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zimovet [89]
3 years ago
13

Mateo is draining a pool at a rate of 1/8 of a gallon every 1/2 hour. If he continues to drain the pool , how much waters will b

e drained in 1 hour?
Mathematics
2 answers:
11Alexandr11 [23.1K]3 years ago
8 0
If he drains 1/8 of a gallon in 1/2, the amount he will drain in one hour is twice as much as 1/8.

Mateo will drain 2/8 (simplified: 1/4) of a gallon in one hour.
masya89 [10]3 years ago
4 0
Just multiply numerator and denominator of the given rate by 2:

2(1/8) gallon        1/4 gallon
-----------------  =  ---------------- = 1/4 gallon per hour
2(1/2) hour)              1 hour
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Which of these statements is correct?
tatuchka [14]

Answer:

The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution is correct.

Step-by-step explanation:

<em>1) The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.</em>

<em>Solve these linear equations simultaneously</em>

<em>Step 1 : Find y in terms of x from any one equation</em>

6x - 5y = 8

y = <u>8 - 6x</u>

        -5

<em>Step 2 : Substitute y in terms of x from step 1 in the second equation.</em>

16x - 6y = 22

16x - 6 (<u>8 - 6x)</u> = 22

              -5

80x - 48 + 36x = 22 x -5

94x = 43

x = 0.457

<em>This statement is incorrect as it does have a solution.</em>

<em>2) The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.</em>

<em>Solve these linear equations simultaneously</em>

<em>Step 1 : Find y in terms of x from any one equation</em>

7x + 2y = 6

y = <u>6 - 7x</u>

        2

<em>Step 2 : Substitute y in terms of x from step 1 in the second equation.</em>

14x + 4y = 16

14x + 4(<u>6 - 7x)</u> = 16

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14x + 12 - 14x = 16

0 ≠ 4

<em>This statement is not true as there are no solutions.</em>

<em>3) The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.</em>

<em>Solve these linear equations simultaneously</em>

<em>Step 1 : Find x in terms of y from any one equation</em>

8x - 3y = 10

x = <u>10 + 3y</u>

        8

<em>Step 2 : Substitute x in terms of y from step 1 in the second equation.</em>

16x - 6y = 22

16(<u>10 + 3y)</u> - 6y = 22

       8

20 + 6y - 6y = 2

0 ≠ -18

<em>This statement is true because there are no solutions</em>

<em>4) The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.</em>

<em>Solve these linear equations simultaneously</em>

<em>Step 1 : Find x in terms of y from any one equation</em>

9x + 6y = 14

x = <u>14 - 6y</u>

        9

<em>Step 2 : Substitute x in terms of y from step 1 in the second equation.</em>

18x + 12y = 26

18 (<u>14 - 6y)</u> + 12y = 26

        9

8 - 12y + 12y = 26

0 ≠ 18

<em>This statement is incorrect because there are no solutions. It does not have infinite number of solutions.</em>

<em>!!</em>

8 0
3 years ago
Read 2 more answers
A man burns 10 calories per minute mountain biking and 7.5 calories per minute in-line skating. His goal is to burn approximatel
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10x = 420
420 / 10 = 42

x = 42 > ( 42,0 )

10(0) + 7.5y = 420
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y = 56 > ( 0,56 )

(42,0) (0,56)

B.) The x intercept means that there was 42 ,minutes spent biking. The y intercept means that there was 56 minutes spent in line skating.

C.) (21 ,28) - (14,37) - (28,18)
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g100num [7]

Answer:8 planes are shown in the figure

Step-by-step explanation:

5 0
3 years ago
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When Javier writes 40 on both accounts they cost him the same amount of money so it should be 41.

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anzhelika [568]
Volume of cylinder:
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1000 = πr²h
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Surface area of cylinder:
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S.A = 2πr² + 2πr(1/πr²)
S.A = 2πr² + 2/r
Now, to minimize surface area, we differentiate the expression with respect to r and equate to 0.
0 = 4πr - 1000/r²
4πr³ - 1000 = 0
r = 4.3 cm
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3 years ago
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