What are the center and radius of the circle defined by the equation
x2 + y2 - 6x+8y +21= 0 ?

Answer:

x = 2

Step-by-step explanation:

Given a line parallel to a side of a triangle and intersecting the other 2 sides then it divides those sides proportionally, that is

[tex]\frac{6}{x+1}[/tex] = [tex]\frac{4}{x}[/tex] ( cross- multiply )

6x = 4(x + 1)

6x = 4x + 4 ( subtract 4x from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Answer:

[tex]x^2 + 6 = 31[/tex]

Step-by-step explanation:

Given

[tex]Painted = 6ft^2[/tex]

[tex]Total = 31ft^2[/tex]

Dimension of unpainted area:

[tex]Length = Width = x[/tex] --- Square

Required

Determine an expression to solve for x

First, calculate the area of the unpainted space;

[tex]Area = Length *Width[/tex]

[tex]Area = x*x[/tex]

[tex]Area = x^2[/tex]

The unpainted area, added to the painted area, equals the total area.

So, we have:

[tex]Area + Painted = Total[/tex]

[tex]x^2 + 6 = 31[/tex]

Hence, the expression is: [tex]x^2 + 6 = 31[/tex]

Answer:

12 centimetres

Step-by-step explanation:

I looked it up

The only table that represents a function is the fourth option.

A function is a relation that maps elements from a set (domain) into elements of another set (range).

Such that each element from the domain can be mapped into only one element from the range.

In the table, the "x" values are from the domain, and the "y" values are from the range.

So, if you see a table with the same value of x being mapped into two different values of y, then that relation is not a function.

With that in mind, the only table that meets this property is table number 4.

If you want to learn more about functions, you can read:

https://brainly.com/question/1770447

Answer:

0.3

Step-by-step explanation:

When we divide by 10, we want to imagine a decimal point going up a place.

Think of it like this:

03.0

When we divide by 10, the decimal goes up a digit:

0.30 or 0.3

Answer:

6.34 years

Step-by-step explanation:

Given data

Principal P=$5,000

Rate r= 8%

Final amount A=  $8,303.00

The expression for the time will be

t= ln(A/P)/r

substitute

t= ln(8,303.00/5000)/0.08

t= ln(1.6606)/0.08

t= 0.507/0.08

t= 6.3375

Hence the time is about 6.34 years

Answer:

11 is the missing number

Answer:

the answer should be 11 your welcome

Answer:

[tex]Volume=56\frac{1}{4}[/tex] cubic feet

Step-by-step explanation:

Given

[tex]L =3\frac{3}{8}ft[/tex] --- Length

[tex]W =13\frac{1}{3}ft[/tex] --- Width

[tex]H =3\frac{3}{4}[/tex] --- Tank

[tex]Water\ level = \frac{2}{3}[/tex]

Required

Space not covered with water

If the water level is:

[tex]Water\ level = \frac{2}{3}[/tex]

Then the empty space is:

[tex]Empty = 1 - Water\ level[/tex] --- Complement rule

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

Take LCM

[tex]Empty = \frac{3-2}{3}[/tex]

[tex]Empty = \frac{1}{3}[/tex]

So, the volume of the empty space is:

[tex]Volume=L*W*H*Empty[/tex]

[tex]Volume=3\frac{3}{8} *13\frac{1}{3}*3\frac{3}{4}*\frac{1}{3}[/tex]

Express fraction as improper fraction

[tex]Volume=\frac{27}{8} *\frac{40}{3}*\frac{15}{4}*\frac{1}{3}[/tex]

Simplify

[tex]Volume=\frac{9}{8} *\frac{40}{3}*\frac{15}{4}[/tex]

Simplify

[tex]Volume=\frac{3}{8} *\frac{40}{1}*\frac{15}{4}[/tex]

Simplify

[tex]Volume=\frac{3}{1} *\frac{5}{1}*\frac{15}{4}[/tex]

[tex]Volume=\frac{3*5*15}{4}[/tex]

[tex]Volume=\frac{225}{4}[/tex]

[tex]Volume=56\frac{1}{4}[/tex]

Answer:

x =417.6

Step-by-step explanation:

0.5x+78.2=287

Subtract 78.2 from each side

0.5x+78.2-78.2=287-78.2

.5x =208.8

Divide each side by .5

.5x/.5 = 280.8/.5

x =417.6

Answer: 17%

Step-by-step explanation: 4/25=16/100=16%, so 17% is bigger.

Answer:

1 sample

Step-by-step explanation:

There is only one sample given for 20%

Answer:

the answer would be

b) 1 sample

Answer:

Step-by-step explanation:

K+4 = 11;

k = 7

Answer:

B is true

Step-by-step explanation:

so use k+4=11 to solve that k+7

Given:

Bl parallel to RA.

To find:

The value of x.

