slove: x = 3y - 7
4x + 5y =- 11
show steps

Given:

The equation of a circle is:

[tex]x^2+y^2-x-2y-\dfrac{11}{4}=0[/tex]

To find:

The center of the circle and its radius.

Solution:

The standard form of a circle is:

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

Where, (h,k) is center and r is the radius of the circle.

The given equation of the circle is:

[tex]x^2+y^2-x-2y-\dfrac{11}{4}=0[/tex]

Write the given equation in standard form of a circle.

[tex](x^2-x)+(y^2-2y)-\dfrac{11}{4}=0[/tex]

[tex]\left(x^2-x+\left(\dfrac{1}{2}\right)^2\right)+(y^2-2y+1^2)-\dfrac{11}{4}-\left(\dfrac{1}{2}\right)^2+1^2=0[/tex]

[tex]\left(x-\dfrac{1}{2}\right)^2+(y-1)^2-\dfrac{11}{4}-\dfrac{1}{4}-1=0[/tex]

[tex]\left(x-0.5\right)^2+(y-1)^2-\dfrac{12}{4}-1=0[/tex]

On further simplification, we get

[tex]\left(x-0.5\right)^2+(y-1)^2-3-1=0[/tex]

[tex]\left(x-0.5\right)^2+(y-1)^2-4=0[/tex]

[tex]\left(x-0.5\right)^2+(y-1)^2=4[/tex]

[tex]\left(x-0.5\right)^2+(y-1)^2=2^2[/tex]            ...(ii)

On comparing (i) and (ii), we get

[tex]h=0.5,k=1,r=2[/tex]

Therefore, the center of the circle is (0.5,1) and radius is 2 units.

Answer:

the answer is 150

Step-by-step explanation:

Answer:

$9,151.38

Hopefully that is correct!!

Answer:

5 games

Step-by-step explanation:

1.50x + 1.25 = 8.75

1.50x = 7.50

x = 5

Answer:

Jacoby is correct.

Step-by-step explanation:

Shop A= $6 ÷ 2 = $3/pound

Shop B= $15 ÷ 5 = $3/pound

Answer:

y = tan-1 (31/23)

Formula: SOHCAHTOA

TOA: tan = opposite/adjacent

31 / 23 = 1.3478

tan-1 of 1.3478 is 53.4264

53.4264 = 53 (rounding to the nearest degree)

y = 53 degrees

Answer:

d

Step-by-step explanation:

Answer:

6 phones and 18 accessories

Step-by-step explanation:

12P + 3.50A = 135

A = 12 + P

12P + 3.50(12 + P) = 135,

12P + 42 +3.50P = 135

15.50P = 93

P = 6 phones

A = 12 + 6 = 18 accessories

Answer:

[tex]\huge\boxed{\text{B) } 22.5 \ \text{feet}}[/tex]

Step-by-step explanation:

We can use basic trigonometric functions to find the closest height of the escalator.

Let's set up a picture from what we already know. The length of the escalator is 30 feet, and it forms a 41 degree angle with the top. Since it will form a 90 degree angle with the ground, we can find the angle between the ground and the beginning of the escalator.

Since all triangles have an angle sum of 180:

Now we know that the triangle looks something like this.

                   /  | 41°

                 /    |

               /      |

            /         |

30      /           |

       /              |                                                

     /                |

  /                   |

/__________| 90°

49°

We need to find the length of the side between the 41 and 90° angle.

To find which trigonometric operation to use on this triangle, we can use the acronym SOH CAH TOA.

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

We can use the sine of the 49 degree angle (opposite / hypotenuse) to find our missing side (since we know the hypotenuse).

Let's set up an equation and solve with our calculator.

We can calculate the sine of 49 with our calculator. We'd end up multiply 30 and that value and get 22.6.

Since the closest value to 22.6 on the answer choices is 22.5, the correct answer would be B) 22.5 feet.

Hope this helped!

Answer:

The answer is B.

