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katen-ka-za [31]
1 year ago
5

Solve each system. (1/2)x + (2/3)y= 1 , (3/4)x - (1/3)y = 2

Mathematics
1 answer:
NeTakaya1 year ago
3 0

The solution of the given system of equations is (3//2, -3/8)

We can solve a system of equations using:

- graphical method

- elimination method

- substitution method

The given system of equations:

(1/2)x + (2/3)y= 1  ......... (1)

(3/4)x - (1/3)y = 2  ..........(2)

Multiply equation (1) by 6

3x + 4y = 6   ..... (3)

Multiply equation (2) by 12

9x - 4y = 24  ...... (4)

Add equation (3) and (4)

3x + 4y = 6  

<u>9x - 4y = 24  </u>+

12x      = 30

   x      = 30/12 = 5/2

Substitute x = 5/2 into equation (3)

3x + 4y = 6  

3. (5/2) + 4y = 6

15/2 +4y = 6

4y = (12 - 15)/2 = -3/2

 y = -3/8

The solution is (3/2, -3/8)

Learn more about how to solve system of equations here:

brainly.com/question/3654260

#SPJ4

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mel-nik [20]

Answer:

Step-by-step explanation:

Given that in a sample of 800 U.S.​ adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement.

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a) The probability that both adults think most celebrities are good role models is ________= Prob of selecting both from 199

= \frac{199C2}{800C2} \\=0.0616

=0.062

b) The probability that neither adult thinks most celebrities are good role models is _______=P(both selecting from 601)

=  \frac{601C2}{800C2} \\=0.5641

=0.564

c) The probability that at least one of the two adults thinks most celebrities are good role models ______

=1-Prob that neither thinks

= 1- 0.564

= 0.436

6 0
3 years ago
Find the integral.......
ICE Princess25 [194]

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1/5(2ln|x|+3*5^1/3)+c

Step-by-step explanation:

4 0
3 years ago
Consider the following functions. f1(x) = x, f2(x) = x2, f3(x) = 7x − 5x2 g(x) = c1f1(x) + c2f2(x) + c3f3(x) Solve for c1, c2, a
Margaret [11]

Answer:

Therefore the solution is = k{-7,5,1} where k ∈R

Step-by-step explanation:

Given that,

f₁(x) =x

f₂(x)= x²

f₃(x)= 7x - 5x²

Also,

g(x) = c₁f₁(x)+c₂f₂(x)+c₃f₃(x)

Putting the values of f₁(x), f₂(x) and f₃(x).

g(x) = c₁.x+c₂x²+c₃(7x-5x²)

Given condition that g(x)= 0

∴ c₁.x+c₂x²+c₃(7x-5x²)=0

⇒(c₁+7c₃)x +(c₂-5c₃)x² = 0

Comparing the coefficients of x and x²

∴c₁+7c₃=0               and       c₂-5c₃ =0

\Rightarrow c_1 =-7c_3                     \Rightarrow c_2=5c_3

Let c₃= k   [k∈R]  

Then c₁ = -7k   and   c₂=5k

Therefore the solution is = { c₁,c₂,c₃}  

                                           = {-7k, 5k, k}

                                            =k{-7,5,1}

5 0
3 years ago
Help with question 3 please
mel-nik [20]
Score = 6x+y

so 6x+y = xy
⇒ 6x = xy-y
⇒ 6x = y(x-1)
⇒ y = 6x/(x-1)

for x=0, y=0
x=1 , not possible
x=2, y = 12
x = 3, y = 9
x = 4, y = 8
x = 5, y = 7.5 (not possible)
x = 6 , y = 7.1 (not possible)
x = 7, y = 7
x = 8, y = 6.85 (not possible)
x = 9, y = 6.75 (not possible)...

Only five scores are possible.


6 0
4 years ago
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kirza4 [7]

Answer:

It's true.

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2(segment ST) = RT

divide both sides by two

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Here's a rough picture of the line.

R _____________S_____________ T

S is in the middle of the line which makes it the midpoint.

It's true. S is the midpoint of RT.

3 0
3 years ago
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