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3 years ago

Does the MVT apply? Explain why or why not. y=x^2/4x + 4 ; [-6, -2]

Mathematics

1 answer:

inysia [295]3 years ago

7 0

Hello!

$\large\boxed{\text{Yes, it does.}}$

In order to use the MVT, the function must be continuous over the given interval.

$y = \frac{x^{2} }{4x}+4$

Simplifies to:

$y = \frac{x}{4} + 4$

This is a linear equation that is continuous on the interval (-∞, ∞), which means that it would also be continuous on the interval [-6, -2]. The MVT would apply to this function.

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What are the vertex and x-intercepts of the graph of the function given below?

madreJ [45]

VERTEX
To determine the vertex (coordinate x) of parabola y = ax² + bx + c, use this following formula
x vertex = $-\dfrac{b}{2a}$

y = x² - 2x - 48
a = 1, b = -2, c = -48
plug in the numbers
x vertex = $-\dfrac{b}{2a}$
x vertex = $-\dfrac{(-2)}{2(1)}$
x vertex = $\dfrac{2}{2}$
x vertex = 1

To find y vertex, substitute the value of x vertex to the parabola equation
y = x² - 2x - 48
y = 1² - 2(1) - 48
y = 1 - 2 - 48
y = -49

The vertex is (1, -49)

X-INTERCEPT
x-intercept located in x axis, that means y = 0. Substitute y = 0 to the parabola equation
x² - 2x - 48 = y
x² - 2x - 48 = 0
(x - 8)(x + 6) = 0
x = 8 or x = -6
The x-intercepts are (8,0) and (-6,0)

The answer is first option

5 0

4 years ago

Read 2 more answers

Which parent functions have an intercept at (0,0)Choose all that are correct.

inessss [21]

Answer:

Linear, Quadratic, Radical, Absolute Value, Cubic, Cube Root

Step-by-step explanation:

To find:

Which functions have an intercept at (0, 0).

That means, when we put a value $x=0$ in the $y =f(x)$ , value of $y=0$ .

Let us discuss each <em>parent</em> function one by one:

1. Linear:

$y = x$

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

2. Quadratic:

$y = x^2$

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

3. Radical:

$y = \sqrt x$

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

4. Absolute Value:

$y = |x|$

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

5. Rational:

$y = \dfrac{1}{x}$

When we put $x = 0\Rightarrow y \rightarrow \infty$

Therefore, it does not have intercept at (0, 0).

6. Exponential:

$y = b^x$

b is any base

When we put $x = 0\Rightarrow y =1$

Therefore, it does not have intercept at (0, 0).

7. Logarithmic:

$y = logx$

When we put $x = 0 \Rightarrow y\rightarrow$ Not defined

Therefore, it does not have intercept at (0, 0).

8. Cubic:

$y = x^3$

When we put $x = 0\Rightarrow y =0$

Therefore, it has intercept at (0, 0).

9. Cube Root:

$y = \sqrt[3]x$

When we put $x = 0\Rightarrow y =0$

Therefore, it has intercept at (0, 0).

3 0

3 years ago

Can Someone please answer and explain. It's just one problem and there a picture. Thank you

Mice21 [21]

Vertices (3,0),(-3,0) co-vertices (0,-5),(0,5)

transverse axis (line passing vertices) is on(or parallel to) x-axis then formula is
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
..notice.. x^2 is on positive / y^2 is on negative

center (h,k) is midway between vertices = (0,0)
we have h = k = 0 and now formula is
x^2/a^2 - y^2/b^2 = 1

a is the distance from a vertex to center = 3
b is the distance from a co-vertex to center = 5

the formula is
x^2/3^2 - y^2/5^2 = 1 ... answer is the 1st

6 0

3 years ago

Coordinate plane with trapezoids TRAP and T prime R prime A prime P prime and points W, X, Y, and Z with points located at T 1 c

k0ka [10]

Answer:

The answer is Z

Step-by-step explanation:

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The number of bacteria, b, in a refrigerated food is given by the function b(t) = 15t2 − 60t + 125, where t is the temperature o

KonstantinChe [14]

Its an undefined value...

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3 years ago