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pogonyaev
3 years ago
14

The sum of the cost of dinner d and a $12 tip divided equally between 3 people

Mathematics
1 answer:
torisob [31]3 years ago
4 0

Answer: 4

Step-by-step explanation:

First you make your equation

3d=12

Divide

You get d=4

Therefore each person pays 4 dollars of the 12 dollar tip

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Renting a porch for the day there is a $50. Fee plus .50 per mile with a budget of $100. How many miles can you go
UkoKoshka [18]

Answer:2

Step-by-step explanation:

3 0
2 years ago
The slope of a line is -1/2 what is the slope of a line that is parallel to it?
Lynna [10]
Parallel lines have the exact same slope ( or else they would eventually run into each other). So the answer is -1/2 is the slope.
5 0
3 years ago
Factor completely. <br> <img src="https://tex.z-dn.net/?f=x%5E%7B8%7D-%5Cfrac%7B1%7D%7B81%7D" id="TexFormula1" title="x^{8}-\fra
Eduardwww [97]

We have 3⁴ = 81, so we can factorize this as a difference of squares twice:

x^8 - \dfrac1{81} = \left(x^2\right)^4 - \left(\dfrac13\right)^4 \\\\ x^8 - \dfrac1{81} = \left(\left(x^2\right)^2 - \left(\dfrac13\right)^2\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)

Depending on the precise definition of "completely" in this context, you can go a bit further and factorize x^2-\frac13 as yet another difference of squares:

x^2 - \dfrac13 = x^2 - \left(\dfrac1{\sqrt3}\right)^2 = \left(x-\dfrac1{\sqrt3}\right)\left(x+\dfrac1{\sqrt3}\right)

And if you're working over the field of complex numbers, you can go even further. For instance,

x^4 + \dfrac19 = \left(x^2\right)^2 - \left(i\dfrac13\right)^2 = \left(x^2 - i\dfrac13\right) \left(x^2 + i\dfrac13\right)

But I think you'd be fine stopping at the first result,

x^8 - \dfrac1{81} = \boxed{\left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)}

6 0
3 years ago
Tickets at a play cost $10 or $14. If 800 tickets were sold and $9,040 was collected by the box office, how many $14 tickets wer
pav-90 [236]
STEP 1:
determine equations needed

x= # of $10 tickets
y= # of $14 tickets

QUANTITY EQUATION
x + y= 800

COST EQUATION
$10x + $14y= $9,040


STEP 2:
multiply quantity equation by -14

-14(x + y)= -14(800)
-14x - 14y= -11,200


STEP 3:
add new quantity equation in step 2 to cost equation of step 1 to solve for x using elimination

-14x - 14y= -11,200
10x + 14y= 9040
y term cancels out

-4x= -2160
divide both sides by -4

x= 540 ten dollar tickets


STEP 4:
substitute x value in step 3 into either original equation

x + y= 800
540 + y= 800
subtract 540 from both sides

y= 260 fourteen dollar tickets


ANSWER: There were 540 $10 tickets and 260 $14 tickets sold.

Hope this helps! :)
5 0
3 years ago
What does y equal when the equation 4y-1=7
asambeis [7]
4y - 1 = 7    / + 1 ;
4y = 8         /÷4 ;
y = 2 ;
7 0
3 years ago
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