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Rom4ik [11]
3 years ago
10

5(2x – 3) = 5 Part A: How many solutions does this equation have? (4 points) Part B: What are the solutions to this equation? Sh

ow your work. (6 points)
Mathematics
1 answer:
Maru [420]3 years ago
7 0

ANSWER

a) One Solution

b) the solution is x=2

EXPLANATION

The given equation is:

5(2x - 3) = 5

We expand to get;

10x - 15 = 5

Group similar terms;

10x = 15 + 5

This implies that,

10x = 20

Divide both sides by 10 to obtain,

x = 2

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Find the max and min values of f(x,y,z)=x+y-z on the sphere x^2+y^2+z^2=81
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Using Lagrange multipliers, we have the Lagrangian

L(x,y,z,\lambda)=x+y-z+\lambda(x^2+y^2+z^2-81)

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L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}
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Substituting the first three equations into the fourth allows us to solve for \lambda:

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For each possible value of \lambda, we get two corresponding critical points at (\mp3\sqrt3,\mp3\sqrt3,\pm3\sqrt3).

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5 0
3 years ago
On a coordinate plane, points (1, 3), (5, 9), and (7, 12) are plotted. Which of the following statements are true about this gra
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