Answer:
The triangles are congruent because:
- QP = ST
- angle P = angle T
- the side PT is in both triangles
We know when 2 sides of two triangles and the angle between them is congruent, the triangles are congruent.
(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} }{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)
= ![[\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
*
*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.
Alex = 6x
Peter = x
6x = x + 50
5x = 50
x = 10
Alex = £60
Peter = £10
together = £70
Answer:
9330
Step-by-step explanation:
6x × 8y + 27x - 6y + 3 = 18 × 536 + 81 - 402 + 3 =
9330