The formula for arithmetic sequence is given by:
an=a+(n-1)d
where:
an=nth term
a=first term
n=number of terms
thus our first term will be:
a1=8
a2=8+(2-1)(-6)=2
a3=8+(3-1)(-6)=-4
a4=8+(4-1)(-6)=-10
a5=8+(5-1)(-6)=-16
a5=-16
thus the sequence will be:
8,2,-4,-10,-16...
Answer:Teo's age = 7 years ,Richard's age = 19 years
Step-by-step explanation:
Step 1
Let Teo's age be represented as x
Such that Richard 's age = 5 + 2x
and their combined ages equaling 26 can be expressed as
x + 5+ 2x = 26
Step 2 --- SOLVING
x + 5+ 2x = 26
3x+ 5= 26
3x= 26-5
3x= 21
x = 21/3
x = 7
Teo's age = 7 years
Richard's age = 5+2x= 5 + 14= 19 years
Answer:
1) There are 13 students in Jerry's study.
2) There are 39 students in Kathy's study.
3) Jerry's study is more trustworthy!
Step-by-step explanation:
1) Jerry's study is the one with the dot plot.
Now, the number of students is calculated by adding the total number of dots in the plot.
We have a total of 13 dots.
Thus, there are 13 students in Jerry's study.
2) Kathy's study is the one with the histogram.
The total number of students is gotten by adding the corresponding number of students on the y-axis for each range of distance on the x-axis.
Total number of students = 9 + 11 + 7 + 12 = 39 students
3) Jerry's study where he used a dot plot is likely to be more trustworthy because it gives exact values of the number of students for each distance represented whereas, Kathy's study where she used a histogram doesn't give exact values but just gives a range of distances for a particular number of people.
Answer: See below
Explanation:
8x + 14 = 10x - 10 (alt. exterior angle)
8x - 10x = -10 - 14
-2x = -24
x = -24/-2
x = 12
Now plug x = 12 in 10x - 10 to find the angle:
10(12) - 10 = 120 - 10 = 110 degree
We have been given angle A as 75 degrees and sides a = 2 and b = 3.
Using Sine rule, we can set up:
Upon substituting the given values of angle A, and sides a and b, we get:
Upon solving this equation for B, we get:
Since we know that value of Sine cannot be more than 1. Hence there are no values possible for B.
Hence, the triangle is not possible. Therefore, first choice is correct.
