A certain circle can be represented by the following equation. x^2+y^2+8x-16y+31=0x 2 +y 2 +8x−16y+31=0x, squared, plus, y, squared, plus, 8, x, minus, 16, y, plus, 31, equals, 0 What is the center of this circle ? ((left parenthesis ,,comma ))right parenthesis What is the radius of this circle ? units

Answers

Answer 1

Answer:

center = [tex](-4,8)[/tex]

Radius = 7 units

Step-by-step explanation:

Given: Equation of circle is [tex]x^2+y^2+8x-16y+31=0[/tex]

To find: Radius and center of the circle

Solution:

Equation of circle is [tex](x-a)^2+(y-b)^2=r^2[/tex]

Here, [tex](a,b)[/tex] is the center and r is the radius.

[tex]x^2+y^2+8x-16y+31=0\\\left [ x^2+2(4)x+4^2 \right ]+\left [ y^2-2(8)y+8^2 \right ]+31=4^2+8^2[/tex]

Use formula [tex](u+v)^2=u^2+v^2+2uv[/tex]

[tex](x+4)^2+(y-8)^2=16+64-31\\(x+4)^2+(y-8)^2=49=7^2[/tex]

On comparing this equation with equation of circle,

center = [tex](-4,8)[/tex]

Radius = 7 units

Answer 2

Answer:

center: (4,-4)

Radius: 9

Step-by-step explanation:

KHAN ACADEMY


Related Questions

Help please someone thanks

Answers

Answer:

16

Step-by-step explanation:

The run is the amount in the x direction

-8 to 8 = 16 units

(8- - 8) = 8+8 = 16

The run is 16

The run would be 16 units


Which equation is NOT an example of a linear function?
A) y = 9 - 2x
B) y = 6/X
C) y = x/2 + 9
D) y = 5/6x - 8

Answers

Answer:

B

Step-by-step explanation:

y = 6/x is not  an example of a linear function

Option B is correct

A linear function can be written in the form ax + by = c

Let us consider the options given and see which of them cannot be expressed in the form ax + by + c

For y  =   9  -  2x

This can also be expressed as

-2x + y  =  9

For y  =  x/2  +  9

This can also be expressed as:

x  -  2y  =  - 18

For y  =  5/6 x - 8

This can also be expressed as:

-5x  +  6y  =  -48

Only y = 6/x cannot be expressed in the form ax + by = c. Therefore, y  = 6/x is not an example of a linear function

Learn more here: https://brainly.com/question/16459885

60. Express - 78 in the form bi where b is a real number.
TIME SENSITIVE‼️‼️‼️

Answers

Answer:

c

Step-by-step explanation:

PLEASE HELLPPP
what is : -4(3-5)+10-3(7+4)+30​

Answers

Answer:

15

Step-by-step explanation:

Use PEMDAS for this:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

-4(3-5)+10-3(7+4)+30 ​= -4(-2)+10-3(11)+30

-4(-2)+10-3(11)+30 = 8+10-33+30

8+10-33+30 = 18-33+30

18-33+30 = -15+30

-15+30 = 15

Step 1: calculate in parentheses
-4•(-2)+10-3•11+30
Step 2: Multiply
8+10-33+30
Step 3: Calculate
=15

Four angles are formed by the intersection of the diagonals of this quadrilateral. Which statement is NOT true?

Answers

I think I don’t know sorry

Answer:

Can’t really understand your question!!

how to simply this equation

Answers

Answer:

[tex]\sqrt[3]{2}[/tex]

Step-by-step explanation:

     18

 9 .     2

3 3

Divide. Write the quotient in lowest terms. 4\dfrac{2}{3} \div 7 =4 3 2 ​ ÷7=4, start fraction, 2, divided by, 3, end fraction, divided by, 7, equals

Answers

Answer:

[tex]\dfrac{2}{3}[/tex]

Step-by-step explanation:

Given the quotient: [tex]4\dfrac{2}{3} \div 7[/tex]

Step 1: Write [tex]4\dfrac{2}{3}[/tex] in improper fraction.

