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taurus [48]
3 years ago
11

Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the

numbers or symbols.
2x+5y=16
-5x-2y=2
Mathematics
1 answer:
kirill [66]3 years ago
6 0

Answer:

\huge\boxed{(2,4)}

Step-by-step explanation:

2x + 5y = 16 ------------------(1)

-5x -2y = 2   ------------------(2)

<u>Multiplying (1) by 5 </u>

5(2x+5y) = 16*5

10x+25y = 80 ----------------(3)

<u>Multiplying (2) by 2</u>

2(-5x-2y) = 2*2

-10x - 4y = 4 -----------------(4)

Adding Eq. (3) and (4)

10x + 25y -10x -4y = 80 + 4

25y - 4y = 84

21y = 84

Dividing both sides by 21

y = 4

\rule[225]{225}{2}

Now, Putting y = 4 in Eq. (1)

2x + 5(4) = 16

2x + 20 = 16

2x = 20 - 16

2x = 4

Dividing both sides by 2

x = 2

\rule[225]{225}{2}

Ordered Pair = (x,y) = (a,b) = (2,4)

\rule[225]{225}{2}

Hope this helped!

<h2>~AnonymousHelper1807</h2>
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rusak2 [61]
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2 years ago
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3 years ago
Percy solved the equation x2 + 7x + 12 = 12. His work is shown below. Is Percy correct? Explain.
antoniya [11.8K]
= > x² + 7x + 12 = 12

= > x² + ( 4 + 3 )x + 12 = 12

= > x² + 4x + 3x + 12 = 12

= > x( x + 4 ) + 3( x + 4 ) = 12

= > ( x + 4 ) ( x + 3 ) = 12


Percy did correct till this step. But by doing like this, Percy can't get the values of the variable x.



Percy should follow the following steps :

= > x² + 7x + 12 = 12


Add -12 on both sides,


= > x² + 7x + 12 - 12 = 12 - 12

= > x² + 7x = 0

= > x( x + 7 ) = 0

= > ( x = 0 ) or ( x + 7 = 0 )

= > ( x = 0 ) or ( x = - 7 )



Hence, required value(s) of x is 0 or -7
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A recent study showed that the length of time that juries deliberate on a verdict for civil trials is normally distributed with
tia_tia [17]

Answer:

Probability that deliberation will last between 12 and 15 hours is 0.1725.

Step-by-step explanation:

We are given that a recent study showed that the length of time that juries deliberate on a verdict for civil trials is normally distributed with a mean equal to 12.56 hours with a standard deviation of 6.7 hours.

<em>Let X = length of time that juries deliberate on a verdict for civil trials</em>

So, X ~ N(\mu = 12.56, \sigma^{2} = 6.7^{2})

The z score probability distribution is given by;

              Z = \frac{X-\mu}{\sigma} ~ N(0,1)

where, \mu = mean time = 12.56 hours

           \sigma = standard deviation = 6.7 hours

So, Probability that deliberation will last between 12 and 15 hours is given by = P(12 hours < X < 15 hours) = P(X < 15) - P(X \leq 12)

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    P(X \leq 12) = P( \frac{X-\mu}{\sigma} \leq \frac{12-12.56}{6.7} ) = P(Z \leq -0.08) = 1 - P(Z < 0.08)

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<em>Therefore, P(12 hours < X < 15 hours) = 0.64058 - 0.46812 = 0.1725</em>

Hence, probability that deliberation will last between 12 and 15 hours is 0.1725.                                                 

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