Answer:
15
Step-by-step explanation:
Set the number of children to n.
The number of adults is, thus, n + 25.
The total price of admission is $720, made up of adult tickets and child tickets.
The children paid $8 per child, or
8 * n
The adults paid $15 per adult, or
15 * (n + 25)
These sum of these is equal to the total cost of $720.
8*n + 15*(n + 25) = 720
8n + 15(n + 25) = 720
Multiplying 15 with both n and 25.
8n + 15n + 25*15 = 720
8n + 15n + 375 = 720
Subtracting 375 from both sides.
8n + 15n + 375 - 375 = 720 - 375
8n + 15n = 345
Adding together 8n and 15n.
23n = 345
Dividing both sides by 23.
n = 345/23 = 15
n = 15
As n is the number of children, there are 15 children in the group.
Answer: 15
Well, the base and height would still be applicable (essentially, base is just width and height is just, uh, height,)
So basically the area of one triangle is 0.5(7*6), which is 21
The area of one triangle is option c., 21.
Answer:
5 cm
Step-by-step explanation:
If AB is tangent to the circle k(O), then radius OB is perpendicular to segment AB.
If BC is tangent to the circle k(O), then radius OC is perpendicular to segment AC.
Consider two right triangles ABO and ACO. In these triangles:
- AO is common hypotenuse;
- ∠OBA=∠OCA=90°, because AB⊥OB, AC⊥OC;
- OB=OC as radii of the circle k(O).
By HL theorem, triangles ABO and ACO are congruent. Then
- ∠OAB=∠OAC=30°;
- AC=AB=5 cm.
Hence, ∠BAC=∠OAB+∠OAC=30°+30°=60°.
Consider triangle ABC, this triangle is isosceles triangle. In isosceles triangles angles adjacent to the base are congruent, thus
∠CBA=∠BCA=1/2(180°-60°)=60°.
Therefore, triangle ABC is an equilateral triangle, so BC=AB=AC=5 cm.
Subtract 2 from 12. 12-2 is 10. You can subtract 10 with 4, and then add 2. (10-4)+2=8.
