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3 years ago

Simplify the expression: 3(4d + 1)

Mathematics

2 answers:

Alexeev081 [22]3 years ago

3 0

Answer:

12d+3

Step-by-step explanation: multiply 3x4d and 3x1 and you get 12d+3

Alex Ar [27]3 years ago

3 0

Answer:

12d + 3

you have to multiply 3 times both of the numbers

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200 σ j=1 2j( j 3) describe the steps to evaluate the summation. what is the sum?

ziro4ka [17]

The sum of the equation is = 5494000.

<h3>What does summation mean in math?</h3>

The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.

<h3>Briefing:</h3>

Distribute 2j to (j+3).

Rewrite the summation as the sum of two individual summations.

Evaluate each summation using properties or formulas from the lesson.

The lower index is 1, so any properties can be used.

The sum is 5,494,000.

<h3>Calculation according to the statement:</h3>

$\sum_{j=1}^{200} 2 j(j+3)$

simplifying them we get:

$\sum_{j=1}^{200} 2 j^{2}+6 j$

Split the summation into smaller summations that fit the summation rules.

$\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j$

$\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}$

The formula for the summation of a polynomial with degree 2

is:

$\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}$

Substitute the values into the formula and make sure to multiply by the front term.

$(2)$$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$$$

we get: 5373400

Evaluating same as above : $6 \sum_{j=1}^{200} j$

we get: 120600

Add the results of the summations.

5373400 + 120600

= 5494000

The sum of the equation is = 5494000.

To know more about summations visit:

brainly.com/question/16679150

#SPJ4

6 0

1 year ago

Can a matrix of dimensions 2 X 4 be added to another matrix with dimensions of 2 X 6?

Rus_ich [418]

Answer:

No.

Step-by-step explanation:

It has different order of matrices .

For Addition or Substraction , both matrices must have the same number of rows and columns .

8 0

3 years ago

How many square feet of outdoor carpet will we need for this hole?

Mamont248 [21]

Answer:

The area of the outdoor carpet = 60 - 6 - 6 = 48 ft²

Step-by-step explanation:

The picture below is what you are referring to .

The whole area of the shape forms a rectangle. A triangle and a rectangle has been cut off from the whole carpet rectangle. The square ft or area of the carpet is the subtraction of the area of the rectangle and triangle cut off from the whole area of the rectangle .

Area of the rectangle = Lb

where

L = 12 ft

b = 5 ft

area = 12 × 5 = 60 ft²

The cut off triangle area

area = 1/2 × base × height

area = 1/2 × 4 × 3

area = 12/2 = 6 ft²

The cut off rectangle area

area = Lb

area = 3 × 2

area = 6 ft²

The area of the outdoor carpet = 60 - 6 - 6 = 48 ft²

7 0

3 years ago

How is the process of this operation? <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%5B6%5D%7Bz%2B5%7D%20%7D%7B%20%5C

Yuki888 [10]

$a^\frac{n}{m}=\sqrt[m]{a^n}\\---------------\\\\ \dfrac{ \sqrt[6]{z+5} }{ \sqrt{z+5} } =(z+5)^\frac{1}{6}:(z+5)^\frac{1}{2}\\\\/use:a^n\cdot a^m=a^{n+m}/\\\\=(z+5)^{\frac{1}{6}+\frac{1}{2}}=(z+5)^{\frac{1}{6}+\frac{3}{6}}=(z+5)^\frac{4}{6}=(z+5)^\frac{2}{3}\\\\=\sqrt[3]{(z+5)^2}=\sqrt[3]{z^2+2z\cdot5+5^2}=\sqrt[3]{z^2+10z+25}$

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3 years ago

A movie theatre sells 3 different sizes of popcorn: small, medium, and large. An order of popcorn comes with 4 different topping

Darina [25.2K]

you can only choose 4 unique ways Step-by-step explanation:

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3 years ago

Simplify the expression: 3(4d + 1) ​

Simplify the expression: 3(4d + 1)