We have an arithmetic progression:
Nth=an
an=a₁+(n-1)d
a₁ is the first term.
n=number of terms.
d=common difference
10,17,24,31...
a₁=10
d=a₂-a₁=17-10=7
Therefore:
Nth=an
an=a₁+(n-1)d
an=10+(n-1)7
an=10+7n-7
an=7n+3.
Therefore: the formula for the nth is, an=a+(n-1), in this case; an=7n+3,
To check:
a₁=7*1+3=10
a₂=7*2+3=17
a₃=7*3+3=24
a₄=7*4+3=31
a₅=7*5+3=38.......
Answer:
There were 14 cartons of size 2 rackets and 24 cartons of size 3 rackets
Step-by-step explanation:
Assume that the number of cartons holding 2 rackets is x and the number of cartons holding 3 rackets is y
∵ There are x cartons of 2 rackets
∵ There are y cartons of 3 rackets
∵ They used 38 cartons
∴ x + y = 38 ⇒ (1)
∵ They packed a total of 100 rackets
∴ 2x + 3y = 100 ⇒ (2)
Let us solve the system of equations
→ Multiply equation (1) by -2 to make the coefficients of x in
the equations equal in values and different is signs
∵ -2(x) + -2(y) = -2(38)
∴ -2x - 2y = -76 ⇒ (3)
→ Add equations (2) and (3)
∴ y = 24
→ Substitute the value of y in equation (1) or (2) to find x
∵ x + 24 = 38
→ Subtract 24 from both sides
∴ x + 24 - 24 = 38 - 24
∴ x = 14
There were 14 cartons of size 2 rackets and 24 cartons of size 3 rackets
Answer:
Step-by-step explanation:
We are given that
Function f decreases from quadrant 2 to quadrant 1 and approaches y=0
It cut the y- axis at (0,6) and passing through the point (1,2).
Function g(x) approaches y=0 in quadrant 2 and increases into quadrant 1.
It passing through the point (-1,2) and cut the y-axis at point (0,6).
Reflection across y- axis:
Rule of transformation is given by
Using the rule then we get
By using
Substitute x=-1
Substitute x=0
Therefore, is true.
X + x + 1 + x + 2 + x + 3 = 330
4x + 6 = 330
4x = 324, x = 81
Smallest number: 81
Biggest number: 81 + 3 = 84
Sum: 81 + 84 = 165
The answer is 165
