amygdaleon305

Let Kelvin and Daniel have \(x\) paper clips at first. 

Now, no. of paper clips left - 

With Kelvin = \(x-17\)

With Daniel = \(x-5\)

According to question, 

\(x-5 = 5(x-17)\)

\(x-5 = 5x -85\)

\(4x = 80\)

\(x=20\)

∴ Daniel had 20 paper-clips at first. 

The points are A(-5,0), B(3,2), C(5,6), D(-3,4) and diagonals are BD and AC. 

Let midpoint of BD be (x,y).

⇒\(x = {3-3 \over 2}\)

   \(x = 0\)

⇒\(y = {2+4 \over 2}\)

    \(y = 3\)

∴ Midpoint of BC = (0,3)

Let midpoint of AD be (x',y')

⇒\(x' = {-5+5 \over 2}\)

   \(x' = 0\)

⇒\(y' = {0+6 \over 2}\)

    \(y' = 3\)

∴ Midpoint of AD = (0,3) 

Thus, diagonals AC and BD bisect each other.

Hence ABCD is a ||gm. 

Total no. of marbles = 3+3+4

                                = 10

P(green marble) = 4/10

                           = 2/5

So this is the question I suppose

Shaded area A - 48= shaded area B

Area of △GHI = 1/2 *10 * 24

                       = 120 cm² 

 

Total area of figure = Area△GHI + Shaded area B

                                     = 120 + Shaded area A - 48

                                     = Shaded area A + 72                                                    ...(1)

 

i.e. from figure, 

Total area of figure = Shaded area A + Area of rectangle EFGH                        ...(2)

 

From (1) and (2) we infer that 

Area of rectangle EFGH = 72 cm² 

 

⇒  72 = EH * HG 

⇒ 72 = EH * 24 

⇒ EH = 3 cm 

 

Perimeter of EFGH = 2( 3 + 24)

                                     = 2 x 27 

                                     = 54 cm 

Let the common ration be \(x\).

So no. of marbles

Kaden gave away = 2\(x\)

Adam gave = 4\(x\)

John gave = 9\(x\)

Now, no. of marbles

Kaden has = 2\(x\) + 2

Adam has = 2(2\(x\) + 2) 

                     = 4\(x\) + 4

John has = 2(4\(x\) + 4) 

                   = 8\(x\) + 8 

 

2\(x\) + 2 + 4\(x\) + 4 + 8\(x\) + 8 = 56

14\(x\) + 14 = 56

14\(x\) = 42

\(x\) = 3

 

Thus John gave away 9*3 = 27 marbles. 

(x² - k)(x + k) = x³ + k(x² - x - 5)

x³ - kx + kx² - k² = x³ + k(x² - x - 5)

x³ + k(x² - x - k) = x³ + k(x² - x - 5)

Comparing both sides, 

 k = 5

Thank you! 

Check this answer https://web2.0calc.com/questions/let-be-a-function-piecewise-defined-as-if-is-negative

value of a is -30.5.

Degree of polynomial is 6.

LMNP is a rectangle and, LN and MP are diagonals.

Since, diagonals of rectangle are equal, 

⇒ 6x + 6 = 9x - 3

⇒9x - 6x = 9 + 3

⇒3x        = 12

⇒x          = 4 

Thus, LN = 6*4 + 6

                = 30

and    MP = 9*4 - 3

                = 33