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Elanso [62]
3 years ago
5

Solve the following equations: 5–(6+9x)=9–(4x–1)

Mathematics
1 answer:
Advocard [28]3 years ago
8 0

Answer:

x=4/13

Step-by-step explanation:

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This is the pond in a shape of a prism, it is completely full of water. Colin uses a pump to empty the pond. The level goes down
AnnZ [28]

Answer:

150 minutes

Step-by-step explanation:

P.S - The exact question is -

Given - This is the pond in a shape of a prism, it is completely full of

             water. Colin uses a pump to empty the pond. The level goes

             down by 20 cm in the first 30 min.

To find - Work put how many minutes Colin has to wait for the pond

               to completely empty.

Proof -

Given that,

Height of prism = 1 m

Also,

Base of the prism is trapezium and

Sides of the trapezium are 0.6 m and 1.4 m

Height of trapezium is 2 m

We know that,

Area of trapezium = \frac{1}{2}× (sum of sides)× height

                             =  \frac{1}{2}× (0.6 + 1.4)× 2

                             =  \frac{1}{2}× (2)× 2

                             =  2 m²

⇒Area of trapezium = 2 m²

Now,

Volume of prism = Area of trapezium × height of prism

                          = 2 m² × 1 m

                          = 2 m³

⇒Volume of prism = 2 m³

Now,

Given that the level goes down by 20 cm in the first 30 min

We know

100 cm = 1 m

⇒1 cm = \frac{1}{100} m = 0.01 m

⇒20 cm = 20×0.01 m = 0.2 m

⇒The level goes down by 0.2 m in the first 30 min.

Also,

we know that height of water = height of prism = 1 m

So, the remaining water left in the pond = 1 m - 0.2 m = 0.8 m

Also,

Volume of Remaining water = Area of trapezium × height

                                           = 2 m² × 0.8 m

                                           = 1.6 m³

⇒Volume of Remaining water = 1.6 m³

Now,

Volume of emptied water = Total Volume - Volume of Remaining water

                                       = 2 m³ - 1.6 m³

                                       = 0.4 m³

⇒Volume of emptied water = 0.4 m³

Now,

0.4 m³ water will be empty in 30 minutes

⇒ 1 m³ water will be empty in \frac{30}{0.4} = 75 minutes

⇒1.6 m³ water will be empty in 1.6 × 75 = 120 minutes

∴ we get

The remaining water is empty in 120 minutes

So,

Total pond is empty in 120 + 30 minutes

⇒Total pond is empty in 150 minutes

5 0
2 years ago
Twice a number decreased by seven is equal to 43
goblinko [34]

2x-7=43

2x=50

x=25

I hope I helped you with your solution! If you could give me brainliest, I would be very thankful!

4 0
3 years ago
Read 2 more answers
A 47-foot-long piece of pipe is to be cut into three pieces. The second piece is three times as long as the first piece, and the
DanielleElmas [232]
A = first piece, b = second piece, c = third piece

a + b + c = 47
b = 3a
c = 5a + 2

a + (3a) + (5a + 2) = 47.....combine like terms
9a + 2 = 47
9a = 47 - 2
9a = 45
a = 45/9
a = 5 ft

b = 3a.....b = 3(5)....b = 15 ft
c = 5a + 2....c = 5(5) + 2.....c = 25 + 2....c = 27 ft

longest piece (c) = 27 ft
7 0
2 years ago
What is 0.8637 rounded to the nearest hundredth?
Wittaler [7]

Answer:

0.87

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Two intersecting lines lie in two planes.<br><br> A. True<br> B. False
Lady_Fox [76]
Intersecting lines can be lying in a plane. An example is the Cartesian coordinate system where systems of equations can be defined by their intesecting points by plotting the equations in the plane coordinate system. In this case, the answer to this problem is B. False
5 0
3 years ago
Read 2 more answers
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