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3 years ago

What is the value of x in this simplified expression? (-j)^-7=1/(-j)^x

Mathematics

1 answer:

e-lub [12.9K]3 years ago

5 0

$x=7\\\\\text{because}\\\\a^{-n}=\dfrac{1}{a^n};\ a\neq0\\\\(-j)^{-7}=\dfrac{1}{(-j)^7}$

$\text{Minus in a power means inverse.}$

$a^{-1}=\dfrac{1}{a}\\\\(-j)^{-7}=(-j)^{7\cdot(-1)}=\left[(-j)^7\right]^{-1}=\dfrac{1}{(-j)^7}\\\\\text{Used:}\\\\(a^n)^m=a^{n\cdot m}$

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Use the graph to determine the domain and range of the relation, and whether the relation is a function

MAVERICK [17]

domain is correct for b and c

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hence answer is B

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3 years ago

Anyone know the area?

Elina [12.6K]

Answer: The area of the triangle is: " 8.5 cm² " ;

or, write as: " 8 $\frac{1}{2}$ cm² " .
_______________________________________________________
Explanation:
_________________________________________________________
The formula {"equation"} for the area of a triangle is:

A = ( $\frac{1}{2}$ ) * b * h ;

in which: A = area;
b = base;
h = [perpendicular] height;
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{also, can be written as: " A = (b * h) / 2 " .}.
______________________________________
Solve for the area, "A" ; by plugging in the known values shown in the figure (image attached):
______________________________________
base, "b" = 13 cm ;
[perpendicular] height, "h" = 5 cm ;
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A = (b * h) / 2 ;

= (13 cm * 5 cm) / 2 ;

= [ (13 * 5) cm²] / 2 ;

= 65 cm² / 2 ;

A = " 8.5 cm² " ; or, write as: " 8 $\frac{1}{2}$ cm² " .
_________________________________________________________
Answer: " 8.5 cm² " ; or, write as: " 8 $\frac{1}{2}$ cm² " .
_________________________________________________________
The area of the triangle is: " 8.5 cm² " ;

or, write as: " 8 $\frac{1}{2}$ cm² " .
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3 years ago

In a certain clothing store,6 shirts and 3 ties cost $79.50 ,and 3 shirts and 2 ties cost $41. determine the cost of each shirt.

Komok [63]

Answer:

Each shirt cost $12

Step-by-step explanation:

First, we have to interpret this question and turn each to an equation, letting shirts represent the letter s and ties represent the letter t.

6 shirts and 3 ties cost $79.50 would be interpreted to 6s+3t=79.5 ,and 3 shirts and 2 ties cost $41 would be interpreted to 3s+2t=41

Hence we have two equations, and we solve them simultaneously.

6s+3t=79.5 (Equation 1)

3s+2t=41 (Equation 2)

We can either use the substitution method or the elimination method but for the sake of this question, we use the Elimination method.

6s+3t=79.5 (Equation 1)

3s+2t=41 (Equation 2)

We multiply equation 1 by 2 and we multiply equation 2 by 3, I'm prefer to eliminate the

2(6s+3t=79.5)

12s+6t=159 Equation 3

3(3s+2t=41)

9s+6t=123 Equation 4

We subtract equation 4 from equation 3.

12s+6t=159

9s+6t=123

12s-9s=3s

6t-6t=0

159-123=36

We therefore have

3s=36

Divide both sides by 3

s=36/3

s=12

One shirt cost $12

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3 years ago

Solve the following exponential equation:<br><br>5^x=2 <br><br>e^x=10

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Number 1.

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Number 2

$e^x=10$ , solve for our exponent, $2.718282^x=10$ , use the logarithmic formula, and we get,

$x=\frac{log(10)}{log(2.718282)}$ , which then we get that $x=2.302585$

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2 years ago

A shopkeeper bought 775 kg of wheat . He wants to divide all the wheat into 8 bags of the same size. How much Wheat Can he store

Arturiano [62]

In order to calculate how much wheat will be stored in each bag, let's divide the total amount of wheat by the number of bags:

$\frac{775}{8}=96.875$

Assuming that the amount of wheat each bag can hold is a whole number, so each bag can hold 96 kg (otherwise, each bag would hold 96.875 kg and there would be no wheat left).

Then, to find how much wheat will be left, let's calculate how much the 8 bags will hold, and then we subtract this value from the total:

$\begin{gathered} 96\cdot8=768 \\ \\ 775-768=7 \end{gathered}$

So there will be 7 kg left.

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11 months ago