Given that,

Vertices of the rectangle are (0, 8), (5, 3), (4, 2), and (- 1, 7).

Hence, the coordinates of the midpoints for each side are calculated by using the above formula,

The midpoint of two points (0, 8) and (5, 3) are,

[tex](\dfrac{(0 + 5)}{2} , \dfrac{(8 + 3)}{2} )[/tex]

[tex](2.5, 5.5)[/tex]

The midpoint of two points (5, 3) and (4, 2) are,

[tex](\dfrac{(5 + 4)}{2} , \dfrac{(3 + 2)}{2} )[/tex]

[tex](4.5, 2.5)[/tex]

The midpoint of two points (4, 2) and (-1, 7) are,

[tex](\dfrac{(4 - 1)}{2} , \dfrac{(2 + 7)}{2} )[/tex]

[tex](1.5, 4.5)[/tex]

The midpoint of two points (-1, 7) and (0, 8) are,

[tex](\dfrac{(-1 + 0)}{2} , \dfrac{(8 + 7)}{2} )[/tex]

[tex](-0.5, 7.5)[/tex]

Therefore, the coordinates of the midpoints for each side are (2.5, 5.5) , (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).

When the coordinates of vertices are rectangular then opposite sides are equal to each other.

So, we can check the length of each side of the coordinates of the midpoints (2.5, 5.5), (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).

Used the distance formula,

The distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

So, The distance between the two points [tex](2.5, 5.5)[/tex] and [tex](4.5, 2.5)[/tex],

[tex]d = \sqrt{(4.5- 2.5)^2 + (2.5 - 5.5)^2}[/tex]

[tex]d = \sqrt{4 + 9}[/tex]

[tex]d = \sqrt{13}[/tex]

The distance between the two points [tex](4.5, 2.5)[/tex] and [tex](1.5, 4.5)[/tex],

[tex]d = \sqrt{(4.5- 1.5)^2 + (2.5 - 4.5)^2}[/tex]

[tex]d = \sqrt{9 + 4}[/tex]

[tex]d = \sqrt{13}[/tex]

The distance between the two points [tex](1.5, 4.5)[/tex] and [tex](-0.5, 7.5)[/tex]

[tex]d = \sqrt{(1.5+ 0.5)^2 + (7.5 - 4.5)^2}[/tex]

[tex]d = \sqrt{4 + 9}[/tex]

[tex]d = \sqrt{13}[/tex]

The distance between the two points[tex](-0.5, 7.5)[/tex] and [tex](2.5, 5.5)[/tex]

[tex]d = \sqrt{(2.5+ 0.5)^2 + (7.5 - 5.5)^2}[/tex]

[tex]d = \sqrt{9 + 4}[/tex]

[tex]d = \sqrt{13}[/tex]

Clearly, All the lengths of each side of the coordinates of the midpoints (2.5, 5.5), (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5) are the same.

Hence, it forms a rectangle, as its opposite sides are also the same in length.

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For this case we must simplify the following expression:

[tex](\frac {n ^ {\frac {3} {2}}} {n ^ {- \frac {1} {6}}}) ^ {- 3}[/tex]

By definition of power properties we have:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, rewriting the expression:

[tex](n ^ {\frac {3} {2}} * n ^ {\frac {1} {6}}) ^ {- 3} =[/tex]

To multiply powers of the same base, we put the same base and add the exponents:

[tex](n ^ {\frac {3} {2} + \frac {1} {6}}) ^ {- 3} =\\(n ^ {\frac {18 + 2} {12}}) ^ {- 3} =\\(n ^ {\frac {20} {12}}) ^ {- 3} =\\(n ^ {\frac {5} {3}}) ^ {- 3} =[/tex]

We multiply the exponents:

[tex]n ^ {\frac {-15} {3}} =\\n^{-5}[/tex]

ANswer:

Option D

What question do you need answered?

Answer:

Option A.

Step-by-step explanation:

Anastasia worked for = 7 hours per day

Number of weeks she worked = 52 weeks

Number of hours she worked = 7×52

= 364 hours

Per hour earning of Anastasia = $20

Total earning of Anastasia = 364×20

= $7280

Let the monthly expenses of Anastasia = $x

Then total expenses = $12x

At the end of the year total saving = Total earning - Total expenses

= $7280 - 12x

Since she saved $2000 in a year therefore, expression that represents the savings will be

2000 = 7280 - 12x

12x = 7280 - 2000

12x = 5280

x = [tex]\frac{5280}{12}[/tex]

x = $440

Option A will be the answer.

Answer:

Choice B is correct

Step-by-step explanation:

The Interquartile Range (IQR) for Florida, 11, is greater than the IQR for Australia, 4.

The spread of a data set is a measure of the dispersion or variability of the data set. The spread can be measured by various statistical quantities depending on the nature of the data (skewed or symmetric);

The IQR

Variance

Standard Deviation

Range

A box plot is a graphical representation of the five number summary;

The minimum, first quartile, median, third quartile, and the maximum value in that order.

