1. Draw a triangle ABC with A(6,10), B(7,6), and C(10,7).

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:

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2 years ago

Having just turned 16 years old, your friend has their mind set on buying a new car by the time they turn 20 years old. They can

DanielleElmas [232]

having just turned 16 years old, your friend has their mind set on buying a new car by the time they turn 20 years old

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3 years ago

What is thesimple interest rate if you borrowed $3000 at 7% for 10 years?

dlinn [17]

Answer:

poopppppppppppppppppppppeeeee

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3 years ago

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185 times 28 please help me

aev [14]

The answer is 5,180! I used a calculator

3 0

3 years ago

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Three ballet dancers are positioned on stage. Elizabeth is straight behind Hannah and directly left of Manuel. If Hannah and Eli

ki77a [65]

Answer: Elizabeth and Manuel have a distance of 4 meters between them.

Step-by-step explanation: Please refer to the picture attached.

From the information given, Elizabeth is directly behind Hannah and directly left of Manuel. That means we have three points which are HEM, that is, we now have triangle HEM. The longest side (hypotenuse) which is the distance between Hannah and Manuel is given as 5 meters while the other side the distance between Hannah and Elizabeth is given as 3 meters.

We shall apply the pythagoras theorem in solving for the unknown side, EM.

The Pythagoras theorem states thus;

AC² = AB² + BC²

Where AC is the hypotenuse, and AB and BC are the other two sides.

Substituting for the known values, we now have;

5² = 3² + EM²

25 = 9 + EM²

Subtract 9 from both sides of the equation

16 = EM²

Add the square root sign to both sides of the equation

√16 = √EM²

4 = EM

Therefore the distance between Elizabeth and Manuel is 4 meters

8 0

3 years ago