hectictar

Note that area in question  =  area of △UYZ  +  area of trapezoid UYXW

m∠VUW + m∠WUY  =  90°

m∠ZUY + m∠WUY  =  90°

So

m∠VUW  =  m∠ZUY

By ASA congruence, △UVW is congruent to △UYZ.

area of △UVW  +  area of trapezoid UYXW  =  area of square UVXY  =  5 * 5  =  25 sq units

Since △UVW is congruent to △UYZ,

area of △UYZ  +  area of trapezoid UYXW  =  area of △UVW  +  area of trapezoid UYXW  =  25 sq units

We can convert  47  base 10 into base 5. This probably isn't the best way to do it but this is the easiest for me...

 _     _     _

25    5     1

how many 25's fit into 47? just 1.

 1     _     _

25    5     1

47 - 25  =  22  so there is 22 left.

how many 5's fit into 22? 4.

 1     4     _

25    5     1

22 - 20  =  2  so there is 2 left.

how many 1's fit into 2? 2.

 1     4     2

25    5     1

47 base 10  =  142 base 5

B = 4

\(\ \phantom{=}\,\dfrac{\frac{u+4}{25}-\frac{u+4}{5}}{\frac{4}{u+4}}\\~\\ =\,(\frac{u+4}{25}-\frac{u+4}{5})\div\frac{4}{u+4}\\~\\ =\,(\frac{u+4}{25}-\frac{u+4}{5})\cdot\frac{u+4}{4}\\~\\ =\,(\frac{u+4}{25}-\frac{u+4}{5}\cdot\frac55)\cdot\frac{u+4}{4}\\~\\ =\,(\frac{u+4}{25}-\frac{5(u+4)}{25})\cdot\frac{u+4}{4}\\~\\ =\,(\frac{1(u+4)-5(u+4)}{25})\cdot\frac{u+4}{4}\\~\\ =\,(\frac{-4(u+4)}{25})\cdot\frac{u+4}{4}\\~\\ =\,\frac{-4(u+4)(u+4)}{4(25)}\\~\\ =\,\frac{-(u+4)(u+4)}{25}\\~\\ =\,\frac{-(u+4)^2}{25} \)

The first one is incorrect. It's not right to use a semicolon to separate items in a series like that.

(a)

slope  =  2

y-intercept  =  15

(b)

The rate of change is 2 baskets per hour. In the equation,  x  is the number of hours, and  y  is the number of baskets. If you add 1 hour to x,  then 2 more is added to the number of baskets. In the equation, you can also see  x  as the number of  2's  that are being added to the number of baskets.

The initial amount is 15 baskets. If no time has passed, the number of hours is 0, and the number of baskets is 15 .

A circle is inscribed in a square with a side length of 9. What is the probability that a randomly chosen point lies in the square, but not in the circle? Express your answer as a percent rounded to the nearest tenth.

probability  =  target area / total area

probability  =  [area of square - area of circle] / [area of square]

probability  =  [ ( 9² )  -  ( pi(9/2)² ) ] / [ 9² ]

probability  =  [ 81 - pi(81/4) ] / 81

probability  =  1 - pi/4

probability  ≈  0.215

probability  ≈  21.5 / 100

probability  ≈  21.5 %

Thank you Melody and CPhill