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2 years ago

How many equations in the same variables must be in a set to solve a system of linear equations?

Mathematics

1 answer:

ira [324]2 years ago

6 0

Answer:

For a unique solution, there must be as many consistent, independent equations as there are variables.

Step-by-step explanation:

Each equation lets you write an expression for one variable in terms of the others in that equation. That expression can be substituted throughout the system, reducing the number of equations and variables by one each.

After n-1 such substitutions in a system of n equations, there will be one equation left. If that is an equation in one variable, then the solution to the system can be easily found. If more than one variable remains (> n variables in n equations), then the system cannot be solved for definitive values of each of the variables.

___

If the equations are inconsistent, there is no solution. If the equations are dependent, then there is no unique solution.

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Which expression is equal to 24 - 18 ÷ 3<br> A) 24 -6<br> B) 6 ÷ 3<br> C) 8 - 18 <br> D) 6 - 3

Westkost [7]

Answer:

Correct Answer is option A.

Step-by-step explanation:

24 - 18 ÷ 3

According to PEMDAS Rule where P stands for parenthesis ,E exponents,M multiplication ,D division , A addtion and S subtraction

so first we divide 18 by 3 we get

24-6

Answer.

7 0

2 years ago

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Diane has a hospital appointment. when she arrives at the hospital, the car park is nearly full. there are a total of 534 car pa

Oksanka [162]

In total there are 534 spaces, but 476 are occupied.
Occupied spots cannot be parked in.
The answer is 534 - 476, which equals 58 available spots.

4 0

3 years ago

the perimeter of an isosceles trapezoid is 62 cm. if three sides are equal in length and the fourth side is 10 cm longer, find t

Alja [10]

Perimeter = sum of all the sides
let x = one side
longer side = x + 10
Perimeter = x + x + x + x + 10
62 = 4x + 10
4x = 52
x = 13
Longer side = 23

Area = (10+23)x2/10
= 6.6

5 0

2 years ago

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Which function has a greater speed and what is the greater speed

lana66690 [7]

Answer:

function a is faster

Step-by-step explanation:

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2 years ago

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If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid

Artist 52 [7]

Check the picture below. Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm². Also, recall, the base is a square, thus, length = width = x.

$\bf \textit{volume of a rectangular prism}\\\\
V=lwh\quad 
\begin{cases}
l = length\\
w=width\\
h=height\\
-----\\
w=l=x
\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\
-------------------------------\\\\
\textit{surface area}\\\\
S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h
\\\\\\
\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\
-------------------------------\\\\
V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3$

so.. that'd be the V(x) for such box, now, where is the maximum point at?

$\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2
\\\\\\
\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100
\\\\\\
x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}$

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.

so, the volume will then be at $\bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3$

6 0

3 years ago