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3 years ago

Find how many natural numbers are there between 80 and 120

Mathematics

1 answer:

Setler [38]3 years ago

6 0

Answer:

Step-by-step explanation:

Natural numbers are numbers that occur commonly in nature and are whole non-negative numbers. Therefore, there are 40 natural numbers between 80 and 120.

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Which expression is equivalent to (81x4y16)12 for all positive values of x and y?<br> 40.5x4y16

IrinaVladis [17]

Answer:

$(81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8$

Step-by-step explanation:

Given

$(81x^4y^{16})^{\frac{1}{2}}$

Required

Determine an equivalent expression

Express 81 as $9^2$

$(9^2x^4y^{16})^{\frac{1}{2}}$

Apply law of indices

$9^2^{\frac{1}{2}} * x^4^{\frac{1}{2}} * y^{16}^{\frac{1}{2}}$

$9^{\frac{2*1}{2}} * x^{\frac{4*1}{2}} * y^{\frac{16*1}{2}}$

$9^{\frac{2}{2}} * x^{\frac{4}{2}} * y^{\frac{16}{2}}$

$9^1 * x^2 * y^8$

$9 * x^2 * y^8$

$9 x^2 y^8$

Hence:

$(81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8$

4 0

2 years ago

A 2.2 kg ball strikes a wall with a velocity of 7.4 m/s to the left. The ball bounces off with a velocity of 6.2 m/s to the righ

Naya [18.7K]

Answer:

The constant force exerted on the ball by the wall is 119.68 N.

Step-by-step explanation:

Consider the provided information.

It is given that the mass of the ball is m = 2.2 kg

The initial velocity of the ball towards left is 7.4 m/s

So the momentum of the ball when it strikes is = $2.2\times 7.4=16.28$

The final velocity of the ball is -6.2 m/s

So the momentum of the ball when it strikes back is = $2.2\times -6.2=-13.64$

Thus change in moment is: $16.28-(-13.64)=29.92$

The duration of force exerted on the ball t = 0.25 s

Therefore, the constant force exerted on the ball by the wall is:

$\frac{29.92}{0.25}=119.68$

Hence, the constant force exerted on the ball by the wall is 119.68 N.

6 0

3 years ago

Help!! Find missing value for each quadratic function

Svetllana [295]

I'll do the first one to get you started. The answer is -3

=================================================

Explanation:

When x = -1, y = 0 as shown in the first column. The second column says that (x,y) = (0,1) and the third column says (x,y) = (1,0)

We'll use these three points to determine the quadratic function that goes through them all.

The general template we'll use is y = ax^2 + bx + c

------------

Plug in (x,y) = (0,1). Simplify

y = ax^2 + bx + c

1 = a*0^2 + b*0 + c

1 = 0a + 0b + c

1 = c

c = 1

------------

Plug in (x,y) = (-1,0) and c = 1

y = ax^2 + bx + c

0 = a*(-1)^2 + b(-1) + 1

0 = 1a - 1b + 1

a-b+1 = 0

a-b = -1

a = b-1

------------

Plug in (x,y) = (1,0), c = 1, and a = b-1

y = ax^2 + bx + c

0 = a(1)^2 + b(1) + 1 ... replace x with 1, y with 0, c with 1

0 = a + b + 1

0 = b-1 + b + 1 ... replace 'a' with b-1

0 = 2b

2b = 0

b = 0/2

b = 0

------------

If b = 0, then 'a' is...

a = b-1

a = 0-1

a = -1

------------

In summary so far, we found: a = -1, b = 0, c = 1

Therefore, y = ax^2 + bx + c turns into y = -1x^2 + 0x + 1 which simplifies to y = -x^2 + 1

------------

The last thing to do is plug x = 2 into this equation and simplify

y = -x^2 + 1

y = -2^2 + 1

y = -4 + 1

y = -3

3 0

3 years ago

Consider the following pair of points.

dedylja [7]

Answer:

The answer is

<h2> $\sqrt{265} \: \: or \: \: 16.28 \: \: \: \: units$ </h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(9,-8) and (-7,-5)

The distance between them is

$d = \sqrt{ ({9 + 7})^{2} + ({ - 8 + 5})^{2} } \\ = \sqrt{ {16}^{2} + ( { - 3})^{2} } \\ = \sqrt{256 + 9} \: \: \: \: \: \: \: \: \: \\ = \sqrt{265} \: \: \: \: \: \: \\ = 16.27882$

We have the final answer as

$\sqrt{265} \: \: or \: \: 16.28 \: \: \: \: units$

Hope this helps you

4 0

3 years ago

Harry fills up his Jeep with gasoline and notes that the odometer reading is miles. The next time he fills up his Jeep, he pays

lukranit [14]

Complete question :

Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,568.7 miles. The next time he fills up his Jeep, he pays for 12.6 gallons of gasoline. He notes his odometer reading is 23,706.3 miles. How many miles per gallon did he get?

Answer:

10.9 miles per gallon

Step-by-step explanation:

Given that :

Odometer reading when filled up with gasoline = 23,568.7 miles

Odometer reading with 12.6 gallons of gasoline = 23,706.3 miles

Miles per gallon gotten :

(Current Odometer reading - reading when filled up) / gallon of gasoline

(23706.3 - 23568.7) / 12.6

= 10.920634

= 10.9 miles per gallon

6 0

2 years ago

Find how many natural numbers are there between 80 and 120​

Find how many natural numbers are there between 80 and 120