Given:
Admission to the local movie theater is $3 for each child and $7 for each adult.
A group of 12 people pay $64 admission.
To find:
The number of children in a group.
Solution:
Let the number of children be x and number of adults be y.
According to the question,
Total persons : ...(i)
Total cost : ...(ii)
Multiply equation (i) by 7 and subtract the result from (ii).
Divide both sides by -4.
Therefore, the number of children is 5.
Answer:
To prove that the triangle is a right- isosceles triangle, prove that
- There is a right angle in the triangle
- Two sides of the triangle are equal in length
Another way to prove that angle YXZ is a right angle is to calculate the length of XY, XZ and YZ using the distance formula. Then show that (YZ)² = (XY)² + (XZ)².
By the inverse of Pythagoras' Theorem, ∡YXZ is a right angle.
*The product of the gradients of 2 perpendicular lines= -1.
Please see the attached pictures for full solution.
