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2 years ago

How many terms are in the arithmetic sequence 1313, 1616, 1919, ……, 7070, 7373?

1 answer:

3 0

The formula in getting the arithmetic sequence:
an = a1 + (n – 1)d.

We can substitute the values in order for us to know how many terms the sequence has.

an = 7373
a1 = 1313
d = 303

an = a1 + (n – 1)d
7373 = 1313 + (n-1) 303
7373 = 1313 + 303n - 303
-303n = 1313 - 303 - 7373
303n = -1313 + 303 + 7373
303n = 6363
n = 21

So, there are 21 terms in the sequence given.

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Write each expression with a single rational exponent. Show each step of your process. Which expressions are equivalent? Justify

Lena [83]

The expression of all the algebra as single rational exponent are; As written below.

<h3>How to Express Exponents?</h3>

1) We want to express ⁴√x³. This can be expressed as;

x^(3/4)

2) We want to express the exponent ¹/x⁻¹. This is expressed as a single rational exponent as; x

3) We want to have the given expression as a single rational exponent. The expression is; ¹⁰√(x⁵ · x⁴ · x²)

We add the exponents to get;

¹⁰√(x¹¹) = x^(¹¹/₁₀)

4) x^(¹/₃) * x^(¹/₃) * x^(¹/₃)

We just add the exponents to get;

x¹ = x

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1 year ago

What’s the answer (no link I give brainly)

mixer [17]

Answer:

I belive it is C

Step-by-step explanation:

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2 years ago

#16 and #19 only Please answer both as soon as possible.

Vlad1618 [11]

Answer:

1. it is not a direct variation because the value k is not kept throughout the ordered pairs

2. -a^5 - 2a³ + 2a², leading coefficient is -1

Step-by-step explanation:

1. to find the direct variation, we will use y/x = k with k representing our constant throughout the chart. if every value is equal to k, it is a direct variation

for this problem we will assume that the cup sizes are x and the cost is y

so the ordered pairs are (8, 0.90), (12, 1.35), (16, 1.80), and (24, 2.25)

.90/8 = 0.1125 <-- this is our k value for which every result has to be equal to

1.35/12 = 0.1125

1.80/12 = 0.1125

2.25/24 = 0.09375

since the value k was not kept throughout the ordered pairs, this is not a direct variation

2. the standard form of a polynomial is the exponents in descending order.

we have the following polynomial: 2a² - a^5 -2a³

to write it in standard form, we will go in descending order of the exponents. the largest exponent being first

-a^5 - 2a³ + 2a²

the leading coefficient of the polynomial is -1, as there is a negative sign in front of the newly formed polynomial

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2 years ago

Chase has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.13 t

riadik2000 [5.3K]

Well the way I see it is he started with 4 villager so I would see the equation to be

1.13x times 17+4 would equal the amount of villagers he could have which would be 23.21 as for the equation it would be 1.13x times 17 plus four equals the number of villagers total

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3 years ago

Hayley has $155 in savings, and her brother Hank has $230. Hayley is saving $10 each week, and her brother is spending $15 each

Sindrei [870]

Answer:

After 3 weeks they both will have the same amount in their savings account.

Step-by-step explanation:

Given:

Amount saved by Haley = $155

Amount saved by Hank = $230

Amount saving each week by Haley = $10

Amount spending each week by Hank = $15

We need to find Number of weeks when both both will have same amount in savings account.

Solution:

Let Number of week be 'x'.

Total Amount of Haley can be calculated by Amount saved by Haley plus Amount saving each week by Haley multiplied by number of weeks.

framing in equation form we get;

Total Amount of Haley = $155+10x$

Also;

Total Amount of Hank can be calculated by Amount saved by Hank minus Amount spending each week by Hank multiplied by number of weeks.

framing in equation form we get;

Total Amount of Hank = $230-15x$

Now we need to find the number of weeks when both will have same amount.

To find the same we will have to make both the equation equal.

So we can say.

$155+10x=230-15x$

On Solving above equation we get;

We will combine the like terms together;

$10x+15x =230-155\\\\25x = 75$

Now Dividing both side by 25 using Division property of equality we get;

$\frac{25x}{25} = \frac{75}{25}\\\\x=3 \ weeks$

Hence, After 3 weeks they both will have the same amount in their savings account.

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2 years ago