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2 years ago

Ariana is opening a new restaurant. She has six entrees. How many different orders can she list them on her menu?

Mathematics

1 answer:

Ksenya-84 [330]2 years ago

4 0

Answer:

if each was used only once, the answer would be 52080

Step-by-step explanation:

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multiply or divide and then simplify (x+1)^2/(x-5)*(x-3)/(x+1) 3x+3/2 divided by 4/9x+9 4a/3a-3*3(a-1)/16a x+2/x-1 divided by 5x

antoniya [11.8K]

$\frac{(x+1)^2}{x-5}\cdot\frac{x-3}{x+1}=\frac{x+1}{x-5}\cdot\frac{x-3}{1}=\frac{(x+1)(x-3)}{x-5}=\frac{x^2-3x+x-3}{x-5}=\frac{x^2-2x-3}{x-5}\\\\D:x\neq5\ \wedge\ x\neq-1$

$\frac{3x+3}{2}:\frac{4}{9x+9}=\frac{3x+3}{2}\cdot\frac{9x+9}{4}=\frac{27x^2+27x+27x+27}{8}=\frac{27x^2+54x+27}{8}\\\\D:x\neq1$

$\frac{4a}{3a-3}\cdot\frac{3(a-1)}{16a}=\frac{1}{3a-3}\cdot\frac{3a-3}{4a}=\frac{1}{4a}\\\\D:a\neq1\ \wedge\ a\neq0$

$\frac{x+2}{x-1}:\frac{5x+10}{x-2}=\frac{x+2}{x-1}\cdot\frac{x-2}{5x+10}=\frac{x+2}{x-1}\cdot\frac{x-2}{5(x+2)}=\frac{1}{x-1}\cdot\frac{x-2}{5}=\frac{x-2}{5x-5}\\\\D:x\neq1\ \wedge\ x\neq2\ \wedge\ x\neq-2$

5 0

3 years ago

Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

AVprozaik [17]

Sorry pics aren't good quality...

7 0

3 years ago

Write the coordinate of the vertices after a translation 8 units left and 13 units down. S(0,10). T(8,10) U(1,5)

Paha777 [63]

Answer:

S(-8,-3), T(0, -3), and U(-7, -8)

Step-by-step explanation:

for all of the coordinates, you would subtract 8 from their X-values, and subtract 13 from their Y-values.

6 0

2 years ago

Please help me answer this question

sergejj [24]

Answer:

72km

Step-by-step explanation:

alex : tomos : annabelle = 2 : 3 : 4

if tomos drove 24km

tomos ratio is 3

so 3 --> 24

1 --> 8

total ratios --> 2 + 3 + 4 = 9

so total journey is 9 --> 9 * 8 = 72km

6 0

2 years ago

Linda won $200,000 in a state lottery. She first paid income tax on 30% on the winnings. She invested some of the rest at 1.5% a

Lady_Fox [76]

She invested $ 50000 at 1.5% rate and $ 90000 at 4% rate.

Explanation

Total amount of winnings = $ 200000

She first paid income tax on 30% on the winnings. So, the amount paid as income tax $=(200000*0.30)dollar=60000$ dollar.

Remaining amount = $ 200000 - $ 60000 = $ 140000

Suppose, she invested $x$ dollar at 1.5% rate.

That means, she invested $(140000-x)$ dollar at 4% rate.

Given that, the total amount of interest earned = $ 4350

So, the equation will be.....

$0.015x+0.04(140000-x)=4350\\ \\ 0.015x+5600-0.04x=4350\\ \\ -0.025x= 4350-5600\\ \\ -0.025x=-1250\\ \\ x= \frac{-1250}{-0.025}=50000$

So, amount of investment at 1.5% rate = $ 50000

and amount of investment at 4% rate = $ 140000 - $ 50000 = $ 90000

5 0

3 years ago