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3 years ago

These are the first four terms of a sequence.

Mathematics

2 answers:

Helga [31]3 years ago

5 0

Answer:

F(x)= 5+3(n-1)

Step-by-step explanation:

5 represents term 1. +3 is demonstrating what you do in the pattern for every resulting number. you multiply by (n-1) because 5+3 already demonstrates the next term, so you subtract the term number by 1

DedPeter [7]3 years ago

3 0

Answer:

2+3n

Step-by-step explanation:

This question is based on a topic called sequence and series,under which we have the arithmetic progression

The formula for arithmetic progression is a+(n-1)d

In which a is the first number,n is the nth term and d is the difference

Back to the question

a=5,n=it's not given,d=3

Using the general formula

a+(n-1)d

5+(n-1)3

Open the bracket first

5+3n-3

Collect like terms

5-3+3n

2+3n

The answer is 2+3n

And it can be solved further only if we are given the value of n...the question even stated that we should solve in terms of n

Therefore the answer is 2+3n

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Anybody know how to do this, it's about angles.

gizmo_the_mogwai [7]

Step-by-step explanation:

45°+90°+60°+X°=360° (being complete angle)

or,195°+X°=360°

or,X°=360°-195°

or,X°=165°

Therefore,valueof X is 165°.

7 0

3 years ago

Read 2 more answers

Work out the nth of this sequence:

Gekata [30.6K]

Answer:

$a_n = -11 +3(n -1)$

Explanation:

The $n$ th term of an arithmetic sequence is explicitly defined as $a_n = a_1 +d(n -1)$ where $a_1$ is the first term of the sequence and $d$ is the the common difference.

From the given first five terms of the sequence we can see that the first term is $11$ so $a_1 = 11$ .

The common difference, $d$ , can be calculated by $a_n - a_{n -1}$ so we'll find the common difference of the given sequence by letting $n = 2$

$d = a_2 - a_{2 -1} \\d = a_2 -a_{1} \\d = -8 -(-11) \\ d = -8 +11 \\ d = 3$ .

Now let's plug everything we know.

$a_1 = -11$

$d = 3$

$a_n = -11 +3(n -1)$

6 0

3 years ago

A normally distributed data set has a mean of 0 and a standard deviation of 2. Which of the following is closest to the percent

frutty [35]

A normally distributed data set has a mean of 0 and a standard deviation of 2. The closest to the percent of values between -4.0 and 2.0 would be 84%.

<h3>What is the empirical rule?</h3>

According to the empirical rule, also known as the 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95%, and 99.7% of the values lies within one, two, or three standard deviations of the mean of the distribution.

$P(\mu - \sigma < X < \mu + \sigma) \approx 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%$

A normally distributed data set has a mean of 0 and a standard deviation of 2.

$Z=(x-\mu)/\sigma$

$P(x=-0.4)\\\\z=(-0.4-0)/2\\\\= -0.2\\\\P(x=2)\\z=(2-0)/2\\\\=1$

$P(-0.4 < x < 2)=p(-0.2 < z < 1)=p(-0.2 < z < 0)+p(0 < z < 1)$ ……….(by symmetry)

=.49865+.3413

.83995…….(by (http://83995…….by) table value)

=.8400 × 100

=84%

Learn more about the empirical rule here:

brainly.com/question/13676793

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4 0

2 years ago

Solve for x:a(a²+b²)x²+b²x-a

m_a_m_a [10]

Answer:

x = a/(a² + b²) or x = -1/a

Step-by-step explanation:

a(a²+ b²)x² + b²x - a =0

Use the quadratic equation formula:

$x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} =\dfrac{-b\pm\sqrt{D}}{2a}$

1. Evaluate the discriminant D

D = b² - 4ac = b⁴ - 4a(a² + b²)(-a) = b⁴ + 4a⁴ + 4a²b² = (b² + 2a²)²

2. Solve for x

$\begin{array}{rcl}x & = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-b^{2}\pm\sqrt{(b^{2}+2a^{2})^{2}}}{2a(a^{2} + b^{2})}\\\\ & = & \dfrac{-b^{2}\pm(b^{2}+ 2a^{2})}{2a(a^{2} + b^{2})}\\\\x = \dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}\\\\x =\dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\\end{array}$

$\begin{array}{rcl}x = \large \boxed{\mathbf{\dfrac{a}{a^{2} + b^{2}}}}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2b^{2}- 2a^{2}}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2(a^{2}+ b^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\large \boxed{\mathbf{-\dfrac{1}{a}}}\\\\\end{array}$

5 0

3 years ago

URGENT PLEASE HELP WILL GIVE BRAINLIEST TO CORRECT ANSWER ABC factory brought a pile of coal. If the factory burns 1500 kilogram

wolverine [178]

Solving a system of equations, we will see that there are 6000 kg of coal on the pile.

<h3>How many kilograms of coal are in the pile of coal?</h3>

Let's say that there are N kilograms of coal, and it is planned to burn it totally in D days, these are our variables.

We know that:

If the factory burns 1500 kilograms per day, it will finish burning the coal one day ahead of planned.
If it burns 1000 kilograms per day, it will take an additional day than planned.

Then we can write the system of equations:

(1500)*(D - 1) = N

(1000)*(D + 1) = N

Because N is already isolated in both sides, we can write this as:

(1500)*(D - 1) = N = (1000)*(D + 1)

Then we can solve for D:

(1500)*(D - 1) = (1000)*(D + 1)

1500*D - 1500 = 1000*D + 1000

500*D = 2500

D = 2500/500 = 5

Now that we know the value of D, we can find N by replacing it in one of the two equations:

(1500)*(D - 1) = N

(1500)*(5 - 1) = N

(1500)*4= N = 6000

This means that there are 6000 kilograms of coal on the pile.

If you want to learn more about systems of equations:

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7 0

2 years ago