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3 years ago

The sum of three consecutive even integers is 126. Let x represent the least consecutive integer.

1 answer:

4 0

Just as an example, three consecutive integers might be 4,5,6.

If x is the least of these (4 in our example), then the other two integers would be x+1, and x+2.

Then the sum of our three integers is x + (x+1) + (x+2).

Addition is commutative so we can switch any two terms, and it is also associative so we can regroup any terms. This lets is rearrange things with all the "x" together and all the numbers together like this:

(x+x+x) + (1+2) OR 3x + 3

According to the problem, the sum is 126, so 3x+3 = 126.
3x = 123
x = 41 (which is the smallest consecutive integer)

Check our answer: 41 + 42 + 43 = 126.

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6. Calculate the area of the octagon in the<br> figure below.

Kryger [21]

Answer:

$41\text{ [units squared]}$

Step-by-step explanation:

The octagon is irregular, meaning not all sides have equal length. However, we can break it up into other shapes to find the area.

The octagon shown in the figure is a composite figure as it's composed of other shapes. In the octagon, let's break it up into:

4 triangles (corners)
3 rectangles (one in the middle, two on top after you remove triangles)

<u>Formulas</u>:

Area of rectangle with length $l$ and width $w$ : $A=lw$
Area of triangle with base $b$ and height $h$ : $A=\frac{1}{2}bh$

<u>Area of triangles</u>:

All four triangles we broke the octagon into are congruent. Each has a base of 2 and a height of 2.

Thus, the total area of one is $A=\frac{1}{2}\cdot 2\cdot 2=2\text{ square units}$

The area of all four is then $2\cdot 4=8$ units squared.

<u>Area of rectangles</u>:

The two smaller rectangles are also congruent. Each has a length of 3 and a width of 2. Therefore, each of them have an area of $3\cdot 2=6$ units squared, and the both of them have a total area of $6\cdot 2=12$ units squared.

The last rectangle has a width of 7 and a height of 3 for a total area of $7\cdot 3=21$ units squared.

Therefore, the area of the entire octagon is $8+12+21=\boxed{41\text{ [units squared]}}$

4 0

3 years ago

£54 is 10% off what is the the original price

Schach [20]

Answer:

48.6

Step-by-step explanation:

50/10=5

4/10=.4

54-5.4=48.6

6 0

2 years ago

Please help me i need help bad

Elena L [17]

Answer:

Line segment A' B' has a length of 2 units, and line segment C' D' has a length of 4 units.

Step-by-step explanation:

All we need to do is count the units in between the line segments.

3 0

2 years ago

Your friends and you notice a classmate who always has brand new clothes, shoes, and electronics. What would you need to know in

sashaice [31]

To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

<h3>What is an asset?</h3>

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

Learn more about assets on:

brainly.com/question/25746199

#SPJ1

5 0

2 years ago

What is: ⅛ ( 64v + 24) =

Illusion [34]

Answer:

8v + 3.

Step-by-step explanation:

1/8 * 64v + 1/8 * 24