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4 years ago

2. How many solutions does this system of equations have?

1 answer:

3 0

Solve using the method comparison method
Then you need to cancel equal terms ---> 3x+4=3x-1 <-----
Then you get this ---> 4= -1
And if you know your math... Like me Lol That equation has no solution Because if you graph these points the lines were parallel
Also, I used Photo math a app to help with math
And my solution is correct

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What is 5% increase of $40,000?

LuckyWell [14K]

Answer:

New value =

40,000 + Percentage increase =

40,000 + (5% × 40,000) =

40,000 + 5% × 40,000 =

(1 + 5%) × 40,000 =

(100% + 5%) × 40,000 =

105% × 40,000 =

105 ÷ 100 × 40,000 =

105 × 40,000 ÷ 100 =

4,200,000 ÷ 100 =

so the answer would be 42,000

3 0

3 years ago

Read 2 more answers

You are in charge of erecting a radio telescope on a newly discovered planet. To minimize interference, you want to place it whe

strojnjashka [21]

Answer:

Step-by-step explanation:

$\text{The equation of the surface of the sphere whose radius is 6 can be represented as:}$

$x^2+y^2+z^2 = 36}$

$So , g(x,y,z) = x^2 + y^2 + z^2 - 36$

$\text{To minimize the function :} \\ \\ M(x,y,z0 = 6x - y^2 +xz + 60$

$\text{by applying lagrange multipliers }$

$\bigtriangledown M (x,y,z) = \lambda \bigtriangledown g(x,y,z)$

$\langle 6+zz,-2y,x \rangle = \lambda \langle 2x,2y,2z \rangle$

$6+z = 2\lambda x$

$-2y = 2 \lambda y$

$\text{from the second equation ;} (\lambda +1)y = 0, \text{so , it is either y =0 or }\lambda = -1$

$Suppose \ \lambda = -1 ; \text{other equation becomes x = -2z and 6+z = -2x}$

$\text{such that; 6+z =4z or z = 2}$

$\text{it implies that: x= -4 and }y = \pm \sqrt{36 - 4-16} = \pm 4$

$\text{Here; there exist two possible points}$

$\text{(-4,-4,2) and (-4,4,2)}$

$\text{In the scenario here y=0,} \lambda \text{ is unknown, then we remove it}$

$x = 2 \lambda z \\ \\ 6+z = 2 \lambda x \\ \\ 6+z = 4 \lambda ^2z \\ \\ 6 = (4 \lambda ^2 -1) z ---(1)$

$z = \dfrac{6}{4 \lambda ^2 -1}$

$x = \dfrac{12 \lambda }{4 \lambda ^2 -1 }$

$\text{recall that; it i possible to divide }4 \lambda ^2 -1 \text{since (1) shows that it cannot be equal to zero.} \\ \\ \text{hence, puttinf this into constraint, whereby y =0, Then:}$