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2 years ago

Please help me with this mathematics worksheet

Mathematics

1 answer:

Tatiana [17]2 years ago

5 0

Answer:

1. 3570

2.-8y+32

3. 8y-(2y^2)(1+y)

4.x-y

5. 4^2−3−^2

Step-by-step explanation:

The distributive property means that you can multiply each number in a set of parentheses by the number outside the parentheses or by the numbers in another set of parentheses instead of doing the multiplication as a whole

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What is the nth term rule of the quadratic sequence below?

Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

$6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136$

As the first differences are not the same, calculate the second differences:

$14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38$

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is: 3n²

Compare 3n² with the given sequence:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

The second operations are different, therefore calculate the differences between the second operations:

$3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18$

As the differences are the same, we need to add 5n as the second operation:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0

1 year ago

Please help and explain very easy good luck

Mars2501 [29]

Answer:

-76

Step-by-step explanation:

A positive digit multiplied by a negative digit will result as a negative digit.

So,

6 · -8 = -48

Now if there is a problem where a number is added by a negative digit number, you turn the "plus" sign into a "negative" sign.

So,

- 48 + (- 28)

-48 - 28

If you subtract a negative by a negative, the answer will be negative BUT you have to ADD those two negative digits together and put the negative sign after.

- 48 - 28 = -76

7 0

2 years ago

Read 2 more answers

Drag the tiles to the boxes to form correct pairs. Match each term to its definition

Illusion [34]

Answer:

Step-by-step explanation:

axiom goes with a given definition assumed to be true

theorem goes with a logical argument showing that a theorem is true

proof is a statement that requires proof

3 0

3 years ago

Read 2 more answers

Which property can you use to show that 3x +{2x+4} is equivalent to {3x + 2x} + 4

yuradex [85]

Answer:

3x+2x=5x but 4 can't add to 3x and 2x

6 0

3 years ago

This question. Help?

Lemur [1.5K]

Answer:

A: venti has a better unit rate at .2275 cents per ounce

B: to get the unit rate you divide the cost by the number of ounces.

Step-by-step explanation:

tall = .2958 cents per ounce

grande = .2656 cents per ounce

venti = .2275 cents per ounce

3 0

3 years ago