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vodka [1.7K]
3 years ago
7

Indicate in standard form the equation of the line passing through the given point and having the given slope. R(4, 0), m = 5

Mathematics
2 answers:
Sergio039 [100]3 years ago
5 0
5x + -1y = 20
You can simplify it to 5x-y=20
adoni [48]3 years ago
3 0

Answer:

5x-y=20

Step-by-step explanation:  

We are asked to find the standard form of the equation of line, which passes through point R(4,0) and having a slope of 5.

First of all, we will write equation of line in point-slope form:

(y-y_1)=m(x-x_1), where,

m=slope of line,

(x_1,y_1) = Coordinates of point that lies on the line.

Upon substituting our given values in point-slope form of equation we will get,

(y-0)=5(x-4)

Now, we will convert our equation into standard form of equation:ax+by=c

Upon using distributive property we will get,

y=5x-20

Now we will subtract 5x from both sides of our equation as:

-5x+y=5x-5x-20

-5x+y=-20

Upon multiplying our equation by -1, we will get,

5x-y=20

Therefore, our required equation would be 5x-y=20.

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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
What property of a rhombus is used in this proof of showing that a triangle is an equilateral triangle?
iragen [17]

Answer:

Step-by-step explanation:

4 0
2 years ago
The table gives predictions of the average costs of a gasoline car after the year 2030. Which graph best represents the relation
kiruha [24]

Answer:

It's the b graph

Step-by-step explanation:

Khan Academy.

4 0
2 years ago
Read 2 more answers
How much simple interest would be paid on a loan of 10,170 at 7.64% for 272 days
Anastasy [175]

Answer:

I'll setup the problem and you can compute the answer

Step-by-step explanation:

The formula for simple:

I = P*r*t

I = interest

P = loan amount

r = interest rate per period (period = days)

n = number of periods

P = 10,170

r = .0764/365

t = 272

6 0
3 years ago
Sue receives a monthly salary of $500. She also receives a sales commision of
artcher [175]

Answer:

2000 because you got to subtract

5 0
2 years ago
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