[tex]4\dfrac{2}{3}=\dfrac{14}{3}[/tex]

Therefore:

[tex]4\dfrac{2}{3} \div 7=\dfrac{14}{3} \div 7[/tex]

Step 2: Change the division sign to multiplication by taking the reciprocal of 7

[tex]\dfrac{14}{3} \div 7 =\dfrac{14}{3} X\dfrac{1}{7} \\$Simplify\\\\=\dfrac{2}{3}[/tex]

Answer:

2/3

Step-by-step explanation:

i did it in khan academy

Select ALL equations that have a solution of 6.

A
x + 6 = 9
3
B
4x + 15 = 29
C
x + 9 = 5
3
D
2(x + 5) = 18

Answers

None, i checked on photomath and it says none. What are we solving for??

The sum of the three numbers is 180. The first number is 10 more than the mean of the three numbers and the second number is 4 less than the mean. What is the third number?

Answers

Answer:

The third number (c) is 54.

The other ones are 70 and 56.

Step-by-step explanation:

We have 3 numbers, let's call them a, b and c.

We know that the sum of the three numbers is 180, thus:

[tex]a+b+c=180[/tex]

We also know that the first number is 10 more than the mean of the three numbers (Note: the mean is the sum of the numbers divided by the number of numbers). Thus:

[tex]a=\frac{a+b+c}{3} +10\\a=\frac{a+b+c+30}{3} \\3a=a+b+c+30\\2a=b+c+30[/tex]

Finally the second number is 4 less than the mean:

[tex]b=\frac{a+b+c}{3}-4\\b=\frac{a+b+c-12}{3} \\3b=a+b+c-12\\2b=a+c-12[/tex]

Now we have our set of equations and we can proceed to solve them:

[tex]a+b+c=180\\2a=b+c+30\\2b=a+c-12[/tex]

Solving for a in our first equation we have: [tex]a=180-b-c[/tex] and substituting this in our second equation we have:

[tex]2a=b+c+30\\2(180-b-c)=b+c+30\\360-2b-2c=b+c+30\\330=3b+3c\\110=b+c[/tex]

Now taking this last result into our first equation we have:

[tex]a+b+c=180\\a+(b+c)=180\\a+110=180\\a=70[/tex]

Now we are going to solve for b in our second equation and substitute this in our third equation: [tex]b= 180-a-c[/tex]

[tex]2b=a+c-12\\2(180-a-c)=a+c-12\\360-2a-2c=a+c-12\\372=3a+3c\\124=a+c[/tex]

But we know that a =70, so we can substitute it in our last line:

[tex]124=a+c\\124=70+c\\54=c[/tex]

Now we just need to find b and we can use our first original equation to do this:

[tex]a+b+c=180\\70+b+54=180\\124+b=180\\b=180-124\\b=56[/tex]

A polynomial p has zeros when x = 1/5, x = -4, and x = 2.
What could be the equation of p?

Answers

Answer:

-3

Step-by-step explanation:

and

= -3

What could be the equation of p?

Choose 1 answer:

©

p(x) = 2(6x + 1)(x+3)

©

p(x) = 2(6x – ) (2 – 3)

© p(x) = + (6 +) (+3)

© pla) = = (***) (2-3)

Answer:

p(x) = (5x - 1) (x + 4) (x - 2)

Step-by-step explanation:

30 POINTS!!!
The math club surveyed 100 students about the number of math courses in which they were enrolled and the weight of their backpacks. Classify the random variables from the survey.

Number of math courses, discrete; weight of backpack, discrete
Number of math courses, discrete; weight of backpack, continuous
Number of math courses, continuous; weight of backpack, discrete
Number of math courses, continuous; weight of backpack, continuous
Unable to determine from information given

Answers

Answer:

As described, the classification of random variables should be:

Number of math courses, discrete; weight of backpack, continuous.

