Show that the 9x^2-24xy+16y^2-12x+16y-12=0 represents a pair of parallel lines .Find the distance between the lines.

Hey there! I'm happy to help!

To find the surface area of a sphere, here is what you do.

You square the radius.

4²=16

You multiply by 4.

16×4=64

And you multiply by pi!

64×π=64π

Therefore, the surface area of the sphere is A. 64π units². It's that easy!

Now you can find the surface area of a sphere! Have a wonderful day! :D

Question :-

Answer :-

[tex] \rule{180pt}{3pt}[/tex]

Diagram :-

[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{4 \: units}}\end{picture}[/tex]

Solution :-

As per the provided information in the given question, we have been given that the radius of the sphere is 4 units. We have been asked to find or calculate the surface area of the sphere.

To calculate the surface area of the sphere, we will use the formula below :-

[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]

Substitute the given values into the above formula and solve for surface area:

[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4 \times \pi \times (4 \: units)^2[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4 \: units)^2 \times 4 \times \pi[/tex]

[tex]\sf:\implies Surface \: Area_{(Sphere)} = 16 \: units^2 \times 4 \times \pi[/tex]

[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 64\pi \: units^2}[/tex]

Therefore :-

[tex]\\[/tex]

Learn more about the surface area of the sphere at https://brainly.com/question/28988747

Have a great day! <33

Answer:

Below

Step-by-step explanation:

For a given shape to be a rhombus, it should satisfy these conditions:

● The diagonals should intercept each others in the midpoint.

● The diagonals should be perpendicular.

● The sides should have the same length.

We will prove the conditions one by one.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's prove that the diagonals are perpendicular:

To do that we will write express them as vectors

The two vectors are EG and DF.

The coordinates of the four points are:

● E(0,2c)

● G (0,0)

● F (a+b, c)

● D (-a-b, c)

Now the coordinates of the vectors:

● EG (0-0,0-2c) => EG(0,-2c)

● DF ( a+b-(-a-b),c-c) => DF (2a+2b,0)

For the diagonals to be perpendicular the scalar product of EG and DF should be null.

● EG.DF = 0*(2a+2b)+(-2c)*0 = 0

So the diagonals are perpendicular.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's prove that the diagonals intercept each others at the midpoints.

The diagonals EG and DF should have the same midpoint.

● The midpoint of EG:

We can figure it out without calculations. Since G is located at (0,0) and E at (0,2c) then the distance between E and G is 2c.

Then the midpoint is located at (0,c)

● The midpoint of DF:

We will use the midpoint formula.

The coordinates of the two points are:

● F (a+b,c)

● D(-a-b,c)

Let M be the midpoint of DF

●M( (a+b-a-b,c+c)

● M (0,2c)

So EG and DF have the same midpoint.

■■■■■■■■■■■■■■■■■■■■■■■■■■

There is no need to prove the last condition, since the two above guarante it.

But we can prove it using the pythagorian theorem.

Answer:

y = 5

Step-by-step explanation:

−x+y=0   −2x+y=−5

Multiply the first equation by -2

-2(-x+y=0)

2x-2y =0

Add this to the second equation

 2x-2y =0

−2x+y=−5

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

0x -y = -5

-y =-5

Multiply by -1

y = 5

Answer:

11, 71, 19, 67, 43.

Step-by-step explanation:

Answer:

( 0,0) is the x intercept

Step-by-step explanation:

y = (2x)/(x-1),

To find the x intercept set y = 0 and solve for x

0 =  (2x)/(x-1)

Multiply by x-1 on each side assuming x does not equal 1

0 = 2x

x = 0

The x intercept is 0

( 0,0) is the x intercept

Answer:

uhfcytuyyytt ryffffffffgtgghhh

Answer:

8

Step-by-step explanation:

Because if x=7 then it would be 7-5 which equals 2 then you would times 2 and 4 together which equals 8 then you would have your answer which is 8.

Answer:

its 8

Step-by-step explanation:

x= 7

so replace the x with the value of 7

4(7-5)

7 minus 5 is 2

4·2

4 multipied by 2 is 8

so the answer is 8

The answer is 200 cm³

The volume of the rectangular prism (V1) is:

V1 = l · w · h                       (l - length,  w - width,  h - height)

It is given:

h = 12 cm

w = l = 5 cm (since it has a square base which all sides are the same size).

Thus: V1 = 12 · 5 · 5 = 300 cm³

The volume of pyramid (V2) is:

V2 = 1/3 · l · w · h                   (l - length,  w - width,  h - height)

It is given:

h = 12 cm

w = l = 5 cm (since it has a square base which all sides are the same size).

