Answer:
x = 6
Step-by-step explanation:
The angle bisector divides the triangle sides proportionally:
(6x -1)/42 = (10x +5)/78
13(6x -1) = 7(10x +5) . . . . multiply by 546 (the LCM of 42 and 78)
78x -13 = 70x +35 . . . . . eliminate parentheses
8x = 48 . . . . . . . . . . . . . . add 13-70x
x = 6 . . . . . . . . . . . divide by 8
_____
<em>Additional comment</em>
The unknown segment lengths are ...
6·6 -1 = 35
10·6 +5 = 65
Then the ratios to the known sides are ...
35/42 = 65/78 = 5/6
I don’t know this but it’ll probably be the second one
Answer:
He add $5 more each month
Step-by-step explanation:
* Lets consider this problem as an arithmetic sequence because
he add every month x dollars more
∵ He start with 50 dollars ⇒ a (1st amount)
∵ He add x dollars every month ⇒ d
∵ He did that for 36 months ⇒ n
∵ He saved 4950 dollars ⇒ Sn
∵ Sn = n/2[2a + (n - 1)d]
* Where Sn is the total money after <em>n</em> months
<em>a</em> is the first amount he saved
<em>d</em> is the money he add more each month
∴ 4950 = 36/2[2(50) + (36 - 1)(x)]
∴ 4950 = 18[100 + 35x]
∴ 4950/18 = 100 + 35x
∴ 35x = 275 - 100 = 175
∴ x = 175/35 = 5 dollars
Answer:
47.91 units²
Step-by-step explanation:
This can be solved using Heron's triangle (see attached)
in this case, your lengths are
a = 3+9=12
b=3+5=8
c=5+9=14
Hence,.
S = (1/2) x (a + b + c) = (1/2) (12+8+14) = 17
(s - a) = 17 -12 = 5
(s - b) = 9
(s - c) = 3
Area = √ [ s (s-a) (s-b) (s-c) ]
= √ [ 17 x 5 x 9 x 3 ] = √2295 = 47.9061 = 47.91 units² (rounded to nearest hundreth)
Answer:
4 : 12 : 15
Step-by-step explanation:
S : J = 1 : 3
J : P= 4 : 5
Using John's ratio to find a common ratio for all
S : J
(1 : 3)4 = 4 : 12
J : P
(4 : 5)3 = 12 : 15
Therefore our ratio is
S : J : P
4 : 12 : 15