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Free_Kalibri [48]
3 years ago
11

What is the equation used to find the nth term of the arithmetic sequence: -9, -4 1, 6, 11...

Mathematics
1 answer:
elena-s [515]3 years ago
4 0

Answer:

a^n=-9+(n-1).5

Step-by-step explanation:

Arithmetic sequence=a+(n-1)d

a=-9

n=?

d=+5

Arithmetic sequence=-9+(n-1)5

=-9+5n-5

Collect like terms

-9-5+5n

-14+5n

So the final answer is

an=-9+(n-1).5

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Subtract 22 on both sides
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3 years ago
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The base of a parallelogram is 18 inches longer than three times the height. The area of the parallelogram is 216 square inches.
nordsb [41]

Answer:

12 inches

Step-by-step explanation:

Let b represent the base

h represents the height

area of the parallelogram = base * height = 216 square inches

From the question'

b = 18 + 3h

Slot in the value of b

216 = (18 + 3h) * h

expand

216 = 18h + 3h^2

subtract 216 from both sides

0 = 18h + 3h^2 - 216

rearrange

3h^2 + 18h - 216 = 0

divide through by 3

h^2 + 6h - 72 = 0

Now, lets solve!

h^2 + 6h - 12h - 72 = 0

h( h + 6 ) - 12(h + 6) = 0

(h - 12) (h + 6) = 0

h - 12 = 0

h = 12

and

h + 6 = 0

h = - 6

Taking the positive value of h

Hence, the height is 12 inches

Lets check

when h = 12 inches

Area of the parallelogram = 18* 12 = 216 square inches     .... correct

when h = -6inches

A = 18 * -6 ≠  216 square inches

So height is 12 inches

5 0
3 years ago
Calculate the Zscore of $80
gayaneshka [121]
The Z-score (z) is calculated according to the formula: z = (x - μ) / σ

Where: x is the raw score value, μ is the mean of the population, σ is the standard deviation of the population.

x = 80, μ = 5, σ = 4

z = (80 - 5) / 4

z = 75 / 4 = 18.7500

Z-score is 18.7500


3 0
2 years ago
A very large study showed that aspirin reduced the rate of heart attacks by 44%. A pharmaceutical company thinks they have a dru
Butoxors [25]

Answer: H_0:\mu=0.44\ ,H_a:\mu

Step-by-step explanation:

Since we have given that

A very large study showed that aspirin reduced the rate of heart attacks by 44%.

we claim that they have a drug that will be more effective than aspirin.

so, our hypothesis would be

H_0:\mu=0.44\\\\H_a:\mu

So, it will be one tail test.

Hence, H_0:\mu=0.44\\\\H_a:\mu

6 0
3 years ago
42x^3+35×^2-36x-30 factor​
Komok [63]

Answer:

(6x + 5)(7x² - 6)

Step-by-step explanation:

Factor the first/second and third/fourth term

42x³ + 35x² - 36x - 30

= 7x²(6x + 5) - 6(6x + 5) ← factor out (6x + 5) from each term

= (6x + 5)(7x² - 6)

4 0
3 years ago
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