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ur wrong

vertex is (2, -7)

The only cube that has no red paint is the one in the middle of the cube. 

Since there are 27 cubes, (3 * 3 * 3), 27 - 1 = 26 cubes that have red paint. 

The question is just asking how many ways to order the kids. 

3! = 6

There are 6 ways. 

Only ONE will NOT have a red face    ...the one in the dead middle     so 26 WILL have a red face

2 out of (3+2)  are boys       2 out of  5    is   2/5 = 40 % are boys

The x coordinate of this dome shaped parabola's vertex will be given by   x = - b/2a      where b = 8     and   a = -  2     

      x = 2

use this value in the equation to calculate the y coordinate as   - 7

Notice that \((x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx\). You could multiply the second equation by 2 and then add the equations up:

\(x^2+y^2+z^2+2xy+2yz+2zx=9+6\cdot2\\(x+y+z)^2=21\)

Take the square root of both sides and you will arrive at the answer.

(notice that the negative square root is extraneous since x, y, and z are all nonnegative)

There is only one 00 year between the dates given   :    2000      

2000 / 900 = 2   remainder 200             so the answer is ONE

Here is a Venn Diagram of the description:     the students who took none will be:     n - (sum of all numbers)            (where n= 100)

Since  f(x)  is of a lesser  degree than  8,  it  must  be  that   g(x)   is of degree  8

"You have linear functions p(x) and q(x). You know p(2) = 3, and p(q(x)) = 4x + 18 for all x. Find q(1). "

"kx^2 - 70x + 2k = 0

Find the maximum integral value of k for which the above quadratic equation has two distinct real roots."

First find the value of k that gives exactly one root, then take the nearest integer saller than that.

To find the value of k that gives exactly one root, set the discriminant to zero.  In this case that is:

70^2 - 4*k*2*k = 0

I'll leave you to solve for k etc.

"integral of sin2x√(1-cosx) dx"

P, Q, R & S form the vertices of a quadrilateral.
∠PQR = 74° and ∠RSP = 121°.
Find the value of ∠SPQ.

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Trapezoid is a quadrilateral!!! 

If ∠PQR = 74° then ∠SPQ = 180 - 74

In the diagram, U = 30 degrees, arc XY is 170 degrees, and arc VW is 112 degrees. Find arc WY, in degrees.

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arc VX + arc WY = 360 - (170 + 112) = 78

30 = 1/2 [(78 - VX) - VX]            arc VX = 9º

Arc WY = 69º

 I'll be sure to keep an eye on this thread. Looking for the same issue. Bumped into your thread. Thanks for creating it. Looking forward for solution.
    

In triangle ABC, angle B = 90 degrees and angle C = 30 degrees. Point D is on line segment BC such that angle ADB = 45 degrees, and DC=10. What is AB?

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∠B = 90º        ∠C = 30º        ∠ADB = 45º        DC = 10

Let E be the point on BC so that DE ⊥ BC.

DE = 10(sin30)

EC = sqrt(10² - 5²)

Angle DBE = 15º

BE = DE / tan15º

AB / BC = DE / EC

AB = 15.77350269 

By Lagrange Interpolation Formula, p(7) = 49.

1356 leaves a remainder of 6 when divided by 27 (you can check using long division.

The problem reduces to: \(3n \equiv 6 (\text{mod 27})\). In other words, what is the smallest number that when multiplied by 3 is equal to 6?

DC = 10

BD = x

By 45 45 90 triangle side ratios, AB = x too. 

By 30 60 90 triangle side ratios, BC/AB = sqrt(3). 

(x+10)/x = sqrt(3)

x + 10 = xsqrt(3)

10 = x(sqrt(3) - 1)

10/(sqrt(3) - 1) = x

(10sqrt(3) + 10)/2 = x

5sqrt(3) + 5 = x

=^._.^=

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