Hope this helps!

:)

Answer:

Number of math courses, discrete; weight of backpack, continuous

Step-by-step explanation:

Hope this helped! stay safe! ;D

An acute ∆ABC is rotated about a point and then dilated by a scale factor of 0.5 to produce ∆A’B’C’. Which statement correctly compares ∆ABC to ∆A’B’C’.

Answers

Answer:

Option given in the top right.

Step-by-step explanation:

If an acute triangle is rotated about a point,

- Angles of the transformed triangle remain unchanged.

If a triangle is dilated by a scale factor of [tex]\frac{1}{2}[/tex],

- Measure of sides of the image will be dilated by a scale factor of 0.5.

Therefore, statement that compares ΔABC to ΔA'B'C' will be,

The angle measures of the triangle A'B'C'are the same of those ΔABC, but the side length of the ΔA'B'C' half the size of those of ΔABC.

Option given in the top right is the answer.

Four families are travelling. Order their speeds from least to greatest.

Sapons
80 km in 2 h

Silvers
180 km in 3 h

Johns
50 km in 1 h

Cunninghams
35 km in 30 min

(please help)​

Answers

Step-by-step explanation:

We're going to convert all of these to km/h.

Sapons: 80km/2h => 40kmh

Silvers: 180km/3h => 60kmh

Johns: 50kmh

Cunninghams: (to get the 30 mins to 60 mins, multiply the top and the bottom by 2) 35km/30min => 70kmh

Now that they're all in the same form we can put them from least to greatest.

Answer:

(Least) - Sapons

- Johns

-Silvers

(Greatest) - Cunninghams

What is the surface area of a cube in which each face of the cube has an area of 7 cm??

Answers

Answer:

42

Step-by-step explanation:

6 faces to a cube

each face has area of 7

6*7 is 42

Answer:

42 is correct

Step-by-step explanation:

give the other person brainliest

Anthony earned the following amount for baby-sitting his brother over winter break: $5, $10, $10, $10, $5, $10, $20, $10, $5, $20, $20, $20, $10, $5, $5. What is the mean and median amount he earned each day?

Answers

Answer:

mean is $11

median is $10

Step-by-step explanation:

Solve the system of equations by the substitution method.
y=5x+6
y=9x+7

Answers

Answer:

When finding the value of x let y be 0 and when finding value of y let x be 0 and get your answers.

The diagram shows a hexagon.
The hexagon has one line
of symmetry
А
B.
FA = BC
EF = CD
Angle ABC = 123
Angle BCD = 2 x angle CDE
Work out the size of angle AFE.
You must show some of your working.
Your final line must say, AFE = ...

Answers

Answer:

158 degrees

Step-by-step explanation:

Step 1:

Let Angle CDE =y

Since Angle BCD = 2 X angle CDE

Angle BCD = 2y

Step 2

Consider Figure 2 attached, each of the figure forms an isosceles trapezoid ABCF and DEFC.

By these properties of Isosceles Trapezoids

Lower Base Angles are CongruentUpper base angles are congruentAny lower base angle is supplementary to any upper base angle

Therefore:

[tex]\angle ABC+\angle BCF=180^\circ\\\angle FCD+\angle CDE=180^\circ\\Therefore:\\\angle ABC+\angle BCF+\angle FCD+\angle CDE=360^\circ\\$But \angle BCF+\angle FCD=\angle BCD\\So:\\\angle ABC+\angle BCD+\angle CDE=360^\circ[/tex]

123+2y+y=360

3y=360-123

3y=237

y=79 degrees

Therefore:

[tex]\angle BCD=2 X 79^\circ=158^\circ\\\angle BCD=\angle AFE=158^\circ\\\angle AFE=158^\circ[/tex]

what is 10 + x = 24?

