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110  112  113  114  115  116  117  118  119  220  221  223  224  225  226  227  228  229  330  331  332  334  335  336  337  338  339  440  441  442  443  445  446  447  448  449  550  551  552  553  554  556  557  558  559  660  661  662  663  664  665  667  668  669  770  771  772  773  774  775  776  778  779  880  881  882  883  884  885  886  887  889  990  991  992  993  994  995  996  997  998  Total =  81 such numbers

Web calc isn't working for me at the moment.

I'm sorry, it seems that I cannot write the rest of the question...

\(x^2+2x-99=\boxed{(x-9)(x+11)}\)

If you click on the link, you will see the question.

From the given information, r_4/r_1 = 1 + 2 + 3 + 4 = 10.

I don't know how to get the image but I can type it for you so you can copy and paste it into google translate:

A bricklayer needs to order 6300 kg of build sand.

a) Write 6300 kg in grams, giving your answer in standard form.

One grain of this sand approximately weighs 7 x 10^-5 g.

b) How many grains of sand are there in 6300kg of sand?

Give your answer in standard form.

Hope this helps! :)

4,5,6,7 because it has to be greater than 3 and less than 8

See geno3141's splendid solution here!

https://web2.0calc.com/questions/this-is-very-confuzzling

This is easy!  Start by letting r be an integer root of P(x).

By similar triangles, DE = 67/2.

Let w = a + bi and z = c + di.  Then

\(\dfrac{w + z}{1 + wz} = \dfrac{a + c + bi + di}{1 + (a + bi)(c + di)}\)

To express this in rectangular form, we can multiply the numerator and denominator by the conjugate:

\(\dfrac{a + c + bi + di}{1 + (a + bi)(c + di)} = \dfrac{(a + c + bi + di)((1 - (a + bi)(c + di))}{(1 + (a + bi)(c + di))(1 - (a + bi)(c + di))}\)

The denominator simplifies to (1 - (a^2 + b^2)(c^2 + d^2)), which is real.  The numerator simplifies to a^2 - b^2 + c^2 - d^2, which is also real.  Therefore, the complex number (w + z)/(1 + wz) is real.

Acute isosceles triangle.
Sides: a = 17 b = 17 c = 16

Area: T = 120
Perimeter: p = 50
Semiperimeter: s = 25
Circumradius

The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. Circumcenter (center of circumcircle) is the point where the perpendicular bisectors of a triangle intersect.

Inradius (r) =Area / Semiperimeter
               r  =120 / 25 =4.8
Circuradius(R) =[17 * 17 * 16] / [4 * 4.8 *25]
                    R = 9.63

Pretty sure this has already been asked before. Maybe go look in all questions? It was on there yesterday I think.

An advantage of James Watt's engine was that:

A.) factory pollution was eliminated.

B. people could work from their homes.

C. factories no longer had to be built near rivers.    Steam engine powered!

D. wider fabrics could be woven at a faster pace.

  !

1/n sinx=?

It is much easier to find the "combinations" first and then calculate the permutations from those combinations:

There are:  {1, 1, 1, 2}, {1, 1, 1, 3}, {1, 1, 1, 4}, {1, 1, 1, 5}, {1, 1, 2, 2}, {1, 1, 2, 3}, {1, 1, 2, 4}, {1, 1, 2, 5}, {1, 1, 3, 4}, {1, 1, 3, 5}, {1, 1, 4, 5}, {1, 2, 2, 3}, {1, 2, 2, 4}, {1, 2, 2, 5}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {1, 3, 4, 5}, {2, 2, 3, 4}, {2, 2, 3, 5}, {2, 2, 4, 5}, {2, 3, 4, 5} = 22 combinations.

Four of them have =4!/3!  x  4       =16 permutations

One of them has    =4!/2!2!            =6 p

Twelve of them have =4!/2!  x 12  =144 p

Five of them have      =4!  x  5       =120 p

So: 16  +  6  + 144  + 120 =286 permutations.

The first sequence sums up to =3/2
The second sequence sums up to =3/4

3/2 x 3/4 = 9/8

These are closed form formulas to sum up the two sequences:

(1 + 1/3 + 1/9 + 1/27 + ...) = sum_(n=1)^∞ 3^(1 - n) = 3/2
(1 - 1/3 + 1/9 - 1/27 + ...) = sum_(n=1)^∞ (-1)^(1 + n) 3^(1 - n) = 3/4

The RHS of  1 + 1/x + 1/x^2 + 1/x^3 + 1/x^4 +.... = x /(x - 1)

Solve for x:
x/(x - 1) = 9/8

Multiply both sides by a polynomial to clear fractions.
Cross multiply:
8 x = 9 (x - 1)

Write the linear polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
8 x = 9 x - 9

Isolate x to the left hand side.
Subtract 9 x from both sides:
-x = -9

Solve for x.
Multiply both sides by -1:

x = 9

Pls note the h at the end is a typo thanks