Answer:
Manuel owes more to Calvin(75 cents) as compared to Lester(50 cents).
Step-by-step explanation:
We are given the following information in the question:
Manuel borrowed 50 cents from Lester and 75 cents from Calvin. Manuel claims that he owes lee to Calvin.
Manuel's claim is wrong.
This could be understood by comparing:
![\displaystyle\frac{-3}{4}~and~\displaystyle\frac{-1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B-3%7D%7B4%7D~and~%5Cdisplaystyle%5Cfrac%7B-1%7D%7B2%7D)
The negative sign here states that this amount is owed to someone, we do not own this money.
![\displaystyle\frac{-3}{4}~and~\displaystyle\frac{-1}{2}\\\\\displaystyle\frac{-3}{4}~and~\displaystyle\frac{-2}{4}\\\\\displaystyle\frac{-3}{4} < \displaystyle\frac{-2}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B-3%7D%7B4%7D~and~%5Cdisplaystyle%5Cfrac%7B-1%7D%7B2%7D%5C%5C%5C%5C%5Cdisplaystyle%5Cfrac%7B-3%7D%7B4%7D~and~%5Cdisplaystyle%5Cfrac%7B-2%7D%7B4%7D%5C%5C%5C%5C%5Cdisplaystyle%5Cfrac%7B-3%7D%7B4%7D%20%3C%20%5Cdisplaystyle%5Cfrac%7B-2%7D%7B4%7D)
![\displaystyle\frac{3}{4}\times \text{1 dollar} = 75\text{ cents}\\\displaystyle\frac{1}{2}\times \text{1 dollar} = 50\text{ cents}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B3%7D%7B4%7D%5Ctimes%20%5Ctext%7B1%20dollar%7D%20%3D%2075%5Ctext%7B%20cents%7D%5C%5C%5Cdisplaystyle%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5Ctext%7B1%20dollar%7D%20%3D%2050%5Ctext%7B%20cents%7D)
Thus, Manuel owes more to Calvin(75 cents) as compared to Lester(50 cents).
Answer:
A
Step-by-step explanation:
Given
![\frac{x}{\sqrt{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B%5Csqrt%7B2%7D%20%7D)
Multiply numerator/ denominator by
to rationalise the denominator
=
=
→ A
Answer:
The graph crosses the x-axis 2 times
The solutions are x = -8 & x = 4
Step-by-step explanation:
Qaudratics are in the form ![ax^2 + bx+ c](https://tex.z-dn.net/?f=ax%5E2%20%2B%20bx%2B%20c)
Where a, b, c are constants
Now, let's arrange this equation in this form:
![4x=32-x^2\\x^2+4x-32=0](https://tex.z-dn.net/?f=4x%3D32-x%5E2%5C%5Cx%5E2%2B4x-32%3D0)
Where
a = 1
b = 4
c = -32
We need to know the discriminant to know nature of roots. The discriminant is:
![D=b^2-4ac](https://tex.z-dn.net/?f=D%3Db%5E2-4ac)
If
- D = 0 , we have 2 similar root and there is 2 solutions and that touches the x-axis
- D > 0, we have 2 distinct roots/solutions and both cut the x-axis
- D < 0, we have imaginary roots and it never cuts the x-axis
Let's find value of Discriminant:
![D=b^2-4ac\\D=(4)^2 -4(1)(-32)\\D=144](https://tex.z-dn.net/?f=D%3Db%5E2-4ac%5C%5CD%3D%284%29%5E2%20-4%281%29%28-32%29%5C%5CD%3D144)
Certainly D > 0, so there are 2 distinct roots and cuts the x-axis twice.
We get the roots/solutions by factoring:
![x^2+4x-32=0\\(x+8)(x-4)=0\\x=4,-8](https://tex.z-dn.net/?f=x%5E2%2B4x-32%3D0%5C%5C%28x%2B8%29%28x-4%29%3D0%5C%5Cx%3D4%2C-8)
Thus,
The graph crosses the x-axis 2 times
The solutions are x = -8 & x = 4
Answer:
900 = 2 * 2 * 3 * 3 * 5 * 5 = 2^2 * 3^2 * 5^2
Step-by-step explanation:
900/2 = 450
450/2 = 225
225/3 = 75
75/3 = 25
25/5 = 5
5/5 = 1
900 = 2 * 2 * 3 * 3 * 5 * 5 = 2^2 * 3^2 * 5^2
I think it would be b or c