Answer:
Step-by-step explanation:
To divide fractions, you just flip around the second fraction and multiply. 2/3 * 5/4 = 10/12.
So the quotient is 10/12, or 5/6.
I hope this helped :)
ANSWER
![B. \: x = \frac{7}{6}](https://tex.z-dn.net/?f=B.%20%5C%3A%20x%20%3D%20%20%5Cfrac%7B7%7D%7B6%7D%20)
EXPLANATION
The given absolute value equation is
![|x + 3| = 7x - 4](https://tex.z-dn.net/?f=%20%7Cx%20%2B%203%7C%20%3D%207x%20-%204)
This implies that, either
![x + 3= 7x - 4](https://tex.z-dn.net/?f=%20x%20%2B%203%3D%207x%20-%204)
Or
![- (x + 3)= 7x - 4](https://tex.z-dn.net/?f=%20%20-%20%28x%20%2B%203%29%3D%207x%20-%204)
![- x - 3 = 7x - 4](https://tex.z-dn.net/?f=%20-%20x%20-%203%20%3D%207x%20-%204)
Group similar terms;
![3 + 4 = 7x - x](https://tex.z-dn.net/?f=3%20%2B%204%20%3D%207x%20-%20x)
or
![- 3 + 4 = 7x + x](https://tex.z-dn.net/?f=%20-%203%20%2B%204%20%3D%207x%20%2B%20x)
Simplify:
![7 = 6x](https://tex.z-dn.net/?f=7%20%3D%206x)
or
![1 = 8x](https://tex.z-dn.net/?f=1%20%3D%208x)
Solve for x.
![x = \frac{7}{6} \: or \: x = \frac{1}{8}](https://tex.z-dn.net/?f=%20x%20%3D%20%20%5Cfrac%7B7%7D%7B6%7D%20%20%5C%3A%20or%20%5C%3A%20x%20%3D%20%20%5Cfrac%7B1%7D%7B8%7D%20)
Check for extraneous solutions.
![| \frac{7}{6} + 3| = 7 \times \frac{7}{6} - 4](https://tex.z-dn.net/?f=%7C%20%5Cfrac%7B7%7D%7B6%7D%20%20%2B%203%7C%20%3D%207%20%5Ctimes%20%20%5Cfrac%7B7%7D%7B6%7D%20-%204)
![\frac{25}{6} = \frac{25}{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B25%7D%7B6%7D%20%20%3D%20%20%5Cfrac%7B25%7D%7B6%7D%20)
Also,
![| \frac{1}{8} + 3| = 7 \times \frac{1}{8} - 4](https://tex.z-dn.net/?f=%7C%20%5Cfrac%7B1%7D%7B8%7D%20%20%2B%203%7C%20%3D%207%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B8%7D%20-%204)
![\frac{25}{8} = - \frac{25}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B25%7D%7B8%7D%20%20%3D%20%20%20%20-%20%5Cfrac%7B25%7D%7B8%7D%20)
This is an extraneous solution.
The only solution is:
![x = \frac{7}{6}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B7%7D%7B6%7D%20)
Answer:
c) -4/5
d) 4/5
Step-by-step explanation:
The given equation is 25x^2 -16 = 0
Adding 16 on both sides, we get
25x^2 = 16
Dividing both sides by 25, we get
x^2 = 16/25
Taking square root on both sides, we get
x = √(16/25)
x = ±4/5
Therefore, x = 4/5 and x = -4/5
Answers: C) and D)
Hope this will helpful to understand the concept.
Thank you.
Yes, we can prove that the given figure is a parallelogram.
From the given figure, we can see that the given quadrilateral opposite angles and congruent. And we know that if a quadrilateral has two opposite angles congruent, then the quadrilateral is a parallelogram.
Therefore, we can say that the given figure is a parallelogram.
From the given options, second option is correct.
Therefore, the correct option is:-
Yes, opposite angles are congruent.