All Answers 358187 Answers

You can adjust that yourself.

\(\frac{1}{12}{y}^{2}-3\)

is this an approximation?
it says simplify as an improper fraction.

OK Here is my best shot :D

There are 280 numbers contain the digit 7 between 0 and 999.

So 280/999

Here to help

:D

By the way, we cannot see google drive because we do not have permission

Please find another way to show us the imagine

Here to help

:D

The front side is a triangle:  A  =  ½·base·height  =  ½·20·21  =

The back side is identical to the front:  A  =

The base is a rectangle:  A  =  20 x 22  =

The slanted side is a rectangle:  A  =  22 x 29  = 

The left side is a rectangle:  A  =  21 x 22  =

You'll need to add these answers together ...

Yes.

Yes.

Yes.

For the function  f(n)  =  2 + 2(n + 1)  =  2 + 2n + 2  =  2n + 4

the oefficient of the variable is  2  and the constant is  4.

I can't draw on this site, or I'd label the diagram.  I'll try to explain it with words. 

The inside triangle is equilateral so all its angles are 60^o  

On the right of the diagram,

the angle of the outside triangle is supplemental to 60^o so it's 120^o  

On the left of the diagram,

the tangent is perpendicular to the radius,so the supplemental angle of the outside triangle is 90^o – 60^o = 30^o 

The sum of those two angles is 150^o.  All the angles of any triangle total 180^o so x is 180^o – 150^o = 30^o  

_.

Since it is an equilateral triangle, each of the interior angles is 60^o.

Look at the large triangle  -- from the center of the circle to the point of tangency to the exterior vertex.

The angle formed by the radius and the tangent is 90^o.

The angle at the center of the circle is 60^o.

Therefore, angle(x) is 30^o.

Using the distance formula:  D  =  sqrt[ (x₂ - x₁)² + (y₂ - y₁)² ]

A to B:  sqrt[ (2 - 0)² + (5 - 1)² ]  =  sqrt[ (2)² + (4)² ]  =  sqrt( 20 )  =  2sqrt(5)

B to C:  sqrt[ (5 - 2)² + (2 - 5)² ]  =  sqrt[ (3)²+ (-3)² ]  =  sqrt( 18 )  =  3sqrt(2)

C to D:  sqrt[ (7 - 5)² + (0 - 2)² ]  =  sqrt[ (2)² + (-2)² ]  =  sqrt( 8 )  =  2sqrt(2)

D to A:  sqrt[ (0 - 7)² + (1 - 0)² ]  =  sqrt[ (-7)² + (1)² ]  =  sqrt( 50 )  =  5sqrt(2)

Can you add these distances together?

The numbers are x, x+2, and x+4 

The equation is                   (x)(x+2) = 3 + (4)[(x+2)+(x+4)] 

                                            x² + 2x = 3 + (4)(2x+6)  

                                             x² + 2x = 3 + 8x + 24 

rearrange                            x² + 2x – 3 – 8x – 24 = 0 

                                            x² – 6x – 27 = 0 

factor                                   (x – 9)(x + 3) = 0 

                                             x = 9  and x =–3  but discard –3 because the problem calls for positive numbers 

                                             The numbers are 9, 11, and 13 

_.

Of course just being a verifier (LOL) 

Let  x,  x + 2,  and  x + 4  represent the three consecutive positive integers.

The product of the smaller two:  x(x + 2)

3 more than four times the sum of the larger two:  3 + 4[ (x + 2) + (x + 4) ]

       x(x + 2)  =  3 + 4[ (x + 2) + (x + 4) ]

        x² + 2x  =  3 + 4[ 2x + 6 ]

        x² + 2x  =  3 + 8x + 24

        x² + 2x  = 27 + 8x

  x² - 6x - 27  =  0

(x - 9)(x + 3)  =  0

x  =  9

x + 2  =  11

x + 4  =  13

Welcome, Mathisgood.....!!!!

Thanks CPhill!

I'm assuming that the slant height   = 10 ft

If so.......we have 4 congruent triangles....each with a base of 10   and a height of 10

Ther total area  = 4 (1/2) base * height  =   4  (1/2) (10) ( 10)  =  200 ft^2  = lateral surface area

Thx, Mathisgood   !!!

We both got the same answer.....always a good omen.......

At both ends we have two circles each with a radius of 4 in 

The area of these  =  2 * pi * 4^2   =   32 pi

The   lateral suface area  ( area of the "side" )   =  2 * pi * radius * height  =

2 * pi * 4 * 15   =  120 pi

Putting this all together the surface area  =  ( 32 + 120)  pi ≈   477.5 in^2 

The answer is 477.5 

Sorry about that. I thought the opposite was true, at least for my old eyes!.

Thx, Kennedy!!!

[ Not the best.....but I try hard     ....  ]