We are provided , Tomas learned <em><u>that a³ + b³ = (a + b ) ( a² - ab + b² )</u></em> , and his teacher writes four products on the board and we have to tell that which product suits the best if <em><u>a = 2x</u></em> and <em><u>b =</u></em><em><u> </u></em><em><u>y</u></em>
Now , putting a = 2x , b = y in the given formula we have :
![{:\implies \quad \bf \therefore \quad \underline{\underline{(2x)^{3}+(y)^{3}=(2x+y)(4x^{2}-2xy+y^{2})}}}](https://tex.z-dn.net/?f=%7B%3A%5Cimplies%20%5Cquad%20%5Cbf%20%5Ctherefore%20%5Cquad%20%5Cunderline%7B%5Cunderline%7B%282x%29%5E%7B3%7D%2B%28y%29%5E%7B3%7D%3D%282x%2By%29%284x%5E%7B2%7D-2xy%2By%5E%7B2%7D%29%7D%7D%7D)
Hence , The product <em>(2x+y) (4x²-</em><em>2</em><em>xy+y²)</em> would result in the sum of cubes of 2x & y :D
Answer:
Option a) 1.6 .
Step-by-step explanation:
We are given that 142 subjects were treated with acupuncture. The numbers of migraine attacks for the treatment group had a mean of 1.8 and a standard deviation of 1.4 which means;
Sample Mean,
= 1.8 , Sample standard deviation, s = 1.4 and Sample size = 142.
Now, 95% confidence interval estimate of the mean number of migraine attacks for all people treated with acupuncture is given by;
⇒
So, the lower bound =
= 1.56 ≈ 1.6
Therefore, option A is correct.
Answer:
x = -4 , x = -1
Explanation:
Multiply by x on both sides to get rid of fraction
x(x + 4/x) = x(-5)
x^2 + 4 = -5x
x^2 + 5x + 4 = 0
Factor
(x+4)(x+1) = 0
x = -4 , x = -1
Answer:
<h2>x = 2 and y = -2</h2>
Step-by-step explanation:
![\left\{\begin{array}{ccc}x-y=4&\text{add}\ y\ \text{to both sides}\\x+2y=-2\end{array}\right\\\\\left\{\begin{array}{ccc}x=4+y&(1)\\x+2y=-2&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\(4+y)+2y=-2\qquad\text{combine like terms}\\\\4+(y+2y)=-2\qquad\text{subtract 4 from both sides}\\\\3y=-6\qquad\text{divide both sides by 3}\\\\y=-2\\\\\text{put the value of}\ y\ \text{to (1):}\\\\x=4+(-2)\\\\x=2](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dx-y%3D4%26%5Ctext%7Badd%7D%5C%20y%5C%20%5Ctext%7Bto%20both%20sides%7D%5C%5Cx%2B2y%3D-2%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dx%3D4%2By%26%281%29%5C%5Cx%2B2y%3D-2%26%282%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7Bsubstitute%20%281%29%20to%20%282%29%3A%7D%5C%5C%5C%5C%284%2By%29%2B2y%3D-2%5Cqquad%5Ctext%7Bcombine%20like%20terms%7D%5C%5C%5C%5C4%2B%28y%2B2y%29%3D-2%5Cqquad%5Ctext%7Bsubtract%204%20from%20both%20sides%7D%5C%5C%5C%5C3y%3D-6%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5Cy%3D-2%5C%5C%5C%5C%5Ctext%7Bput%20the%20value%20of%7D%5C%20y%5C%20%5Ctext%7Bto%20%281%29%3A%7D%5C%5C%5C%5Cx%3D4%2B%28-2%29%5C%5C%5C%5Cx%3D2)
Hello!
The first one has just 4 right angles, along with parallel sides. It is a rectangle.
The second one has four right angles, congruent sides, and parallel sides. It is a square.
The third one has four congruent sides. It is a rhombus.
The fourth has parallel sides. It is a parallelogram.
a. Rectangle
b. Square
c. Rhombus
d. Parallelogram
I hope this helps!