Answers

Answer:

x=14

Step-by-step explanation:

subtract 10 on both sides

24-10=14

x=14

Answer:

x = 14

Step-by-step explanation:

10 + x = 24

-10

x=14

( You subtract 10 from both sides. 24-10 =14. Therefore x =14

Does anyone know what 6.04 x 10^-3

Answers

Answer:

.00604

Step-by-step explanation:

when multiplying by a negative exponent move the decimal to the left

10^-3 move the decimal 3 spaces to left

.00604

Suppose you arrange 50 counters into rows. The first row has 4 counters. Each row after that has 3 more counters than the row before. How many rows do you need to make to use all 50​ counters? nothing rows

Answers

Answer:

20

Step-by-step explanation:

hope it right not the best with counting

❗️ASKED ONCE AND NO ONE ANSWERED, WILL MARK BRAINLIEST,,,,,,,,,,❗️. Five men and eight women work in a firm’s PR office. Their employer must choose two of them to attend a conference in Chicago. What is the probability of choosing one woman and one man to attend the conference?

A. 15/28
B. 6/13
C. 20/39
D. 8/15

MUST PROVIDE EXPLANATION

Answers

Answer:

I DONT KNOW BUTTTTTTT CAN YOU MARK ME BRANINLIST

Answer:

20/39

Step-by-step explanation:

Choose 2 out of 13 which is the total. this is 13C2

5 * 8 for one man and one women.

divide.

Can you please help me with this question please please help me

Answers

It’s the third one. Hope that helped!

Answer:

i think the answer is [tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \geq \neq \sqrt{x} x^{2} \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \leq x_{123} \\\int\limits^a_b {x} \, dx[/tex]

Step-by-step explanation:

[tex]x^{2} \int\limits^a_b {x} \, dx \sqrt{x} \sqrt[n]{x} \frac{x}{y} \alpha x_{123}[/tex]

Can i get some help pwease

Answers

Answer:

Hey!

Your answer is Y=-5x-6

Step-by-step explanation:

Using the formula y=mx+c...

m=slope c=y-intercept

The coordinate s(the c) it's given you are the coordinates for the y-intercept so we only write the y-value down (the -6)

The m is the slope do we write the slope value (-5)

Which forms y=-5x-6

HOPE THIS HELPS!!

Complete the equation to show the relationship between the number of buses, x, and the number of people that can be transported, y. At this rate, how many people can be transported on 40 buses?

Answers

Answer:

[tex]y = 40\cdot k[/tex]

Step-by-step explanation:

Let suppose that each bus has the same capacity and exists a direct proportionality between the amount of people that is transported and the number of buses:

[tex]y \propto x[/tex]

[tex]y = k \cdot x[/tex]

Where [tex]k[/tex] is the proportionality constant, which is equivalent to the maximum capacity of each bus. In that case, the quantity of people that is transported on 40 buses is:

[tex]y = 40\cdot k[/tex]

Answer:

The first answer is ''y=45 x''

1800 people for the second one

The hardware store is having a 15% off sale on lawn mowers this weekend.If x is the original price of the lawn mower,what will be the final sales price,excluding tax?

Answers

Answer:

Final price f = 0.85x

Step-by-step explanation:

Let f represent the final price and

x is the original price of the lawn mower

Given;

The hardware store is having a 15% off sale on lawn mowers this weekend;

the final sales price,excluding tax will be equal to the original price minus 15% of the original price.

Final price f = 100% of x - 15% of x

Final price f = x - 0.15x

Final price f = 0.85x

Answer:

WHAT IS THE ANSWER?

Step-by-step explanation:

help mehhh

Plis help I need help

Answers

Answer:

meee tooo

Step-by-step explanation:

helpplppppppp

Answer: 8) All points with an x-coordinate of 0 means that the slope of the graph is 0 and all the points will always lie on the y-axis.

  9) All points with a y-coordinate of 0 will always lie on the x axis.

