Determine the center and radius of the following circle equation:
+ y2 – 123 + 8y – 48 = 0

9514 1404 393

Answer:

  ±√58 ≈ ±7.616

Step-by-step explanation:

The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.

  |x| = √(3² +7²) = √58

The motion is bounded between positions ±√58.

_____

Here's a way to get to the relation used above.

The sine of the sum of angles is given by ...

  sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)

If this is multiplied by some amplitude A, then we have ...

  A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)

Comparing this to the given expression, we find ...

  A·cos(c) = 3   and   A·sin(c) = -7

We know that sin²+cos² = 1, so the sum of the squares of these values is ...

  (A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²

That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...

  x = A·sin(θ +c) . . . . for some angle c

  x = (√58)sin(θ +c)

This has the bounds ±√58.

Answer:

ok hiiiiiiiiiiiiiiiiiiiiiii

Step-by-step explanation:

Answer:

Option C, No real solutions

Hope this helps!

Answer:

А.The system has two solutions, but only one is viable because the other results in a negative width.

Step-by-step explanation:

Given

Let:

[tex]L_A \to[/tex] length of play area A

[tex]W_A \to[/tex] width of play area A

[tex]L_B \to[/tex] length of play area B

[tex]W_B \to[/tex] width of play area B

[tex]x \to[/tex] Area of A

[tex]y \to[/tex] Area of B

From the question, we have the following:

[tex]L_A = 1 + 4W_A[/tex]

[tex]W_B = 2 + W_A[/tex]

[tex]L_B = 2 + 3W_B[/tex]

[tex]x = y[/tex]

The area of A is:

[tex]x = L_A * W_A[/tex]

This gives:

[tex]x = (1 + 4W_A) * W_A[/tex]

Open bracket

[tex]x = W_A + 4W_A^2[/tex]

The area of B is:

[tex]y = L_B * W_B[/tex]

[tex]y = (2 + 3W_B) * ( 2 + W_A)[/tex]

Substitute: [tex]W_B = 2 + W_A[/tex]

[tex]y = (2 + 3(2 + W_A)) * ( 2 + W_A)[/tex]

Open brackets

[tex]y = (2 + 6 + 3W_A) * ( 2 + W_A)[/tex]

[tex]y = (8 + 3W_A) * ( 2 + W_A)[/tex]

Expand

[tex]y = 16 + 8W_A + 6W_A + 3W_A^2[/tex]

[tex]y = 16 + 14W_A + 3W_A^2[/tex]

We have that:

[tex]x = y[/tex]

This gives:

[tex]W_A + 4W_A^2 = 16 + 14W_A + 3W_A^2[/tex]

Collect like terms

[tex]4W_A^2 - 3W_A^2 + W_A -14W_A - 16 =0[/tex]

[tex]W_A^2 -13W_A - 16 =0[/tex]

Using quadratic calculator, we have:

[tex]W_A = -14.1[/tex] or [tex]W = 1.13[/tex] --- approximated

But the width can not be negative; So:

[tex]W = 1.19[/tex]

Answer:

y=-3x-4

Step-by-step explanation:

i solved it by the two points

Answer:

14.379

Step-by-step explanation:

1. Line up from left to right

2. Make sure that the decimals are lined up

3. Add the thousandths and hundredths with 0

4. Add 3 in the tenths place

5. Add up 9 and 5 to make 14

*IF YOU DID THE STEPS RIGHT, THEN YOU SHOULD HAVE 14.379 AS YOUR ANSWER*

Answer:

9.079

+5.300

_______

14.379

Step-by-step explanation:

Just line the decimals up and add zeros for 5.3 to 5.300 because you can't do 9.079

   +5.3   because your decimal will be in the wrong spot and your answer will come out wrong

Answer: 114

Step-by-step explanation:

Plug in the numbers. 5*5+2*5*8/2*2+3*3=25+80+9=114

Answer: 30 degrees

Step-by-step explanation: Vertical angles are always congruent. If Angle A and Angle B are vertical then they are equal to each other. They both will way thirty degrees.

Answer:

[tex]P(2)=(32,46)[/tex]

Step-by-step explanation:

From the question we are told that:

Height of robot [tex]h=12 inches[/tex]

Weight of robot [tex]W=4[/tex]

Start position [tex]P(1)=(4,4)[/tex]

Per minute distance [tex]d=(4,6)[/tex]

Total time [tex]T=7min[/tex]

Generally the distance traveled in 7 minutes [tex]d_T[/tex] is mathematically given by

 [tex]d_T=d*T[/tex]

 [tex]d_T=(4.6)*7[/tex]

 [tex]d_T=(28,42)[/tex]

Generally the position of the robot after 7 minutes is  mathematically given by

 [tex]P(2)=P(1)+d_T[/tex]

 [tex]P(2)=(4,4)+(28,42)[/tex]

 [tex]P(2)=(32,46)[/tex]

