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Answer:

1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]

2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]

3) For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex],  the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]

4) For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex],  the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]

5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex],  the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]

6) For[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]

Step-by-step explanation:

This can be done using the completing the square method.

The standard equation of a circle is given by [tex](x - a)^2 + (y-b)^2 = r^2[/tex]

1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex]

[tex]x^2 - 4x + y^2 + 12y = 20\\x^2 - 4x + 2^2 + y^2 + 12y + 6^2 = 20 + 4 + 36\\(x-2)^2 + (y+6)^2 = 60\\[/tex]

Therefore, for [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]

2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex]

[tex]x^2 + 6x + y^2 - 8y = 10\\x^2 + 6x + 3^2 + y^2 - 8y + 4^2 = 10 + 9 + 16\\(x + 3)^2 + (y- 4)^2 = 35\\[/tex]

Therefore, for [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]

3)  For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex]

Divide through by 3

[tex]x^2 + y^2 + 4x + 6y = 5[/tex]

[tex]x^2 + y^2 + 4x + 6y = 5\\x^2 + 4x + 2^2 + y^2 + 6y + 3^2 = 5 + 4 + 9\\(x + 2)^2 + (y+ 3)^2 = 18\\[/tex]

Therefore, for [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex],  the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]

4)  For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex]

Divide through by 5

[tex]x^2 + y^2 - 2x + 4y = 6[/tex]

[tex]x^2 + y^2 -2x + 4y = 6\\x^2 - 2x + 1^2 + y^2 + 4y + 2^2 = 6 + 1 + 4\\(x - 1)^2 + (y+ 2)^2 = 11\\[/tex]

Therefore, for [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex],  the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]

5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex]

Divide through by 2

[tex]x^2 + y^2 - 12x - 8y = 4[/tex]

[tex]x^2 + y^2 - 12x - 8y = 4\\x^2 - 12x + 6^2 + y^2 - 8y + 4^2 = 4 + 36 + 16\\(x - 6)^2 + (y+ 4)^2 = 56\\[/tex]

Therefore, for [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex],  the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]

6) For [tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex]

[tex]x^2 + 2x + y^2 - 12y = 9\\x^2 + 2x + 1^2 + y^2 - 12y + 6^2 = 9 + 1 + 36\\(x+1)^2 + (y-6)^2 = 46\\[/tex]

Therefore, for[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]

For Plato / Edmentum

Just to the test and got it right ✅

Answer:

sorry please....what is the end of the question ....no task to do

Answer:

$280 dollars

Step-by-step explanation:

When they were leaving

[tex]\$1 \approx \frac{7}{10}$ Euro\\Therefore:\\\$1000 \approx \dfrac{7}{10}\times 1000 =700$ Euro[/tex]

When they returned home, they brought 196 Euros.

[tex]If\:\:\$1 \approx \frac{7}{10}$ Euro\\Then: 1 Euro $=\$ \dfrac{10}{7}\\\\$Therefore:\\\\196 Euros = \$ 196 \times \dfrac{10}{7} =\$280[/tex]

They brought back $280 dollars to the United States.

Answer:

They brought back 280 dollars.

Step-by-step explanation:

From the question, one United States dollar was worth about $\frac{7}{10}$ of a euro implies that:

$1 = 7/10 euro, or 0.70 euro. That is, the exchange rate is $1:0.70 euro.

The equivalence of the exchange $1:0.70 euro can also be obtained by dividing both sides by 0.70 as follows:

$1 / 0.7 = 0.7 / 0.7 => $1.43:1 euro. That is, $1.43 is equal to one euro.

Since they returned with 196 euros and $1.43 is equal to one euro, we will simply multiply 196 euros by $1.43 to obtain the amount of dollars they brought back as follows:

Amount of dollars they brought back = $1.43 * 196 = $280 to the nearest dollar.

Therefore, they brought back 280 dollars.

Answer:

x=23/3

Step-by-step explanation:

x=c+ay

7=c+3a     | *(-1)

9=c+6a

-7=-c-3a

9=c+6a

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

9-7=c-c+6a-3a

2=3a

a=2/3

7=c+3*2/3

7=c+2

-2   -2

5=c

so   x=5+2/3*y

when y=4 then  x=5+2/3*4=5+8/3

x=15/3+8/3

x=23/3

Equal steps mean each number is the same distance from the previous one

From -2 to 28 is 28 units

There are 4 spaces between the numbers

28/4 = 7

Each number is in increase of 7

-2 + 7 = 5

5+7 = 12

12+7 = 19

19+7 = 26

The third number would be 12

Answer:

Solution,

[tex]10 {x}^{2} - 17x + 3 \\ = 10 {x}^{2} - (15 + 2) x+ 3 \\ = 10 {x}^{2} - 15x - 2x + 3 \\ = 5x(2x - 3) - 1(2x - 3) \\ = (2x - 3)(5x - 1)[/tex]

Hope this helps..

