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2 years ago

Find the vertex of y=5-4x-x^2

Mathematics

2 answers:

SSSSS [86.1K]2 years ago

3 0

The answer is (h,k)
(-2,9)

Levart [38]2 years ago

3 0

Answer:

(-2,9)

Step-by-step explanation:

rewrite in vertex form: y= -(x+2)^2+9

(-2,9)

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2 years ago

Four mathematicians, three physicists, and an engineer are to be seated equally spaced around a circular table. How many differe

Vesna [10]

First, we can choose the seats for the four mathematicians. Then we seat the physicits, then the engineer. There are 4! ways to seat the mathematicians, then 3! ways to seat the physicists, then 1! ways to seat the engineer. But then we must divide by 8, because we can rotate the table, so there are 8!*4!*3!/8 = 725760 ways to seat everyone.

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2 years ago

Write the decimal .0006 as a fraction

marysya [2.9K]

Answer:

6/1000

Step-by-step explanation:

.0006 times 10,000

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2 years ago

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

Can someone help me please !!

masya89 [10]

Answer:

I think you answer is 85

Step-by-step explanation:

7 0

2 years ago