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aliya0001 [1]
3 years ago
9

100 POINTS!!! What is the sum of 1/2 x-1/3 and 5x^2-2x+6? Write your answer in standard form

Mathematics
2 answers:
Nat2105 [25]3 years ago
5 0

\\ \sf\Rrightarrow \left(\dfrac{1}{2}x-\dfrac{1}{3}\right)+5x^2-2x+6

\\ \sf\Rrightarrow \left(\dfrac{x}{2}-\dfrac{1}{3}\right)+5x^2-2x+6

\\ \sf\Rrightarrow \dfrac{3x-2}{6}+5x^2-2x+6

\\ \sf\Rrightarrow \dfrac{3x-2+30x^2-12x+36}{6}

\\ \sf\Rrightarrow \dfrac{30x^2+3x-12x-2+36}{6}

\\ \sf\Rrightarrow \dfrac{30x^2-9x+34}{6}

Nutka1998 [239]3 years ago
4 0

<em><u>The PM is the head of the British government and the President is the head of the American government. ... Whilst the Prime Minister is the head of the government, it's the ruling monarch who's the head of state. The head of state is the person who has the finally say about what happens in the country.</u></em>

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Rachna borrowed a certain sum at the rate of 15% per annum. if she paid at the end of the two years Rs.1290 as interest Compound
Natalija [7]

Given info:

Compound Interest = Rs.1290

Rate of Interest = 15% p.a

Time = 2 years

<h3>Formula we have to know:-</h3>

\dag{\underline{\boxed{\sf{C.I = P  \bigg(1  + \dfrac{R}{100} \bigg)^{n}  - 1}}}}

<u>Where</u>

C.I = Compound Interest

P = Principle

R = Rate of Interest

N = Time

\textsf{ \underline{Solution-}}\\

Here

C.I = Rs.1290

R = 15%

N = 2 years

Principle = ?

Now,Calculating the sum (Principle) borrowed by Rachna

\quad{: \implies{\sf{C.I =  \Bigg[P  \bigg(1  + \dfrac{R}{100} \bigg)^{n}  - 1 \Bigg]}}}

Substituting the given values

\quad{: \implies{\sf{1290 =  \Bigg[P  \bigg(1  + \dfrac{15}{100} \bigg)^{2}  - 1 \Bigg]}}}

\quad{: \implies{\sf{1290 =  \Bigg[P  \bigg(\dfrac{(1 \times 100) + 15}{100} \bigg)^{2}  - 1 \Bigg]}}}

\quad{: \implies{\sf{1290 =  \Bigg[P  \bigg(\dfrac{115}{100} \bigg)^{2}  - 1 \Bigg]}}}

\quad{: \implies{\sf{1290 =  \Bigg[P  \bigg(\dfrac{115}{100} \times \dfrac{115}{100}  \bigg)  - 1 \Bigg]}}}

\quad{: \implies{\sf{1290 =  \Bigg[P  \bigg(\dfrac{13225}{10000} \bigg) - 1 \Bigg]}}}

\quad{: \implies{\sf{1290 =  \Bigg[P  \bigg( \cancel{\dfrac{13225}{10000}} \bigg) - 1 \Bigg]}}}

\quad{: \implies{\sf{1290 =  \Bigg[P  \bigg({1.3225 - 1} \bigg) \Bigg]}}}

\quad{: \implies{\sf{1290 =  P  \times  {0.3225}}}}

\quad{: \implies{\sf{\dfrac{1290}{0.3225}  =  P}}}

\quad{: \implies{\sf{\dfrac{1290 \times 1000}{0.3225 \times 1000}  =  P}}}

\quad{: \implies{\sf{\dfrac{12900000}{3225}  =  P}}}

\quad{: \implies{\sf{\cancel{\dfrac{12900000}{3225}}  =  P}}}

\quad{: \implies{\sf{Rs.4000  =  P}}}

\quad{\dag{\underline{\boxed{\tt{\blue{Principle} =  \purple{Rs.4000 }}}}}}

\begin{gathered}\end{gathered}

<u>Hence,</u>

The sum (Principle) is Rs.4000.

3 0
3 years ago
How to show you can use Distributive Property to rewrite and find (32×4)+(32×4).
ELEN [110]

Answer:

32x4= 128 x 2= 256

Multiplied by two because you're adding the same equation

Step-by-step explanation:

6 0
3 years ago
Explain why sine ratio has a macimum value of 1??
Goshia [24]

Answer:

The maximum length of the opposite side of a right triangle equals the length of the hypotenuse.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Find Surface Area! WILL MARK BRANLIEST PLEASE HURRY!
TiliK225 [7]

Answer:

1164

Step-by-step explanation:

Surface area is the sum of the areas for all the faces. So 20×15= 300 since there is another one like that you multiply that answer by 2. Then 16×12= 192 then repeat and multiply 192 by 2. Then 12×15= 180 and since there is only one you dont multiply it by 2. Now add (192×2) + (300×2) + 192.

384 + 600 + 192 = 1164

8 0
3 years ago
Suppose you pay a dollar to roll two dice. if you roll 5 or a 6 you Get your dollar back +2 more just like it the goal will be t
LiRa [457]

Answer:

(a)$67

(b)You are expected to win 56 Times

(c)You are expected to lose 44 Times

Step-by-step explanation:

The sample space for the event of rolling two dice is presented below

(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)\\(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)\\(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)\\(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)

Total number of outcomes =36

The event of rolling a 5 or a 6 are:

(5,1), (6,1)\\ (5,2), (6,2)\\( (5,3), (6,3)\\ (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)

Number of outcomes =20

Therefore:

P(rolling a 5 or a 6)  =\dfrac{20}{36}

The probability distribution of this event is given as follows.

\left|\begin{array}{c|c|c}$Amount Won(x)&-\$1&\$2\\&\\P(x)&\dfrac{16}{36}&\dfrac{20}{36}\end{array}\right|

First, we determine the expected Value of this event.

Expected Value

=(-\$1\times \frac{16}{36})+ (\$2\times \frac{20}{36})\\=\$0.67

Therefore, if the game is played 100 times,

Expected Profit =$0.67 X 100 =$67

If you play the game 100 times, you can expect to win $67.

(b)

Probability of Winning  =\dfrac{20}{36}

If the game is played 100 times

Number of times expected to win

=\dfrac{20}{36} \times 100\\=56$ times

Therefore, number of times expected to loose

= 100-56

=44 times

8 0
4 years ago
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