Good luck on your assignment...

Answer:

The answer would be letter B. This is because the problem wants you to find the equation that is not necessarily true. In this case G'G does not equal 8 units.

Answer:

58.43%

Step-by-step explanation:

In this case we have that the probability that they are different is the opposite of the probability that they are the same, therefore, in each case it would be:

P (plain, plain) = (12/20) (11/19)

P (p, p) = 132/380

P (chocolate, chocolate) = (5/20) (4/19) = 20/380

P (ch, ch) = 20/380

P (currant, currant)= (3/20) (2/19) = 6/380

P (c, c) = 6/380

The probability that they are equal is the sum of each:

P (equal) = 132/380 + 20/380 + 6/380

P (equal) = 0.4157

Therefore, the probability that they are different is:

P (different) = 1 - 0.4157

P (different) = 0.5843 = 58.43%

It means that the probability is 58.43%

Answer:111/190

Step-by-step explanation:

Answer:

Area of rectangle = H × B

Area of rectangle = 10(H)

Step-by-step explanation:

Given:

Base (B) = 10

Height = H

Find:

Area of rectangle

Computation:

Area of rectangle = Height × Base

Area of rectangle = H × B

So,

Area of rectangle = H × B              [Base (B) = 10]

⇒ Area of rectangle = H × 10

⇒ Area of rectangle = 10(H)

Answer:

The expression that represents the area of this rectangle is 8b

When b = 10, the area of the rectangle is 80 square units.

Step-by-step explanation:

The rectangle’s base is b units, and its height is 8 units. The area of the rectangle is the product of its base and height, which is 8b.

To find the area of the rectangle when b = 10, substitute 10 for b in the expression:

8b= 8(10)

    =80

Answer:

Step-by-step explanation:

We can use the intercept form of the equation of a line, then solve for y.

Intercept form

  x/(x-intercept) +y/(y-intercept) = 1

  x/-4 +y/8 = 1

__

Solving for y, we have ...

  -2x +y = 8 . . . . multiply by 8

  y = 2x +8 . . . .  add 2x

The coefficient of x is 2, so the slope is 2.

__

The graph shows you the rise is 8 for a run of 4, so ...

  slope = rise/run = 8/4

  slope = 2

Answer:  a) 110√2 meters

                b) 2.42 hectares

Step-by-step explanation:

a) Since it is a square, the diagonal cuts the square into two 45-45-90 triangles where the diagonal is the hypotenuse.  Therefore, the sides are length x and the diagonal is length x√2.

[tex]x\sqrt2=220\\\\\\x=\dfrac{220}{\sqrt2}\\\\\\x=\dfrac{220}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\x=\large\boxed{110\sqrt2}[/tex]

b) Area of a square is side squared.    10,000 meters² = 1 hectare

   [tex]A=(110\sqrt2)^2\\\\.\quad =(110)^2(\sqrt2)^2\\\\.\quad =12100(2)\\\\.\quad =24200\ \text{meters}^2\\\\.\quad =\large\boxed{2.42\ \text{hectares}}[/tex]

Answer:

Option C

Step-by-step explanation:

Answer:

B.

You need to subtract 1 term because you don't include the starting 5

4^10 - 1 =  4^9

You multiply 5 by 4 each time for 9 times so it is 5 x 4^9

Hope this helps

Step-by-step explanation:

Answer:

D. No, there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.

Step-by-step explanation:

Two figures are congruent if their vertices can be mapped into one another by appropriate rigid transformation or combination of rigid transformations. Examples of the transformation are; reflection, dilation, rotation and translation.

Comparing the two figures, it would be observed that they are not congruent. Since there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.

Answer:

it is D just took the test

Step-by-step explanation:

Answer:10

Step-by-step explanation:

8/80=1/10*100=10

Answer:

m∠x = 98°

Step-by-step explanation:

Step 1: Find the supplementary angle in the triangle

180 - (53 + 45) = 82

Step 2: Use Supplementary Angles to solve for x

180 - 82 = 98°

Answer: 5/55

Step-by-step explanation:

1/11 x 5 = 5/55

So, the fifth equivalent fraction to 1/11 is 5/55.

