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3 years ago

If the nth term of a number sequence is n^2 + 2,find the first 3 terms and the 10th term

Mathematics

1 answer:

Nady [450]3 years ago

8 0

Answer:

The first three terms are $3,6,11$

The 10th term is $102$

Step-by-step explanation:

An ordered list of numbers is known as a sequence such that each number in the sequence is called a term.

The nth term is $a_n=n^2+2$ .

To find the first 3 terms, put $n=1,2,3$

$a_1=1^2+2=1+2=3\\a_2=2^2+2=4+2=6\\a_3=3^2+2=9+2=11$

To find the 10th term, put $n=10$ in $a_n=n^2+2$

$a_{10} =(10)^2+2=100+2=102$

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3 years ago

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3 years ago

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4 years ago

Simone has 5 in her flower shop.Each employee works 6 4/15 hours a day how many hours in total do the 5 empoyees work per day?

kodGreya [7K]

To figure out the total amount of hours an employee works, we have to multiply the total amount of employees by the amount of hours each employee would work.

To simplify the mixed fraction of hours they work, convert the mixed fraction into an improper fraction:

$6 \frac{4}{15}$

Multiply the whole number by the denominator:

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Add this number to the numerator to convert the mixed fraction into an improper fraction:

$90 + 4 = 94$

$6 \frac{4}{15} = \frac{94}{15}$

Now we can multiply the two numbers together (note that a whole number can be treated as the number above the denominator 1):

5 employees working 94/15 hours a day:

$\frac{5}{1} \times \frac{94}{15} = \frac{470}{15}$

To simplify this fraction, divide the numerator by the denominator:

$470 \div 15 = 31 R 5$

The whole number stays as a number, and the remainder is the new numerator:

$31 \frac{5}{15}$

The fraction can be further simplified by dividing both the numerator and denominator by the greatest common factor:

Factors of 5: {1,5}
Factors of 15: {1,3,5,15}

$\frac{5}{15} \div \frac{5}{5} = \frac{1}{3}$

$31 \frac{5}{15} = 31 \frac{1}{3}$

The 5 employees will work a total of 31 and 1/3 hours a day.

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3 years ago

How do you write (-2,-4),(-3,-3) into slope intercept form

zzz [600]

Answer- $y=−3x+9$

Step-by-step explanation:

First, we will write and equation in point-slope form and then convert to slope-intercept form.

To use the point-slope form we must first determine the slope.

The slope can be found by using the formula : $m=y2−y1x2−x1$

<em>Where </em> $m$ is the slope and $(x1,y1) and (x2,y2$ ) are the two points on the line.

Substituting the values from the points in the problem gives: $m=3−−32−4m=3+32−4m=6−2=−3$

We can now use this calculated slope and either point to write the equation in point-slope form.

The point-slope formula states: $(y−y1)=m(x−x1)$

Where $m$ is the slope and $(x1y1)$ is a point the line passes through.

Again, substituting gives: $(y−−3)=−3(x−4) (y+3)=−3(x−4)$ We can now convert this to slope-intercept form.

The slope-intercept form of a linear equation is: $y=mx+b$

Where $m$ is the slope and $b$ is the y-intercept value.

We can solve our equation for $y:$

$(y+3)=−3(x−4) y+3=(−3×x)−(−3×4)y+3=−3x−(−12)y+3=−3x+12y+3−3=−3x+12−3y+0=−3x+9y=−3x+9$

This took me so long to type lol, hope this helps you and have a great day noon or night! <3 ❤️

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2 years ago

If the nth term of a number sequence is n^2 + 2,find the first 3 terms and the 10th term ​

If the nth term of a number sequence is n^2 + 2,find the first 3 terms and the 10th term