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2 years ago

What is the value of the 20th term in this sequence? f(n)=6n−18

Mathematics

1 answer:

babunello [35]2 years ago

4 0

The value of the 20th term in this sequence will be 102

Since we are given f(n)=6n−18.

In this case, we have been given n to be 20. Therefore, f(n)=6n−18 will then be written as:

f(n)=6n−18

f(20) = 6(20) - 18

f(20) = 120 - 18

f(20) = 102

In conclusion, value of the 20th term in this sequence will be 102

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Find the perimeter RST. Round answer to the nearest tenth Show all the work

kow [346]

Answer:

35.1 units

Step-by-step explanation:

Imagine a right-angled triangle with RS as hypotenuse. The base would be 3 units and the height would be 6 units. By Pythagorus:

RS²=3²+6²

RS= $\sqrt{45}$ ≈6.7 units

Imagine a right-angled triangle with RT as hypotenuse. The base would be 9 units and the height would be 12 units. By Pythagorus:

RT²=9²+12²

RT= $\sqrt{225}$ = 15 units

Imagine a right-angled triangle with TS as hypotenuse. The base would be 12 units and the height would be 6 units. By Pythagorus:

TS²=12²+6²

TS= $\sqrt{180}$ ≈13.4 units

Perimeter=RS+RT+TS

=6.7+15+13.4

=35.1 units

6 0

3 years ago

From the 12 players who will travel, the coach must select her starting line-up. She will select a player for each of the five p

gizmo_the_mogwai [7]

Answer:

990

Step-by-step explanation:

The center position can be selected in 3 different ways, the other 4 players can be selected in combinations of 11 players (the center is already selected) taken 4 at a time.

By the Fundamental Principle of Counting, there are

$3\displaystyle\binom{11}{4}=3*\displaystyle\frac{11!}{4!(11-4)!}=3*\displaystyle\frac{11!}{4!7!}=990$

ways for her to select the starting line-up.

7 0

3 years ago

I need help with this plss

Zigmanuir [339]

Answer:

Point F is at -3

Step-by-step explanation:

8 0

2 years ago

Find all roots: x^3 + 7x^2 + 12x = 0 Show all work and check your answer.

Aliun [14]

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

Solution:

We have been given a cubic polynomial.

$x^{3}+7 x^{2}+12 x=0$

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

$x^{3}+7 x^{2}+12 x=0$

$x\left(x^{2}+7 x+12\right)=0$ ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

$x^{2}+7 x+12=0$

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

$\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}$

Therefore, the two roots are:

$\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}$

And,

$\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}$

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

4 0

3 years ago

What is the distance, to the nearest hundredth, from (6, 5) to (−3, −8)?

Olin [163]

Answer:

15.81

Step-by-step explanation:

Use the distance formula:

So the distance formula for two given points is

Distance= sqrt((x2-x1)^2 +(y2-y1)^2 ) =sqrt((-3-6)^2 +(-8-5)^2 )

=sqrt((-9)^2 +(-13)^2 )

=sqrt(81+169)

=sqrt(250)

=15.81

Hope this helped

5 0

3 years ago