The equation x2+y2−16x+6y+73=100 can be rewritten as [g(x)]2+(y+3)2=100.Write an expression for g(x).

Answers

Answer 1

Answer: g(x) = (x - 8)

Step-by-step explanation:

We start with the equation:

x^2 + y^2 - 16*x + 6*y + 73 = 100.

And we want to write this as:

g(x)^2 + (y + 3)^2 = 100.

So both equations are equal, then we can write this as:

x^2 + y^2 - 16*x + 6*y + 73 = g(x)^2 + (y + 3)^2

First we can expand the right side:

g(x)^2 + (y + 3)^2 = g(x)^2 + y^2 + 2*3*y + 9

Then we have:

x^2 + y^2 - 16*x + 6*y + 73 = g(x)^2 + y^2 + 6*y + 9

Now we can cancel the equal terms in each side, like y^2 and 6*y

x^2 - 16*x + 73 = g(x)^2 + 9

Now let's subtract 9 in each side:

x^2 - 16*x + 73 - 9 = g(x)^2

x^2 - 16*x + 64 = g(x)^2

Then we can assume that g(x) = (x - a)

then:

x^2 - 16*x + 64 = (x - a)^2 = x^2 - 2*a*x + a^2

-16*x + 64 = -2*a*x + a^2

now we must find the value of a, we have two equations:

-2*a = -16

a^2 = 64

and each equation yields to:

a = -16/-12 = 8.

a = √64 = 8

Then we have: g(x) = (x - 8)

Answer 2

Completing the squares, it is found that: [tex]g(x) = x - 8[/tex]

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

The expression given is:

[tex]x^2 + y^2 - 16x + 6y + 73 = 100[/tex]

To complete the squares:

First, each first order term(-16 and 6) are divided by 2.Then, we write as the square of (x - 8) and (x + 3).Then, we have to find the squares on the other side of the equality.

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

Doing these steps:

[tex](x - 8)^2 + (y + 3)^2 = 100 - 73 + 8^2 + 3^2[/tex]

[tex](x - 8)^2 + (y + 3)^2 = 100 - 73 + 64 + 9[/tex]

[tex](x - 8)^2 + (y + 3)^2 = 100[/tex]

Which means that:

[tex]g(x) = x - 8[/tex]

A similar problem is given at https://brainly.com/question/16269892


Related Questions

Three fair, standard six-sided dice are rolled. What is the probability that the sum of the numbers on the top faces is 18? Express your answer as a common fraction.

Answers

Answer: 1/216

Explanation:

There is only one way to get a sum of 18 and that is rolling three '6's to get 6+6+6 = 18.

There are 6*6*6 = 216 different ways to roll three dice.

Divide the two values to get 1/216

please help like nobody has helped me on my other questions and i dont wanna fail this test

Answers

Answer: d=70; f=45; e=65

Step-by-step explanation:

NUMBER 1 WAY

110+d=180

      d=70

135+f=180

       f=45

d+f+e=180

70+45+e=180

            e=65

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

NUMBER 2 WAY

concept to know: exterior angle theorem

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

System of equation

d+e=135

f+e=110

d+e+f=180

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

d=135-e

f=110-e

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

d+e+f=180

(135-e)+e+(110-e)=180

135-e+e+110-e=180

245-e=180

e=65

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

d=70

e=65

f=45

Point C'(-4,-3)C

(−4,−3)C, prime, left parenthesis, minus, 4, comma, minus, 3, right parenthesis is the image of C(-2,-3)C(−2,−3)C, left parenthesis, minus, 2, comma, minus, 3, right parenthesis under a translation

Answers

Answer:

The slope of the line through the points is -5/7

Step-by-step explanation:

Here, we want to calculate the value of the slope through the lines

Mathematically;

m = y2-y1/(x2-x1)

Where (x1,y1) = (-4,2)

and (x2,y2) = (3,-3)

Substituting these values, we have;

m = (-3-2)/(3-(-4)) = -5/7 = -5/7

Answer:

2 units to the LEFT

Step-by-step explanation:

i used khan

find the distance points (7,-2) (3,1)

Answers

Answer:

5

or

square root of 25

Step-by-step explanation:

I used my ti-84 plus ce calculator to solve

>download DISTMID

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>DISTENCE

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B(7, 2) and C(-1,-9) are the endpoints of a line segment. What is the midpoint M of that line
segment?

