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2 years ago

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What is the area of the playground shown? The edges of the playground meet at right angles, except for the edge whose length is

not given. Show all work.

1 answer:

Dennis_Churaev [7]2 years ago

3 0

Answer:

520,000

Step-by-step explanation:

1400 x 200 = 280000

(400 + 800) x 400 /2 = 240000

240000 + 280000 = 520000

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Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Prope

ziro4ka [17]

Given:

Expression is

$3r^2-2r+4$

To prove:

If r is any rational number, then $3r^2-2r+4$ is rational.

Step-by-step explanation:

Property 1: Every integer is a rational number. It is Theorem 4.3.1.

Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.

Let r be any rational number.

We have,

$3r^2-2r+4$

It can be written as

$3(r\times r)-2r+4$

Now,

3, -2 and 4 are rational numbers by property 1.

$r^2=r\times r$ is rational by Property 3.

$3r^2\text{ and }-2r$ are rational by Property 3.

$3r^2+(-2r)+4$ is rational by property 2.

So, $3r^2-2r+4$ is rational.

Hence proved.

6 0

2 years ago

Howie sorkin can travel 8 miles upstream in the same time it takes him to go 12 miles downstream. His boat goes 15 mph in still

lozanna [386]

Answer: the speed of the current is 2.5 mph

Step-by-step explanation:

Let the speed of the boat be x miles per hour

Let the speed of the current be y miles per hour

Speed = distance / time

Time = distance/speed

If the boat goes 12miles downstream(in still water) at 15 mph then, the time is

12/ 15 = 0.8 hours

In still water, it means that it moved in the same direction with the current.

The total speed would be x + y. Therefore

x + y = 15 - - - - - - -1

If the boat goes 8 miles upstream in 0.8 hours, the the speed is

8/ 0.8 = 10 miles per hour

Assuming it moved in the opposite direction to the current.

The total speed would be x -y. Therefore

x - y = 10 - - - - - - -2

Adding equation 1 and equation 2, it becomes

2x = 25

x = 25/2 = 12.5

y = 15 - x

y = 15 - 12.5 = 2.5 miles per hour

8 0

3 years ago

A normal probability distribution

julia-pushkina [17]

Answer:

Option B) is a continuous probability distribution

Step-by-step explanation:

Properties of a normal probability distribution:

The mean, mode and median of the data is same.
It is a continuous probability distribution.
The area under the curve is 1.
The probability that any random variable X at a particular value is zero.

Thus, from the properties of normal distribution, the correct answer is:

Option B) is a continuous probability distribution

6 0

3 years ago

Find the volume of a cylinder with a radius of 4.8 cm and a height of 14.6 cm. [Use it =

juin [17]

Answer:

1056.24 cm^3

Step-by-step explanation:

The volume of a cylinder is $\pi r^2h$ . The problem says to use $\pi$ =3.14

Plug in your numbers $3.14*4.8^2*14.6=1056.24$

6 0

2 years ago

6. Which type of angle pair are LSM and OSN?

Elina [12.6K]

6. vertical

7. LSM and MSN are vertical angles

8. MSN

8 0

3 years ago

Read 2 more answers