Step-by-step explanation:

B. 22.5 feet

Answer:

about 62%

Step-by-step explanation:

add all of the numbers

subtract the number of purple skittles

do 16÷26

multiply your answer by 100

get 61.5

round up

Answer:

Earth : Moon

1 : 27

Step-by-step explanation:

24 hrs = 1 day

so the ratio is up there

Hope I helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

Step-by-step explanation:

Pathagory and Theorem

a^2+b^2=c^2

(x-3)^2+(x-4)^2=6^2

expand:

2x^2-14x+25=36

2x^2-14x-11=0

x=(\sqrt{71}+7)/2

perimeter=(x-3)+(x-4)+6=2x-1

insert the value for x into 2x-1

[tex]\sqrt{71}[/tex]+6=perimeter

Hope that helps :)

9514 1404 393

Answer:

  2x -1

Step-by-step explanation:

The perimeter is the sum of the side lengths.

  P = 6 + (x -4) + (x -3)

  P = 2x -1 . . . . . . collect terms

The perimeter is 2x -1.

_____

Additional comment

There is nothing in the problem statement that suggests this is a right triangle. Without knowing at least one angle, we cannot solve for a numerical value for the perimeter. The problem title suggests we're to leave the result in polynomial form.

Answer:

8^2-60 ,   11^1   , 2^2x5

Step-by-step explanation:

2^2= 4

4 x 5 = 20

11^1= 11

8^2= 64

64-60 = 4

Answer:

E, 297.1

Step-by-step explanation:

First, find the area of the triangle using the formula a= (bh) / 2

Base x height would be 16 x 12, which is 192

192 / 2 is 96 sq meters

Then, find the area of the circle using the formula a= Pi (r^2)

If the diameter is 16, the radius would be 8 because you divide by 2

8^2 is 64, 64 times Pi is approximately 201.1

Finally, add the areas together, 96 + 201.1 is 297.1 or E

Answer:

Please Provide the an attachment.Then i can show u my answer

Answer:

30f+25 I hope it is a right answers

I hope this answers is useful for you

Answer:

Here is the answer I solved.

Answer:

Trapezoid

Step-by-step explanation:

They're showing us (with red arrows/triangles) that the bottom and top are parallel, but do not state anything like it for the sides.

That means it's at least a trapezoid.

As nothing suggests the sides are parallel, it's likely not a parallelogram (and it doesn't look like one).

It's also not a kite, as there is no indication that pairs of neighboring sides are equal in length.

As we don't think it's a parallelogram, it's thus not a rectangle (every rectangle is a parallelogram).

Similar with rhombus (every rhombus is a parallelogram) and square (every square is a parallelogram AND a rhombus).

Answer:

I think it's vertex bestie not sure tho lmk if it's wrong

Answer:

There are 231 ;)

Step-by-step explanation:

Answer:

231:)

Step-by-step explanation:

Answer:

c

a fraction bar Is just a division bar, it's c.

Answer:

D.   2 ≤ x ≤ 5

Step-by-step explanation:

Notice that there are no points on the graph for x ≤ 2 and x ≥ 5.  Or another way to look at it is that the x's are between 2 and 5, inclusive.

The domain is the set of possible x values.  Therefore,  2 ≤ x ≤ 5 is the set of  values for the domain

Answer:

3(x+5) is the answer.

Answer:

i think is is 64a

Step-by-step explanation:

Answer:

[tex](8 - 3a)(8 - 3a) \\ 8(8 - 3a) - 3a(8 - 3a) \\ 64 - 24a - 24a + 6a {}^{2} \\ 64 - 48a + 6a {}^{2} \\ 6a {}^{2} - 48a + 64[/tex]

Answer:

do math

Step-by-step explanation:

Answer:

The unit rate is 2.20. For a single pound of cat food it would cost $2.20

Answer:

Step-by-step explanation:

1) Area of garden = side * side

                             = 10* 10

                             = 100 Sq.m

2) Area of each flowerbed = 1*1 = 1 sqm

3)  Area of 4 flowerbed = 1 * 4 = 4 sqm

 Area of the remaining garden = Area of garden - area of 4 flower bed

                                                    = 100 - 4

                                                    = 96 sq.m

4) Length of the fence = 4 *side

                                      = 4 * 10 = 40 m

5)  Cost of planting in the remaining garden = 96 * 20

                                                                          = ₹ 1920