Answer:
Expanded: (y-3)(y-3)(y-3)
Simplified: ![y^{3}-9y^{2}+27y-27](https://tex.z-dn.net/?f=y%5E%7B3%7D-9y%5E%7B2%7D%2B27y-27)
Step-by-step explanation:
Expanded: (y-3)(y-3)(y-3)
Simplified:
![y^{2} -3y-3y+9(y-3)\\y^{2} -6y+9(y-3)](https://tex.z-dn.net/?f=y%5E%7B2%7D%20-3y-3y%2B9%28y-3%29%5C%5Cy%5E%7B2%7D%20-6y%2B9%28y-3%29)
![y^{3} -3y^{2}-6y^{2} +18y+9y-27](https://tex.z-dn.net/?f=y%5E%7B3%7D%20-3y%5E%7B2%7D-6y%5E%7B2%7D%20%20%2B18y%2B9y-27)
![y^{3}-9y^{2} +27y-27](https://tex.z-dn.net/?f=y%5E%7B3%7D-9y%5E%7B2%7D%20%2B27y-27)
Using the properties of operations the given pair of expressions are not equivalent
<u>Solution:</u>
Given that, we have to use the properties of operations to determine if each pair of expressions is equivalent
<em><u>And the two expressions are:</u></em>
![\frac{1}{2}(4-2 x) \text { and } 2-2 x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%284-2%20x%29%20%5Ctext%20%7B%20and%20%7D%202-2%20x)
Now, we know that, there are four (4) basic properties of operations:
<em>Commutative, Associative, Distributive and Identity. These properties only apply to the operations of addition and multiplication.</em>
So, if we observe we can apply distributive property on 1st expression
The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
![\begin{array}{l}{\frac{1}{2}(4-2 x) \rightarrow \frac{1}{2}(4)-\frac{1}{2}(2 x)} \\\\ {\rightarrow 2-x}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Cfrac%7B1%7D%7B2%7D%284-2%20x%29%20%5Crightarrow%20%5Cfrac%7B1%7D%7B2%7D%284%29-%5Cfrac%7B1%7D%7B2%7D%282%20x%29%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%202-x%7D%5Cend%7Barray%7D)
Here the resulting expression is 2 – x and it is not equivalent to 2 – 2x
Hence, the given two expressions are not equal.
Answer:
No
Step-by-step explanation:
Answer:
15.9
Step-by-step explanation:
If you add 15.8 and 0.1 together, it equals to 15.9.
15.8
+ 0.1
-------------
15.9
Answer:
325
Step-by-step explanation:
You must have heard about Arithmetic Progressions (AP)
Arithmetic progressions are a series of numbers such that every successive number is the sum of a constant number and the previous number.
Our very own counting numbers form AP
For example :-
2 = 1 + <u>1</u>
3 = 2 + <u>1</u>
4 = 3 + <u>1</u>
The number in bold (1) is that constant number which is added to a number to form its successive number.
To find the sum of series forming AP, we use the formula :-
![sum = \frac{n}{2} \{ a + a _{n} \}](https://tex.z-dn.net/?f=sum%20%3D%20%20%5Cfrac%7Bn%7D%7B2%7D%20%5C%7B%20a%20%20%2B%20a%20%20_%7Bn%7D%20%20%5C%7D%20)
here,
- n is the number of terms
- a is the first number of the series
- an is the last number of the series
So we'll use all this information to find the sum of continuous numbers from 1 to 25 where 1 is the first term(a) and 25 is the last(an).
and n is 25
![S = \frac{25}{2}\{ 1 +25\}](https://tex.z-dn.net/?f=S%20%20%3D%20%20%20%5Cfrac%7B25%7D%7B2%7D%5C%7B%201%20%20%2B25%5C%7D%20%20)
![= \frac{25 \times 26}{2}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B25%20%5Ctimes%2026%7D%7B2%7D%20)
![= 25 \times 13](https://tex.z-dn.net/?f=%20%3D%2025%20%20%5Ctimes%2013)
![= 325](https://tex.z-dn.net/?f=%20%3D%20325)
So, the value of S comes out to be 325.