Let h(x)=2x+5, g(x)=8−3x. What is the value of h(g(1.5))?

1 answer:

6 0

So your equation is a composite function. It means to plug 1.5 as x into g(x), then the answer you get for that, plug into h(x).

So.

g(1.5)=8-3(1.5)

=8-4.5

=3.5

Then.

H(3.5)=2x+5

=2(3.5)+5

=7+5=12

Your final answer is 12.

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Find the values of x and y. 40 sy 40 xº X = y= 0

Helga [31]

Answer:

x = 30°

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Step-by-step explanation:

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Therefore, x is a base triangle of the isosceles, thus:

x = ½(180 - (180 - 60))

x = ½(180 - 120)

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x = 30°

Let's find y.

8y = 40 (sides of an equilateral ∆ are equal)

Divide both sides by 8

y = 5

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Molodets [167]

Answer:

500 type A; 3500 type B

Step-by-step explanation:

The method of Lagrange multipliers can solve this quickly. For objective function f(x, y) and constraint function g(x, y)=0 we can set the partial derivatives of the Lagrangian to zero to find the values of the variables at the extreme of interest.

These functions are ...

$f(x,y)=4x+2y\\g(x,y)=2x^2+y-4$

The Lagrangian is ...

$\mathcal{L}(x,y,\lambda)=f(x,y)+\lambda g(x,y)\\\\\text{and the partial derivatives are ...}\\\\\dfrac{\partial \mathcal{L}}{\partial x}=\dfrac{\partial f}{\partial x}+\lambda\dfrac{\partial g}{\partial x}=4+\lambda (4x)=0\ \implies\ x=\dfrac{-1}{\lambda}\\\\\dfrac{\partial \mathcal{L}}{\partial y}=\dfrac{\partial f}{\partial y}+\lambda\dfrac{\partial g}{\partial y}=2+\lambda (1)=0\ \implies\ \lambda=-2$

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