The points (4, 1) and (x, -6) lie on the same line. If the slope of the line is 1 what is the value of x?

The answer is:

The center of the circle is located on the point (-9,-2) and the radius is 6 units.

To solve the problem, we need to use the given equation which is in the general form.

We are given the circle:

[tex]x^{2}+y^{2}+18x+4y+49=0[/tex]

We know that a circle can be written in the following form:

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

Where,

h is the x-coordinate of the center of the circle

k is the y-coordinate of the center of the circle

r is the radius of the circle.

So, to find the center and the radius, we need to perform the following steps:

- Moving the constant to the other side of the equation:

[tex]x^{2}+y^{2}+18x+4y=-49[/tex]

- Grouping the terms:

[tex]x^{2}+18x+y^{2}+4y=-49[/tex]

- Completing squares for both variables, we have:

We need to sum to each side of the equation the following term:

[tex](\frac{b}{2})^{2}[/tex]

Where, b, for this case, will the coefficients for both terms that have linear variables (x and y)

So, the variable "x", we have:

[tex]x^{2} +18x[/tex]

Where,

[tex]b=18[/tex]

Then,

[tex](\frac{18}{2})^{2}=(9)^{2}=81[/tex]

So, we need to add the number 81 to each side of the circle equation.

Now, for the variable "y", we have:

[tex]y^{2} +4y[/tex]

Where,

[tex]b=4[/tex]

[tex](\frac{4}{2})^{2}=(2)^{2}=4[/tex]

So, we need to add the number 4 to each side of the circle equation.

Therefore, we have:

[tex](x^{2}+18x+81)+(y^{2}+4y+4)=-49+81+4[/tex]

Then, factoring, we have that the expression will be:

[tex](x+9)^{2}+(y+2)^{2}=36[/tex]

- Writing the standard form of the circle:

Now,  from the simplified expression (after factoring), we can find the equation of the circle in the standard form:

[tex](x+9)^{2}+(y+2)^{2}=36[/tex]

Is also equal to:

[tex](x-(-9))^{2}+(y-(-2))^{2}=36[/tex]

Where,

[tex]h=-9\\k=-2\\r=\sqrt{36}=6[/tex]

Hence, the center of the circle is located on the point (-9,-2) and the radius is 6 units.

Have a nice day!

Answer:

A scale drawing is a drawing that shows the size of an object reduced or enlarged by a certain amount. The most common example is a map.

If we were to create a real size map of a house it would be a HUGE map. We wouldn't be able to grab it using our hands, and it wouldn't be useful either. The idea of a map is to have a diagrammatic representation of something.

Intead, we create maps where the size of the house is reduced by a certain scale. So we can see the distribution of the house, and -at the same time- know the measures of it.

I am attaching an example of a map. It's the map of mexico, and you can see the scale of the map at the bottom.

Answer:

D. -2x+3y=12

Step-by-step explanation:

ANSWER

D. -2x+3y=12

EXPLANATION

The given line passes through:

(0,4) and (-6,0)

These are the x and y intercepts.

The equation is given by :

[tex] \frac{x}{a} + \frac{y}{b} = 1[/tex]

where a= -6 is the x-intercept and b=4 is the y-intercept.

We substitute the values to get,

[tex]\frac{x}{ - 6} + \frac{y}{4} = 1[/tex]

Multiply through by 12,

[tex]\frac{x}{ - 6} \times 12 + \frac{y}{4} \times 12 = 1 \times 12[/tex]

[tex] - 2x + 3y = 12[/tex]

The correct answer is D .

Answer:1

Step-by-step explanation:

Answer:

11.7 cm

Step-by-step explanation:

10^2 + 6^2 = c^2

100+36= 136

find the square root of 136 and you get 11.7 cm

For this case, we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

A: It's the radio

h: The height of the cylinder

We have the values:

[tex]r = 6 \ cm\\h = 15 \ cm[/tex]

Substituting:

[tex]V = \pi * (6 ^ 2) * 15\\V = \pi * 36 * 15\\V = 1696.46 \ cm ^ 3[/tex]

Answer:

[tex]V = 1696.46 \ cm ^ 3[/tex]

ANSWER

a=1 and b=-12

EXPLANATION

The hyperbola has a hole at:

x=3

and a vertical asymptote at x=-4.

