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3 years ago

Simplify the following expression: 2(3g-4)-(8g+3)

Mathematics

2 answers:

Luden [163]3 years ago

8 0

<span>First you have to do with simplify.

2(3g-4)-(8g+3)

= -2g-11

Answer is = -2g-11</span>

Firlakuza [10]3 years ago

7 0

(6g-8) - (8g+3)

-2g-11

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rodikova [14]

Associative property is a+(b+c)=(a+b)+c

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3 years ago

(1 point) (a) Find the point Q that is a distance 0.1 from the point P=(6,6) in the direction of v=⟨−1,1⟩. Give five decimal pla

natima [27]

Answer:

following are the solution to the given points:

Step-by-step explanation:

In point a:

$\vec{v} = -\vec{1 i} +\vec{1j}\\\\|\vec{v}| = \sqrt{-1^2+1^2}$

$=\sqrt{1+1}\\\\=\sqrt{2}$

calculating unit vector:

$\frac{\vec{v}}{|\vec{v}|} = \frac{-1i+1j}{\sqrt{2}}$

the point Q is at a distance h from P(6,6) Here, h=0.1

$a=-6+O.1 \times \frac{-1}{\sqrt{2}}\\\\= 5.92928 \\\\b= 6+O.1 \times \frac{-1}{\sqrt{2}} \\\\= 6.07071$

the value of Q= (5.92928 ,6.07071 )

In point b:

Calculating the directional derivative of $f (x, y) = \sqrt{x+3y}$ at P in the direction of $\vec{v}$

$f_{PQ} (P) =\fracx{f(Q)-f(P)}{h}\\\\$

$=\frac{f(5.92928 ,6.07071)-f(6,6)}{0.1}\\\\=\frac{\sqrt{(5.92928+ 3 \times 6.07071)}-\sqrt{(6+ 3\times 6)}}{0.1}\\\\= \frac{0.197651557}{0.1}\\\\= 1.97651557$

$\vec{v} = 1.97651557$

In point C:

Computing the directional derivative using the partial derivatives of f.

$f_x(x,y)= \frac{1}{2 \sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{2 \sqrt{22}}\\\\f_x(x,y)= \frac{1}{\sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{\sqrt{22}}\\\\f_{(PQ)}(P)= (f_x \vec{i} + f_y \vec{j}) \cdot \frac{\vec{v}}{|\vec{v}|}\\\\= (\frac{1}{2 \sqrt{22}}\vec{i} + \frac{1}{\sqrt{22}} \vec{j}) \cdot \frac{-1}{\sqrt{2}}\vec{i} + \frac{1}{\sqrt{2}} \vec{j}$

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3 years ago

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Svetach [21]

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3 years ago

The rate of discount, R, can be determined using the formula, where P is the regular price of an item and D is the discount or a

astraxan [27]

Answer:

B.0.31

Step-by-step explanation:

% of change = amount of change/original price

R=(P-D)÷P

39-27=12

12÷39=.307

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3 years ago

What is the solution to the system of equations below?<br>2x+3y = 17<br>3x+6y= 30

brilliants [131]

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}2x+3y=17&\text{multiply both sides by (-2)}\\3x+6y=30\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-4x-6y=-34\\3x+6y=30\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-x=-4\qquad\text{change the signs}\\.\qquad x=4\\\\\text{put the value of x to the first equation:}\\\\2(4)+3y=17\\8+3y=17\qquad\text{subtract 8 from both sides}\\3y=9\qquad\text{divide both sides by 3}\\y=3$

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3 years ago

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