Only 3(a−b) and 3a−3b are equivalent
Further explanation:
We have to evaluate each expression to evaluate if the expressions are equivalent or not.
So,
<u>For 3(a−b)</u>
![3(a-b)\\Distributing\ 3\ in\ bracket\\3.a-3.b\\=3a-3b](https://tex.z-dn.net/?f=3%28a-b%29%5C%5CDistributing%5C%203%5C%20in%5C%20bracket%5C%5C3.a-3.b%5C%5C%3D3a-3b)
As we can see that 3(a-b) results in 3a-3b so these are equivalent
<u>For 2a(2+b)</u>
![2a(2+b)\\Distributing\ 2a\\2a.2+2a.b\\=4a+2ab](https://tex.z-dn.net/?f=2a%282%2Bb%29%5C%5CDistributing%5C%202a%5C%5C2a.2%2B2a.b%5C%5C%3D4a%2B2ab)
As we can see that 2a(2+b) doesn't result in 4ab so these are not equivalent
Hence,
Only 3(a−b) and 3a−3b are equivalent
Keywords: Equivalent expression, Polynomials
Learn more about polynomials at:
#LearnwithBrainly
Let's see.
4x/5 + 4/3 = 2x
First we have to make each denominator the same, so I'll multiply 4x/5 by 3/3, 4/3 by 5/5, and 2x by 15/15
Now we have 12x/15 + 20/15 = 30x/15
With everything in the same denominator we can solve the new equation of
12x + 20 = 30x
20 = 18x
10 = 9x
X= 10/9
D. About 122 units I just took the test
Consider the absolute value, because we only worry about the quadrant later.
![\text{Consider: } sin(A) = |-\frac{\sqrt{3}}{4}|](https://tex.z-dn.net/?f=%5Ctext%7BConsider%3A%20%7D%20sin%28A%29%20%3D%20%7C-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B4%7D%7C)
![sin(A) = \frac{\sqrt{3}}{4}](https://tex.z-dn.net/?f=sin%28A%29%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B4%7D)
Thus, we know that the hypotenuse has a length of 4 units, and the side opposite the angle, A is √3, because this is the nature of the sine function in relation to its triangular component.
The missing side can be found using Pythagoras' Theorem:
4² - (√3)² = x²
16 - 3 = x²
13 = x²
x = √13
![\therefore tan(A) = \pm \sqrt{\frac{3}{13}}](https://tex.z-dn.net/?f=%5Ctherefore%20tan%28A%29%20%3D%20%5Cpm%20%5Csqrt%7B%5Cfrac%7B3%7D%7B13%7D%7D)
Since angle A is in the third quadrant, the tangent function will produce a positive angle.
![tan(A) = \sqrt{\frac{3}{13}}](https://tex.z-dn.net/?f=tan%28A%29%20%3D%20%5Csqrt%7B%5Cfrac%7B3%7D%7B13%7D%7D)
![\text{Rationalise the denominator: } \frac{\sqrt{3}}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}](https://tex.z-dn.net/?f=%5Ctext%7BRationalise%20the%20denominator%3A%20%7D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B13%7D%7D%20%5Ccdot%20%5Cfrac%7B%5Csqrt%7B13%7D%7D%7B%5Csqrt%7B13%7D%7D)
Answer: #1 Answer is D
Step-by-step explanation: Welcome!
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