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matrenka [14]
3 years ago
6

15 points and brainliest!! please help !!

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
3 0
This will be solved by solving for x first. Firstly you multiply the top equation by 2 and the bottom by -3. This will change both equation to (top)-10x+6y=-54 and (bottom) 27x-6y=-57. Now when you add the factors the y-values cancel out leaving you with; 17x=-3. now you have to divide by 17 on both sides giving you x=-0.17647058823 (not the prettiest solution but you can round if you want to). After that pick an equation to solve for y (I'm picking the top); the equation will be 5(-0.17647058823)+3y=-27. multiply the negative decimal and 5 to get -0.88235294117 (again not the prettiest). Add that to both sides which will give you 3y=-26.1176470588. After this divide both sides by 3 which will give you y=-8.70588235294. Your answer is (-0.17647058823,-8.70588235294) You can divide to the second or third decimal if needed-----remember that as you round from left to right on a decimal if it's below five you leave it and if it's above 5 then round up 1. I hope this help :)
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If f(1)=3 and f(n)=-2f(n-1)+ 1, then f(5)=
AlladinOne [14]
Our function is f(n)=-2f(n-1)+1.
We want to find f(5).
Let's substitute 5 for n.
f(5) = -2f(5-1) + 1
f(5) = -2f(4) + 1
We need to know f(4).
f(4) = -2f(4-1) + 1
f(4) = -2f(3) + 1
We need to know f(3).
f(3) = -2f(3-1) + 1
f(3) = -2f(2) + 1
We need to know f(2).
f(2) = -2f(2-1) + 1
f(2) = -2f(1) + 1
We know that f(1) = 3
f(2) = -2(3) + 1
f(2) = -6 + 1
f(2) = -5
Now we can use f(2) = -5 to find f(3)...
f(3) = -2(-5) + 1
f(3) = 10 + 1
f(3) = 11
Now we can use f(3) = 11 to find f(4)...
f(4) = -2(11) + 1
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7 0
2 years ago
Read 2 more answers
Janet worked 3 hours more than David and 7 hours less than Kate. David earned $7.50 per hour, Janet earned $6 per hour, and Kate
grandymaker [24]

We want to write and solve a system of equations to see how much each person earns.

What each one earned is:

  • Janet = $78
  • Kate =  $180
  • David = $75

Let's define:

  • J = number of hours that Janet worked.
  • D = number of hours that David worked.
  • K = number of hours that Kate worked.

The information is:

<em>"Janet worked 3 hours more than David and 7 hours less than Kate"</em>

From this we can write:

J = D + 3

J = K - 7

We know that:

  • David earned $7.50 per hour.
  • Janet earned $6 per hour.
  • Kate earned $9 per hour.

Finally, we know that Kate earned $27 more than David an Janet combined, then we can write:

$9*K = $27 + ($7.50)*D + $6*J

Then we have a system of equations:

J = D + 3

J = K - 7

$9*K = $27 + ($7.50)*D + $6*J

We can rewrite the first and second equations to get:

D = J - 3

K = J + 7

Now we can replace these two in the other equation to get:

$9*(J + 7) = $27 + ($7.50)*(J - 3)+ $6*J

Now we can solve this for J:

$9*J + $63 = $27 + $7.50*J - $22.50 + $6*J

$9*J - $7.50*J - $6*J = $27 - $63 - $22.50

-$4.50*J = -$58.60

J = (-$58.60)/(-$4.50) = 13

This means that Janet worked for 13 hours.

And with:

K = J + 7 = 13 + 7 = 20

D = J - 3 = 13 - 3 = 10

We can see that Kate worked for 20 hours and David for 10 hours.

Then each one of them earned:

Janet = 13*$6 = $78

Kate = 20*$9 = $180

David = 10*$7.50 = $75

If you want to learn more, you can read:

brainly.com/question/9351049

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Sidana [21]
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Diano4ka-milaya [45]

Answer:

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Solve the system using a matrix.
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Answer:

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