The 5th equivalent fraction should be [tex]5\div 55[/tex]

Since the fraction is [tex]1\div 11[/tex]

So here the 5th equivalent should be

[tex]= 1\div 11 \times 5\div 5[/tex]

= [tex]5\div 55[/tex]

Here 5 represent the numerator and 55 represent the denominator.

Therefore, we can concluded that The 5th equivalent fraction should be [tex]5\div 55[/tex]

Learn more about fraction here: https://brainly.com/question/1786648

Answer:

The Area of the required figure is  [tex]315\:cm^2[/tex]

Step-by-step explanation:

[tex]Area = (21\times 7)+(14\times 7) + (7\times 10)\\\\=147+98+70\\\\=315[/tex]

Best Regards!

Answer:

6) g = 11p

7) This equation is an example of direct variaction because it is proportional because can make a slanted line with the equation C = 6g + 15

Step-by-step explanation:

Well to find g we seperate g and combine like terms,

[tex]81 = 6g + 15[/tex]

So we subtract 15 from both sides 66 = 6g,

66/6 = 11.

So g = 11.

hope it will be helpful.......

Answer:

y = csc (x) + 2

Step-by-step explanation:

From the graph, we can derive the parent function y = csc(x). Notice how there are asymptotes at x = 2πk and x = π + 2πk, which is where csc(x) is undefined.

Finally, we can see a vertical shift of 2 which we can see from the mid-line of the graph which is at y = 3.

Answer:

c

Step-by-step explanation:

edg 2021

Answer:

x = 12

Step-by-step explanation:

We can use the Cross Products Property.

9 / 12 = x / 16

12x = 9 * 16

x = 9 * 16 / 12 = 12

Answer:

x = 12

Step-by-step explanation:

→ First we work out the multiplier between 16 and 12 so,

16 ÷ 12 = 1.3 recurring

→ Multiply this multiplier by 9

9 × 1.3 recurring = 12

→ x = 12

Answer:

I think it is C

Step-by-step explanation:

Answer:

b-4/5b

Step-by-step explanation:

b is decreased by 80%

dat is 80/100×b

= b-80/100b

b-4/5b

Answer:

10 inches

Step-by-step explanation:

Length of photograph, L1 = 3 inches; Length of enlarged photograph, L2 = 15 inches; Width of photograph, W1 = 2 inches; Width of photograph, W2 = ?

Hence, L1/L2 = W1/W2

∴ W2 = (L2*W1)/L1 = (15 X 2)/3 = 10 inches

Hey there! :)

Answer:

y + 32 = 3(x + 8)

Step-by-step explanation:

Begin by finding the slope of the line using the slope formula:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the coordinates of the points into the equation:

[tex]m = \frac{1 - (-32)}{3 - (-8)}[/tex]

Simplify:

[tex]m = \frac{33}{11}[/tex]

m = 3.

Point-slope form is:

y-y₁=m(x-x₁)

Plug in the coordinates of the first point, as well as the slope:

y - (-32) = 3(x - (-8)

y + 32 = 3(x + 8)

Answer:    y+32=3(x+8)

Step-by-step explanation:

First  you need to find the slope.The slope is the change in y divided by the change in x values.

-32 - 1 = -33

-8 - 3 =    -11  

-33/-11 = 3   the slope is 3  

and in point-slope form is  like y-b= m(x-a) where b is a y coordinate and a is the x coordinate.

it could be like   y-1=3(x-3) or y+32= 3(x+8)

Answer: 0.0009

Step-by-step explanation:

Given : Babies born in a large hospital have a mean weight of 3366 grams, and a variance of 244,036.

i.e. [tex]\mu=3366[/tex]  and [tex]\sigma^2 = 244036\Rightarrow\ \sigma= \sqrt{244036}=494[/tex]

Sample size = 1118

Let [tex]\overline{X}[/tex] be the sample mean weight of babies.

Then, the probability that the mean weight of the sample babies would be greater than 3412 gram:

[tex]P(\overline{X}>3412)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3412-3366}{\dfrac{494}{\sqrt{1118}}})\\\\=P(Z>\dfrac{46}{14.7743})\ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\\approxP(Z>3.11)\\\\= 1-P(Z<3.11)\\\\=1-0.9991=0.0009[/tex]

Hence, the required probability = 0.0009

Answer:

it is the second option

Step-by-step explanation:

Step-by-step explanation:

The first differences are 7,9,11,13,15,17 and the second differences are 2.

This means that the first term of the sequence is n^2.

Subtracting n^2 from the sequence gives 6,10,14,18,22,26, which has nth term of 4n + 2.

So putting these together gives a nth term of the quadratic sequence of n^2 + 4n + 2.

Hope it helped and tell me if I went wrong :)