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3 years ago

The sum of 5 consecutive even numbers is 100. What is the first number in this sequence?

Mathematics

1 answer:

gayaneshka [121]3 years ago

4 0

Answer:

Step-by-step explanation:

Let's represent this with an equation, where x is the first number. The next number must be x+2, because it has to be even, not x+1, and the rest continue the same way:

x+(x+2)+(x+4)+(x+6)+(x+8) = 100

Solve for x.

5x+20 = 100

5x = 80

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Determine if the given side lengths could be used to form a unique triangle, many different triangles, or no triangles. explain

ehidna [41]

Given sides of length 300 mm or 190 mm, you can form 4 different triangles:

equilateral with sides 190 mm
equilateral with sides 300 mm
isosceles with two sides 190 mm and one side 300 mm
isosceles with two sides 300 mm and one side 190 mm

The triangle inequality requires the sum of the lengths of any two sides be not less than the length of the third side. Since 2×190 > 300, you can mix and match these side lengths any way you want. With three sides and 2 choices for each, there are only a limited number of possibilities.

In the above, we have not listed ones that are simply rotations or reflections of a congruent triangle. (A 190-190-300 triangle looks the same as a 190-300-190 triangle, for example.)

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3 years ago

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2 years ago

The Patronete Winery's tastiest wine must have a 12% alcohol content. How many gallons of wine with a 9% alcohol content must be

erik [133]

Answer: 3000 gallon

Step-by-step explanation:

Here, The total quantity of 15% alcohol content = 3000 gallon

And, in which quantity of alcohol = 15% of 3000 gallon = 450 gallon.

Let the total quantity of 9% alcohol content = x

In which quantity of alcohol = 9% of x gallon= 9x/100 gallon

Now, according to the question, The wine with a 9% alcohol content will be mixed with 3,000 gallons of wine with a 15% alcohol content in order to achieve the desired 12% alcohol content.

Thus, the total quantity of mixture of 12% alcohol content = The total quantity of 15% alcohol content + total quantity of 9% alcohol content

= 3000 + x

In which quantity of alcohol = 12 % of ( 3000+x) = (360 + 12x/100) gallon ---(1)

But, the quantity of alcohol in 12 % of alcohol content = quantity of alcohol in 15% of alcohol content + quantity of alcohol in 9% of alcohol content

The quantity of alcohol in 12 % of alcohol content = (450 + 9x/100) gallon ---(2)

On equating equation (1) and (2)

We get, 360 + 12x/100 = 450 + 9x/100

⇒ 3x/100 = 90

⇒ x = 3000

Therefore, The total quantity of the mixture of 9% alcohol content = 3000

6 0

3 years ago

the table shows the number of minutes Tim has for lunch and study hall. he calculates that these two periods account for 18% of

EleoNora [17]

Tim spends 500 minutes at the school.

Step-by-step explanation:

Given,

Time for lunch = 45 minutes

Time for study hall = 45 minutes

Total = 45+45 = 90 minutes

This represents 18% of the total minutes Tim spend at school.

Let,

x be the total minutes Tim spend at school.

18% of x = 90 minutes

$\frac{18}{100}x=90\\\\0.18x=90$

Dividing both sides by 0.18

$\frac{0.18x}{0.18}=\frac{90}{0.18}\\x=500$

Tim spends 500 minutes at the school.

Keywords: percentage, division

Learn more about division at:

#LearnwithBrainly

5 0

3 years ago

A bedroom has a length of x+ 3 feet and a width of x-1 feet. Write a polynomial to express the area of the bedroom. Then calcula

jekas [21]

Answer:

Step-by-step explanation:

Length = x+3

Width = x-1

Area = l*b

where l is the length of the bedroom

and b is the breadth or width of the bedroom

The polynomial can be written as:

Area=(x+3)(x-1)

Now we will find the area of the room when x=10

First we will find the values of length and width.

Length = x+3

Length = 10+3 = 13

Width = x-1

Width = 10-1=9

Now put the values in the formula:

Area=l*b

Area=13*9

Area = 117 square feet....

3 0

3 years ago