MATHEMATICS HIGH SCHOOL

find the indicated terms of the arithmetic sequence with the given description. the 50th term is 1001, and the common difference is 6. find the first and second terms.

Answers

Answer 1

Answer:

Answer:

a₁ = 707 a₂ = 713

Step-by-step explanation:

the nth term of an arithmetic sequence is

$a_(n)$ = a₁ + (n - 1)d

a₁ is the first term, d the common difference , n the term number

given

a₅₀ = 1001 , then

a₁ + 49d = 1001 ← substitute d = 6

a₁ + 49(6) = 1001

a₁ + 294 = 1001 ( subtract 294 from both sides )

a₁ = 707

and a₂ = a₁ + d = 707 + 6 = 713

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Toshi and owen need to add 4.9 x 10^9 and 4.1 x 10^7. toshi says they must use the expression (490 x 10^7 ) (4.1 x 10^7), but owen says they must use the expression (4.9 x 10^9) (0.041 x 10^9). are neither, one, or both students correct? explain

Answers

Final answer:

When adding numbers in scientific notation, the exponents must be the same. Owen is correct and Toshi is incorrect.

Explanation:

When adding numbers in scientific notation, the exponents must be the same.

Toshi suggests using the expression (490 × 10⁷) + (4.1 × 10⁷), but this is incorrect because the exponents do not match.

Owen suggests using the expression (4.9 × 10⁹) + (0.041 × 10⁹), and this is correct because the exponents are the same.

So, Owen is correct and Toshi is incorrect.

Learn more about scientific notation here:

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Both are correct. You add any two numbers in scientific notation if the exponents on the 10 are equal.

Use the Distributive Property to expand -3 (8x - 4).

Answers

-3(8x-4). With D property, that would be
-24x + 12

Final answer:

The Distributive Property is applied to -3(8x - 4) by multiplying -3 by each term inside the parenthesis, which gives the expanded form -24x + 12.

Explanation:

To use the Distributive Property to expand -3(8x - 4), you need to multiply each term inside the parenthesis by -3.

Multiply -3 by 8x: -3 × 8x equals -24x
Multiply -3 by -4: -3 × -4 gives +12, because when two negative numbers are multiplied, the answer has a positive sign.

Now combine the two products you obtained:

-24x + 12

Therefore, the expanded form of -3(8x - 4) using the Distributive Property is -24x + 12.

Learn more about Distributive Property here:

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I REALLY NEED HELP !!!The number of hours, t, that bacteria spread 10-fold can be modeled by the equation B(t) = B0(10)^3t. There are five bacteria present initially and a biologist wishes to find out how many hours will elapse until there are 2,000 bacteria present. What is the exact value for the number of hours elapsed, t, in the equation 2,000 = 5(10)^3t?

t equals start fraction log of forty over three end fraction
t equals start fraction log of two thousand over three times log of fifty end fraction
t equals start fraction log of four hundred over log of three end fraction
t equals start fraction log of four hundred over three end fraction

Answers

I think the answer is c

The answer is t=2/5

Im sorry if this is incorrect! Tried my best at least! Good luck :)

Write the expression as either the sine, cosine, or tangent of a single angle.cosine of pi divided by five times cosine of pi divided by seven plus sine of pi divided by five times sine of pi divided by seven.

Answers

The expression is:
cos (π / 5) cos (π/7) + sin (π/5) sin(π/7)

This expression can be reduced into a trigonometric function with one angle if we make use of the trigonometric identities. The appropriate identity is:
cos (A - B) = cos A cos B + sin A sin B

If we let
A = π / 5
B = π / 7

Therefore,
cos (π / 5) cos (π/7) + sin (π/5) sin(π/7) = cos (π/5 - π/7) = cos (2π/35)

Hello! I could use some help with this algebra question:)

Answers

Answer:

f(-2) = -14

f(4) = -13

Step-by-step explanation:

(in picture)

Marian se deplaseaza ,cu automobilul,pe autostrada.La ora 10 si 35 minute el se afla la kilometrul 25 .Dupa un interval de timp,la ora 11 si 15 minute,el se afla la kilometrul 100.Calculati :durata deplasarii,distanta parcursa de Marian si viteza medie a acestuia(exprimata in unitati de SI)

Answers

Step-by-step explanation:

If Marian travels, by car, on the highway. At 10 and 35 minutes he is at kilometer 25. After a period of time, at 11 and 15 minutes, he is at kilometer 100.

Total distance covered = 25km + 100km

Total distance covered by Marian = 125km

Total time taken by marian = 10hr 35min + 11hr + 15min

Total time taken by marian = (10+11)hr + (35+15)min

Total time taken by marian = 21hr 50mins

Total time taken by marian = 21 * 50/60 hr

Total time taken by marian (Duration) = 21.833hr

Average speed = Total distance covered/Total time taken

Average speed = 125/21.833

Average speed = 5.725km/hr

Convert to m/s

5.725km/hr = 5.725*1000/3600