This implies that the denominator of the rational function is

(x-3)(x+4)

We expand to get;

[tex] {x}^{2} + 4x - 3x - 12[/tex]

This simplifies to:

[tex]{x}^{2} + x - 12[/tex]

comparing to

[tex] {x}^{2} + ax + b[/tex]

We have a=1 and b=-12

Answer:

D 81 pi units^2

Step-by-step explanation:

The circumference of a circle  is given by

C = 2 * pi *r

18 pi = 2 * pi *r

Divide each side by 2 * pi

18 pi / (2 pi) = 2 pi * r/ (2 pi)

9 = r

Now we can find the area.  Area is given by

A = pi r^2

A = pi * 9^2

A = 81 pi units^2

Circumference = [tex]2\pi r[/tex]

[tex]\frac{18\pi}{2\pi} = \frac{2\pi r }{2\pi }[/tex]

18 ÷ 2 = 9

r = 9

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

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

= [tex]\pi (9)^{2}[/tex]

= 81[tex]\pi[/tex] units².

Answer:

The answer is $63.6 for a coat

Step-by-step explanation:

80 (times) 0.75 = 60

60 (times) 1.06 = 63.6

25% = 0.75

adding 6% = 1.06

Answer:

The answer is $63.6 for a coat

Step-by-step explanation:

Answer:

Changing value of "b" changes the period of the cosine graph.

Step-by-step explanation:

Question says to find about how does the b-value affect your cosine graph.

General equation of cosine function can be given as:

[tex]y=a\cdot\cos\left(bx-c)\right)+d[/tex]

In that formula, value of  "[tex]\frac{2 \pi}{b}[/tex]" gives period.

So changing value of "b" changes the period of the cosine graph.

Answer:

[tex]\left[\begin{array}{cc}-\frac{1}{2}&\frac{1}{6}\\-\frac{1}{2}&\frac{1}{3}\\\end{array}\right][/tex]

Step-by-step explanation:

If a 2x2 matrix is given as:

[tex]\left[\begin{array}{cc}a&b\\c&d\\\end{array}\right][/tex]

The inverse is:

[tex]\frac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right][/tex]

Our matrix given is:

[tex]\left[\begin{array}{cc}-4&2\\-6&6\\\end{array}\right][/tex]

Using the formula, let's find the inverse:

[tex]\frac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]\\=\frac{1}{(-4)(6)-(-6)(2)}\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=\frac{1}{-12}\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=\left[\begin{array}{cc}-\frac{1}{2}&\frac{1}{6}\\-\frac{1}{2}&\frac{1}{3}\\\end{array}\right][/tex]

Answer:

12+4/8

Step-by-step explanation:

sum means add and you need to divide 8 by whatever 12 and 4 equal

12+4= 16

16/8=2

2

For this case we must represent the expression given above algebraically.

We have that the sum of 8 and 12 is represented as:

[tex]8 + 12[/tex]

We must divide the sum by 4:

[tex]\frac {8 + 12} {4} =\\\frac {20} {4} =\\5[/tex]

Finally, the result of the expression is 5.

ANswer:

5

[tex]\text{Hey there!}[/tex]

[tex]\text{What is the greatest common factor of 86 and 43?}[/tex]

[tex]\text{Factors of 86}\rightarrow\text{1, 2, 43, 86}[/tex]

[tex]\text{Factors of 43}\rightarrow\text{1, 43}[/tex]

[tex]\text{Common factors of BOTH NUMBERS: 1, 2, 43}[/tex]

[tex]\text{Out all the common factors of those we listed just now, 43 is the biggest one}[/tex]

[tex]\boxed{\boxed{\text{Answer: 43}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

The Greatest Common Factor(GCF) of 86 and 43 is 1 because 43 is a prime number and does not have any other factors apart from 1 and itself, and 43 does not divide evenly into 86.

To find the Greatest Common Factor (GCF) of 86 and 43, we first need to understand what a GCF is. The GCF of two or more numbers is the largest number that divides evenly into each of the numbers. The GCF for these numbers is 1 because the number 43 is a prime number and does not have any other factors apart from 1 and itself. In addition, 43 does not divide evenly into 86, leaving us with 1 as the higher factor that divides both 43 and 86.

So, the Greatest Common Factor of 86 and 43 is 1.

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Answer:

11 : 15

Step-by-step explanation:

Given

$5.5 : 7.5 ← divide both parts by 5

= 1.1 : 1.5 ← multiply both parts by 10

= 11 : 15 ← in simplest form

So a basic function is y=mx+b where m is a rate and b is the constant. His goal is 150 so y is 150 and the rate of his baking is 16 so m is 16, finally he has already 22 done so 22 remains constant. Plugging all these in you should get the following equation:

150=16x+22

Final answer:

Hou's goal is to bake at least 150 cookies, and he has already baked 22. If he bakes an average of 16 cookies every half hour, the equation representing the total cookies baked is Cookies baked = 16t + 22. The inequality to ensure he meets his goal is 16t + 22 >= 150.