The IQR is defined as;

third quartile - first quartile

With this definition, the Interquartile Range (IQR) for Florida is;

28 - 17 = 11

while the Interquartile Range (IQR) for Australia is;

14 - 10 = 4

Therefore, the Interquartile Range (IQR) for Florida, 11, is greater than the IQR for Australia, 4.

Answer:

-6 -4 -2 4

Step-by-step explanation:

A B C F

Answer:

A. B. C. F.

Step-by-step explanation:

2.5 x 32.50 = 81.25 a week

Answer:

32.50× 2 = 65

32.50 ÷ 2 = 16.25

65+16.25 = 81.25(this is the answer)

Answer:

∠4 and ∠5

Step-by-step explanation:

we know that

If a is parallel to b

then

∠5=∠1 -----> by corresponding angles

∠4=∠1 -----> by alternate interior angles

Answer:

[tex]f(g)=25g[/tex]

Step-by-step explanation:

Let [tex]g[/tex] be the number of gallons so [tex]f(g)[/tex] is the number of miles traveled per [tex]g[/tex] gallons.

We know for our problem that Brian's car gets 25 miles per gallon. Since the gallons is represented by [tex]g[/tex], his car will travel a total distance of 25g (where g is the number of gallons.

We also know that the total distance is given by [tex]f(g)[/tex], so we can put the two expressions together to get our function:

[tex]f(g)=25g[/tex]

Let's check:

- If he uses 1 gallon (g=1), so

[tex]f(1)=25(1)[/tex]

[tex]f(1)=25[/tex] miles

He will travel 25 miles with one gallon.

- If he uses 2 gallons (g=2), so

[tex]f(2)=25(2)[/tex]

[tex]f(2)=50[/tex]

He will travel 50 miles with two gallon.

Answer:

The volume of the shape is 343 cm

Step-by-step explanation:

Because the formula is length x width x height

Answer:

343 cm³

Step-by-step explanation:

V = lwh

V = 7·7·7, since the sides are all 7

V = 49·7 because 7·7 = 49

V = 343 cm³

Answer:

None of these

Step-by-step explanation:

the answer can't have anything to do with perpendicular because you don't know if any of the angles are 90 degrees (and honestly none of them look right anyways... pun intended) and the only answer that isn't perpendicular is wrong because the lines are intersececting.

Answer:

∠7 = 34°

Step-by-step explanation:

Since a and b are parallel lines then

∠3 and ∠7 are corresponding angles and congruent, so

∠7 = ∠3 = 34°

Answer:

34 degrees

Step-by-step explanation:

For this case we have the following expression:

[tex]\frac {10p-5} {5 + 3 (p-1)}[/tex]

We must find the value of the expression when c[tex]p = 2[/tex].

Substituting the value of "p" we have:

[tex]\frac {10 (2) -5} {5 + 3 ((2) -1)} =\\\frac {20-5} {5 + 3 (1)} =\\\frac {20-5} {5 + 3} =\\\frac {15} {8}[/tex]

Thus, the value of the expression when [tex]p = 2, is\ \frac {15} {8}[/tex]

ANswer:

[tex]\frac {15} {8}[/tex]

Answer:

Since is the total amount of students now and m were the students before, you subtract them both (n-m) and divide that by m. Then, since to get a percentage from a fraction you have to multiply by 100, your answer should look like this: n-m/m*100

Answer:

D

Step-by-step explanation:

It's easiest to divide everything by 3.

The best variable to solve for is x in the first equation.

Let 3x+6y=9 be equation (1)

and 2x-10y=13 be equation (2)

2x-10y=13

10y = 2x - 13

y =[tex]\frac{2x - 13}{10}[/tex]  

substitute the value of y in equation (1)

3x+6y=9

3x + [tex]6(\frac{2x - 13}{10})[/tex] = 9

3x + [tex]3(\frac{2x - 13}{5})[/tex] = 9

[tex]\frac{15x + 6x - 39}{5}[/tex] = 9

21x - 39 = 45

21x = 84

x = [tex]\frac{84}{21}[/tex]

x = 4

Therefore, option D) x in the first equation is the correct answer

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Answer:

32

Step-by-step explanation:

Answer:

Tn = -4^n/2

Step-by-step explanation:

The formula for nth tern of a geometric sequence is given as:

Tn = ar^n-1 where;

a is the first term

r is the common ratio

n is the number of terms

Since we are looking for the nth term if the geometric sequence, we will write our answer as a function if 'n'.