Solution:

In triangle ATR and ITB,

[tex]\angle ATR\cong \angle ITB[/tex]              [Common angles]

[tex]\angle ART\cong \angle IBT[/tex]              [Corresponding angle]

[tex]\triangle ATR\sim \triangle ITB[/tex]              [AA property of similarity]

We know that the corresponding sides of a similar triangle are proportional. So,

[tex]\dfrac{AT}{IT}=\dfrac{AR}{IB}[/tex]

[tex]\dfrac{x}{x+8}=\dfrac{12}{18}[/tex]

[tex]\dfrac{x}{x+8}=\dfrac{2}{3}[/tex]

On cross multiplication, we get

[tex]3(x)=2(x+8)[/tex]

[tex]3x=2x+16[/tex]

[tex]3x-2x=16[/tex]

[tex]x=16[/tex]

Therefore, the correct option is C.

Answer:

[tex]BC=12.8,\\AC=15.1[/tex]

Step-by-step explanation:

In right triangles only, the tangent of an angle is equal to its opposite side divided by its adjacent side.

Therefore, we have the following equation:

[tex]\tan 58^{\circ}=\frac{BC}{8}[/tex]

Solving, we get:

[tex]BC=8\tan 58^{\circ}\approx \boxed{12.8}[/tex]

Also in right triangles only, the cosine of an angle is equal to its adjacent side divided by the hypotenuse of the triangle.

[tex]\cos 58^{\circ}=\frac{8}{AC},\\AC=\frac{8}{\cos 58^{\circ}},\\AC\approx \boxed{15.1}[/tex]

We can also use the Pythagorean theorem now that we've found BC. However, if you choose to do so, make sure you don't use a rounded value for BC, as that could cause a notable deviation in your final answer.

Using the Pythagorean theorem to verify our answers:

[tex]8^2+(8\tan 58^{\circ})^2=\left(\frac{8}{\cos 58^{\circ}}\right)^2\:\checkmark[/tex]

Answer:

x=25, 120

Step-by-step explanation:

The two angles form a straight line so they add to 180

60 + 4x +20 =180

Combine like terms

4x+80 = 180

Subtract 80 from each side

4x+80-80 =180-80

4x= 100

Divide by 4

4x/4 =100/4

x= 25

The exterior angle is

4x+20 = 4*25+20 =100+20 =120

Answer:

x=25, 120

Step-by-step explanation:

The two angles form a straight line so they add to 180

60 + 4x +20 =180

Combine like terms

4x+80 = 180

Subtract 80 from each side

4x+80-80 =180-80

4x= 100

Divide by 4

4x/4 =100/4

x= 25

The exterior angle is

4x+20 = 4*25+20 =100+20 =120

- 8 / 20 = y / - 4

y = - 4 × - 8 / 20

y = 4 × 8 / 4 × 5

y = 8 / 5

Answer:

A translation 1 unit left and 2 units up

Step-by-step explanation:

1) look at the point at the very bottom-we can call that point A

2) that point on figure C would be at (3,-5)

3) if you move it to the left one and up two, you get that same point but on figure D

So, the answer is the second option

Answer:

arts: movement and flexibility  Music: communication and rhythm

Answer:

$120,000

Step-by-step explanation:

Given that

The price of the new car is $750,000

And, the saving percent is 16%

We need to find out the saving amount for the deposit

SO, the saving amount is

= $750,000 × 16%

= $120,000

We simply multiply these two to each other so that the saving amount could come

Step-by-step explanation:

[tex]A = x^2-xy+y^2\\C =x^4+x^2y^2+y^4[/tex]

We will now divide C with A.

[tex]\frac{x^4+x^2y^2+y^4}{x^2-xy+y^2}[/tex]

Divide x^2, -xy, y^2. Remember that dividing exponents results in subtracting.[tex]x^4 / x^2 = x^2\\4 - 2 = 2[/tex]

So:

[tex]\frac{1}{x^2+xy+y^2}[/tex]

Answer:

The dot plot shows that most planes fly below the optimal cruising speed. This means that the airline isn’t being as efficient as it can be. So, the manager needs to have a discussion with the pilots to determine why they aren’t reaching the optimal cruising speed or check the planes to make sure everything is running at full capacity.

Step-by-step explanation:

the answer that is given on edmentum

Answer:

Step-by-step explanation:

Answer:

You must find the diameter then half it, so the radius, and then multiply it by 3.14152

Step-by-step explanation:

Answer:

2 2/3 kilometers

Step-by-step explanation:

t = 3y

let t = 8

8 = 3y

Divide each side by 3

8/3 = 3y/3

8/3 = y

2 2/3 kilometers

Answer:

2 2/3 kilometers

Step-by-step explanation:

Answer:It's 1

Step-by-step explanation:

Step-by-step explanation:

3(3a+4b)+4(2a-5b)

=9a+12b+8a-20b

=17a-8b

Answer:

x = 9

Step-by-step explanation:

x + 3 = 12

subtracting both sides by 3

x + 3 - 3 = 12 - 3

x + 0 = 9

x = 9

Answer:

x = 9

Step-by-step explanation:

x + 3 = 12

x (+ 3 - 3) = 12 - 3

x = 9

Answer:

In summary, the translation and scale factor are:

Translation: (x,y)↦(x+5,y+4)

Scale factor: 2

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

3+7+2

12

12/3

4