I think number 6 it should be right I think
Answer:
D.) If soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.
Step-by-step explanation:
Let us assume x = selling price of each soccer ball
y = daily profit earned from selling of soccer balls
Given that
Y= ![-6x^2+100x-180](https://tex.z-dn.net/?f=-6x%5E2%2B100x-180)
where,
a = -6
b = 100
c = -180
Now we have to applied the formula which is as follows
x ![= \frac{-b\pm\sqrt{b^2-4ac}}{2a}$](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%24)
![= \frac{-100\pm\sqrt{100^2-4\times -6\times -180}}{2\times -6}$](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B-100%5Cpm%5Csqrt%7B100%5E2-4%5Ctimes%20-6%5Ctimes%20-180%7D%7D%7B2%5Ctimes%20-6%7D%24)
![= \frac{-100\pm\sqrt{10,000 - 4,320}}{-12}$](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B-100%5Cpm%5Csqrt%7B10%2C000%20-%204%2C320%7D%7D%7B-12%7D%24)
![= \frac{-100\pm\sqrt{5.680}}{-12}$](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B-100%5Cpm%5Csqrt%7B5.680%7D%7D%7B-12%7D%24)
![= \frac{-100 + 75.3658}{-12}$](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B-100%20%2B%2075.3658%7D%7B-12%7D%24)
![= \frac{24.6342}{-12}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B24.6342%7D%7B-12%7D)
x^1 = -2.05285
Now
x^2 ![= \frac{-100 - 75.3658}{-12}$](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B-100%20-%2075.3658%7D%7B-12%7D%24)
![= \frac{- 175.3658}{-12}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B-%20175.3658%7D%7B-12%7D)
x^2 = 14.6138
Based on this the option D is most appropriate as per the given situation
Answer:
The answer is 3.
Step-by-step explanation:
Given that the Indices Law is,
![{a}^{m} \div {a}^{n} = {a}^{m - n}](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7Bm%7D%20%20%5Cdiv%20%20%7Ba%7D%5E%7Bn%7D%20%20%3D%20%20%7Ba%7D%5E%7Bm%20-%20n%7D%20)
![{a}^{0} = 1](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B0%7D%20%20%3D%201)
So the expression is :
![3 \times {5}^{2} \div {5}^{2}](https://tex.z-dn.net/?f=3%20%5Ctimes%20%20%7B5%7D%5E%7B2%7D%20%20%5Cdiv%20%20%7B5%7D%5E%7B2%7D%20)
![= 3 \times {5}^{2 - 2}](https://tex.z-dn.net/?f=%20%3D%203%20%5Ctimes%20%20%7B5%7D%5E%7B2%20-%202%7D%20)
![= 3 \times {5}^{0}](https://tex.z-dn.net/?f=%20%3D%203%20%5Ctimes%20%20%7B5%7D%5E%7B0%7D%20)
![= 3 \times 1](https://tex.z-dn.net/?f=%20%3D%203%20%5Ctimes%201)
![= 3](https://tex.z-dn.net/?f=%20%3D%203)
The volume of cube and rectangular prism are same. Option B.
Step-by-step explanation:
Given,
The length of the edge of the cube (a) = 5 cm
The dimension of rectangular prism (l×b×h) = 5 cm×25 cm×1 cm
To find the relation between the volume of cube and rectangular prism.
Formula
The volume of a cube = a³ cube cm
The volume of rectangular prism = l×b×h cube cm
Now,
The volume of a cube = 5³ cube cm = 125 cube cm
The volume of rectangular prism = 5×25×1 cube cm = 125 cube cm
Hence,
The volume of cube and rectangular prism are same.