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3 years ago

If the sum of three consecutive integers is 36, what is the smallest of these integers?

Mathematics

1 answer:

DedPeter [7]3 years ago

5 0

Let the three consecutive equals:
x, x+1, x+2

sum:
x+(x+1)+(x+2) = 36
3x + 3 = 36
x+1 = 36/3
x+1 = 12
x=12-1
x=11

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Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction. Samuel traveled 3km/h fa

12345 [234]

Samuel was going with 40 km/h and Heather was going with 37 km/h

Step-by-step explanation:

Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction

Samuel traveled 3 km/h faster than Heather
After 3.5 h Samuel stopped for a half-hour break, but Heather kept going
Heather was 8 km ahead of Samuel

We need to find how fast each was going

Assume that Heather's speed is x km/h

∵ Heather's speed = x km/h

∵ Samuel traveled 3 km/h faster than Heather

∴ Samuel's speed = x + 3 km/h

The formula of the distance is distance = speed × time

∵ Samuel travel for 3.5 hours

- Find the distance that Samuel traveled in 3.5 h

∴ Samuel distance = (x + 3) × 3.5

- Multiply the bracket by 3.5 to simplify

∴ Samuel distance = 3.5x + 10.5

∵ Samuel took a break for half hour

∵ Heather kept going

∵ At the end of the break, Heather was 8 km ahead of Samuel

- That means Heather was going for 4 hours (3.5 + 0.5), and her

distance is longer than Samuel distance by 8 km

∴ Heather distance = x × 4 = 4x

- Subtract the distance of Samuel from the distance of Heather

and equate the difference by 8

∵ 4x - (3x + 10.5) = 8

∴ 4x - 3x - 10.5 = 8

- Add the like terms in the left hand side

∴ 0.5x - 10.5 = 8

- Add 10.5 to both sides

∴ 0.5x = 18.5

- Divide both sides by 0.5

∴ x = 37

∵ x represents Heather's speed

∴ Heather's speed = 37 km/h

∵ x + 3 represents Samuel's speed

∴ Samuel's speed = 37 + 3 = 40 km/h

Samuel was going with 40 km/h and Heather was going with 37 km/h

Learn more:

You can learn more about the equation of motion in brainly.com/question/568302

#LearnwithBrainly

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3 years ago

Brand A scooter has a top speed that goes 2 miles per hour faster than Brand B. if after hours, Brand A scooter traveled 24 mile

Leni [432]

Your answer would be 22mph

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3 years ago

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Sin(2x+30°)=1 <br> Tìm x <br> Cảm ơn vì giúp đỡ

Pie

Answer:

Step-by-step explanation:

This question is asking us to find where sin(2x + 30) has a sin of 1. If you look at the unit circle, 90 degrees has a sin of 1. Mathematically, it will be solved like this (begin by taking the inverse sin of both sides):

$sin^{-1}[sin(2x+30)]=sin^{-1}(1)$

On the left, the inverse sin "undoes" or cancels the sin, leaving us with

2x + 30 = sin⁻¹(1)

The right side is asking us what angle has a sin of 1, which is 90. Sub that into the right side:

2x + 30 = 90 and

2x = 60 so

x = 30

You're welcome!

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3 years ago

- 7(2-1) = 28<br> The solution is?

Aneli [31]

Answer:

Is there a x somewhere or is that litteraly how the equation is?

If so, -7 multiplied by 2 is -14,

-1 times -7 is 7,

add it together and you get

-7=28,

you could add 7 to both sides or subtract 28 from both sides and you'll get either 0=35 or -35=0

which would make the solution false since both sides are not the same

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3 years ago

THIS IS URGENT! PLZ HELP!

Yanka [14]

Answer:

Step-by-step explanation:

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