Answer:
the star is quadrant 2
Step-by-step explanation:
Answer:
(- 3.5, - 5.5 )
Step-by-step explanation:
Given the 2 equations
y = x - 2 → (1)
y = 3x + 5 → (2)
Substitute y = 3x + 5 into (1)
3x + 5 = x - 2 ( subtract x from both sides )
2x + 5 = - 2 ( subtract 5 from both sides )
2x = - 7 ( divide both sides by 2 )
x = - 3.5
Substitute x = - 3.5 into either of the 2 equations and evaluate for y
Substituting into (1)
y = - 3.5 - 2 = - 5.5
Solution is (- 3.5, - 5.5 )
Answer:the total number of horses in the herd is 36
Step-by-step explanation:
Let x represent the total number of horses in the herd.
One fourth of the herd of horses was seen in the forest. This means that the number of horses that was seen in the forest would be
1/4 × x = x/4
Twice the square root of the herd had gone to the mountain slopes. This means that the number of horses that had gone to the mountain slopes would be
2 × √x = 2√x
Three times five horses remained on the riverbank. This means that the number that remained would be
3 × 5 = 15
Therefore
x/4 + 2√x + 15 = x
x - x/4 - 15 = 2√x
(4x - x - 60)/4 = 2√x
(3x - 60)/4 = 2√x
Cross multiplying,
3x - 60 = 8√x
Squaring both sides of the equation, it becomes
(3x - 60)(3x - 60) = 64x
9x² - 180x - 180x + 3600 = 64x
9x² - 360x - 64x + 3600 = 0
9x² - 424x + 3600 = 0
Applying the quadratic equation
x = (- b ±√b² - 4ac)/2a
x = ( - - 424 ± √-424² - 4(9 × 3600)/2 × 9
x = (424 ± √179776 - 129600)/18
x = (424 ±√50176)/18
x = (424 + 224)/18 or
x = (424 - 224)/18
x = 36 or x = 11.11
the number of horses must be whole number. Therefore, the number of horses is 36
There are many reasons one may want to simplify, rearranging to find specific values - or maybe just making it simpler
Well, let's do some examples:
y(x(3+2)) +2 = -2y +2 <span>< I just made this one up, it looks really complicated right now, none the less it can be simplified easily
</span>y(3x+2x) + 2 = - 2y +2
3xy + 2xy + 2 = -2y +2
5xy + 2 = -2y +2 <-- the +2's dissapear because they cancel out
5xy = -2y
<span>And there we have it, that long expression has been simplified to something really simple.
</span>
Another example:
3(4(x+3(2 +z)) - 5)= 3y <span><- you can start where ever, I like starting in the middle
</span>3 * (4 * (x + 3*(2 + z)) - 5 ) = 3y <span><- here it is spaced out, we get a much better view
</span><span>3 * (4 * (x + 6 + 3z) - 5 ) = 3y</span>
3 * (4x + 24 + 12z - 5) = 3y <- divide both sides by 3 ..
4x + 24 + 12z - 5 = y <- much better
<span>
</span>Note: Simplify means solving to a degree, but you can't solve it because it has unknowns
That would just mean you have to divide 15 and 7
answer:2.1 or 2pounds
