This point falls on none of your possible answers.
We can first tell that it falls neither positive or negative in terms of x since the x value is 0.
We can also tell the y term is negative. Therefore, it would fall on the negative y-axis.
Answer: The correct statements are 'The equation 2n = p should be 2p = n' , 'The actual cost of the onions is $3.00 per pound' and 'Potatoes cost $1.50 per pound.'
Step-by-step explanation:
Here, p represents cost of one potato and n represents the cost of one onion.
And, According to the question, He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18.
Therefore, 6p +3n = 18 ------(1)
And, Onions cost twice as much as potatoes.
Therefore, n= 2p ---------(2)
Putting the values of n from 2) in equation 1),
we get, 6p+3(2p)=18
⇒6p+6p=18 ⇒ 12p =18 ⇒ p = 1.5 dollar.
Thus cost of one potato= $1.5
And cost of one onion = $ 2× 1.5= $ 3.00
Thus with help of above explanation we can say that Options first, third and fifth are correct.
Answer:
Step-by-step explanation:
The geometric mean relations for this geometry tell you the length of each segment (x or y) is the root of the product of the hypotenuse segments it touches.
x = √(9×5) = (√9)(√5) = 3√5
y = √(9×(9+5)) = (√9)(√14) = 3√14
_____
<em>Additional comment</em>
The geometric mean of 'a' and 'b' is √(ab).
The geometric mean relations derive from the fact that the three triangles in this geometry are similar. That means corresponding sides are proportional.
Segment x is both a long side (of the smallest triangle) and a short side (of the medium-size triangle). Then it will be involved in proportions involving the relationship of the long side and the short side of the triangles it is part of:
long side/short side = x/5 = 9/x
x² = 5·9
x = √(9×5) . . . . as above
In like fashion, y is both a long side and a hypotenuse, so we have ...
long side/hypotenuse = y/(9+5) = 9/y
y² = (9+5)(9)
y = √(9×14) . . . . . as above
The same thing holds true on the other side of the triangle. The unmarked segment is both a short side and a hypotenuse, so its measure will be the geometric mean of 14 and 5, the hypotenuse and its short segment.
<u>Answer:</u>
are two roots of equation ![-3 x^{2}-x-3=0](https://tex.z-dn.net/?f=-3%20x%5E%7B2%7D-x-3%3D0)
<u>Solution:</u>
Need to solve given equation using quadratic formula.
![-3 x^{2}-x-3=0](https://tex.z-dn.net/?f=-3%20x%5E%7B2%7D-x-3%3D0)
General form of quadratic equation is ![a x^{2}+b x+c=0](https://tex.z-dn.net/?f=a%20x%5E%7B2%7D%2Bb%20x%2Bc%3D0)
And quadratic formula for getting roots of quadratic equation is
![x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E%7B2%7D-4%20a%20c%7D%7D%7B2%20a%7D)
In our case b = -1 , a = -3 and c = -3
Calculating roots of the equation we get
![\begin{array}{l}{x=\frac{-(-1) \pm \sqrt{(-1)^{2}-4(-3)(-3)}}{2 \times-3}} \\\\ {x=-\frac{1}{6} \pm\left(-\frac{\sqrt{-35}}{6}\right)}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7Bx%3D%5Cfrac%7B-%28-1%29%20%5Cpm%20%5Csqrt%7B%28-1%29%5E%7B2%7D-4%28-3%29%28-3%29%7D%7D%7B2%20%5Ctimes-3%7D%7D%20%5C%5C%5C%5C%20%7Bx%3D-%5Cfrac%7B1%7D%7B6%7D%20%5Cpm%5Cleft%28-%5Cfrac%7B%5Csqrt%7B-35%7D%7D%7B6%7D%5Cright%29%7D%5Cend%7Barray%7D)
Since
is equal to -35, which is less than zero, so given equation will not have real roots and have complex roots.
![\begin{array}{l}{\text { Hence } x=-\frac{1}{6}-\frac{\sqrt{35}}{6} i \text { and } x=-\frac{1}{6}+\frac{\sqrt{35}}{6} i \text { are two roots of equation - }} \\ {3 x^{2}-x-3=0}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Ctext%20%7B%20Hence%20%7D%20x%3D-%5Cfrac%7B1%7D%7B6%7D-%5Cfrac%7B%5Csqrt%7B35%7D%7D%7B6%7D%20i%20%5Ctext%20%7B%20and%20%7D%20x%3D-%5Cfrac%7B1%7D%7B6%7D%2B%5Cfrac%7B%5Csqrt%7B35%7D%7D%7B6%7D%20i%20%5Ctext%20%7B%20are%20two%20roots%20of%20equation%20-%20%7D%7D%20%5C%5C%20%7B3%20x%5E%7B2%7D-x-3%3D0%7D%5Cend%7Barray%7D)
Answer:
Step-by-step explanation:
First