V2 = 1/3 · 12 · 5 · 5 = 1/3 · 300 = 100 cm³

The volume of the space outside the pyramid but inside the prism (V) is a difference between the volume of the rectangular prism (V1) and the volume of the pyramid (V2):  

V = V1 - V2 = 300 cm³ - 100 cm³ = 200 cm³

Answer:

4 I guess

Step-by-step explanation:

Because

3-1=2

2^2=2*2=4

Answer:

18w+8

Step-by-step explanation:

[tex]2(4 + 9w) \\ = 2(4) + 2(9w) \\ 8 + 18w \\ = 18w + 8[/tex]

Answer:

8+18w [tex]\huge\checkmark[/tex]

Step-by-step explanation:

Hi! Hope you are having an amazing day! :)

Distribute 2 by multiplying everything inside the parentheses by 2:

[tex]\huge\mathrm{2(4+9w)}[/tex]

[tex]\huge\mathrm{8+18w}[/tex] (Answer)

Hope you find it helpful.

Feel free to ask if you have any doubts.

[tex]\bf{-MistySparkles^**^*}\star[/tex]

Answer:

37x - 13

Step-by-step explanation:

Hello!

The product of 37 and x mean multiply so we can write it as

37x

13 less means subtract so we put that at the end

37x - 13

The answer is 37x - 13

Hope this helps!

Answer:

37 * x - 13

This answer is here according to your question It said that 37*x - 13 Please mark this answer The brainliest one

Answer:

x = - 2, y = - 8

Step-by-step explanation:

Given the 2 equations

13x - 6y = 22 → (1)

x = y + 6 → (2)

Substitute x = y + 6 into (1)

13(y + 6) - 6y = 22 ← distribute and simplify left side

13y + 78 - 6y = 22

7y + 78 = 22 ( subtract 78 from both sides )

7y = - 56 ( divide both sides by 7 )

y = - 8

Substitute y = - 8 into (2) and evaluate for x

x = - 8 + 6 = - 2

Thus x = - 2, y = - 8

Answer:

as ratio of two type of fabric is different .

hence, the relationship between the number of square yards and the cost

is not proportional between the two types of fabric

Step-by-step explanation:

For a relation to be proportional

a:b = c:d

in other form

a/b = c/d

______________________________________________

Ratio for first type of fabric

cost of fabric/ area of fabric = 31.25/5 = 6.25

Ratio for other type of fabric

cost of fabric/ area of fabric = 71.50/11 = 6.5

as ratio of two type of fabric is different .

hence, the relationship between the number of square yards and the cost

is not proportional between the two types of fabric

Answer:

Hey there!

A simple way to think about slope is rise over run. Between any two points on this line, the rise is 3, and the run is -1.

3/-1=-3, so  the slope is -3.

Let me know if this helps :)

Answer:

45% that either would occur, or a 5% chance both would occur.

Step-by-step explanation:

There is one overlap, 15, so it must be subtracted from one of the number lists.

3 6 9 12 15 18

5 10 15 20

6/20 + 3/20 = 9/20 = 0.45 = 45%

15 is the ONLY overlap number, so 1/20 times both would occur.

1/20 = 0.05 = 5%

Answer:

The '=' sign.

Step-by-step explanation:

The equals sign ( = ). for example:

3x + 1 = 8.

The  equals sign was invented by Robert Recorde of Tenby, South Wales, UK in the early part of the 16th century.

Answer:

The correct option is;

3 + (-9) = -6, because -6 is 9 units to the left of 3

Step-by-step explanation:

The given information are;

Kelvin's score after the first round is shown at point K on the number line

The range of numbers on the number line = -10 to +10

The position of point K after the first round = +3

The number of points Kevin lost in the second round = 9 points

Therefore, Kevin's cumulative score = +3 - 9 = -6

Therefore, the expression that shows how many total points he has at the end is of round 2 = 3 + (-9) = -6, because -6 is 9 units to the left of 3.

Answer:

B. (6,-2)

Step-by-step explanation:

The equation of a circle is (x-h)^2+(y-k)^2=r^2

The center of the circle is (h,k)

So, in this problem, h is 6 and k is -2, so the center of this circle is (6,-2).

Answer: The number of sets contain any 4 numbers = 210

Step-by-step explanation:

Given: Universal set = {0,1,2,3,4,5,6,7,8,9}.

i.e. Total choices = Numbers in set = 10

By combinations, the number of sets contain any 4 numbers =[tex]^{10}C_4[/tex]

[tex]=\dfrac{10!}{4!6!}\ \ \ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{10\times9\times8\times7\times6!}{4\times3\times2\times1 \times6!}\\\\=210[/tex]

Hence, the number of sets contain any 4 numbers = 210

Answer as an inequality:  [tex]x > 0[/tex]

Answer in interval notation:  [tex](0, \infty)[/tex]

Answer in words: Set of positive real numbers

All three represent the same idea, but in different forms.

======================================================

Explanation:

Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is [tex]f^{-1}(x) = \log_b(x)[/tex]

For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.

Because of this, [tex]\log_b(x)[/tex] has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.

The domain of [tex]\log_b(x)[/tex] is x > 0 which in interval notation would be [tex](0, \infty)[/tex]. This is the interval from 0 to infinity, excluding both endpoints.

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

The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.

So,

[tex]\log_e(x) = \text{Ln}(x)[/tex]

allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.

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

In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.

Answer:

x = -2

Step-by-step explanation:

-14 = x - 12

-14 + 12 = x

-2 = x

check:

-14 = -2 - 12

Answer:

The points for this will be:

A: (1, -4)

B: (-4, -2)

C: (-5, 4)

D: (-2, 1)

Step-by-step explanation:

If we reflect a shape over the x-axis, all of it’s points y values will be negated.

