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3 years ago

2x-6y=12 and -5x+15y=-30 elimination

Mathematics

1 answer:

Reptile [31]3 years ago

8 0

Answer:

unsolvable because the second equation is just -2.5 times the first equation.

Step-by-step explanation:

2x-6y=12 then 2x=12+6y x=6+3y

-5x+15y=-30

substitute x

-5(6+3y)+15y=-30

-30-15y+15y=-30

y=y

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Step-by-step explanation:

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3 years ago

A manager is assessing the correlation between the number of employees in a plant and the number of products produced yearly. Th

Contact [7]

Answer:

A)there is a strong positive correlation

B)A function that best fits the data is $\widehat{y}=6x+10$

C)Slope indicates the rate of change of Number of products per employee

y intercept indicates number of products when number of employees are 0

Step-by-step explanation:

Number of employees (x) 0 25 50 75 100 125 150 175 200

Number of products (y) 10 160 310 460 610 760 910 1060 1210

Part A: Is there any correlation between the number of employees in the plant and the number of products produced yearly?

Mean of x values = $\frac{0+25 + 50 + 75 + 100 + 125 + 150 + 175 + 200}{9}=900$

Mean of y values = $\frac{10+160+ 310+ 460+ 610+ 760+ 910+ 1060+ 1210}{9} =610$

$\sum(x-\bar{x})^2= 37500$

$\sum(y - \bar{y})^2 = 1350000$

N =No. of observations= 9

$\sum(x - \bar{x})(y-\bar{y}) = 225000$

R Calculation

$r = \frac{\sum((x-\bar{x})(y - \bar{y}))}{\sqrt{\sum(x - \bar{x})^2(y-\bar{y})^2}}$

$r=\frac{225000}{\sqrt{(37500)(1350000)}}\\r= 1$

So, there is a strong positive correlation

B: Write a function that best fits the data.

Regression Equation = ŷ = bx + a

$b = \frac{225000}{37500} = 6\\a = \bar{y} -b \bar{x} = 610 - (6 \times 100) = 10\\ \widehat{y}= 6x + 10$

So, a function that best fits the data is $\widehat{y}=6x+10$

C)What does the slope and y-intercept of the plot indicate?

Slope indicates the rate of change of Number of products per employee

y-intercept indicates the y-coordinate of a point where a line, curve, or surface intersects the y-axis.

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4 years ago

Pleaseeee help ASAP!!!!!!

erik [133]

Question:

The taxi company charged a pick-up fee of $4.30 plus $1.25 per mile. The total fare was $35.55, not including the tip. How many miles was the taxi ride?

Answer:

total miles 25

Prove:

35.55-4.30=31.25

31.25/1.25= 25

<em><u>OR Explained</u></em>

sub 4.30 35.55 - 4.30 = 31.25

Divide 1.25 31.25/1.25 = 25

Final answer is 25

After dividing what you subtracted, you will successfully get your answer.

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3 years ago

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Describe the transformation f(x)= x-2; g(x)= f(x)+3 please help asap

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The parent function is the simplest form of the type of function given.
f(x)=x^2

The transformation being described is from f(x)=x^2
to g(x)=(x−5)^2+3

******************************************************************************

By definition,
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f(x)=x^2→g(x)=(x−5)^2+3

The horizontal shift depends on the value of h. The horizontal shift is described as:
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Hence, in the question above, Horizontal Shift: Right 5 Units

The vertical shift depends on the value of k. The vertical shift is described as:
g(x)=f(x)+k - The graph is shifted up k units.
g(x)=f(x)−k - The graph is shifted down k units.

Therefore, in the question above, Vertical Shift: Up 3 Units

The graph is reflected about the x-axis when g(x)=−f(x)
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Reflection about the x-axis: None
The graph is reflected about the y-axis when g(x)=f(−x)
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Reflection about the y-axis: None
Compressing and stretching depends on the value of 'a'
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When 'a' is greater than 1 : Vertically stretched
When 'a' is between 0 and 1 : Vertically compressed
Vertical Compression or Stretch: None

****************************************************************************
Comparing and listing the transformations as follows:

Parent Function: f(x)=x^2
Horizontal Shift: Right 5 Units
Vertical Shift: Up 3 Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None

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