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dalvyx [7]
3 years ago
9

Need help ASAP please

Mathematics
1 answer:
nirvana33 [79]3 years ago
6 0

Answer:

x=5.75 ; price of a single popcorn

y=2.25 ; price of a drink

system of equations

2*x+3*y= 18.25

4*x+2*y=27.50

Step-by-step explanation:

x= price of popcorn

y= price of drink

2*x+3*y= 18.25 ; this is information for Mohamed

4*x+2*y=27.50 ; this is informtion for miguel

solve an equation for y

2y=27.50-4x

y=13.75-2x

substitue into other equation

2*x+3(13.75-2x)=18.25

2*x+41.25-6x=18.25

-4x+41.25=18.25

-4x=-23

x=5.75 ; price of a single popcorn

swap x=5.75 into the other equation

4*5.75+2*y=27.50

2y=4.5

y=2.25 ; price of a drink

put back in to check work

2*5.75+3*2.25

11.5+6.75=18.25

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e-lub [12.9K]

Answer:

X=-3/2

Step-by-step explanation:

1/4+1/2+X=-3/4

X=-3/4-1/4-1/2

X=-3/2

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(2 x 1 )+ (6 x 1/1000) in a standard form
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Answer:

(2 x 1) + (6 x 1/1,000)  

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Step-by-step explanation:

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2 years ago
Read 2 more answers
Write the following comparison as a ratio reduced to lowest terms.<br> 114 hours to 13 days
kicyunya [14]

The ratio of 114 hours to 13 days is 19:52.

<h3>How to calculate the ratio?</h3>

It should be noted that ratio is simply used to show the comparison between two things that are illustrated.

In this case, we want to calculate the ratio of 114 hours to 13 days. It should be noted that 24 hours make one day. Therefore, 13 days will be:

= 13 × 24 = 312 hours.

The ratio of 114 hours to 13 days will be:

= 114 / 312

= 19 / 52

The ratio is 19:52.

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6 0
1 year ago
Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator
SpyIntel [72]
\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}
\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)

When x=3, you're left with

147=49a_1\implies a_1=\dfrac{147}{49}=3

When x=\sqrt2 or x=-\sqrt2, you're left with

\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}

Adding the two equations together gives -10=2a_5, or a_5=-5. Subtracting them gives 2\sqrt2=2\sqrt2a_4, a_4=1.

Now, you have

5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)
5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)
2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that a_2x^4=2x^4 and a_3(-3)(-2)=6a_3=-6. These alone tell you that you must have a_2=2 and a_3=-1.

So the partial fraction decomposition is

\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}
7 0
3 years ago
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