Answers

Answer:

(3,-3.5)

Step-by-step explanation:

[tex]Mid-point formula : \frac{ x_{1} +x_{2}} {2}, \frac{y_{1}+y_{2} }{2} \\\\x=\frac{7+(-1)}{2} , y= \frac{2+(-9)}{2} \\x= \frac{6}{2} , y= \frac{-7}{2} \\x=3 , y= -3.5[/tex]

Midpoint M of the line segment is (3,-3.5)

Find the value of x
Pls help me :(

Answers

Answer:

i think is 10

Step-by-step explanation:

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If sets A and B have the same number of terms, is the standard deviation of set A greater than the standard deviation of set B? 1.The range of set A is greater than the range of set B. 2. Sets A and B are both evenly spaced sets.

Answers

Step-by-step explanation:

(1) The range of set A is greater than the range of set B.

This statement  gives only the range which means only outermost values but what about the other values. For example-11,0,0,0,11 and -10,-10,0,10,10

Clearly, Former one has higher range but lower standard deviation.

(2) Sets A and B are both evenly spaced sets.

Evenly spaced is fine. However, we don't know the spacing since that is required to know the deviation.

For, example, sets A{2,4,6,8,10} and B {1,2,3,4,5} so in this case SD of A> SD of B. Or,  we can have B{2,4,6,8,10} and A{1,2,3,4,5} so in this case SD of B> SD of A.

Given: g (x) = StartFraction 1 Over x + 2 EndFraction and h (x) = 3 x Check all restrictions on the domain of g circle h. x not-equals 0 x not-equals negative 2 x not-equals negative two-thirds There are no restrictions.

Answers

Answer:2/3 is the same

Step-by-step explanation:

What is 0/7 Simplified A. 7 B. 70 C. 0 D. Undefined

Answers

Answer:

C

Step-by-step explanation:

Dividing zero by any value gives a result of zero, thus

[tex]\frac{0}{7}[/tex] = 0 → C

Answer:

C. 0

Step-by-step explanation:

0/7.  It means 7 divided by 0, which is 0.  

But if it was 7/0, it would be undefined.

7/0= undefined

0/7= 0

The answer is c, 0.  :)

PLEASE HELP!
Find the value of z. A. 40 B. 80 C. 56 D. 62

Answers

Answer:

A

Step-by-step explanation:

The secant- tangent angle 50° is half the difference of the measures of the intercepted arcs, that is

[tex]\frac{1}{2}[/tex](210 - x) = 50 ( multiply both sides by 2 )

210 - x = 100 ( subtract 210 from both sides )

- x = - 110 ( multiply both sides by - 1 )

x = 110°

The sum of the 3 arcs on the circle = 360°

210 + x + z = 360

210 + 110 + z = 360

320 + z = 360 ( subtract 320 from both sides )

z = 40°

what is the slope of a line that passes through the points ( 3,7) and(12,7)?​

Answers

Answer:

The slope is 0.

Step-by-step explanation:

To find the slope, we can do (7 - 7) / (12 - 3) = 0 / 9 = 0. This makes sense because if we look at the points, they both have the same y-coordinate, so we know that as x increases / decreases, y never changes. Because y never changes, the slope is 0.

Answer:

m=0

Step-by-step explanation:

To find slope, it is y2-y1/x2-x1

Therefore, x1=3, x2=12, y1=7 and y2=8

Plugging those variables in,

(7-7)/(12-3)=

7-7=0

12-3=9

0/9=0

Therefore, slope of the line that passes through points (3,7) and (12,7) is 0

Multiply
(2y²-1) by (2y³+5y²)
please dasdo ​

Answers

Answer:

4[tex]y^{5}[/tex] + 10[tex]y^{4}[/tex] - 2y³ - 5y²

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

2y²(2y³ + 5y²) - 1(2y³ + 5y²) ← distribute both parenthesis

= 4[tex]y^{5}[/tex] + 10[tex]y^{4}[/tex] - 2y³ - 5y²

What List of 7 numbers that round to 300?

Answers

Answer:

The numbers 250-259 can be rounded to 300. Also 301-349 can be rounded down to 300. This works if you are rounding by the nearest hundreds place.

