A bubble may be enclosed in a square whose side
length is equal to the bubble's diameter. Four bubbles
in squares collide and merge into one large bubble in
a square. The area of the large bubble is equal to the
sum of the areas of the small bubbles. How is the side
length of the large square related to the side length of
one small square?

Answer:

8x^2 + 18x - 35.

Step-by-step explanation:

Area = (4x - 5)(2x + 7)

= 8x^2 + 28x - 10x - 35

= 8x^2 + 18x - 35.

Answer:

1 .4x2-9= 2x+3,2x-3

2 .16x2-1=4x-1,4x+1

3 .16x2-4=4(2x+1)(2x-1)

4 .4x2-1=(2x+1)(2x-1)

Step-by-step explanation:

16x² − 1  = (4x − 1)(4x + 1) ;  16x² − 4  = 4(2x + 1)(2x − 1); 4x² − 1  = (2x + 1)(2x − 1) ;

4x² − 9 = (2x + 3)(2x − 3)

16x² − 1  is the difference of squares.  This is because 16x² is a perfect square, as is 1.  To find the factors of the difference of squares, take the square root of each square; one factor will be the sum of these and the other will be the difference.

The square root of 16x² is 4x and the square root of 1 is 1; this gives us (4x-1)(4x+1).

16x² − 4 is also the difference of squares.  The difference of 16x² is 4x and the square root of 4 is 2; this gives us (4x-2)(4x+2).  However, we can also factor a 2 out of each of these binomials; this gives us

2(2x-1)(2)(2x+1) = 2(2)(2x-1)(2x+1) = 4(2x-1)(2x+1)

4x² − 1  is also the difference of squares.  The square root of 4x² is 2x and the square root of 1 is 1; this gives us (2x-1)(2x+1).

4x² − 9 is also the difference of squares.  The square root of 4x² is 2x and the square root of 9 is 3; this gives us (2x-3)(2x+3).

Answer:

Have a great rest of your day :)

Step-by-step explanation:

Answer:

x^3-2x^2-5x+6

Step-by-step explanation:

Answer:

D. y= 2/3x-2

Step-by-step explanation:

y=6-2x/-3

-2+2/3x

2/3x-2=y

Answer:

The two numbers are 9 and 11

Answer:

148

Step-by-step explanation:

Answer:

1 Adult ticket=$35

1 Children ticket=$20

Step-by-step explanation:

21C+15A=945

6C+6A=330

we find adult tickets 1st

42C+30A=1890

42C+42A=2310

12A=420

A=35

we will find children ticket next

42c+30a=1890

30c+30a=1650

12c=240

C=20

Answer:

20%

Step-by-step explanation:

4+5+3 equals 12. in all, all of the frequencies combined is 30. because of that, it equals 20%. pls give brainliest

Step-by-step explanation:

Since there are 3 w's and a 1 on one side and 7 1's on the other and the hanger diagram shows they are even, we can set them equal to each other.

3w + 1 = 7 Subtract 1 from both sides

3w = 6 Divide 3 from both sides

w = 2

Answer:

B

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

the 2 triangles are proportionately identical.

the larger one is 1/3 larger, so x would be 9 plus 1/3 of 9- 12

Answer:

3

Step-by-step explanation:

ill reply to this gimmie a moment

Answer:

(-∞, 3] or x[tex]\leq[/tex]3

Step-by-step explanation:[tex]inf[/tex]

we treat it like a normal linear problem.

We can add 3 on both sides to get:

-10w[tex]\leq[/tex]-30

we can divide both sides by -10 to get...

w[tex]\leq[/tex]3

Or if nessessary, the interval notation is (-∞, 3]

Hope this helped!

Answer:

43

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Find the vertex

¼(x-5) = (y-2)²

x-5 = 4(y-2)²

x = 4(y-2)² + 5

This is a right-opening parabola with vertex (5,2).

focal length p = 1/(4·coefficient of y²) = 0.0625

directrix: x = 5-p = 4.9375

D

The equation of directrix of the parabola will be x = 4, i.e. Option A.

Directrix is a straight line distance to which from any point of a conic section is in fixed ratio to the distance from the same point to a focus. The directrix is perpendicular to the axis of symmetry and does not touch the parabola.

We have,

[tex]\frac{1}{4} (x - 5) = (y - 2)^2[/tex]

Now,

Rewrite as,

[tex](x - 5) = 4(y - 2)^2[/tex]

Now,

[tex]x= 4(y - 2)^2+5[/tex]

Now,

Comparing it with the vertex form,

i.e.

[tex]x = a ( y - h )^ 2 + k[/tex]

Vertex of parabola = (2, 5),

So,

Focus at (a, 0),

So,

Focus of the parabola = (4, 0),

i.e., a = 4

Now,

The Equation of directrix is given by x = a

So,

The equation of the directrix of this parabola,

x - a = 0,

i.e.

x - 4 = 0

⇒

x = 4

Hence, we can say that the equation of directrix of the parabola will be x = 4, i.e. Option A.

To know more about directrix click here

https://brainly.com/question/4333610

#SPJ2

Answer:

i think

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

The total number is 12 (assuming the dice would be rolled 12 times) 7 is a number in the range and it will appear once in the 12 rolls because each number shows each time. 1 (how many times 7 will show)/ 12(total number of rolls)

Probability of [tex]7[/tex] when a dice (showing numbers 1 throught 7) is thrown is equal to [tex]\boldsymbol{\frac{7}{12}}[/tex] as a dice is rolled.

Probability refers to chances of occurrence of any event.

Value of probability lies in the interval [tex]\boldsymbol{\left [ 0,1 \right ]}[/tex]

Total number of numbers on a dice [tex]=12[/tex]

Probability is equal to number of favorable outcomes divided by the total number of outcomes.

Probability of [tex]7=\frac{7}{12}[/tex]

Find out more information about probability here:

https://brainly.com/question/11234923?referrer=searchResults

Answer:

30 ft^2

Step-by-step explanation:

Break the figure into smaller pieces:

5*2=10

10*2=20

Add the areas

20+10=30

The are of the figure is 30 ft^2

Answer:

A's coordinates are:

A. (-4, 3)

Step-by-step explanation:

Because the x  always goes first,

So that will mean -4 will go first.

After you have -4 down, you will see that A's point on the graph is (-4, ?)

To answer the ?, you will have to check the y.

Because remember, The x-coordinate always comes first, followed by the y-coordinate.

So, it will be (-4, 3)

and 3 will be the fill in for y.

I hope this helps     :)

Answer:

41/91

Step-by-step explanation:

edggggge

Answer:

Step-by-step explanation:

Where are the graphs?

Answer:

2

There is a picture the website is Math-way I use it all the time to help out or just to check my answers.

Answer:

i was abt to answer but too late prolly

Step-by-step explanation:

if u still wanna know,

Answer:

23

Step-by-step explanation:

20+3=23

Answer:

[tex] 11.25\: {in}^{3} [/tex]

Step-by-step explanation:

Since, box contains two layers of cubes and each layer has 15 cubes.

So, length = 15*1/2 in = 7.5 in,

width = 3*1/2 in = 1.5 in

height = (1/2 + 1/2) = 1 inch

Volume of box = lbh

= 7.5* 1.5 *1

= 11.25 cubic inches

Answer:

Da^^ good luck that looks hard

Step-by-step explanation:

Answer:

√{395×395}=√395²=395 is your answer

Answer:

Answer:

The graph shows a relation and a function

Step-by-step explanation:

Because there is one value of y for every value of x, this is a relation and a function.

Answer:

relation because the x does not repeat