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Naddika [18.5K]
3 years ago
11

Solve by substitution x-2y= -25 and 3x-y=0

Mathematics
1 answer:
andreev551 [17]3 years ago
5 0

Answer:

x=5 and y=15

Step-by-step explanation:

x−2y=−25

x−2y+2y=−25+2y(Add 2y to both sides)

x=2y−25

Step: Substitute2y−25forxin3x−y=0:

3x−y=0

3(2y−25)−y=0

5y−75=0(Simplify both sides of the equation)

5y−75+75=0+75(Add 75 to both sides)

5y=75

5y

5

=

75

5

(Divide both sides by 5)

y=15

Step: Substitute 15fory in x=2y−25:

x=2y−25

x=(2)(15)−25

x=5(Simplify both sides of the equation)


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eimsori [14]

Answer:

<em>(7, 5.25)</em> lies on the graph.

Step-by-step explanation:

We are given the following values

x = 4,   6,  8, 12 and corresponding y values are:

y = 3, 4.5, 6, 9

Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.

Equation of a line passing through two points (x_1,y_1) and (x_2,y_2) is given as:

y=mx+c

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(x,y) are the coordinates from where the line passes.

c is the y intercept.

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m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}

Now, the equation of line becomes:

y=\dfrac{3}{4}x+c

Putting the point (4,3) in the above equation to find <em>c</em>:

3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0

So, final equation of given function is:

y=\dfrac{3}{4}x

OR

4y=3x

As per the given options, the point <em>(7, 5.25) </em>satisfies the equation.

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6 0
3 years ago
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3 0
3 years ago
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Bumek [7]

Using the normal distribution, the area underneath the shaded region <u>between the two z-scores</u> is given by:

C. 0.6766.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
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Hence, for this problem, the area is the <u>p-value of z = 0.75 subtracted by the p-value of z = -1.3</u>.

Looking at the z-table, the p-values are given as follows:

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Then:

0.7734 - 0.0968 = 0.6766.

Which means that option C is correct.

More can be learned about the normal distribution at brainly.com/question/15181104

#SPJ1

3 0
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