PLZ HELP! Determine the value of k. Round your answer to the nearest hundredth if necessary.

13. If 6 times the 6th term of an A.P. is equal to

romanna [79]

Answer:

see explanation

Step-by-step explanation:

The n th term of an AP is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given

6(a₁ + 5d) = 13(a₁ + 12d) ← distribute parenthesis on both sides

6a₁ + 30d = 13a₁ + 156d ( subtract 13a₁ from both sides )

- 7a₁ + 30d = 156d ( subtract 30d from both sides )

- 7a₁ = 126d ( divide both sides by - 7 )

a₁ = - 18d

Now

a₁₉ = a₁ + 18d = - 18d + 18d = 0 ← as required

7 0

3 years ago

An actor invests some money at 7%, and $24000 more than four times the amount at 8%. The total annual interest earned from the i

natita [175]

Answer:

$70,000 at 7%
$304,000 at 8%

Step-by-step explanation:

Given:

Total interest earned on two investments is $29,220.

An amount is invested at 7%.

$24,000 more than 4 times that amount is invested at 8%.

Find:

The amount invested at each rate.

Solution:

Our strategy will be to define a variable representing the amount invested at 7%, use that variable to write an expression for the amount invested at 8%, then write an equation for the total return on the investments.

Let x represent the amount invested at 7%. Then (24,000+4x) will be the amount invested at 8%. The total interest earned will be ...

interest on 7% account + interest on 8% account = total interest

0.07x + 0.08(24000+4x) = 29220

0.39x + 1920 = 29220 . . . . . . . . . . . simplify

0.39x = 27300 . . . . . . . . . . . . . . . . . .subtract 1920

x = 27300/0.39 = 70000 . . . . . . . . . divide by the coefficient of x

24,000 +4x = 24,000 +280,000 = 304,000 . . . . amount invested at 8%

He invested $70,000 at 7% and $304,000 at 8%.

Check

The answer must satisfy ...

7% interest + 8% interest = 29,220

0.07×70,000 +0.08×304,000 = 4,900 +24,320 = 29,220 . . . . as required

_____

Comment on 6-step method

We have tried to hit the highlights. Your steps appear to be ...

Identify the given information (Given)
Identify the question you are asked to answer (Find)
Identify the useless information in the problem statement (is none)
Decide on a strategy. Make a model or drawing. (model equation shown)
Solve and show work (Solution)
Explain why the answer makes sense (Check)

6 0

3 years ago

1. Noah had $ 5.25 and Lin had $ 8.95. How much did they have altogether?

amid [387]

1. 5.25 + 8.95 = 14.20

2. 21.32 - 9.50 = 11.82

3. 24.50 × 5 = 122.5

4. 85.20 ÷ 4 = 21.3

Hope this helped! Please comment if you have any questions regarding how I got my answers. Stay safe.

4 0

2 years ago

DO NOT SKIP!! Let’s see who’s smart enough to work out the problem if u get it correct I’ll mark u as BRAINLIEST SHOW THE WORK P

forsale [732]

Answer:

y=10.1(x)

x= $\frac{y}{10.1}$

Step-by-step explanation:

It is said in the problem that y would represent how much money she earns and x represents the number hours she works.

so it also said that the amount of Jessa earns is proportional to the amount of time she works .

finding y will be easy dividing 252.50 by 25 will give you 10.1

so how did we get that equation

y will represent the amount and x will represent the hours

4 0

2 years ago

Choose one of the factors of 6x^3 + 6

ivanzaharov [21]

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

$6x^3+6$

Now, by factorising , we get

$6x^3+6\\=6(x^3+1)$

Now, we use the formula i.e.

$a^3+b^3=(a+b)(a^2-ab+b^2)$

By using this, we get ,

$6(x^3+1)\\=6(x+1)(x^2-x+1)$

So,

$(x+1) \text{ is the factor of }6x^3+6.$

6 0

2 years ago

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