Answer:

Step-by-step explanation:
The nth term of an arithmetic sequence is given by the formula,

We were given that the 9th term is
.





The sum of the first n-terms is given by the formula,

To find
, we substitute
,
and
.





The correct answer is D
The length of the KN is 4.4
Step-by-step explanation:
We know from Pythagoras theorem
In a right angle ΔLMN
Base² + perpendicular² = hypotenuse
²
From the properties of triangle we also know that altitudes are ⊥ on the sides they fall.
Hence ∠LKM = ∠NKM = 90
°
Given values-
LM=12
LK=10
Let KN be “s”
⇒LN= LK + KN
⇒LN= 10+x eq 1
Coming to the Δ LKM
⇒LK²+MK²= LM²
⇒MK²= 12²-10²
⇒MK²= 44 eq 2
Now in Δ MKN
⇒MK²+ KN²= MN²
⇒44+s²= MN² eq 3
In Δ LMN
⇒LM²+MN²= LN²
Using the values of MN² and LN² from the previous equations
⇒12² + 44+s²= (10+s)
²
⇒144+44+s²= 100+s²+20s
⇒188+s²= 100+s²+20s cancelling the common term “s²”
⇒20s= 188-100
∴ s= 4.4
Hence the value of KN is 4.4
The equation we can use is
3 + 1/4c = 9
To find the total number of pieces, we would just solve the equation.
3 + 1/4c = 9
3 - 3 +1/4c = 9 - 3
1/4c = 6
inverse of division is multiputcation
4/1 *1/4c = 6*4
c = 24
There were 24 pieces of cake in total.
Answer:
g(x) = -|x|
Step-by-step explanation:
Are you familiar with the absolute value function y = |x|?
Its graph is v-shaped and opens up.
If the graph is turned upside down (so that it opens down), then g(x) = -|x|.
Answer:
D) 6
Step-by-step explanation:
set Q has 16 values which are all even values from 4 to 36
set Z has 11 values that are multiples of 3 from 4 to 36 (6,9,12,15,etc.) however, we have to eliminate the odd ones, leaving the following six:
6, 12, 18, 24, 30, 36