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3 years ago

Identify the vertex, focus, and directrix for the parabola in the figure.

Mathematics

1 answer:

adell [148]3 years ago

5 0

The answers are

focus: (−2,3)

directrix: y=7

vertex: (−2,5)

The vertex is at the point (−2,5), the focus is at the point (−2,3), and the directrix is the line at y=7.

Hope this helps

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you placed a 13.2% down payment on a new home. given that the amount of the down payment was $25,623.10, determine the price of

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4 years ago

(1 point) Use the graph below to find exact values of the indicated derivatives, or state that they do not exist. If a derivativ

svetlana [45]

Derivatives can be calculated from graphed functions.

The values of the derivatives are:

The given parameter is:

$\mathbf{h(x) = f(g(x))}$

Start by calculating the equations of f(x) and g(x)

<u>Graph f(x)</u>

The slopes of f(x) are: 3/2 and -3/2

So, the equations are:

$\mathbf{f(x) = \frac{3}{2}x,\ 0 \le x \le 2}$

$\mathbf{f(x) = -\frac{3}{2}x,\ x \ge 2}$

<u>Graph g(x)</u>

The slope of g(x) is: -1/2

So, the equation is:

$\mathbf{g(x) = -\frac 12x}$

So, we have:

$\mathbf{h(x) = f(g(x))}$

Where:

$\mathbf{f(x) = \frac{3}{2}x\ 0 \le x \le 2}$ and $\mathbf{g(x) = -\frac 12x}$

$\mathbf{h(x) = f(g(x))}$ becomes

$\mathbf{h(x) = \frac{3}{2}(-\frac{1}{2}x)}$

Open brackets

$\mathbf{h(x) = -\frac{3}{4}x}$

Differentiate

$\mathbf{h'(x) = -\frac{3}{4}}$

So:

$\mathbf{h'(1) = -\frac{3}{4}}$

$\mathbf{h'(2) = -\frac{3}{4}}$

For x = 3, we have:

$\mathbf{h(x) = f(g(x))}$

Where:

$\mathbf{f(x) = -\frac{3}{2}x\ x \ge 2}$ and $\mathbf{g(x) = -\frac 12x}$

$\mathbf{h(x) = f(g(x))}$ becomes

$\mathbf{h(x) = -\frac{3}{2}(-\frac{1}{2}x)}$

$\mathbf{h(x) = \frac{3}{4}x}$

Differentiate

$\mathbf{h'(x) = \frac{3}{4}}$

Substitute 3 for x

$\mathbf{h'(3) = \frac{3}{4}}$

Hence, the values of the derivatives are:

$\mathbf{h'(1) = -\frac{3}{4}}$ , $\mathbf{h'(2) = -\frac{3}{4}}$ and $\mathbf{h'(3) = \frac{3}{4}}$

Read more about graphed functions at:

brainly.com/question/11804653

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What is the solution to this inequality?

solong [7]

Answer: x>−4

Step-by-step explanation:

Let's solve your inequality step-by-step.

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6x−5+5>−29+5

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Step 2: Divide both sides by 6.

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