Convert the following decimal to a fraction. Be sure to simplify your fraction 0.378​

Answers

Answer:

189/500

Step-by-step explanation:

[tex]0.378\\\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}\\\\\mathrm{There\:are\:}3\\\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\\\:therefore\:multiply\:and\:divide\:by\:1000}\\\\=\frac{0.378\timess \:1000}{1000}\\\\=\frac{378}{1000}\\\\\frac{378}{1000}:\quad \frac{189}{500}[/tex]

189/500 because it is the correct answer

M is between N and O . MO = 15, and MN = 76. Find NO

Answers

Answer:

                  91        

Step-by-step explanation:

N___________________M_______O

               76                                 15

NO = MN + MO = 76 + 15 = 91

PLZ HELP ME I.NEED.HELP ASP
Question 10
If QR=21 and PR=88, find PQ.

Answers

Answer:

67

Step-by-step explanation:

Hello!

To find PQ we subtract the length of the whole line by QR

88 - 21 = 67

The answer is 67

Hope this helps!

Write the set of real numbers from - 10 through 10 in interval notation.
The interval notation is

Answers

Answer:

1) [tex](-10,10)[/tex] - Greater than -10 and less than 10.

2) [tex][-10, 10][/tex] - Greater than or equal to -10 and less than or equal to 10.

3) [tex][-10, 10)[/tex] - Greater than or equal to -10 and less than 10.

4) [tex](-10, 10][/tex] Greater than -10 and less than or equal to 10.

Step-by-step explanation:

There are four form of describing that set in interval notation, which presented below:

1) [tex](-10,10)[/tex] - Greater than -10 and less than 10.

2) [tex][-10, 10][/tex] - Greater than or equal to -10 and less than or equal to 10.

3) [tex][-10, 10)[/tex] - Greater than or equal to -10 and less than 10.

4) [tex](-10, 10][/tex] Greater than -10 and less than or equal to 10.

8 plus 3 cubed over 12-7

Answers

Answer:

7

Step-by-step explanation:

8+3³/12-7

8+27/5

35/5

7

Evaluating expression 4/a + b/3 when a = 4 and b = 3.​

Answers

Answer:

2

Step-by-step explanation:

Hello!

It is asking us to solve when a = 4 and b = 3 so we put those values in for a and b

4/4 + 3/3

When the numerator and denominator are the same that fraction can be shown as 1

1 + 1 = 2

The answer is 2

Hope this helps!

Answer:

The answer is 2

Step-by-step explanation:

[tex] \frac{4}{a} + \frac{b}{3} [/tex]

a = 4 and b = 3

Substitute the values of a and b into the expression

That's

[tex] \frac{4}{4} + \frac{3}{3} = 1 + 1[/tex]

We have the final answer as

2

Hope this helps you

simplify (-2)(-3)+(4)(-8)​

Answers

Step-by-step explanation:

[tex]( - 2)( - 3) + (4 )( - 8) \\ - 2 \times - 3 + 4 \times - 8 \\ 6 + ( - 64) \\ 6 - 64 \\ - 58[/tex]

A group of 4 friends likes to golf together, and each friend keeps track of her all-time lowest score in a single round. Their low scores are all between 90 and 100, except for Angie, whose low score is 80. Angie then golfs a great round and has a new low score of 75. How will decreasing Angie's low score affect the mean and median?

Answers

Answer: Mean get decreased and median remains same.

Step-by-step explanation:

Given: The low scores of all 4 friends  are all between 90 and 100, except for Angie, whose low score is 80.

i.e. Angie is an outlier.

[An outlier is an extreme value which lies far from the other data values.]

Angie then golfs a great round and has a new low score of 75.

i.e. more lower value.

Since Mean gets effected by an outlier but median remains same.

Here, value of new outlier(75) is less than the previous one (80), so mean score will get decreased, where as median (middle most value in ordered data) remains the same.