Step-by-step explanation:

Explain what the similarities and difference between y=2cosx and y=2cosx-3.

Answers

Answer:

(See explanation for further details)

Step-by-step explanation:

Similarities: Both expression have the same slope for the same values of x.

Difference: The second expression is a translated form of the first function in -3 units.

Rachel is making nachos for a party. The recipe calls for 23 cup of cheese for each plate of nachos. Part A How many full plates of nachos can Rachel make with 5 cups of cheese?

Answers

Answer: 0.22 plates

Step-by-step explanation:

Given that The recipe calls for 23 cup of cheese for each plate of nachos

1 plate = 23 cups

X plate = 5 cups

Cross multiply

5 = 23x

Make the x the subject of formula

X = 5/23

X = 0.22

Or 5/23 plate

Which algebraic expression has like terms? 9 n cubed minus 2 n + 3 minus 4 n squared 7 n cubed + 3 n minus 3 minus 6 n squared 7 n cubed + 4 n minus 3 n cubed minus 5 n squared 6 n cubed minus 4 n Superscript 4 Baseline + 6 n minus 5 n squared

Answers

Question

Which algebraic expression has like terms?

[tex]9n^3 - 2n + 3 - 4n^2[/tex]

[tex]7n^3 + 3n - 3 - 6n^2[/tex]

[tex]7n^3 + 4n - 3n^3 - 5n^2[/tex]

[tex]6n^3 - 4n^4 + 6n - 5n^2[/tex]

Answer:

A. [tex]9n^3 - 2n + 3 - 4n^2[/tex]

B. [tex]7n^3 + 3n - 3 - 6n^2[/tex]

Step-by-step explanation:

Given:

The above expressions

Required:

Expressions with like terms

Algebraic expressions are said to have like terms if and only if the have the equivalent exponents;

Like terms are dependent on the exponents and are independent on the sign of each terms.

Listing out the exponents of each options;

A. [tex]9n^3 - 2n + 3 - 4n^2[/tex]

The exponents of n are 3 1 0 2

Rearrange: 0 1 2 3

B. [tex]7n^3 + 3n - 3 - 6n^2[/tex]

The exponents of n are 3 1 0 2

Rearrange: 0 1 2 3

C. [tex]7n^3 + 4n - 3n^3 - 5n^2[/tex]

The exponents of n are 3 1 3 2

Rearrange: 1 2 3 3

D. [tex]6n^3 - 4n^4 + 6n - 5n^2[/tex]

The exponents of n are 3 4 1 2

Rearrange: 1 2 3 4

From the list of exponents above, only A and B are equal;

Hence, the following expressions have the like terms

A. [tex]9n^3 - 2n + 3 - 4n^2[/tex] and B. [tex]7n^3 + 3n - 3 - 6n^2[/tex]


Let ∠A, ∠B, and ∠C be acute angles. Use a calculator to approximate the measures of ∠A, ∠B, and ∠C to the nearest tenth of a degree.

cos A = 0.31, sin B = 0.89, tan C = 0.52

Answers

Answer:

1. ∠A =  71.9°

2. ∠B =  62.9°

3. ∠C = 27.5°

Step-by-step explanation:

By using a calculator, we have;

cos A = 0.31

sin B = 0.89

tan C = 0.52

1. Therefore, ∠A = cos⁻¹(0.31), inputting the digits in the calculator and looking for the inverse sign, we have;

∠A = cos⁻¹(0.31) = 71.94° = 71.9° to the nearest tenth of a degree.

2. For sin B = 0.89, we have;

∠B = sin⁻¹0.89 = 62.873° ≈ 62.9° with the answer rounded to the nearest tenth of a degree.

3. Similarly, for tan C = 0.52, inputting the values in the calculator and pressing the tan⁻¹ button, we have;

∠C = tan⁻¹(0.52) = 27.474°, which is 27.5° rounded to the nearest tenth of a degree.

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