(a) ![[\frac{9}{2.6} - \frac{2.5^{2} }{2.5} ]^{2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B9%7D%7B2.6%7D%20%20-%20%5Cfrac%7B2.5%5E%7B2%7D%20%7D%7B2.5%7D%20%5D%5E%7B2%7D)
Answer:
= ![[\frac{9}{2.6} - \frac{2.5*2.5 }{2.5} ]^{2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B9%7D%7B2.6%7D%20%20-%20%5Cfrac%7B2.5%2A2.5%20%7D%7B2.5%7D%20%5D%5E%7B2%7D)
= ![[\frac{9}{2.6} - \frac{2.5}{1} ]^{2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B9%7D%7B2.6%7D%20%20-%20%5Cfrac%7B2.5%7D%7B1%7D%20%5D%5E%7B2%7D)
*canceling 2.5 in numerator and denominator*
![= [\frac{9-(2.5)(2.6)}{2.6} ]^2\\*Using L.C.M of 2.6 and 1 which comes out to be '2.6'= [\frac{9-(6.5)}{2.6} ]^2\\= [\frac{2.5}{2.6} ]^2\\*multiplying and dividing by '10'= [\frac{2.5*10}{2.6*10} ]^2\\= [\frac{25}{26} ]^2\\= \frac{25^2}{26^2}\\= \frac{625}{676}\\= 0.925](https://tex.z-dn.net/?f=%3D%20%5B%5Cfrac%7B9-%282.5%29%282.6%29%7D%7B2.6%7D%20%5D%5E2%5C%5C%3C%2Fp%3E%3Cp%3E%2AUsing%20L.C.M%20of%202.6%20and%201%20which%20comes%20out%20to%20be%20%272.6%27%3C%2Fp%3E%3Cp%3E%3D%20%5B%5Cfrac%7B9-%286.5%29%7D%7B2.6%7D%20%5D%5E2%5C%5C%3D%20%5B%5Cfrac%7B2.5%7D%7B2.6%7D%20%5D%5E2%5C%5C%3C%2Fp%3E%3Cp%3E%2Amultiplying%20and%20dividing%20by%20%2710%27%3C%2Fp%3E%3Cp%3E%3D%20%5B%5Cfrac%7B2.5%2A10%7D%7B2.6%2A10%7D%20%5D%5E2%5C%5C%3D%20%5B%5Cfrac%7B25%7D%7B26%7D%20%5D%5E2%5C%5C%3D%20%5Cfrac%7B25%5E2%7D%7B26%5E2%7D%5C%5C%3D%20%5Cfrac%7B625%7D%7B676%7D%5C%5C%3D%200.925)
Properties used:
Cancellation property of fractions
Least Common Multiplier(LCM)
The least or smallest common multiple of any two or more given natural numbers are termed as LCM. For example, LCM of 10, 15, and 20 is 60.
(b) ![[[\frac{3x^{a}y^{b}} {-3x^{a} y^{b} } ]^{3} ] ^{2}](https://tex.z-dn.net/?f=%20%5B%5B%5Cfrac%7B3x%5E%7Ba%7Dy%5E%7Bb%7D%7D%20%7B-3x%5E%7Ba%7D%20y%5E%7Bb%7D%20%7D%20%5D%5E%7B3%7D%20%20%20%20%5D%20%5E%7B2%7D%20)
Answer:
![[[\frac{3x^{a}y^{b}} {-3x^{a} y^{b} } ]^{3}] ^{2}\\](https://tex.z-dn.net/?f=%5B%5B%5Cfrac%7B3x%5E%7Ba%7Dy%5E%7Bb%7D%7D%20%7B-3x%5E%7Ba%7D%20y%5E%7Bb%7D%20%7D%20%5D%5E%7B3%7D%5D%20%5E%7B2%7D%5C%5C)
*using ![[x^{a}]^b = x^{ab}](https://tex.z-dn.net/?f=%5Bx%5E%7Ba%7D%5D%5Eb%20%3D%20x%5E%7Bab%7D)
*
![= [\frac{3x^{3a}y^{3b}} {-3x^{3a} y^{3b} }] ^{2}](https://tex.z-dn.net/?f=%3D%20%5B%5Cfrac%7B3x%5E%7B3a%7Dy%5E%7B3b%7D%7D%20%7B-3x%5E%7B3a%7D%20y%5E%7B3b%7D%20%7D%5D%20%5E%7B2%7D)
*Again, using *
![= \frac{3x^{2*3a}y^{2*3b}} {-3x^{2*3a} y^{2*3b} } \\= (-1)\frac{3x^{6a}y^{6b}} {3x^{6a} y^{6b} }\\[\tex]*taking -1 common, denominator and numerator are equal*[tex]= -(1)\frac{1}{1}\\= -1](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B3x%5E%7B2%2A3a%7Dy%5E%7B2%2A3b%7D%7D%20%7B-3x%5E%7B2%2A3a%7D%20y%5E%7B2%2A3b%7D%20%7D%20%20%5C%5C%3D%20%28-1%29%5Cfrac%7B3x%5E%7B6a%7Dy%5E%7B6b%7D%7D%20%7B3x%5E%7B6a%7D%20y%5E%7B6b%7D%20%7D%5C%5C%5B%5Ctex%5D%3C%2Fp%3E%3Cp%3E%2Ataking%20-1%20common%2C%20denominator%20and%20numerator%20are%20equal%2A%3C%2Fp%3E%3Cp%3E%5Btex%5D%3D%20-%281%29%5Cfrac%7B1%7D%7B1%7D%5C%5C%3D%20-1)
Property used: 'Power of a power'
We can raise a power to a power
(x^2)4=(x⋅x)⋅(x⋅x)⋅(x⋅x)⋅(x⋅x)=x^8
This is called the power of a power property and says that to find a power of a power you just have to multiply the exponents.
Angles 1, 2, and 3 are all 90°.
10x = 90
.. x = 9
x +y = 90
.. y = 81
5z = 90
.. z = 18
The values of (x, y, z) are (9, 81, 18).
Answer:
2x - 6 = 4
Step-by-step explanation:
Firstly, let's assume the number is x
Then, twice the number is 2 times x = 2x
6 less than twice the number is four
2x - 6 = 4
2x - 6 + 6 = 4 + 6
2x = 10
2x/2 = 10/2
x = 5
Answer:
3
Step-by-step explanation:
First we must find the total boxes of pens
15 + 9 = 24
Then we can divide the total cost by the total number of boxes of pens
$72 / 24 boxes = 3
Answer:
%18 tip
Step-by-step explanation:
The dinner cost was $29 before tip
after tip it was $32.22
34.22-29= $5.22 she tipped
$29 * %x = $5.22
After solving this equation, the x is %18
