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Helen [10]
3 years ago
5

Yan has already finished 3/5 of the 45 math problems he was assigned today. Each math problem took him 1 4/5 of a minute to comp

lete. If this pace continues, how much more time, to the nearest minute, will the rest of the problems take him to finish?
Mathematics
1 answer:
kobusy [5.1K]3 years ago
3 0

Answer:

He will finish the rest of the problems in 32.4 minutes.

Step-by-step explanation:

Since we are given that Yan has completed 3/5 of 45 problems i.e.

\frac{3}{5}*45

27

Thus he has completed 27 problems

Remaining no. of problems are 45-27 = 18

Since he complete each problem in minutes = 1\frac{4}{5} =\frac{9}{5} =1.8

So, he completes 18 problems in minutes = 18 *1.8 = 32.4 minutes

Hence , He will finish the rest of the problems in 32.4 minutes.


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Svetlanka [38]
I suppose the answer is b. Graph the system to show all possible solutions
8 0
3 years ago
Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value
MArishka [77]

Answer:

  • y = 81-x
  • the domain of P(x) is [0, 81]
  • P is maximized at (x, y) = (54, 27)

Step-by-step explanation:

<u>Given</u>

  • x plus y equals 81
  • x and y are non-negative

<u>Find</u>

  • P equals x squared y is maximized

<u>Solution</u>

a. Solve x plus y equals 81 for y.

  y equals 81 minus x

__

b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.

  P equals x squared left parenthesis 81 minus x right parenthesis

__

c. Find the domain of the function P found in part b.

  left bracket 0 comma 81 right bracket

__

d. Find dP/dx. Solve the equation dP/dx = 0.

  P = 81x² -x³

  dP/dx = 162x -3x² = 3x(54 -x) = 0

The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...

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7 0
3 years ago
3x+10y=13<br> 4(-2y+x)-9x=13
mart [117]

Answer:

x=-9

y=4

Step-by-step explanation:

3x+10y=13 ← Equation 1

4(-2y+x)-9x=13\\

By simplifying the above equation we get,

-8y+=4x-9x=13 (Simplifying the brackets)

-8y-5x=13 (By subtracting -9x from +4x) ← Equation 2

Multiply Equation 1 by 5 and Equation 2 by 3 and add them together.

Equation 1 multiplied by 5 will give,

15x+50y=65

Equation 2 multiplied by 3 will give,

-24y-15x=39

Add those together,

15x+50y-24y-15x=65+39

26y=104 (After simplifying x values)

Therefor y=4

By substituting y=4 to Equation 1 we get,

3x+10*4=133x+40=13\\3x=-27\\x=-9

Therefor we can say,

x=-9

y=4

8 0
3 years ago
1( m² + 15m + 56) = (____) (m+8)<br>2 a² +5ab + 6b²=(a +2b (_____)<br><br>pastor po ​
Nutka1998 [239]

Step-by-step explanation:

1.

{m}^{2}  + 15m + 56 = ( \:  \:  \:  \:  \: )(m + 8) \\ solution \\  \:  \: taking \: lhs \\   = {m}^{2}  + 15m + 5 \\   = {m}^{2}  + (7 + 8)m + 56 \\ \:  \:  \: \:    = {m}^{2}  + 8m + 7m + 56 \:  \:  \\ now \: taking \: common \: factor \\  m(m + 8) + 7(m + 8) \\ (m + 7)(m + 8) \\ now \\  {m}^{2}  + 15m + 56 = (m + 7)(m + 8)

2.

{a}^{2}  + 5ab +  6 {b}^{2} = ( a + 2b)( \:  \:  \:  \:  \:  \:  \:  \: ) \\ solution \\ taking \:  \: lhs \\  =  {a}^{2}  + 5ab + 6 {b}^{2} \\ =  {a}^{2}  + ( 3+ 2)ab + 6 {b}^{2} \\  =  {a}^{2}  + 3ab + 2ab + 6 {b}^{2}  \\now \: taking \: common \: factor \\ a(a + 3b) + 2b(a + 3) \\ (a + 2b)(a + 3) \\ now \\ {a}^{2}  + 5ab +  6 {b}^{2} = ( a + 2b)( a + 3) ans

this may help you(:

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2 years ago
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Gemiola [76]
The slope is 1/6. y= mx + b
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