What is 3÷11= A. 11/3 B. 3/11 C. 3/8 D. 8/3
2 answers:
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Answer:
Step-by-step explanation:
Since Quadrilateral ABCD ~ PQRS, therefore:
Let's find the value of x by using the ratio of two corresponding sides of both quadrilaterals. Let's use:
CD = 5
RS = 4.5
DA = 4
SP = x
Cross multiply
Divide both sides by 5
After 2 hours time , both Abe and Gabe to cost the same amount .
<u>Step-by-step explanation:</u>
Here we have , a car needs fixing and Abe can fix it for $70 per hour with a $60 part, but Gabe can fix it for $80 an hour with a $40 part. We need to find How long will it take for both Abe and Gabe to cost the same amount .Let's find out:
Let the time for which both Abe and Gabe to cost the same amount be x hours, so according to question scenario we will have equation as :
⇒
⇒
⇒
⇒
⇒
⇒
Therefore , After 2 hours time , both Abe and Gabe to cost the same amount .
Answer:
The nth term rule of the quadratic sequence is .
Step-by-step explanation:
We are given the following quadratic sequence below;
4, 15, 30, 49, 72, 99, 130,...
As we know that the formula for the nth term of the quadratic sequence is given by =
Firstly, we will find the difference between the term of the given sequence;
1st difference of the given sequence;
(2nd term - 1st term), (3rd term - 2nd term), (4th term - 3rd term), (5th term - 4th term), (6th term - 5th term), (7th term - 6th term)
= (15 - 4), (30 - 15), (49 - 30), (72 - 49), (99 - 72), (130 - 99),....
= (11, 15, 19, 23, 27, 31,.....)
Now, we will find the second difference of the given sequence, i.e;
= (15 - 11), (19 - 15), (23 - 19), (27 - 23), (31 - 27),....
= (4, 4, 4, 4, 4)
Since the differences are same now, so to find the value of a we have to divide the value of second difference by 2, i.e;
The value of a = = 2
SO, the first term of the nth term rule equation is =
.
Now, in the term , put the value of n = 1, 2, 3, 4 and 5 and then form the sequence, i.e;
If n = 1, then =
= 2
If n = 2, then =
= 8
If n = 3, then =
= 18
If n = 4, then =
= 32
If n = 5, then =
= 50
SO, the sequence formed is (2, 8, 18, 32, 50).
Now, find the difference of this sequence and the original quadratic sequence, i.e;
= (4 - 2), (15 - 8), (30 - 18), (49 - 32), (72 - 50)
= (2, 7, 12, 17, 22)
Now, as we can see that the above sequence resembles the general form of (5n - 3) because:
If we put n = 1, then (5n - 3) = 5 - 3 = 2
If we put n = 2, then (5n - 3) = 10 - 3 = 7 and so on....
From this, we concluded that the value of b and c are 5 and (-3) respectively.
Hence, the nth term rule for the given quadratic sequence is .