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3 years ago

Solving system of equations by substitution

1 answer:

5 0

Y=3x-10 and 3x+2y=16
y=3x-10
subsitute 3x-10 for y in other equation

3x+2y=16
3x+2(3x-10)=16
distribute
3x+6x-20=16
9x-20=16
add 20 both sides
9x=36
divide both sides by 9
x=4

sub back

y=3x-10
y=3(4)-10
y=12-10
y=2

x=4
y=2
(4,2) is soluiton

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Lines k and n are perpendicular.if the slope of line k is -6,what is the slope of line n?

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Answer:

1/6

Step-by-step explanation:

Well perpendicular lines are reciprocals of each other,

meaning if like k has a slope of -6 then line n will have a slope of positive 1/6.

Thus,

line n has a slope of 1/6.

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Belle walks 7/10 mile each morning, and 1, 4/10 miles each evening.

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Answer:

10.5 miles.

Step-by-step explanation:

If she walks 7/10 of a mile each morning, and 1, 4/10 of a mile each day, Belle walks a total of 2 1/10 of a mile each day (2.1) miles each day)

We can just multiply the amount of miles per day by 5, (2.1 x 5) and we get 10.5 miles total.

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2 years ago

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777dan777 [17]

Answer:

$0 < p ≤ $25

Step-by-step explanation:

We know that coach Rivas can spend up to $750 on 30 swimsuits.

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C ≤ $750

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C = 30*p

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30*p ≤ $750.

To find the possible values of p, we just need to isolate p in one side of the inequality.

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(30*p)/30 ≤ $750/30

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And we also should add the restriction:

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3 years ago

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Oliga [24]

Answer:

Part A)

The height of the water level in the rectangular vessel is 2 centimeters.

Part B)

4000 cubic centimeters or 4 liters of water.

Step-by-step explanation:

We are given a cubical vessel that has side lengths of 10cm. The vessel is completely filled with water.

Therefore, the total volume of water in the cubical vessel is:

$V_{C}=(10)^3=1000\text{ cm}^3$

This volume is poured into a rectangular vessel that has a length of 25cm, breadth of 20cm, and a height of 10cm.

Therefore, if the water level is h centimeters, then the volume of the rectangular vessel is:

$V_R=h(25)(20)=500h\text{ cm}^3$

Since the cubical vessel has 1000 cubic centimeters of water, this means that when we pour the water from the cubical vessel into the rectangular vessel, the volume of the rectangular vessel will also be 1000 cubic centimeters. Hence:

$500h=1000$

Therefore:

$h=2$

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To find how how much more water is needed to completely fill the rectangular vessel, we can find the maximum volume of the rectangular vessel and then subtract the volume already in there (1000 cubic centimeters) from the maximum volume.

The maximum value of the rectangular vessel is given by :

$A_{R_M}=20(25)(10)=5000 \text{ cm}^3$

Since we already have 1000 cubic centimeters of water in the vessel, this means that in order to fill the rectangular vessel, we will need an additional:

$(5000-1000)\text{ cm}^3=4000\text{ cm}^3$

Sincer 1000 cubic centimeters is 1 liter, this means that we will need four more liters of water in order to fill the rectangular vessel.

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