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3 years ago

I need the answer of this with steps and solutions fast plz

Mathematics

1 answer:

Natali [406]3 years ago

6 0

Answer:

$1 \dfrac{13}{15}$

Step-by-step explanation:

$2 \dfrac{1}{5} - \dfrac{1}{3} =$

$= \dfrac{11}{5} - \dfrac{1}{3}$

$= \dfrac{33}{15} - \dfrac{5}{15}$

$= \dfrac{28}{15}$

$= 1 \dfrac{13}{15}$

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Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms

miv72 [106K]

Hint :-

Break the given sequence into two parts .
Notice the terms at gap of one term beginning from the first term .They are like $\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ . Next term is obtained by multiplying half to the previous term .
Notice the terms beginning from 2nd term , $4,7,10,13$ . Next term is obtained by adding 3 to the previous term .

Solution :- 

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

$\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ .

We can see that this is in Geometric Progression where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

$\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]$

Notice the term $\dfrac{1}{2^{25}}$ will be too small , so we can neglect it and take its approximation as 0 .

$\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]$

$\\\implies \boxed{ S_1 \approx 1 }$

$\rule{200}2$

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

$\implies S_2=\dfrac{n}{2}[2a + (n-1)d]$

Substitute ,

$\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}$

Hence sum = 908 + 1 = 909

7 0

3 years ago

Help please thank you!

Maslowich

the error is that they didnt add the exponets

6 0

3 years ago

2. Graph the function y=x^2+2x-3 . Draw a chart to show at least three ordered pairs that are on the graph.

lidiya [134]

You'd have to draw a table of x and y values first to be able to graph.
Step 1: Pick any number for x. Let's pick 2.
Step 2: Plug in 2 into the equation: y = 2^2 + 2(2) - 3
Step 3: Solve for y: 4 + 4 - 3 = 5
Step 4: So the point (ordered pair) would be (x, y) ⇒ (2, 5). You can plot that on the graph.

Follow these steps 2 more times to get at least three ordered pairs.

Make sure you have enough points to know where the graph curves, then you can connect the dots and now there you have a graph and chart :)

6 0

3 years ago

Select the correct answer. Which of the following sets of ordered pairs represents a function?

iogann1982 [59]

Answer: {(-8, -14), (-7,-12), (-6,-10), (-5,-8)}

Step-by-step explanation: A function is a relation in which each x-coordinate corresponds to exactly one y-coordinate.

In the relations show here, notice that the first set

of ordered pairs is the only set where each x-coordinate

appears once with a different y-coordinate.

In the other ordered pairs, there is an x-coordinate that appears more

than once and it corresponds to a different y-coordinate.

For example, in the second relation,

the x-coordinate -9 appears twice.

In one case, -9 corresponds to -12 and

in the other case, it corresponds to -8.

So, this is not a function.

3 0

4 years ago

Can someone please help me with math.

krek1111 [17]

Answer:

Step-by-step explanation:

1) Number of nickels = x

Number of quarter = y

x + y = 7 ----------------------(I)

x = 7 - y ------------------------(II)

0.05x + 0.25y = 0.55 -----------(III)

Substitute s = 7 - y in equation (III)

0.05*(7 - y) + 0.25y = 0.55

0.05*7 - 0.05*y + 0.25y = 0.55

0.35 - 0.05y + 0.25y = 0.55 {Combine like terms}

0.35 + 0.20y = 0.55 {Subtract 0.35 from both sides}

0.2y = 0.55 - 0.35

0.2y = 0.2 {Divide both sides by 0.2}

y = 0.2/0.2

y = 1

Substitute y =1 in equation (II)

x = 7 - 1

x = 6

Number of nickels = 6

Number of quarter = 1

2) Number of children tickets = x

Number of adult tickets = y

x + y = 40 -----------------(I)

x = 40 - y -----------------(II)

2x + 5y = 170 -----------------(III)

Substitute x = 40 - y in equation (III)

2*(40-y) + 5y = 170

2*40 - 2*y + 5y = 170

80 - 2y + 5y = 170 {Combine like terms}

80 + 3y = 170 {Subtract 80 from both sides}

3y = 170 - 80

3y = 90 {Divide both sides by 3}

y = 90/3

y = 30

Substitute y = 30 in equation (II)

x = 40 - 30

x = 10

Number of children tickets = 10

Number of adult tickets =30

3 0

3 years ago

I need the answer of this with steps and solutions fast plz​

I need the answer of this with steps and solutions fast plz