Kendrick is using a compass and straightedge to copy angle M the figure shows the portion of the construction that he has already completed where should Kendrick place the center of the compass to do the next step of the construction

Answers

Answer:

The next step of the construction is;

Place the compass at point N and adjust the width to the point where the arc crosses the other side leg of the angle

Step-by-step explanation:

The steps to copy an angle are;

1) Mark the point C of the vertex of the new angle

2) Draw a ray from C in the desired direction

3) With the compass placed at M of the original angle, draw an arc that crosses both sides of the original angle. Mark the crossing points N and O

4) With the same compass width from the arc drawn in the above step, draw a similar arc that crosses the ray from C at point D

5) Place the compass at point N and adjust the width to point O, the point where the arc crosses the other side of the angle

6) While the adjusted compass width is held to remain the same, place the compass at point D and draw an arc to cross the previous arc drawn from C and label the intersection point E

7) With the straight edge, draw a ray FC that passes through E to point C to complete the copied angle.

NEED HELP ASAP algebra 2​

Answers

Answer:

[tex]8\sqrt{2}[/tex]

Step-by-step explanation:

Step 1: Use Pythagorean Theorem to find the length of the hypotenuse

[tex]a^{2}+b^{2} =c^{2}[/tex]

[tex]9^{2}+7^{2} =c^{2}[/tex]

[tex]81+47 =c^{2}[/tex]

[tex]128 =c^{2}[/tex]

[tex]\sqrt{c^{2} } =\sqrt{128}[/tex]

[tex]c=\sqrt{128}[/tex][tex]\sqrt{128} =8\sqrt{2}[/tex]

Therefore the third side is [tex]8\sqrt{2}[/tex]

A researcher received 9 shipments of 3.49 x 1010 cells to go along with the 1.2 x 109 cells she had already received. How many total cells has she received? A. 4.57 x 1010 B. 3.129 x 1011 C. 3.153 x 1011 D. 3.29 x 1011

Answers

Answer:7.84 X 10-3 m2

Step-by-step explanation:

A researcher received 9 shipments of 3.49 x 1010 cells to go along with the 1.2 x 109 cells she had already received. How many total cells has she received? A. 4.57 x 1010 B. 3.129 x 1011 C. 3.153 x 1011 D. 3.29 x 1011

4.57 x 1010 B. 3.129 x 1011 C. 3.153 x 1011 D. 3.29 x 1011

=7.84 X 10-3 m2


what’s the answer choice?

Answers

Answer:

C. -1/2, 2, √5, √16, 4,05

Step-by-step explanation:

When ordering numbers from least to greatest first comes negative values then we compare all positive expressions

2 is smaller than √5 because it's approximately 2.2 and then comes √16 because it's equal to 4 and finally comes 4.05

Please help: Using graph paper, determine the line described by the given point and slope. Click to show the correct graph below. (0, 0) and 2/3 What would the graph look like?

Answers

Answer:

SINCE I DONT HAVE GRAPH PAPER ILL SHOW YOU ON MY COMPUTER

Step-by-step explanation:

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

Y=2/3X+0 OR Y=2/3X

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The graph of a linear equation is a straight line.

The graph has a positive slope and it passes through the origin

The given parameters are:

[tex]\mathbf{m =\frac 23}[/tex]

[tex]\mathbf{(x,y)= (0,0)}[/tex]

A linear equation is represented as:

[tex]\mathbf{y = mx + b}[/tex]

[tex]\mathbf{m =\frac 23}[/tex]

So, we have:

[tex]\mathbf{y = \frac 23 x + b}[/tex]

[tex]\mathbf{(x,y)= (0,0)}[/tex] represents the y-intercept (i.e. b = 0).

So, we have:

[tex]\mathbf{y = \frac 23 x + 0}[/tex]

[tex]\mathbf{y = \frac 23 x}[/tex]

See attachment for the graph of [tex]\mathbf{y = \frac 23 x}[/tex]

The graph has a positive slope and it passes through the origin

Read more about linear equations at:

https://brainly.com/question/11897796

Determine whether the following statement is true or false. Explain your reasoning. Jordan says that when solving the equation 4b+3=11, the best first step is to apply the Division Property of Equality.

.

A. The statement is false. Since there is a coefficient on the variable, the Multiplication Property of Equality should be used first.
.
B. The statement is true. The Division Property of Equality should always be the first property of equality used when solving linear equations.
.
C. The statement is false. The Subtraction Property of Equality should be used first to remove the constant term before dividing.
.
D. The statement is true. Since there is a coefficient on the variable, the Division Property of Equality must be used first.

