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4 years ago

-x+7y=5,-4x+y=-7 System of equations substitution

Mathematics

1 answer:

Leno4ka [110]4 years ago

5 0

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}-x+7y=5\\-4x+y=-7&\text{add}\ 4x\ \text{to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}-x+7y=5&(1)\\y=4x-7&(2)\end{array}\right\qquad\text{subtritute (2) to (1)}\\\\-x+7(4x-7)=5\qquad\text{use the distributive property}\\\\-x+(7)(4x)+(7)(-7)=5\\\\-x+28x-49=5\qquad\text{add 49 to both sides}\\\\-x+28x=5+49\qquad\text{combine like terms}\\\\27x=54\qquad\text{divide both sides by 27}\\\\\boxed{x=2}$

$\text{Put the value of}\ x\ \text{to (2):}\\\\y=4(2)-7\\\\y=8-7\\\\\boxed{y=1}$

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Find expressions for the partial derivatives of the following functions:

nlexa [21]

Answer:

Step-by-step explanation: partial derivative is the differentiation of one variable e.g. X while leaving the values of the other variable e.g. Y

These four questions A, B, C and D have different functions separated by commas. I will not assume the commas to be something else like a plus sign.

A. f(x) = g'(x).k(y) , g'(x) + h(y)

f(y) = k'(y).g(x) , g(x) + h'(y)

B. f(x) = g'x (x+y)

f(y) = g'y (x+y) , h'y (y+z)

f(z) = h'z (y+z)

C. f(x) = f'x (xy) , f'x (zx)

f(y) = f'y (xy) , f'y (yz)

f(z) = f'z (yz) , f'z (zx)

D. f(x) = f'x (x) , g'(x) , h'x (x,y)

f(y) = h'x (x,y)

These are the partial derivative expressions for each variable in each function. You will need to pay a lot of attention to understand:

* while differentiating X alone, functions in Y which are separated by commas from the functions in X, are ignored totally because they are different questions

* In functions where X added to Y is in a bracket e.g. (x+y), to find the derivative of X, Y isn't thrown away because they are joined (by a plus sign) the derivative of X alone in this case would be f'x (x+y)

* f(x), just like g(x), simply means/represents a function in X hence f'(x) means the differentiation of all X-terms in that function

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3 years ago

Is (11,9), (11,5), (9,3) a function

Marina86 [1]

Answer:

$\huge{ \boxed{ \sf{No}}}$

✑ Question :

Is ( 11 , 9 ) , ( 11 , 5 ) , ( 9 , 3 ) a function ?

No , it's not a function.

✎ Reason :

This is not a function because one element 11 of set A is associated to elements 9 and 5 of set B.

♨ Explore about function :

↪ Function is a special type of relation. It is the refinement of relation. In a relation from A to B , every element of set A should have only one ( distinct ) image in B to be a function. In other words , if no two different ordered pairs have the same first component , then it is a function.

Hope I helped!

Have a wonderful day ! ツ

~ $\sf{TheAnimeGirl}$ ♡

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3 years ago

Find the sum of 2x 2 + 3x - 4, 8 - 3x, and -5x 2 + 2

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

The table below represents a linear function f(x) and the equation represents a function g(x):

notsponge [240]

(0,0)(1,3) = (3 - 0) / (1 - 0) = 3

slope = 3
equation for this line is y = 3x...and since u have (0,0) as a point on this line, ur y int is (0,0)

g(x) = 7x + 2...slope here is 7 and y int is (0,2)
==========================
The slope of f(x) = 3. I found this using the slope formula (y2 - y1) / (x2 - x1).
The slope of g(x) = 7. Because in y = mx + b form, the slope is in the m position.
g(x) has a steeper slope.
=========================
f(x) has a y int of (0,0)...the line cuts thru the origin.

g(x) has a y int of (0,2)...because in y = mx + b form, the y int will be in the b position.

So, g(x) has a greater y int.

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3 years ago