Explanation:

Hou has set a goal to bake 150 cookies for a fundraiser and has already baked 22 cookies. He averages about 16 cookies every half hour. To represent this situation mathematically, we can use an equation related to the number of cookies baked over time.

Let's define the variable t to represent the number of half-hour segments Hou bakes. The total number of cookies Hou will have baked after t half-hour segments can be calculated by multiplying the number of segments by the average number of cookies baked in each half-hour segment and then adding the 22 cookies already baked.

The equation representing this situation is:

Cookies baked = 16t + 22

Hou's goal is to bake at least 150 cookies, so we create an inequality to represent the situation:

16t + 22 ≥ 150

Answer:

[tex]142\ tiles[/tex]

Step-by-step explanation:

step 1

Find the total tiles in the square board

The total area of the square board is equal to

[tex]A=14^{2}=196\ in^{2}[/tex]

Remember that each tile is 1-inch-square

so

by proportion

The total tiles is equal to

[tex]196\ tiles[/tex]

step 2

Find the number of gray tiles in the square board

The total area of gray tiles in the square board is equal to

[tex]A=3[(3)(3)]=27\ in^{2}[/tex]

Remember that each tile is 1-inch-square

so

by proportion

The total gray tiles is equal to

[tex]27\ tiles[/tex]

step 3

Find the number of white tiles in the square board

Subtract the number of gray tiles from the total number of tiles

[tex]196-27=169\ tiles[/tex]

step 4

Find out how more white tiles than gray tiles will Zoey use

Subtract the number of gray tiles from the number of white tiles

[tex]169-27=142\ tiles[/tex]

Hello! :)

While they don't give nearly enough information on sampling size to be credible data or how many kids vs how many adults, the simplistic answer is (B) a greater percentage of kids experienced side effects among their peers than the adults among their peers.  The sneaky thing about statistics is you can make the data say anything you want. 

Hope I helped and answered in time!

Good luck!

~ Destiny ^_^

A greater percentage of kids experienced side effects among their peers than the adults among their peers.

The relative frequency helps us to see the number of the population studied that can be associated with a particular class.

From the relative frequency table, we can see that; a greater percentage of kids experienced side effects among their peers than the adults among their peers.

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12x^2y^2+2xy-2 with problems like these use the app “Photomath” it will help you a lot.

The answer is:

[tex](3xy-1)(4xy+2)=12(xy)^{2}+2xy-2[/tex]

or

[tex](3xy-1)(4xy+2)=12x^{2}y^{2}+2xy-2[/tex]

To solve the problem and identify the resultant expression, we need to apply the distributive property, and the, add or subtract like terms.

Describing the distributive property:

[tex](a+b)(c+d)=a*c+a*d+b*c+b*d[/tex]

Remember, like terms are the terms that share the same variable and same exponent, for example:

[tex]a^{2} +3a^{2}+a^{3}=4a^{2}+a^{3}[/tex]

We were able to add only the terms that have the same exponent (2).

We are given the expression:

[tex](3xy-1)(4xy+2)[/tex]

Now, solving we have:

[tex](3xy-1)(4xy+2)=(3xy*4xy)+(3xy*2)-(1*4xy)-2\\\\(3xy*4xy)+(3xy*2)-(1*4xy)-2=12(xy)^{2}+6xy-4xy-2\\\\12(xy)^{2}+6xy-4xy-2=12(xy)^{2}+2xy-2[/tex]

Hence, we have that:

[tex](3xy-1)(4xy+2)=12(xy)^{2}+2xy-2[/tex]

or

[tex](3xy-1)(4xy+2)=12x^{2}y^{2}+2xy-2[/tex]

Have a nice day!

Answer:

30 gms

Step-by-step explanation:

half life time means time taken for material to become half of its quantity

120 gms will become 60 gms in 10 mins

then in 20 mins, it will be 30 gms

After 20 minutes 30 grams amount of radioactive form of nitrogen left.

Given

The total amount radioactive form of nitrogen = 120 grams

The time is taken for the radioactivity of a specified isotope to fall to half its original value:

The formula is used to calculate half-life is;

[tex]\rm Half \ life = \dfrac{Amount \ of \ substance}{2}[/tex]

The half-life of the nitrogen after 10 minutes;

[tex]\rm Half \ life = \dfrac{Amount \ of \ Nitrogen}{2} \\\\ Half \ life = \dfrac{120}{2}\\\\\rm Half \ life = 60 \ grams[/tex]

The half-life of the nitrogen after 10 minutes is 60 grams.

