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yulyashka [42]
3 years ago
6

The first line in a system of linear equations has a slope of 3 and passes through the point (-1 , -8). The second line passes t

hrough the points (-6 , 3) and (10 , -1).
What is the solution to the system?

Mathematics
1 answer:
gregori [183]3 years ago
7 0
The equation of the first line can be written in point-slope form as
.. y = 3(x +1) -8
or
.. 3x -y = 5

The equation of the second line can be written in 2-point form as
.. y = (-1-3)/(10-(-6))*(x +6) +3
.. y = (-1/4)(x +6) +3
or
.. x +4y = 6

A graph shows the solution to this system is (x, y) = (2, 1).

_____
The second equation can be used to write an expression for x:
.. x = 6 -4y
This can be substituted into the first equation.
.. 3(6 -4y) -y = 5
.. 18 -13y = 5 . . . . . . . collect terms
.. 13 = 13y . . . . . . . . . add 13y-5
.. 1 = y . . . . . . . . . . . . divide by 13
From the above equation for x
.. x = 6 -4*1 = 2

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Answer:

Change in productivity will be 50%

So option (b) will be correct option

Step-by-step explanation:

It is given that it takes 8 hour to bake 800 pretzels

And there is a shift of 8 hours

So hourly production = \frac{800}{8} =100

Now the production is increases to 1200

Now hourly production = \frac{1200}{8}=150

So change in productivity  = \frac{150-100}{100}=50 %

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3 years ago
Describe the graph of y=3/4x-12 as compared to the graph of y=1/x
Eddi Din [679]

Answer:

Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.

Step-by-step explanation:

We are asked to describe the transformation of function y=\frac{3}{4x-12} as compared to the graph of y=\frac{1}{x}.

We can write our transformed function as:

y=\frac{3}{4(x-3)}

y=\frac{3}{4}*\frac{1}{(x-3)}

Now let us compare our transformed function with parent function.

Let us see rules of transformation.  

f(x-a)\rightarrow\text{Graph shifted to the right by a units},

f(x+a)\rightarrow\text{Graph shifted to the left by a units},

Scaling of a function: a*f(x)

If a>1 , so function is stretched vertically.

If 0<a<1 , so function is compressed vertically.

As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.

As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.

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3 years ago
The cost of 7 books was $154.40. How much does each book cost?
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Answer:

22.057

Round to 22

154.4/7 = 22.057

3 0
2 years ago
Read 2 more answers
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