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OverLord2011 [107]
3 years ago
10

Use the equation an = a1 + (n – 1)d to write a rule for the arithmetic sequence 32, 41, 50, . …

Mathematics
1 answer:
jarptica [38.1K]3 years ago
3 0

Answer: an = 9n + 23

Step-by-step explanation:

The formula for determining the nth term of an arithmetic sequence is expressed as

an = a1 + (n - 1)d

Where

a1 represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 32

d = 9

Therefore, the equation or rule for the given arithmetic sequence would be

an = 32 + (n - 1)9

Expanding the brackets, it becomes

an = 32 + 9n - 9

an = 9n + 32 - 9

an = 9n + 23

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Fully Factor 3x^2 – 16x + 20
ryzh [129]

Answer:

C. (3x2 - 10) (x - 2)

Step-by-step explanation:

3x^2 - 16x +20

Step 1: Sum = - 16x

Product = 60x^2

Step 2: Find 2 numbers that their sum is -16 and their product is 60. If you do that correctly, then you will get two numbers: 10 and -6

Step 3: Replace -16x with the two numbers found in step 2, then you will have; 3x^2 - 6x - 10x + 20

Step 4: Factorise the equation in step 3, like so;

(3x^2 - 6x)(- 10x + 20)

3x(x - 2) -10(x - 2)

(3x - 10)(x - 2)

To check if the answer is correct, expand the bracket: (3x - 10)(x - 2)

If the bracket is opened properly, you will get 3x^2 - 16x + 20

4 0
3 years ago
What is the value of x in the diagram below? 2 right triangles are stacked. The bottom triangle has a side length of 9 units and
ehidna [41]

Answer:

18 sqrt2/ sqrt3

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
-6x-16 < 2x please help asap! and help me solve it
ICE Princess25 [194]

1. Divide both sides by 2

2. Add 16 to each side

Answer  x > -2

         

3 0
3 years ago
4(-5.4) SHOW WORK PLS
Nana76 [90]

Answer:

-21.6

Step-by-step explanation:

-5.4    

x  4               4x 4=16 so you carry the one to 5x4= 20 + 1 that was carried

--------           keep it negative

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6 0
3 years ago
3x^2+kx=-3 What is the value of K will result in exactly one solution to the equation?
Scorpion4ik [409]

Answer:

For k = 6 or k = -6, the equation will have exactly one solution.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = (x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

If \bigtriangleup = 0, the equation has only one solution.

In this problem, we have that:

3x^{2} + kx + 3 = 0

So

a = 3, b = k, c = 3

\bigtriangleup = b^{2} - 4ac

\bigtriangleup = k^{2} - 4*3*3

\bigtriangleup = k^{2} - 36

We will only have one solution if \bigtriangleup = 0. So

\bigtriangleup = 0

k^{2} - 36 = 0

k^{2} = 36

k = \pm \sqrt{36}

k = \pm 6

For k = 6 or k = -6, the equation will have exactly one solution.

3 0
3 years ago
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