The half-life of nitrogen after 20 minutes;

[tex]\rm Half \ life = \dfrac{Amount \ of \ Nitrogen}{2} \\\\ Half \ life = \dfrac{60}{2}\\\\\rm Half \ life = 30 \ grams[/tex]

Hence, after 20 minutes 30 grams amount of radioactive form of nitrogen left.

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Answer:

which fraction equals -9/16--------->An equivalent fraction is nothing but, when the numerator and denominator of the fraction are equal when written in lowest terms. The fraction 3/9 is equal to 1/3 when reduced to lowest terms.

Step-by-step explanation:

-18/32, -27/48 are the fractions which are equivalent fractions of -9/16.

Numerical value that is a part of a whole is called as Fraction. It is evaluated by dividing a whole into number of parts.

We have to find an equivalent fraction of -9/16

To find the equivalent fraction  multiply both the numerator and denominator by the same number.

Multiply both the denominator and numerator of -9/16 by 2

(-9 x 2)/(16 x 2)

= -18/32

Now let us multiply both the numerator and denominator of -9/16 by 3, we get:

(-9 x 3)/(16 x 3)

= -27/48

Therefore,  -18/32, -27/48 are the fractions which are equivalent fractions of -9/16.

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Answer: 10

Step-by-step explanation:

1. Add all the types of meat, cheese, and bread

2. 10 Is your answer because it’s asking for 1 and 10 of all the items will be in 1 meal consisting all the types.

About $290.83.

Hope this helps!

The police officer will earn approximately $290.83 more each month in his second year, as his annual salary will raise from $26,400 to $29,890.

In this scenario, we are dealing with a salary raise and how it affects the overall monthly income. The first year, the police officer is earning $2,200 per month, which translates to an annual salary of $26,400 (since there are 12 months in a year, you can simply multiply the monthly income by 12 to find this). The second year, his annual salary will be raised to $29,890.

To see how much more they will be making a month, subtract the first year's annual salary from the second year's total ($29,890 - $26,400 = $3,490). This is the total raise for the year, but we want to find out how much more the officer will be making a month. Since the raise is distributed over 12 months, simply divide this total by 12 to get the answer. $3,490 ÷ 12 = approximately $290.83. So, the police officer will be making around $290.83 more each month in the second year.

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Answer:

a)

[tex]4x {}^{2} - 9 = (2x + 3)(2x - 3)[/tex]

b) g - 3m = am + 5

am + 3m = 5 - g

m (a + 3) = 5 - g

m =

[tex] \frac{5 - g}{a + 3} [/tex]

Step-by-step explanation:

[tex]a {}^{2} - b {}^{2} = (a + b)(a - b)[/tex]

Answer:

see explanation

Step-by-step explanation:

(a)

4x² - 9 ← is a difference of squares which factors in general as

a² - b² = (a + b)(a - b)

4x² = (2x)² ⇒ a = 2x and 9 = 3² ⇒ b = 3, thus

4x² - 9 = (2x + 3)(2x - 3)

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

(b)

g - 3m = am + 5 ( collect the terms in m together )

Add 3m to both sides

g = am + 3m + 5 ( subtract 5 from both sides )

g - 5 = am + 3m ← factor out m from each term

g - 5 = m(a + 3) ← divide both sides by (a + 3)

m = [tex]\frac{g-5}{a+3}[/tex]

Answer:

They are proportional

Step-by-step explanation:

becaue the length of one of the square's sides is 1/4 the perimeter

Answer:

(5,-37/9)

Step-by-step explanation:

Divide the first equation by 2 and the second equation by 2.

8x=3-9y, -5x=-12+9y

Isolate the 9y's

8x-3=-9y, -5x-12=9y

Add the equations together so that the two y's cancel out

8x-3=-9y

-5x-12=9y   +

3x-15=0

Solve this equation to get...

x=5

Plug that in to the original equations to get y=-37/9

Answer:

(x,y) = (-3,3)

Step-by-step explanation:

16x=6-18y

-10x=-24+18y

We need to solve the above equations to find the values of x and y.