So, (1, 4) becomes (1, -4)

(-4, 2) becomes (-4, -2)

(-5, -4) becomes (-5, 4)

and (-2, -1) becomes (-2, 1)

Hope this helped!

New coordinates of the quadrilateral are A' is (1, -4), B' is (-4, -2), C' is (-5, 4) and D' is (-2, 1)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The coordinates of quadrilateral ABCD are A is (1, 4), B is (-4, 2), C is (-5, -4) and D is (-2, -1)

After reflecting across the x-axis , the x-coordinates of the vertices will remain the same, but the signs of their y-coordinates will change.

Therefore, the new coordinates of the vertices will be:

A' is (1, -4)

B' is (-4, -2)

C' is (-5, 4)

D' is (-2, 1)

Hence,  new coordinates of the quadrilateral are A' is (1, -4), B' is (-4, -2), C' is (-5, 4) and D' is (-2, 1)

To learn more on Graph click:

https://brainly.com/question/17267403

#SPJ3

Answer:

x = 3

Step-by-step explanation:

j(x) = 4/5(-5) + 7

= -4 + 7

= 3

Answer:

15

Step-by-step explanation: -4/5 x has to be -12 because -12+7 equals 5. Since we want to figure out x, we have to flip -4/5 x to 4/5x which would change the -12 to 12. What is a fourth of 12? It is three. 12+3 equals 15. This is the first right answer on all of the internet for this question!

Answer:

What we need to do is simply multiply the values in both columns e.g 4 * 3/36 = 12/36

Please check explanation for complete answer

Step-by-step explanation:

Here, we are concerned about filling the empty columns of the table.

What we want to do here is simply straightforward. All we need to do is to

multiply the values of x by the values of P(x) in each of the individual rows.

Also recall, we do not need to reduce the fractions.

So we have;

2. 3 * 2/36 = 6/36

3. 4 * 3/36 = 12/36

4. 5 * 4/36 = 20/36

5. 6 * 5/36 = 30/36

6. 7 * 6/36 = 42/36

7. 8 * 5/36 = 40/36

8. 9 * 4/36 = 36/36

9. 10 * 3/36 = 30/36

10. 11 * 2/36 = 22/36

11. 12 * 1/36 = 12/36

Answer:

Step-by-step explanation:

  We already establish an understand  that, for Brooke to graduate she needs nothing less than 132 credit hours.

Now a semester has 15 credit hours, she has 4 semester completed already.

Hence 15*4= 60 credit hours done and dusted

This means that she has 132-60 = 72 credit hours to go

Since "c" is the number of credit hours that Brooke needs to complete in order to graduate college.

The inequality can be modeled as,

60 + c > 132

c= 132-60

c= 72

Step-by-step explanation:

If a line segment AB of length 6.6cm is drawn, bisecting it perpendicularly at N, we have two lines AN and NB of length 3.3cm each.

Because the line is bisected perpendicularly, the angles formed at the point of bisection are 90 degrees.

Answer:

linear equation to express the price is:

y=0.72x+0.21

An eight quarts will cost :  $5.97

Step-by-step explanation:

linear equation represent y=mx+b

let x=quarts ( x=4, x=2)

y= price (3.09 and y=1.65 )

two points (4,3.09) and (2,1.65)

need to find the slope m:

y2-y1/x2-x1

(1.65-3.09)/(2-4) ⇒ m=0.72

y=0.72x+b  find b at point (2,1.65)

1.65=0.72(2) +b  ⇒ b=0.21

y=0.72x +0.21

check : point (4,3.09)

y=0.72(4) +0.21

y=3.09  ( correct)

An eight quarts will cost :

y=0.72(8)+0.21

y=5.97 dollars

Answer:

The steps to construct a a line parallel to another line from a point includes

1) From the given line draw a transversal through the point

2) With the compass, copy the angle formed between the transversal and the given line to the point P

3) Draw a line through the intersection of the arcs of the angle construction to get the parallel line through the point P

Step-by-step explanation:

Answer:

The length of the steel frame will be approximately 44 feet

Step-by-step explanation:

We can solve this problem by calculating the circumference of the steel frame. We are working with the fact that the steel frame was welded into a circular shape.

The circumference of the steel frame can be calculated using

[tex]circumference = \pi \times d[/tex]

where d diameter of the steel frame = 14 feet

[tex]circumference = 3.14 \times 14=43.96ft[/tex]

Therefore, the length of the steel frame will be approximately 44 feet

Answer:

12

Step-by-step explanation:

1 inch = 20 miles

240 miles ÷ 20 miles =

12 inches

Answer:

12 inches

Step-by-step explanation:

Hey there!

Well to solve the given question we need to use fractions,

if 1 inch is 20 milles, we can set up the following.

[tex]\frac{1}{20} = \frac{x}{240}[/tex]

Cross multiply

240 = 20x

Divide both sides by 20

x = 12

So it is 12 inches in the map.

Hope this helps :)