Given the second and fifth terms to be -8 and 512, respectively, this can be interpreted as;

T2 = ar^2-1 = -8

T5 = ar^5-1 = 512

From the equations above, we have;

ar = -8... (1)

ar⁴ = 512

Dividing both equation, we have;

ar⁴/ar = -512/8

r³ = -64

r = -4

Substituting r = -4 into equation 1, we have;

a(-4) = -8

-4a = -8

a = 2

Since nth term Tn = ar^n-1

Substituting the value of a and r into the equation will give;

Tn = 2(-4)^n-1

2(-4^n × -4^-1)

2(-4^n × -1/4)

= -4^n/2

Answer:

as you all saw the rating of the above answer, it is incorrect. here is the correct answer with proof down in the photo below

The point-slope equation of the line passing through the points (-5,4) and (1,6) is y - 6 = 1/3(x - 1). This is derived from the standard point-slope formula y - y1 = m(x - x1) where m is the slope of the line.

In mathematics, specifically in linear algebra, the point-slope formula is used to determine the equation of a line given a point on the line and its slope. The point-slope equation of the line through the points (-5,4) and (1,6) is found by first calculating the slope between these two points, defined as the change in y divided by the change in x. So, y2 - y1 divided by x2 - x1. In this case, (6-4) / (1 - (-5)) = 2/6 = 1/3. So, the slope of the line is 1/3. We can then use one of these coordinates (for instance, 1, 6) and the slope in the point-slope formula: y - y1 = m(x - x1). Therefore, the point-slope equation of the line through (-5,4) and (1,6) is y - 6 = 1/3(x - 1).

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Answer:

# x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

# 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

# 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

# x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Step-by-step explanation:

* Lets study the problem to solve it

- Use the terms of x and y in the general form to find the standard form

∵ x² + y² - 4x + 12y - 20 = 0

- Use the term x term

∵ -4x ÷ 2 = -2x ⇒ x × -2

∴ (x - 2)²

- Use the term y term

∵ 12y ÷ 2 = 6y ⇒ y × 6

∴ (y + 6)²

∵ (-2)² + (6)² + 20 = 4 + 36 + 20 = 60

∴ x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

∵ x² + y² + 6x - 8y + 10 = 0

- Use the term x term

∵ 6x ÷ 2 = 3x ⇒ x × 3

∴ (x + 3)²

- Use the term y term

∵ -8y ÷ 2 = -4y ⇒ y × -4

∴ (y - 4)²

∵ (3)² + (-4)² - 10 = 9 + 16 - 10 = 5

∴ x² + y² + 6x - 8y + 10 = 0 ⇒ (x + 3)² + (y - 4)² = 5 ⇒ not in answer

∵ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ divide all terms by 3

∴ x² + y² + 4x + 6y - 5 = 0

- Use the term x term

∵ 4x ÷ 2 = 2x ⇒ x × 2

∴ (x + 2)²

- Use the term y term

∵ 6y ÷ 2 = 3y ⇒ y × 3

∴ (y + 3)²

∵ (2)² + (3)² + 5 = 4 + 9 + 5 = 18

∴ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

∵ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ divide both sides by 5

∴ x² + y² - 2x + 4y - 6 = 0

- Use the term x term

∵ -2x ÷ 2 = -x ⇒ x × -1

∴ (x - 1)²

- Use the term y term

∵ 4y ÷ 2 = 2y ⇒ y × 2

∴ (y + 2)²

∵ (-1)² + (2)² + 6 = 1 + 4 + 6 = 11

∴ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ (x - 1)² + (y + 2)² = 11 ⇒ not in answer

∵ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ divide both sides by 2

∴ x² + y² - 12x - 8y - 4 = 0

- Use the term x term

∵ -12x ÷ 2 = -6x ⇒ x × -6

∴ (x - 6)²

- Use the term y term

∵ -8y ÷ 2 = -4y ⇒ y × -4

∴ (y - 4)²

∵ (-6)² + (-4)² + 4 = 36 + 16 + 4 = 56

∴ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

∵ x² + y² + 2x - 12y - 9 = 0

- Use the term x term

∵ 2x ÷ 2 = x ⇒ x × 1

∴ (x + 1)²

- Use the term y term

∵ -12y ÷ 2 = -6y ⇒ y × -6

∴ (y - 6)²

∵ (1)² + (-6)² + 9 = 1 + 36 + 9 = 46

∴ x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Answer:

9^2 = 81

12^2 = 144

63^= 3969

A^2 + B^2 = C^2

81 + 144 = 225

so these numbers do not make a right triangle

Final answer:

The numbers square root of 63, 9, and 12 do make a right triangle as their squares satisfy the Pythagorean theorem. The sum of the squares of 9 and square root of 63 equals the square of 12, which validates that we have a right triangle.

Explanation:

To determine if the numbers square root of 63, 9, and 12 make a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longest side (the hypotenuse). Let's calculate the squares of each provided number:

Since the longest side here must be 12 (as it is the largest number), the Pythagorean theorem for these numbers would be as follows:
81 + 63 = 144?

That simplifies to:
144 = 144?

This is a true statement, which means that these numbers do indeed represent the sides of a right triangle.