Rearranging the above equations

16x + 18y - 6 = 0 => eq(1)

-10x -18y +24 =0 => eq(2)

Adding eq(1) and eq(2)

16x + 18y - 6 = 0

-10x -18y +24 =0

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

6x + 18 =0

6x = -18

x= -18/6

x= -3

Putting value of x in eq(1) i.e

16x + 18y - 6 = 0

x= -3

16(-3) + 18y - 6 =0

-48 + 18y -6 =0

18y - 54 = 0

18y = 54

y= 54/18

y= 3

So, value of x = -3 and y = 3

(x,y) = (-3,3)

The answer is:

The general form of the circle is:

[tex]x^{2} -2x+y^{2} +4y=0[/tex]

We are given the standard form of a circle, so, to calculate the general form, we need to solve notable products.

We must remember the way to solve the notable product:

[tex](a+b)^{2}=a^{2}+2ab+b^{2} \\\\(a-b)^{2}=a^{2}-2ab+b^{2}[/tex]

So,

We are given the equation:

[tex](x-1)^{2}+(y+2)^{2}=5[/tex]

Then, solving the notable products, and adding/subtracting like terms, we have:

[tex]x^{2} -2*1x+1+y^{2}+2*2y+4=5\\x^{2} -2x+1+y^{2} +4y+4=5\\\\x^{2} -2x+y^{2} +4y+1+4-5=0\\\\x^{2} -2x+y^{2} +4y=0[/tex]

Hence,  have that the general form of the circle is:

[tex]x^{2} -2x+y^{2} +4y=0[/tex]

Have a nice day!

Answer

$1.38

OR 11.5 cents per bag

Ok lets start

the bulk chips has a total of 10.50

the individual cost 0.99 each

Multiply 0.99 by 12 so everything is fair

0.99 x 12 =11.88

The bulk chips ae 10.50

To find the difference we subtract

10.50 from 11.88  (remember, 10.50 is the cost of buying in bulk!)

11.88-10.50 = 1.38

divide 1.38 by 12

We save $1.38 by buying in bulk or

11.5 cents per bag by buying bulk

Hope this answers your question,

~Jeron

Answer:

Step-by-step explanation:

Given that the bulk chips has a total of 10.50

The individual cost 0.99 each

To compare both

Multiply 0.99 by 12

[tex]0.99 x 12 =11.88[/tex]

The bulk chips ae 10.50

11.88 is more than 10.50

Hence purchasing in bulk is cheaper by 1.38 dollars.

To find the difference we subtract

10.50 from 11.88

[tex]11.88-10.50 = 1.38[/tex]

Evaluating the expression step-by-step, the final answer is 14. This indicates there may be a misinterpretation or error in the options as 14 is not listed among the provided choices.

Let's break down the expression step-by-step to evaluate –(31 + 2) + 72 – (–5)2.

Therefore, the correct evaluation of the expression is 14, which is not among the provided options, indicating a possible error in the question or the options provided.

Answer:

Full question attached below.

Yes, the system of equations on line 4 has the same solution set as the system of equations on line 1

Step-by-step explanation:

There is no difference between the systems of line 1 and 4

1st system

5x + 3y = 14

4x - 2y = -2

4th system

10x + 6y = 28

12x - 6y = -6

In the fourth system, we factor number 2 from the first line, and number 3 from the second line

4th system

2[5x + 3y] = 2[14]

3[4x - 2y] = 3[-2]

If we simplify,

4th system

[5x + 3y] = [14]

[4x - 2y] = [-2]

We get the same system as the 1st

Therefore, the solution is the same.

Answer: Its C

Step-by-step explanation: its equivalent

Answer:

C, $3,555.63

Step-by-step explanation:

to answer this, we have to use the compound interest formula which is:

A = P(1 + r/n)^nt

the meanings of each variable are:

A = result

P = principal amount

r = rate (in decimal form)

n = the number of compound periods (eg: annually, quarterly, etc)

t = time

in the word problem, we need to solve for A. we are given P, r, n, and t.

P = 2,400

r = 0.0395 also known as 3.95%

n = 4 keyword being quarterly which is equal to the value of 4

t = 10

we can plug these values into the formula:

A = 2400(1 + 0.0395/4)^(4)(10)

we can use a calculator to calculate this easier but ill break it down:

A = 2400(1 + 0.0395/4)^(4)(10)

A = 2400(1 + 0.0395/4)^40

A = 800(1.009875)^40

A = 2400(1.48151088)

A ≈ 3555.626

we can round 3555.626 to the nearest hundredth which is $3555.63

you would have earned $3555.63 in 10 years

our answer would be C

Answer:

Putting 5x^2 +2 = 4x into standard form:

5x^2 -4x  +2 = 0

a=5 b= -4 c=2

Step-by-step explanation:

Answer

A= 5

B= -4

C= 2