Answer:
x can take any value and are viable in this situation if and only if it is a positive number
Step-by-step explanation:
We know that the area of a rectangle is given by:
A = x * y
So if we replace we have:
12 ≤ x * y ≤ 36
We divide by y, and we have:
12 / y ≤ x ≤ 36 / y
Which means that the value of x depends on y, that is to say if y is worth 1, the inequality would be:
12 ≤ x ≤ 36
In the event that y is equal to 2:
12/2 ≤ x ≤ 36/2
6 ≤ x ≤ 18
Which means, that depending on y, x can take any value and are viable in this situation if and only if it is a positive number.
Answer:
Four raised to the one-sixth power
Step-by-step explanation:
We want to simplify: ![\dfrac{\sqrt{4} }{\sqrt[3]{4} }](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B4%7D%20%7D%7B%5Csqrt%5B3%5D%7B4%7D%20%7D)
First, we apply the fractional law of indices to each term.
![\text{If } a^{1/x}=\sqrt[x]{a},$ then:\\\sqrt{4}=4^{1/2}\\\sqrt[3]{4}=4^{1/3}](https://tex.z-dn.net/?f=%5Ctext%7BIf%20%20%7D%20a%5E%7B1%2Fx%7D%3D%5Csqrt%5Bx%5D%7Ba%7D%2C%24%20then%3A%5C%5C%5Csqrt%7B4%7D%3D4%5E%7B1%2F2%7D%5C%5C%5Csqrt%5B3%5D%7B4%7D%3D4%5E%7B1%2F3%7D)
We then have:
![\dfrac{\sqrt{4} }{\sqrt[3]{4} }=\dfrac{4^{1/2} }{4^{1/3} }\\$Applying the division law of indices: \dfrac{a^m }{a^n }=a^{m-n}\\\dfrac{4^{1/2} }{4^{1/3} }=4^{1/2-1/3}\\\\=4^{1/6}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B4%7D%20%7D%7B%5Csqrt%5B3%5D%7B4%7D%20%7D%3D%5Cdfrac%7B4%5E%7B1%2F2%7D%20%7D%7B4%5E%7B1%2F3%7D%20%7D%5C%5C%24Applying%20the%20division%20law%20of%20indices%3A%20%5Cdfrac%7Ba%5Em%20%7D%7Ba%5En%20%7D%3Da%5E%7Bm-n%7D%5C%5C%5Cdfrac%7B4%5E%7B1%2F2%7D%20%7D%7B4%5E%7B1%2F3%7D%20%7D%3D4%5E%7B1%2F2-1%2F3%7D%5C%5C%5C%5C%3D4%5E%7B1%2F6%7D)
The correct option is B.
Answer:
35 pounds of $8.00 tea and 15 pounds of $6.00 tea
Step-by-step explanation:
Let x represent the pounds of tea of the $8 kind. 8x would represent the total cost of that type of tea. We can also say 50 - x is the pounds of tea of the $6 kind, so 6(50 - x) is the total cost of that type of tea. 50 * 7.4 represents the total cost of all the tea, and the expression 8x + 6(50 -x) would also represent the same thing. We can write this as an equation,
8x + 6(50 -x) = 50 * 7.4
simplify,
8x + 300 - 6x = 370
2x + 300 = 370
and solve.
2x = 70
x = 35
This means there is 35 pounds of the $8 kind.
We can subtract that from 50 to find,
50 - 35 = 15,
15 pounds is the amount of the $6 kind.
This problem can be expressed through the equation:
x+3x+10= 90
To solve it we subtract 10 on both sides
→x+3x=80
Add x and 3x
→4x=80
And divide each side by 4
→x=80/4
→x=20
ANSWER:
20
