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Firlakuza [10]
3 years ago
6

Find the inverse of the function.

Mathematics
1 answer:
erik [133]3 years ago
4 0

Answer:

X=y-8................

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Mr. Kohl has a breaker containing n milliliters of solution to distribute to the students in his chemistry class. If he gives ea
77julia77 [94]

Answer:

There were 26 students in his class and the teacher had 83 ml of the solution.

Step-by-step explanation:

Mr. Kohl has a "x" amount of solution, if he divides it by the number of students "n" he'll give each student 3 milliliters  and have a left over of 5 milliliters. If the amount of solution Mr. Kohl had was "x + 21" then he'd be able to give each student 4 milliliters of the solution. From these informations we have:

x = 3*n + 5

(x + 21)/n = 4

x + 21 = 4*n

x = 4*n - 21

Now that we have two equations and two variables we can solve the system of equations, as seen bellow:

3*n + 5 = 4*n - 21

3*n - 4*n = -21 - 5

-n = -26

n = 26

x = 4*26 - 21 = 83 ml

There were 26 students in his class and the teacher had 83 ml of the solution.

3 0
3 years ago
If x^2+1/x^2=3 find the value of x^2/(x^2+1)^2<br> Express answer as a common fraction.<br> Thanks!!
timama [110]

x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0

By the quadratic formula,

x^2=\dfrac{3\pm\sqrt5}2\implies x^2+1=\dfrac{5\pm\sqrt5}2

Then

(x^2+1)^2=\dfrac{25\pm10\sqrt5+5}4=\dfrac{15\pm5\sqrt5}2

\implies\dfrac{x^2}{(x^2+1)^2}=\dfrac{\frac{3\pm\sqrt5}2}{\frac{15\pm5\sqrt5}2}=\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}

Multiply numerator and denominator by the denominator's conjugate:

\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}\cdot\dfrac{15\mp5\sqrt5}{15\mp5\sqrt5}=\dfrac{45\pm15\sqrt5\mp15\sqrt5-25}{15^2-(5\sqrt5)^2}=\dfrac{20}{100}=\dfrac15

3 0
3 years ago
If you earn $1200 per month and you expect your earnings to increase by 10% per year, what monthly salary would you be making in
Sergio [31]
So u turn the percent into a decimal.
0.10 
Now multiply 1200 * 0.10
1200*0.10= 120 ( 120 is the amount that is gonna increase)
So if it says 5 years, than your gonna multiply 120 * 5 
120*5 =600
So your gonna add 600 to 1200.
So in five years your gonna be making 1,800.
An easier way would be to use prt
Principle * rate * time
1200 * 0.10* 5
= 600
So now you just add 600 to 1200
= 1800

7 0
3 years ago
Find a vector 3 units long in the opposite direction from v = 〈3, 1,-4).
lutik1710 [3]

Unit vector along the direction v = <3,1,-4> is :

\hat{v} = \dfrac{3i + j  -4k}{\sqrt{3^2 + 1^2 + 4^2}}\\\\\hat{v} = \dfrac{3i + j -4k}{5.1}

So, unit vector opposing the \hat{v} is :

\hat{v'} = -\hat{v}\\\\\hat{v'} = -( \dfrac{3i + j -4k}{5.1})\\\\\hat{v'} = \dfrac{-3i - j +4k}{5.1}

so, vector of magnitude 3 units in opposite direction from v is :

\vec{V} = 3\hat{v'}\\\\\vec{V} = \dfrac{3}{5.1}( -3i -j+4k)

Hence, this is the required solution.

5 0
3 years ago
Which point can be used to find f(3)
Andreas93 [3]

Commonly the horizontal axis represent the x-axis. So, you need the point that means x = 3 (positive 3), so, it is the point A.

3 0
3 years ago
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