You have to simplify each equation. You can do that by adding similar values to each other:
(the first equation)
8x²y + 7x² - 5y² + 3x - 2 + 2x²y - x² - 2y² + 3x - 4
To make it easier, arrange the values around so that similar ones are beside each other:
8x²y + 2x²y + 7x² - x² - 5y² - 2y² + 3x + 3x - 2 - 4
then add the similar values together:
8x²y + 2x²y = 10x²y
7x² - x² = 6x²
- 5y² - 2y² = -7y²
3x + 3x = 6x
(- 2)+ (- 4) = -6
and if you put them together:
10x²y + 6x² - 7y² + 6x - 6
This isn't the answer to the equation, because it's different. So repeat the process with all the other equations until you find one that is identical to the simplified version.
The answer is the second one: 8x²y + 7x² - 5y² + 3x - 2 + 2x²y - x² - 2y² - 3x - 4
Answer:
The solution of the inequation
is
.
Step-by-step explanation:
First of all, let simplify and factorize the resulting polynomial:



Roots are found by Quadratic Formula:
![r_{1,2} = \frac{\left[-\left(-\frac{11}{6}\right)\pm \sqrt{\left(-\frac{11}{6} \right)^{2}-4\cdot (1)\cdot \left(-\frac{10}{6} \right)} \right]}{2\cdot (1)}](https://tex.z-dn.net/?f=r_%7B1%2C2%7D%20%3D%20%5Cfrac%7B%5Cleft%5B-%5Cleft%28-%5Cfrac%7B11%7D%7B6%7D%5Cright%29%5Cpm%20%5Csqrt%7B%5Cleft%28-%5Cfrac%7B11%7D%7B6%7D%20%5Cright%29%5E%7B2%7D-4%5Ccdot%20%281%29%5Ccdot%20%5Cleft%28-%5Cfrac%7B10%7D%7B6%7D%20%5Cright%29%7D%20%5Cright%5D%7D%7B2%5Ccdot%20%281%29%7D)
and 
Then, the factorized form of the inequation is:

By Real Algebra, there are two condition that fulfill the inequation:
a) 


b) 


The solution of the inequation
is
.
Answer: 4.2495 feets
Step-by-step explanation:
Given the following :
Rate of change (speed) when rock hits the lake surface = - 3in/s
Distance or depth after 5 seconds :
Distance = rate of change * time
Distance = (- 3 in/s × 5) = - 15 inches
1 inch = 0.0833 feet
15 inches = (-15 * 0.0833) = - 1.2495 feets
Distance between Lisa's hand and lake surface = 3 feets :
Distance between Lisa's hand and rock after 5 seconds :
(3 feets + 1.2495 feets) = 4.2495 feets
Answer:
Slope- intercept form y = 200 x + 500
Step-by-step explanation:
Given that the equation
200x - y + 500 = 0
where y, the number of pairs of skates the factory has in the warehouse, and x be the number of hours
The slope-intercept form
y = m x +C
Given equation 200x - y + 500 = 0
200 x + 500 =y
y = 200 x + 500
Slope of the equation m = 200 and y-intercept 'C' = 500
Answer:
x = 2sqrt(5)
Step-by-step explanation:
We can use the Pythagorean theorem to solve
The legs are x and 8/2 =4
and the hypotenuse is 6
a^2 + b^2 = c^2
x^2 +4^2 = 6^2
x^2 +16 = 36
Subtract 16 from each side
x^2 +16-16=36-16
x^2 = 20
Take the square root of each side
sqrt(x^2) = sqrt(20)
x = sqrt(4*5)
x = sqrt(4) sqrt(5)
x = 2sqrt(5)