Answer:
3.08 km/h.
Step-by-step explanation:
We know that,
Ali traveled at a speed of s km/h for 2.5 hours.
Let d be the distance and t be the time.
...(1)
On his return journey, he increased his speed by 4 km/h and saved 15 minutes. So, distance is d and times is t-15.
...(2)
From (1) and (2), we get
Put t=40 in (1).
So, t=40 and d=100.
Now,
Total distance = d + d = 100 + 100 = 200
Total time = t + t - 15 = 40 + 40 - 15 = 65
So, the average speed is
Therefore, the average speed is 3.08 km/h.
The student mixed the letters. If you swicth the order of the letters then the equation would be true. y=4x. So if you plug in all the numbers into the equation you get the correct value for why. For example 4×2=8, 4×4=16, and so on.
Hello!
![\large\boxed{(4, -150)}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%284%2C%20-150%29%7D)
We can solve for the vertex by completing the square. Begin by factoring out 6 from the equation to simplify the process:
6(x² - 8x) - 54 = 0
To complete the square, we must look at the first two terms (x² - 8x).
Remember that squaring a binomial uses the format a² + 2ab + b². We are already given a² and 2ab², so solve for b:
-8 / 2 = -4. This is the value of b.
We can rewrite this as:
(x - 4)²
However, this produces +16 which much be taken into account. Substitute (x - 4)² into the original equation:
6(x - 4)² - 54 = 0
Multiply 16 by the term in the front and subtract to cancel out this term:
6(x - 4)² - 54 - (6 · 16) = 0
Simplify:
6(x - 4)² - 150 = 0
In this form, the vertex is given as:
a(x - h)² + k, where h = x-coordinate and k = y-coordinate of the vertex.
In this instance, h = 4 and k = -150, so the coordinates of the vertex are:
(4, -150)
Answer:
see explanation
Step-by-step explanation:
Given the sequence
1, 3, 6, 10, 15
(a)
This is the sequence of triangular numbers.
After the first term the pattern is
+ 2, + 3, + 4, + 5, ............
(b)
Using this pattern then
a₆ = a₅ + 6 = 15 + 6 = 21
a₇ = a₆ + 7 = 21 + 7 = 28
a₈ = a₇ + 8 = 28 + 8 = 36
(c)
The n th term formula for triangular numbers is
=
n(n + 1)
(d)
Substitute n = 21 into the formula
a₂₁ =
× 21 × 22 = 21 × 11 = 231