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ELEN [110]
2 years ago
8

an employee adds 160 fluid ounces of chemical to a feature that holds 120,000 gallons of water. did the employee add yhe correct

amount?
Mathematics
1 answer:
Hitman42 [59]2 years ago
5 0
We are given a volume of 160 fluid ounces of chemical which is added to a container that holds 120,000 gallons of water. Assuming that the chemical has the same density as water, we just need to convert 120,000 gallons to ounces.

A conversion factor is taken from literature, 1 gallon is equivalent to 128 fluid ounces. So 160 fluid ounces is only 1.25 gallons, thus occupying minimal space in the container. The employee could add more of the chemical in the container. He can actually add 15360000 fluid ounces in total. 
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Find an explicit formula for the arithmetic sequence 12, 5, -2, -9,...12,5,−2,−9,...12, comma, 5, comma, minus, 2, comma, minus,
Andrew [12]

Answer:

A(n) = 19 - 7n

Step-by-step explanation:

12, 5, -2, -9,...

First term, a = 12

Common difference, d = a2 - a1

a2 = 5

a1 = 12

Common difference, d = a2 - a1

= 5 - 12

= -7

d = -7

A(n) = a + (n - 1)d

A(n) = 12 + (n - 1) -7

= 12 + (-7n + 7)

= 12 - 7n + 7

= 12 + 7 - 7n

= 19 - 7n

A(n) = 19 - 7n

5 0
2 years ago
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What algebraic expression represents GK, if GK =37, what are GH and JK. GJ=4x+2 and HK=6x-1
torisob [31]

Answer:

The answer is "GK=37, GH=14, and JK=19 ".

Step-by-step explanation:

In the question, an attachment file is missing.so, please find its attached file.

Given values:

GJ=4x+2

HK=6x-1

GK =37

Find:

HJ=?

GK = GJ+JK

     = GJ+(HK-HJ)

     = 4x+2+((6x-1)-x)

     = 4x+2+6x-1-x

     =  

9x+1...(a)

Solve equation (a) and put the value of x in the equation:

      =9(4)+1

       =36+1

       =37

find GH and JK=?

Given:

GK=37

Formula:  

GH = GJ-HJ

      = 4x+2- x

      = 3x+2....(b)

Solve equation (a):

GK= 9x+1

37=9x+1

36=9x

x=4....(c)

put the value of equation (b) in equation (c)

GH = 3x+2

      = 3(4)+2

      = 12+2

      = 14

Formula:

JK= HK-HJ

    = 6x-1- x

    = 5x-1

put the value of x in the above equation:

     = 5(4)-1

     = 20-1

     =19

8 0
2 years ago
Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form? Y = 3 (x minus seven-halves) squared minus StartFraction 27
densk [106]

Answer: y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction

or

y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}

Step-by-step explanation:

Vertex form of equation : f (x) = a(x - h)^2 + k,where (h, k) is the vertex of the parabola.

y=3(x-2)^2-(x-5)^2\\\\=3(x^2+4-4x)-(x^2+25-10x)\\\\=3x^2+12-12x-x^2-25+10x\\\\=2x^2-2x-13\\\\=2(x^2-x-\dfrac{13}{2})\\\\=2(x^2-x+\dfrac{1}{4}-\dfrac{1}{4}-\dfrac{13}{2})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{1+26}{4})\\\\=2((x-\dfrac{1}{2})^2-\dfrac{27}{4})=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}

Hence, the vertex form of the equation is y=2((x-\dfrac{1}{2})^2)-\dfrac{27}{2}

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What input value produces the same output value for the two functions on the graph ?
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we know that

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so

the point of intersection is (4,3)

for an input value equal to 4

the output value for both functions is 3

therefore

<u>the answer is the option</u>

X= 4

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