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3 years ago

You want to buy a new video game for $48.99. If there is a 6% sales tax, how much will you need total?

Mathematics

1 answer:

S_A_V [24]3 years ago

8 0

Answer:

$51.93

Step-by-step explanation:

$48.99 x 1.06 = $51.9294

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How is the series 5+11+17…+251 represented in summation notation?

NISA [10]

Answer:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

Step-by-step explanation:

Given:

Series 5+11+17+...+251

To find:

Summation notation of the given series

Summation Notation:

$\displaystyle \large{\sum_{k=1}^n a_k}$

Where n is the number of terms and $\displaystyle \large{a_k}$ is general term.

First, determine what kind of series it is, there are two main series that everyone should know:

Arithmetic Series

A series that has common difference.

Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

11-5 = 6
17-11 = 6

Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:

<u>Arithmetic Sequence</u>

$\displaystyle \large{a_n=a_1+(n-1)d}$

Where $\displaystyle \large{a_n}$ is the nth term, $\displaystyle \large{a_1}$ is the first term and $\displaystyle \large{d}$ is the common difference:

So for our general term:

$\displaystyle \large{a_n=5+(n-1)6}\\\displaystyle \large{a_n=5+6n-6}\\\displaystyle \large{a_n=6n-1}$

And for number of terms, substitute $\displaystyle \large{a_n}$ = 251 and solve for n:

$\displaystyle \large{251=6n-1}\\\displaystyle \large{252=6n}\\\displaystyle \large{n=42}$

Now we can convert the series to summation notation as given the formula above, substitute as we get:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

5 0

2 years ago

Compute the value of the discriminant and give the number of real solutions of the quadratic equation.

Sergio039 [100]

$-2x^2+6x-3=0 \\ \\
a=-2 \\ b=6 \\ c=-3 \\ \Delta=b^2-4ac=6^2-4 \times (-2) \times (-3)=36-24=12$

The value of the discriminant is 12.
Since the discriminant is greater than zero, the equation has two real solutions.

4 0

3 years ago

Find the zeros and the axis of symmetry of the parabola.

emmainna [20.7K]

Answer:

ok i think its D

Step-by-step explanation:

2,4; x= 3

i am not 100% but like i looked up examples and that seems to be the only one that looks right

6 0

3 years ago

Read 2 more answers

the sum of two consecutive integers is -49 write an equation that models this situation and find the values of the two integers

hodyreva [135]

Х is the first <span>integer
</span>(x+1) is the second integer

x + x + 1 = -49
2x + 1 = - 49
2x = -49 - 1
2x = -50
x = -25 first integer
-25 + 1 = -24 second integer

Answer: -25 and -24

7 0

4 years ago

Read 2 more answers

Convert 40/6 to a mixed number in simplest form

alex41 [277]

The answer would be six and 1 tenths or 6 and 1/10

8 0

3 years ago