Let's call Maura's age now M and Cara's age now C.
We know Maura is five years younger than Cara. In symbols that is, M - 5 = C
We also know that 7 years ago Maura's age was half of Cara's. Maura's age 7 years ago was M-7 and Cara's age seven years ago was C-7. Since Maura's age (7 years ago) was half of Cara's we can write in symbols:

Let's take that last equation and substitute C - 5 for M (this is because according to our first equation these are equal). When we do this we get an equation with only C as the variable and solve for C as follows:







Cara is 17. Since Maura is 5 years younger she is 12.
As a check, seven years ago Cara was 10 and Maura was 5. It is the case that Maura was half Cara's age seven years ago.
Answer:
k = 5 and (6,2).
Step-by-step explanation:
Since (1,-1) is a solution of the equation 3x - ky = 8, so the point (1,-1) will satisfy the equation above.
Hence, putting x = 1 and y = -1 in the equation will give left-hand side = right-hand side.
So, 3(1) - k(-1) = 8
⇒ 3 + k = 8
⇒ k = 5 (Answer)
Therefore, the equation of the straight line is 3x - 5y = 8 ....... (1)
Now, putting x = 6 , then from equation (1) we get y = 2
Therefore, (6,2) is also a point on the graph of equation (1). (Answer)
Well the way I see it is he started with 4 villager so I would see the equation to be
1.13x times 17+4 would equal the amount of villagers he could have which would be 23.21 as for the equation it would be 1.13x times 17 plus four equals the number of villagers total
Answer:
4.5
miles
Step-by-step explanation:
Well, he runs
3
miles in
28
minutes. Also, see that
42
=
28
⋅
1.5
.
So, his journey would just be running
1.5
times, with each time running
28
minutes.
So, he runs a total of
1.5
⋅
3
=
4.5
miles
F = t ⇨ df = dt
dg = sec² 2t dt ⇨ g = (1/2) tan 2t
⇔
integral of t sec² 2t dt = (1/2) t tan 2t - (1/2) integral of tan 2t dt
u = 2t ⇨ du = 2 dt
As integral of tan u = - ln (cos (u)), you get :
integral of t sec² 2t dt = (1/4) ln (cos (u)) + (1/2) t tan 2t + constant
integral of t sec² 2t dt = (1/2) t tan 2t + (1/4) ln (cos (2t)) + constant
integral of t sec² 2t dt = (1/4) (2t tan 2t + ln (cos (2t))) + constant ⇦ answer