Therefore the position of the robot after 7 minutes is

 [tex]P(2)=(32,46)[/tex]

Answer:

A) One Solution

Step-by-step explanation:

3x + 4 = -x

4 = -4x

x = -1

y = 3(-1)+4

y = 1

One Solution

Answer:

∠A= 80°

Step-by-step explanation:

if they are supplementary then put them equal to 180

7x + 3 +7x + 23 = 180

14x + 26 = 180

14x = 154

x= 11

now plug in

7(11)+3

77+3= 80

Answer:

No

Step-by-step explanation:

7 3/4 x 3 = 22 1/2

Answer:

open bracket

7j - 35 = 14

7j = 14 + 35

7j = 49

divide thru by 7

7j / 7 = 49 / 7

j = 7

I think the first one c and the second one a

Answer:

the right answer is

tan D=80/18

Answer:

C

Step-by-step explanation:

Process of elimination

Answer:

92°÷^®√™÷√÷^π^π^^π^π°π°^÷

Answer:95

Step-by-step explanation:

Answer:

[tex]10f - 5-5f +2 =5f -3= -3+5f[/tex]

last option

Answer:

C

Step-by-step explanation:

If we solve 10f-5f+8+69+4, We get 5f+81 (put in comments if you want a step by step explanation on how i solved this).  

Let's try to solve each of the options.  

A) 15f + 14g + 4  

It would not be option A because there isn't a variable such as g in the expression.  

B) 15f + 8 + 10g

C) 5f + 69 + 12

5f+ 81  

This one is correct because the expression also equals 5f+81  

D) 5f + 149 +4​

5f+ 153  

D would be wrong as well

Hope this helps! <3

Answer:

It has 5 terms

Step-by-step explanation:

Terms are the numbers or values in a equation, so this Equation has 5 terms

x + 5y - 17 - 2y + x.

1. x

2.5y

3.17

4. 2y

5.x  

(I listed the terms)

Answer:

24

Step-by-step explanation:

8 correct for every 2 wrong

multiply both sides by 3

24 correct and 6 wrong

which adds up to 30

Answer:

C

Step-by-step explanation:

The transitive property states that a line is congruent to itself.

Answer:

The answer is, (C) transitive property.

Step-by-step explanation:

The (interior) bisector of an angle, also called the internal angle bisector  is the line or line segment that divides the angle into two equal parts. The angle bisectors meet at the incenter. , which has trilinear coordinates.

Then, For angle bisector construction, a statement column proof is given.

Justification for Statement.

CPCTC and MBP have the same angle.

NBP angle

Since SSS established congruence for the two triangles in the preceding sentence,

The next step is to ensure that matching angles are identical and that congruent triangle portions are congruent.

A line is congruent to itself if it has the transitive attribute.

To know more angle bisector here, https://brainly.com/question/24334771

#SPJ2

Answer:

Step-by-step explanation:

I hope this helps you

Rectangular Prism Volume is

Height. Width. Height

(6.25).(7.5).(8)

375

Answer:

$125

Step-by-step explanation:

if there was a discount of 20%, the sales price is 100 - 20 = 80% of the original price

let a = original price

this equation can be used to represent the question

a x 0.8 = 100 ]]divide both sides by 0.8

a = 100 / 0.8 = 125

Answer:

50% increase

Step-by-step explanation:

4050-2700 = 1350

1350/2700 = 0.5

Convert to a percentage:

0.5*100 = 50

Answer:

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

Step-by-step explanation:ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

Answer:

[tex]4m ^{2} = 4 \times 5 \times 5 = 100[/tex]

Answer:

[tex]y=-\frac{1}{2} x-3[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

[tex]x+2y=18[/tex]

Rearrange this equation into slope-intercept form (this will make it easier for us to identify the slope)

Subtract x from both sides to isolate 2y

[tex]x+2y-x=-x+18\\2y=-x+18[/tex]

Divide both sides by 2 to isolate y

[tex]y=-\frac{1}{2} x+9[/tex]

Now, we can see clearly that [tex]-\frac{1}{2}[/tex] is in the place of m. Because parallel lines have the same slope, [tex]-\frac{1}{2}[/tex] is therefore the slope of the line we're currently solving for. Plug [tex]-\frac{1}{2}[/tex] into [tex]y=mx+b[/tex]:

[tex]y=-\frac{1}{2} x+b[/tex]

2) Determine the y-intercept

[tex]y=-\frac{1}{2} x+b[/tex]

Plug in the point (8,-7)

[tex]-7=-\frac{1}{2} (8)+b\\-7=-4+b[/tex]

Add 4 to both sides

[tex]-7+4=-4+b+4\\-3=b[/tex]

Therefore, the y-intercept is -3. Plug this back into [tex]y=-\frac{1}{2} x+b[/tex]:

[tex]y=-\frac{1}{2} x-3[/tex]

I hope this helps!