Problem solving real world 14. 13. jerome is making prizes for a game at the school fair. he has two bags of different candies, one with 15 pieces of candy and one with 20 pieces. every prize will have one kind of candy, the same number of pieces, and the greatest number of pieces possible. how many candies should be in each prize? 2 candies

There are 5 candies of first type and 4 candies of second type.

Step-by-step explanation:

Since we have given that

Number of pieces of candy of first type = 15

Number of pieces of candy of second type = 20

We need to find the greatest number of pieces possible.

So, Greatest number of pieces = H.C.F. of 15 and 20 = 5

So, there are 5 greatest number of pieces possible.

Number of candies of first type in this piece =

Number of candies of second type in this piece =

Hence, there are 5 candies of first type and 4 candies of second type.

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.