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photoshop1234 [79]
3 years ago
14

What is the solution to the system of equations of linear equations 2x + 4y = 38 and 10x + 3y = 105

Mathematics
1 answer:
nata0808 [166]3 years ago
6 0
<span>A) 2x + 4y = 38
B) 10x + 3y = 105
Multiplying A) by -5
A) -10x -20y = -190 then adding it to B)
</span><span>B) 10x + 3y = 105

-17y = -85
y = 5
x = 9


</span>
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Solve the following systems by Elimination
Alenkasestr [34]

Answer:

The solutions for both system of equations are as follows:

  1. (5,2)
  2. (2,-1)

Step-by-step explanation:

The first set of equations is:

4x+6y=32\\3x-6y=3\\

It can clearly be seen that the coefficients of y are already same in magnitude with different signs so we have to add both equations

So adding both equations, we get

4x+6y+3x-6y = 32+3\\7x = 35\\\frac{7x}{7} = \frac{35}{7}\\x = 5

Putting x=5 in equation 1

4(5)+6y = 32\\20+6y = 32\\6y = 32-20\\6y = 12\\\frac{6y}{6} = \frac{12}{6}\\y = 2

The solution is (5,2)

The second set of simultaneous equations is:

-3x+5y=-113x+7y=-1

We can see that the coefficients of x in both equations are same in magnitude with opposite signs so

Adding both equations

-3x+5y+3x+7y = -11-1\\12y = -12\\\frac{12y}{12} = \frac{-12}{12}\\y = -1

Putting y= -1 in first equation

-3x+5(-1)=-11\\-3x-5=-11\\-3x=-11+5\\-3x=-6\\\frac{-3x}{-3} = \frac{-6}{-3}\\x = 2

The solution is: (2,-1)

Hence,

The solutions for both system of equations are as follows:

  1. (5,2)
  2. (2,-1)
3 0
3 years ago
Abigail bought some mangoes at 3 for GH¢ 0.90 and sold all at 4 for GH¢ 1.60.If she made a profit of GH¢ 35.00,how many mangoes
umka21 [38]

Answer:

2

Step-by-step explanation:

Total costs = 4 + (3 * 2) + 5 + 15  

Total costs = 4 + 6 + 5 + 15  

Total costs = $ 30  

Substituting values we have:  

Total change = 32 - 30  

Total change = 2 $

6 0
3 years ago
Which is a characteristic of a studio apartment?
GenaCL600 [577]

Answer:d

its a apartment thats just one big room

8 0
3 years ago
Test scores of the student in a school are normally distributed mean 85 standard deviation 3 points. What's the probability that
Mrrafil [7]

Answer:

The probability that a random selected student score is greater than 76 is \\ P(x>76) = 0.99865.

Step-by-step explanation:

The Normally distributed data are described by the normal distribution. This distribution is determined by two <em>parameters</em>, the <em>population mean</em> \\ \mu and the <em>population standard deviation</em> \\ \sigma.

To determine probabilities for the normal distribution, we can use <em>the standard normal distribution</em>, whose parameters' values are \\ \mu = 0 and \\ \sigma = 1. However, we need to "transform" the raw score, in this case <em>x</em> = 76, to a z-score. To achieve this we use the next formula:

\\ z = \frac{x - \mu}{\sigma} [1]

And for the latter, we have all the required information to obtain <em>z</em>. With this, we obtain a value that represent the distance from the population mean in standard deviations units.

<h3>The probability that a randomly selected student score is greater than 76</h3>

To obtain this probability, we can proceed as follows:

First: obtain the z-score for the raw score x = 76.

We know that:

\\ \mu = 85

\\ \sigma = 3

\\ x = 76

From equation [1], we have:

\\ z = \frac{76 - 85}{3}

Then

\\ z = \frac{-9}{3}

\\ z = -3

Second: Interpretation of the previous result.

In this case, the value is <em>three</em> (3) <em>standard deviations</em> <em>below</em> the population mean. In other words, the standard value for x = 76 is z = -3. So, we need to find P(x>76) or P(x>-3).

With this value of \\ z = -3, we can obtain this probability consulting <em>the cumulative standard normal distribution, </em>available in any Statistics book or on the internet.

Third: Determination of the probability P(x>76) or P(x>-3).

Most of the time, the values for the <em>cumulative standard normal distribution</em> are for positive values of z. Fortunately, since the normal distributions are <em>symmetrical</em>, we can find the probability of a negative z having into account that (for this case):

\\ P(z>-3) = 1 - P(z>3) = P(z

Then

Consulting a <em>cumulative standard normal table</em>, we have that the cumulative probability for a value below than three (3) standard deviations is:

\\ P(z

Thus, "the probability that a random selected student score is greater than 76" for this case (that is, \\ \mu = 85 and \\ \sigma = 3) is \\ P(x>76) = P(z>-3) = P(z.

As a conclusion, more than 99.865% of the values of this distribution are above (greater than) x = 76.

<em>We can see below a graph showing this probability.</em>

As a complement note, we can also say that:

\\ P(z3)

\\ P(z3)

Which is the case for the probability below z = -3 [P(z<-3)], a very low probability (and a very small area at the left of the distribution).

5 0
3 years ago
Holly missed 6 of 181 school days this year. Approximately what percent of school days was Holly in attendance?
Natasha2012 [34]
181-6=175\\\\\frac{175}{181}\cdot100\%=\\\\\frac{17500}{181}\%=\\\\96.7\%\approx97\%\\\\Answer\ C
4 0
3 years ago
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