Answers

Answer:

The correct option is;

C. The statement is false. The Subtraction Property of Equality should be used first to remove the constant term before dividing

Step-by-step explanation:

In other to solve the equation 4·b + 3 = 11, we have;

By the subtraction property of equality, we have;

Firstly we subtract 3 from both sides gives;

4·b + 3 - 3= 11 - 3

Next we apply the division property of equality, we have;

Both sides of an equation remain equal when we divide both sides of the equation by the same, non-number,

Dividing both sides by 4, gives;

4·b/4 = 8/4

b = 8/4 = 2

The solution to the equation, 4·b + 3 = 11 is b = 2.

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Which best describes the dimensions of a line?
Vx
O Aline has zero dimensions because it represents a location on the coordinate plane.
O Aline has one dimension because it is made up of all points that extend infinitely in either direction.
O Aline has two dimensions because it is made up of three noncollinear points.
O Aline has multiple dimensions depending on how many labeled points it contains.
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Answers

Answer:

B

Step-by-step explanation:

Which of the following is correct based on this picture? A. tan D=31/24 B. sinD=31/24 C. cosK=31/24 D. tanK=31/24

Answers

Answer:

D. tanK = 31/24

I'll explain why

4. Match the polynomial in the left column with its descriptive feature in the
right column
A x + 3x2 - 2x + 7
B. 3abº
C. 3x – 9x + 5x®
D. 7ab2 + 18ab-c-9a
E 2x - 9x + 8x
F. 4x - 7x? +9
G. x? -7
L. 9th degree monomial
II. Constant term of -7
III. 7 degree polynomial
IV. Leading coefficient of 4
V. Four terms
VI. 5th degree polynomial
VII. Equivalent to 5x + 3x+ - 9x​

Answers

Complete question is;

Match the polynomial in the left column with its descriptive feature in the

right column

A.) x³ + 3x² - 2x + 7

B.) 3a³ b ^(6)

C.) 3x⁴ – 9x³ + 5x^(8)

D.) 7a³ b ² + 18ab² c – 9a³

E.) 2x^(5) – 9x³ + 8x^(7)

F.) 4x^(8) – 7x² + 9

G.) x² − 7

I. 9th degree monomial

II. Constant term of −7

III. 7th degree polynomial

IV. Leading coefficient of 4

V. Four terms

VI. 5th degree polynomial

VII. Equivalent to 5x^(8) + 3x⁴ – 9x³

Answer:

A) For polynomial x³ + 3x² - 2x + 7 : Option V - 4 Terms

B) For polynomial 3a³ b ^(6) : option I - 9th degree monomial

C) For the polynomial 3x⁴ – 9x³ + 5x^(8) : Option VII - Equivalent to 5x^(8) + 3x⁴ – 9x³

D) For the polynomial 7a³b² + 18ab²

c – 9a³ : Option VI - 5th degree polynomial.

E) For the polynomial 2x^(5) – 9x³ + 8x^(7) : Option III - 7th degree polynomial.

F) for the polynomial 4x^(8) – 7x² + 9 : Option IV - Leading coefficient of 4

F) For the polynomial x² − 7 : Option II - Constant term of −7

Step-by-step explanation:

A) Most appropriate matching descriptive feature for the polynomial x³ + 3x² - 2x + 7 is Option V - 4 Terms

B) Most appropriate matching descriptive feature for the polynomial 3a³ b ^(6) is option I - 9th degree monomial. This is because the sum of the powers of a and b is 9.

C) Most appropriate matching descriptive feature for the polynomial 3x⁴ – 9x³ + 5x^(8) is Option VII - Equivalent to 5x^(8) + 3x⁴ – 9x³

D) Most appropriate matching descriptive feature for the polynomial 7a³ b ² + 18ab² c – 9a³ is Option VI - 5th degree polynomial. This is because the highest sum of powers attached to a and b in a figure is 2 + 3 = 5.

E) Most appropriate matching descriptive feature for the polynomial 2x^(5) – 9x³ + 8x^(7) is Option III - 7th degree polynomial. This is because the highest power of x is 7.

F) Most appropriate matching descriptive feature for the polynomial 4x^(8) – 7x² + 9 is Option IV: Leading coefficient of 4. This is because the coefficient attached to the largest power of x is 4.

G) Most appropriate matching descriptive feature for the polynomial

x² − 7 is Option II - Constant term of −7

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