Explanation: In my notes you’ll see the formula for how to find slope under “Formulas”.
How to use this formula: In the first graph you have points (2,3) and (6,8)
So y2 would be 8, and y1 would be 3.
x2 would be 6, and x1 would be 2.
1. Sub points into formula
2. subtract y2 by y1
3. Subtract x2 by x1
4. Divide top by bottom
And you’ve got your slope! (Rise/run)
If you need further clarification, feel free to ask me in the comments. Hope this helps :)
Answer:
7.1%
Step-by-step explanation:
The formula for percentage relative change =
[Final value - Initial value/Initial value] × 100
From the above question
Initial value = 42 %
Final value = 45%
= 45 - 42/ 42 × 100
= 3/42 × 100
= 7.1428571429 %
Therefore, approximately to the nearest tenth, the percentage relative change = 7.1%
<span>binomial </span>is an algebraic expression containing 2 terms. For example, (x + y) is a binomial.
We sometimes need to expand binomials as follows:
(a + b)0 = 1
(a + b)1 = a + b
(a + b)2 = a2 + 2ab + b2
(a + b)3 = a3 + 3a2b + 3ab2 + b3
<span>(a + b)4</span> <span>= a4 + 4a3b</span><span> + 6a2b2 + 4ab3 + b4</span>
<span>(a + b)5</span> <span>= a5 + 5a4b</span> <span>+ 10a3b2</span><span> + 10a2b3 + 5ab4 + b5</span>
Clearly, doing this by direct multiplication gets quite tedious and can be rather difficult for larger powers or more complicated expressions.
Pascal's Triangle
We note that the coefficients (the numbers in front of each term) follow a pattern. [This was noticed long before Pascal, by the Chinese.]
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
You can use this pattern to form the coefficients, rather than multiply everything out as we did above.
The Binomial Theorem
We use the binomial theorem to help us expand binomials to any given power without direct multiplication. As we have seen, multiplication can be time-consuming or even not possible in some cases.
<span>Properties of the Binomial Expansion <span>(a + b)n</span></span><span><span>There are <span>\displaystyle{n}+{1}<span>n+1</span></span> terms.</span><span>The first term is <span>an</span> and the final term is <span>bn</span>.</span></span><span>Progressing from the first term to the last, the exponent of a decreases by <span>\displaystyle{1}1</span> from term to term while the exponent of b increases by <span>\displaystyle{1}1</span>. In addition, the sum of the exponents of a and b in each term is n.</span><span>If the coefficient of each term is multiplied by the exponent of a in that term, and the product is divided by the number of that term, we obtain the coefficient of the next term.</span>
Answer:
96 and 288
Step-by-step explanation:
So, we need to find 2 numbers such that their sum is 8 and they do not have common factor (Relatively prime). Both these numbers will be divisible by 48 but there would be no other common divisor (after dividing by 48).
Such order independent pairs are (1,7) and (3,5).
Difference between them would be (7–1)*48=6*48 and (5–3)*48=2*48 respectively.
The differences are 6*48=288 and 2*48=96.
We have found difference without finding numbers.
Ans.: 96 and 288
p.s.: The number pairs (again order neutral) would be (48, 336) and (144, 240)
Difference for 48 and 336 add up to 384, their HCF is 48. These two numbers match the conditions. Their difference is 288.
Difference of 144 and 240 add up to 384, their HFC is 48 (the numbers are 48*3 and 48*5, common factor is 48 and no other common factor for 3 and 5; 48 is HCF). The difference is 96.
The whole field is square, and its total area is 25 acres.
It's divided up into 25 little sections.
Each little section is a square, and its area is 1 acre.
So the whole thing looks like a square tray with 25 little square blocks in it.
The blocks are in 5 rows, and there are 5 blocks in each row.
There are 16 blocks around the edge of the square tray, and 9 in the middle
that don't touch the edge.
Every block costs $1,200 to start out. But the ones around the edge are
more expensive. Anything on the edge costs an extra $150 for each side
of the little block that touches the edge.
Most of the 16 little blocks around the outside have only 1 side that touches
the edge. But the ones in the
<em>corners</em> of the tray have 2 sides along the edge.
You may want to have a look at the picture I attached.
That should be plenty to put you in a position to work out the costs.
