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1 year ago

7

Ashley spent 3x + 2hours on her science project and Adam spent 4x - 6 hours on his science project. If they spent a total of 31

hours on their projects, find the value of x

1 answer:

miv72 [106K]1 year ago

6 0

Answer:

x = 5

Step-by-step explanation:

Ashley and Adam spent a total of 31 hours on their projects so: 3x+2+4x-6 = 31

3x+2+4x-6 = 31

7x-4 = 31

7x = 35

x = 5

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Beaker A contains 1 liter which is 30 percent oil and the rest is vinegar, thoroughly mixed up. Beaker B contains 2 liters which

alekssr [168]

Answer:

1.25 liters of oil

Step-by-step explanation:

Volume in Beaker A = 1 L

Volume of Oil in Beaker A = 1*0.3 = 0.3 L

Volume of Vinegar in Beaker A = 1*0.7 = 0.7 L

Volume in Beaker B = 2 L

Volume of Oil in Beaker B = 2*0.4 = 0.8 L

Volume of Vinegar in Beaker B = 1*0.6 = 1.2 L

If half of the contents of B are poured into A and assuming a homogeneous mixture, the new volumes of oil (Voa) and vinegar (Vva) in beaker A are:

$V_{oa} = 0.3+\frac{0.8}{2} \\V_{oa} = 0.7 \\V_{va} = 0.7+\frac{1.2}{2} \\V_{va} = 1.3$

The amount of oil needed to be added to beaker A in order to produce a mixture which is 60 percent oil (Vomix) is given by:

$0.6*V_{total} = V_{oa} +V_{omix}\\0.6*(V_{va}+V_{oa} +V_{omix}) = V_{oa} +V_{omix}\\0.6*(1.3+0.7+V_{omix})=0.7+V_{omix}\\V_{omix}=\frac{0.5}{0.4} \\V_{omix}=1.25 \ L$

1.25 liters of oil are needed.

6 0

2 years ago

Part A: The area of a square is (9x2 − 12x + 4) square units. Determine the length of each side of the square by factoring the a

Sladkaya [172]

Answer:

Part A: The length of each side is $3x-2$ units long.

Part B: The dimensions are 5x-4 and 5x+4 units long.

Step-by-step explanation:

Part A:

--> $9x^2-12x+4$

--> Multiply 9 times 4 to see the factors of that product

--> 9 times4 = 36

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

Use the factor 6 and make it negative so -6

add another -6

Keep in mind that it is -6x

--> 9x^2-6x-6x+4

Separate the four terms into two different binomials

--> 9x^2-6x and -6x+4

Factor the binomials

With 9x^2-6x you can factor a 3x

So it will 3x(3x-2)

Do the same thing with -6x+4

You can factor out a -2

-2(3x-2)

The reason you factor out a -2 and not 2 is because it has to be same so in this case it is (3x-2)

Take the two numbers that you factored and put them to make an expression so (3x-2)

--> (3x-2)(3x-2) or (3x-2)^2

3x-2 is the length of each side so it is 3x-2 units long

Part B:

-->25x^2-16y^2

Use the difference of squares

take the square root of 25x^2

that is 5x

take the square root of 16y^2

that is 4y

write it in this way (5x+4y)(5x-4y)

These are the dimensions of the rectangle

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2 years ago

Convert a speed of 651 mi/hr to units of feet per minute. also show the unit analysis by dragging components into the unit-facto

ladessa [460]

We know that 60 minutes = 1 hour and 1 mile = 5280 feet. We just need to multiply and simplify:

651 miles/hour = 651 *5280/60 feet/minutes = 651*88 feet/minutes = 57288 feet/minutes

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3 years ago

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Please find it <br>please help

Sedbober [7]

Answer:

29/30

Step-by-step explanation:

11/12 + 1/20

220+12/240

232/240 ........divide it by 8

29/30

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2 years ago

Which expression is equivalent to 10k+17-7j-18-11k?

balu736 [363]

Answer:

B. -7j-k-1

Step-by-step explanation:

Simplify:

1. IDENTIFY LIKE TERMS

<em>10k</em>+17-7j-18-<em>11k</em>

<em>10k and -11k are like terms since they have the same variable.</em>

17 and -18 are like terms since they are regular numbers.

-7j has no like terms.

2. COMBINE LIKE TERMS

-7j-<em>k</em>-1

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2 years ago

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