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AlladinOne [14]
3 years ago
8

Solve the following system of equations -3x+2y=8 6x-2y=-20

Mathematics
1 answer:
Elanso [62]3 years ago
6 0
2 [-3x+2y=8]
6x-2y=-20

-6x + 4y = 16
6x - 2y = -20
2y = -4
y = -2

use the first eq (u can use any) then substitute the value of y

-3x + 2(-2) = 8
-3x -4 = 8
-3x = 12
x = -4

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A bag contains some white and black balls . The probability of picking two white balls one after other without replacement from
FromTheMoon [43]

Answer:

2/35

Step-by-step explanation:

Let w and b be the numbers of white and black balls in the bag respectively.

So, the total numbers of the balls in the bag is

n=w+b\;\cdots(i)

As the bag can hold maximum 15 balls only, so

n\leq15 \;\cdots(ii)

Probability of picking two white balls one after other without replacement

=Probability of the first ball to be white and the probability of second ball to be white

=(Probability of picking first white balls) x( Probability of picking 2nd white ball)

Here, the probability of picking the first white ball =\frac{w}{n}

After picking the first ball, the remaining

white ball in the bag = w-1

and the remaining total balls in the bag =n-1

So, the probability of picking the second white ball =\frac{w-1}{n-1}

Given that, the probability of picking two white balls one after other without replacement is  14/33.

\Rightarrow \frac{w}{n} \times \frac{w-1}{n-1}=\frac{14}{33}

\Rightarrow \frac{w(w-1)}{n(n-1)} =\frac{14}{33}

Here, w and n are counting numbers (integers) and 14 and 33 are co-primes.

Let, \alpha be the common factor of the numbers w(w-1) (numerator) and n(n-1) (denominator), so

\frac{w(w-1)}{n(n-1)} =\frac{14\alpha}{33\alpha}

\Rightarrow w(w-1)=14\alpha\cdots(iii)

And n(n-1)=33\alpha.

As from eq. (ii), n\leq 15, so, the possible value of \alpha for which multiplication od two consecutive positive integers (n and n-1) is 33\alpha is 4.

n(n-1)=11\times (3\alpha)

\Rightarrow n(n-1)=12\times11 [as \alpha=4]

\Rightarrow n=12

So, the number of total balls =12

From equation (iv)

w(w-1)=7\times (2\alpha)

\Rightarrow w(w-1)=8\times7

\Rightarrow w=8

So, the number of white balls =8

From equations (i), the number of black balls =12-8=4

In the similar way, the required probability of picking two black balls one after other in the same way (i.e without replacement) is

=\frac{b}{n} \times \frac{b-1}{n-1}

= \frac{4}{15} \times \frac{4-1}{15-1}

= \frac{4}{15} \times \frac{3}{14}

= \frac{2}{35}

probability of picking two black balls one after other without replacement is 2/35.

6 0
3 years ago
Two angles are complementary. two times the measure of one is equal to 40% of the measure of the other. find the measure of both
Nostrana [21]

The measure of both angles are 112.5 and 68.5 degrees

<h3>Complementary angles</h3>

The sum of two complementary angles is 90 degrees.

If two angles are complementary, then;

x + y = 90

x = 90 - y..........1

where x and y are the angles

If  two times the measure of one is equal to 40% of the measure of the other then;

2x = 0.4y ............2

Substitute equation 1 into 2

2(90-y) = 0.4y

180 - 2y = 0.4y

180 = -0.4y + 2y

1.6y = 180

Divide both sides by 1.6

1.6y/1.6 = 180/1.6

y = 112.5 degrees

For the other angle

x= 180 - y

x = 180 -112.5

x = 68.5 degrees

Hence the measure of both angles are 112.5 and 68.5 degrees

Learn more on complementary angles here: brainly.com/question/16281260

#SPJ1

8 0
10 months ago
The longest side of an obtuse triangle measures 20 cm. The two shorter sides measure x cm and 3x cm. Rounded to the nearest tent
tankabanditka [31]
Obtuse triangle Pythagorean Theorem

c² > a² + b²

20² > x² + 3x²
400 > 4x²
<u>÷4      ÷4</u>
<u> 100 > x²</u>
   10 > x
  
400 > 4(7.1)²
400 > 4(50.41)
400 > 201.64

The greatest possible value of x is 7.10
6 0
3 years ago
Read 2 more answers
What is the equation of the following line
Alex_Xolod [135]
Its B 
rise over run dictates that its 2/8 which simplifies to 1/4
and its at an upward angle from left to right therefore its positive.
3 0
3 years ago
Read 2 more answers
A factory makes tennis balls. Every tennis ball must meet a quality standard, or it will be rejected. The percentage that meets
Anettt [7]
The answer you're looking for is 40 tennis balls.
Hope this helped!
3 0
3 years ago
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