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3 years ago

HELP ASAP! Use the quadratic equation y = –2x^2 + 4x +5 to complete the statements.

Mathematics

1 answer:

gregori [183]3 years ago

4 0

Answer:

Step-by-step explanation:

Given quadratic equation is,

y = -2x² + 4x + 5

y = -2(x² - 2x) + 5

y = -2(x² - 2x + 1 - 1) + 5

y = -2(x² - 2x + 1) + 2 + 5

y = -2(x - 1)² + 7

This equation is in the vertex form of the quadratic equation,

y = a(x - h)² + k

where, (h, k) is the vertex of the parabola.

Therefore, vertex of the given quadratic equation is (1, 7)

The equation can be rewritten as y = -2(x - 1)² + 7.

Therefore, the vertex of the graph of the function y = -2x² + 4x + 5 in the xy-coordinate plane is located at the point (1, 7).

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Select all of the following expressions that are equivalent to 0.25.. . 1. (0.5)2. 2. (-0.2) + (-0.05). 3. |-3 + 2.75|. 4. -(-0.

shepuryov [24]

The solutions for the following expressions are:
1. 0.5*2 = 1
2. -0.2+-0.05= -0.25
3. absolute value of (-3+2.75) = 0.25
4. -(-0.25) = 0.25
5. 2x-1.75x = 0.25x

The expression equivalent to 0.25 is numbers 3 and 4.

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3 years ago

Calcylate the volume of this regular solid

MatroZZZ [7]

Answer:

V = 270 cm³

Step-by-step explanation:

Remember your volume formula: V=lwh

So, plug in all your variables and multiply:

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4 years ago

F(x)=3x 2 +9f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 9 and g(x)=\dfrac{1}{3}x^2-9g(x)= 3 1 x 2

34kurt

Answer:

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

$g(f(x)) = 3x^4 + 18x^2 + 18$

f(x) and g(x) and not inverse functions

Step-by-step explanation:

Given

$f(x) = 3x^2 + 9$

$g(x) = \dfrac{1}{3}x^2 - 9$

Required

Determine f(g(x))

Determine g(f(x))

Determine if both functions are inverse:

Calculating f(g(x))

$f(x) = 3x^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)(\frac{1}{3}x^2 - 9) + 9$

Expand Brackets

$f(g(x)) = (x^2 - 27)(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = x^2(\frac{1}{3}x^2 - 9) - 27(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = \frac{1}{3}x^4 - 9x^2 - 9x^2 + 243 + 9$

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

Calculating g(f(x))

$g(x) = \dfrac{1}{3}x^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)(3x^2 + 9) - 9$

$g(f(x)) = (x^2 + 3)(3x^2 + 9) - 9$

Expand Brackets

$g(f(x)) = x^2(3x^2 + 9) + 3(3x^2 + 9) - 9$

$g(f(x)) = 3x^4 + 9x^2 + 9x^2 + 27 - 9$

$g(f(x)) = 3x^4 + 18x^2 + 18$

Checking for inverse functions

$f(x) = 3x^2 + 9$

Represent f(x) with y

$y = 3x^2 + 9$

Swap positions of x and y

$x = 3y^2 + 9$

Subtract 9 from both sides

$x - 9 = 3y^2 + 9 - 9$

$x - 9 = 3y^2$

$3y^2 = x - 9$

Divide through by 3

$\frac{3y^2}{3} = \frac{x}{3} - \frac{9}{3}$

$y^2 = \frac{x}{3} - 3$

Take square root of both sides

$\sqrt{y^2} = \sqrt{\frac{x}{3} - 3}$

$y = \sqrt{\frac{x}{3} - 3}$

Represent y with g(x)

$g(x) = \sqrt{\frac{x}{3} - 3}$

Note that the resulting value of g(x) is not the same as $g(x) = \dfrac{1}{3}x^2 - 9$

Hence, f(x) and g(x) and not inverse functions

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Answer:

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Step-by-step explanation:

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4 years ago

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ivolga24 [154]

Continue: root3 + root2 + root3 - root2 - 2 = 2root2 - 2 => rootx-(1/rootx) = root(2root2 - 2);

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3 years ago