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3 years ago

Find four consecutive multiples of 3 such that the product of the first, third, and fourth is 1080

Mathematics

1 answer:

Dovator [93]3 years ago

7 0

Answer:

Therefore, we have 6, 9, 12, and 15, that are the first, second, third and fourth consecutive multiples of 3, such the product of 6, 12 and 15 is 1,080.

Step-by-step explanation:

Let's find the factors of 1,080, as follows:

1,080 Dividing by 2 (1,080/2)

540 Dividing by 2 (540/2)

270 Dividing by 2 (270/2)

135 Dividing by 3 (135/3)

45 Dividing by 3 (45/3)

15 Dividing by 3 (15/3)

5 Dividing by 5 (5/5)

In consequence, we have:

5 * 3 * 3 * 3 * 2 * 2 * 2

Let's find out what multiples of 3 there are:

5 * 3 = 15 is a multiple of 3,

And 3 * 3 * 2 * 2 * 2 is remaining.

3 * 2 = 6 is also a multiple of 3,

And 3 * 2 * 2 is remaining

3 * 2 * 2 = 12 is also a multiple of 3.

Therefore, we have 6, 9, 12, and 15, that are the first, second, third and fourth consecutive multiples of 3, such the product of 6, 12 and 15 is 1,080.

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To rent a certain meeting room, a college charges a reservation fee of $ 46 and an additional fee of $ 6.40 per hour. The chemis

lisabon 2012 [21]

Answer:

Up to 5 hours

Step-by-step explanation:

Given:

One off fee = $46
Hourly rent = $6.4 / hr
Amount limitation= $78

Equation to reflect the condition:

78 = 46 + 6.4t
6.4t = 78 - 46
6.4t = 32
t = 32/6.4
t = 5 hours max

So, the meeting room can be rented for up to 5 hours with $78

8 0

2 years ago

S the following statement always, sometimes, or never true?

liubo4ka [24]

The statement “The supplement of an acute angle is an obtuse angle.” is always true because the sum of any two supplementary angles is 180°, so if one of them less than 90° (acute), then the other must be greater than 90° (obtuse)

Step-by-step explanation:

Let us revise some facts about the supplementary angles

Supplementary angles are two angles the sum of their measure is 180°
The two angles could be right angles or one of them is acute and the other is obtuse
The two angles can not be acute angles or obtuse angles

Let us take some examples to explain the facts above

∵ One of two supplementary angles is a right angle

∵ The measure of the right angle is 90°

∵ The sum of the measures of the supplementary angles is 180°

∴ 90 + the measure of the supplement angle = 180

- Subtract 90 from both sides

∴ The measure of the supplement angle = 90°

∴ The supplement of a right angle must be a right angle

∵ One of two supplementary angles is 70°

∵ Its measure less than 90°

∴ This angle is an acute angle

∵ The sum of the measures of the supplementary angles is 180°

∴ 70 + the measure of the supplement angle = 180

- Subtract 70 from both sides

∴ The measure of the supplement angle = 110°

∵ Its measure greater than 90°

∴ The supplement angle is an obtuse angle

∴ The supplement of an acute angle must be an obtuse angle

The two supplementary angles can not be acute angles because their sum is less than 180°

The two supplementary angles can not be obtuse angles because their sum is greater than 180°

The statement “The supplement of an acute angle is an obtuse angle.” is always true because the sum of any two supplementary angles is 180°, so if one of them less than 90° (acute), then the other must be greater than 90° (obtuse)

Learn more:

You can learn more about the supplementary angles in brainly.com/question/11175936

#LearnwithBrainly

4 0

3 years ago

Read 2 more answers

Nichol walks at a constant pace of 1.2 m/s and takes 15 minutes to get to school.

liraira [26]

Answer:

The difference between the distances they walked is 600 meters.

Step-by-step explanation:

Let's calculate the distance traveled by Nichol and Sakura with the following equation:

$d = v*t$

Where:

v: is the speed

t: is the time

The distance traveled by Nichol is:

$d_{n} = 1.2 m/s*15min*\frac{60 s}{1 min} = 1080 m$

And the distance traveled by Sakura is:

$d_{s} = 1.4 m/s*20 min*\frac{60 s}{1 min} = 1680 m$

Hence, the difference between the distances they walked is:

$d_{t} = d_{s} - d_{n} = 1680 m - 1080 m = 600 m$

Sakura traveled 600 meters more than Nichol.

Therefore, the difference between the distances they walked is 600 meters.

I hope it helps you!

4 0

2 years ago

A scale drawing of a building is one foot to 1/4 inch. What is the actual length of the building if the scale drawing shows that

Rom4ik [11]

$1\quad foot\quad :\quad \frac { 1 }{ 4 } \quad inch\\ \\ 4\quad \cdot \quad 1\quad foot\quad :\quad \frac { 1 }{ 4 } \quad inch\quad \cdot \quad 4\\ \\ 4\quad feet\quad :\quad 1\quad inch$

This means that:

$4\quad feet\quad :\quad 1\quad inch\\ \\ \frac { 27 }{ 2 } \cdot \quad 4\quad feet\quad :\quad \frac { 27 }{ 2 } \cdot \quad 1\quad inch\\ \\ \frac { 108 }{ 2 } \quad feet\quad :\quad \frac { 27 }{ 2 } \quad inches\\ \\ 54\quad feet\quad :\quad \frac { 27 }{ 2 } \quad inches\\ \\$

13 + 1/2 inches is the same as 54 feet

4 0

3 years ago

Read 2 more answers

The number of a certain company's video stores can be approximated by the linear equation y= -264x+4682, where x is the number o

ahrayia [7]

Answer:

Missing co-ordinate for the ordered pair is $(7,2834)$

Y-intercept is $(0,4682)$

X-intercept is $(17.73,0)$

Step-by-step explanation:

The number of a certain company's video stores can be approximated by the linear equation

$y= -264\ x+4682$

where $y$ is the number of stores and $x$ represents the number of years after 1990.

To find the missing co-ordinate for the ordered pair solution $(7,?)$

For the ordered pair, we are given the $x$ value which is =7 i.e 7 years after 1990. Thus we will plugin $x=7$ in the linear equation to get the $y$ value which is number of stores after 7 years from 1990.

$y= -264\ (7)+4682$

$y= -1848+4682$

$y= 2834$

Thus the ordered pair is $(7,2834)$

To find y-intercept which is the point where the line touches the y-axis, we would plugin $x=0$ in the equation as the x-coordinate is 0 at y-axis.

$y= -264\ (0)+4682$

$y= 0+4682$

$y=4682$

Thus y-intercept is at point $(0,4682)$

To find x-intercept which is the point where the line touches the x-axis, we would plugin $y=0$ in the equation as the y-coordinate is 0 at x-axis and thus for $x$