In the above problem, you want to find the number of multiples of 7 between 30 and 300.
This is an Arithmetic progression where you have n number of terms between 30 and 300 that are multiples of 7. So it is evident that the common difference here is 7.
Arithmetic progression is a sequence of numbers where each new number in the sequence is generated by adding a constant value (in the above case, it is 7) to the preceding number, called the common difference (d)
In the above case, the first number after 30 that is a multiple of 7 is 35
So first number (a) = 35
The last number in the sequence less than 300 that is a multiple of 7 is 294
So, last number (l) = 294
Common difference (d) = 7
The formula to find the number of terms in the sequence (n) is,
n = ((l - a) ÷ d) + 1 = ((294 - 35) ÷ 7) + 1 = (259 ÷ 7) + 1 = 37 + 1 = 38
You could try dividing like example 54° ÷3
Answer:
The sequence is arithmetic with a common difference of -10
Step-by-step explanation:
From the question, we want to determine if the sequence is arithmetic or geometric
From the question
f(1) = 5
f(2) = -5
f(3) = -15
Mathematically for the common difference;
f(3) - f(2) = f(2) - f(1)
Since;
-15-(-5) = -5-5
-10 = -10
Since the common difference here is same , then the sequence is arithmetic with a common difference of -10
Answer:
Peter's company uses on:
Monday = 4 gallons
Tuesday = 4 gallons
Wednesday = 4 gallons
Thursday = 8 gallons
Step-by-step explanation:
If they made a total of 20 gallons over the course of these four days, how many gallons did they make each day? Monday
Let the gallons of paint used be Peter's company on Monday, Tuesday, and Wednesday since it is the same amount be represented by x
On Thursday, they made twice as many as any of the previous days.
= 2x
Hence:
x + x + x + 2x = 20 gallons
5x = 20 gallons
x = 20 gallons/5
x = 4 gallons
Note that:
Thursday = 2x
Hence, = 2 × 4 gallons = 8 gallons
Hence, Peter's company uses on:
Monday = 4 gallons
Tuesday = 4 gallons
Wednesday = 4 gallons
Thursday = 8 gallons
Answer:
63degrees
Step-by-step explanation:
Using the theorem which states that the measure of angle at the vertex is half the angle of its intercepted arc.
Given
angle of its intercepted arc = 126 degree
Required
angle at the vertex = x =<XYZ
According to the theorem;
x = 1/2(126)
x = 126/2
x = 63
Hence the measure of <XYZ is 63degrees
