Recall that A = 1/2bh.
We are given that h = 4+2b
So, putting it all together:
168 = 1/2 b(4+2b)
168 = 1/2(4b + 2b^2)
168 = 2b + b^2
b^2 + 2b - 168 = 0.
Something that multiplies to -168 and adds to 2? There's a trick to this.
Notice 13^2 = 169. So, it's more than likely in the middle of the two numbers we're trying to find. So let's try 12 and 14. Yep. 12 x 14 = 168. So this factors into (b+14)(b-12) So b = -14 or b =12. Is it possible to have a negative length on a base? No. So 12 must be our answer.
Let's check this. If 12 is our base, then according to our problem, 2*12 + 4 would be our height... or 28. so what is 12 * 28 /2?
196. Check.
Hope this helped!
The extraneous root is
x = 2
Let ticket be x and meal be y
So $0.50 for each movie ticket = 0.50x
$2 for each meal = 2y
He purchased 22 tickets, so x = 22
0.50 * 22 = $ 11
Now the total value is $25 (with both ticket and meal)
total = t
0.50x + 2y = t
you know x = 22 and t = 25
11 + 2y = 25
Part A)
2y = 25 -11
y = 14/2
y = 7
Number of meal is 7
Part B)
(don't know about part B)
0.50x + 2y = 25
0.50(22) + 2(7) = 25
11 + 14 = 25
25 = 25
8/15 or somthing like that it you might be souposed to solve it diferent than i did
Answer:
(a) ΔARS ≅ ΔAQT
Step-by-step explanation:
The theorem being used to show congruence is ASA. In one of the triangles, the angles are 1 and R, and the side between them is AR. The triangle containing those angles and that side is ΔARS.
In the other triangle, the angles are 3 and Q, and the side between them is AQ. The triangles containing those angles and that side is ΔAQT.
The desired congruence statement in Step 3 is ...
ΔARS ≅ ΔAQT
