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DiKsa [7]
3 years ago
15

During one month, a homeowner used 600 units of electricity and 100 units of gas for a total cost of $344. The next month, 400 u

nits of electricity and 250 units of gas were used for a total cost of $299. Find the cost per unit of gas.
Mathematics
1 answer:
leonid [27]3 years ago
4 0

Answer: the cost per unit of gas is $0.38

Step-by-step explanation:

Let x represent the cost per unit of electricity.

Let y represent the cost per unit of gas.

During one month, a homeowner used 600 units of electricity and 100 units of gas for a total cost of $344. It means that

600x + 100y = 344- - - - - - - - - -1

The next month, 400 units of electricity and 250 units of gas were used for a total cost of $299.

It means that

400x + 250y = 299- - - - - - - - - -1

Multiplying equation 1 by 400 and equation 2 by 600, it becomes

240000x + 40000y = 137600

240000x + 150000y = 179400

Subtracting, it becomes

- 110000y = - 41800

y = - 41800/- 110000

y = 0.38

Substituting y = 0.38 into equation 1, it becomes

600x + 100 × 0.38 = 344

600x + 38 = 344

600x = 344 - 38 = 306

x = 306/600

x = 0.51

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Step-by-step explanation:

multiply 150 by 50

8 0
2 years ago
Anyways I’m so close! Sleep here I come lol
a_sh-v [17]

Answer:

558

Step-by-step explanation:

930

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Hope this helped!

3 0
3 years ago
Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t
Tresset [83]

Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = xyz

with subject to x+2y+3z=9

So, let z=\dfrac{9-x-2y}{3}

So, Volume becomes,

V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}

Partially derivative wrt x and y we get that

9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9

By solving these two equations, we get that

x=3,y=\dfrac{3}{2}

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So, Volume of largest rectangular box would be

xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5

Hence, the volume of largest rectangular box is 4.5 units.

4 0
3 years ago
PLZ HELP / FILL IN THE BLANK
klemol [59]

Answer:

16

Step-by-step explanation:

Divide 20 by 100 then multiply it by 80, which gives you 16.

5 0
2 years ago
How many terms are in the arithmetic sequence 1313, 1616, 1919, ……, 7070, 7373?
Nataliya [291]
To find the number of terms in the arithmetic sequence, we need to use the formula 
a_{n}= a_{1}+(n-1)d    
where a_{n} is the nth number, a_{1} is the first number, n is the number of terms and d is the difference of the two consecutive numbers.
7373 = 1313 + (n - 1)(303)
7373 = 1313 + 303n - 303
7373 = 1010 + 303n
7373 - 1010 = 303n
6363 = 303n
6363 ÷ 303 = n
n = 21

Therefore, there are 21 terms in the arithmetic sequence given.
7 0
3 years ago
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