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3 years ago

(fog)(2) if f(x) = 3x + 1 and g(x) = x ^ 2 + 2

Mathematics

1 answer:

miss Akunina [59]3 years ago

8 0

Answer:

(fog)(x)=f(g(x))=2(3x+2)−1=6x+4−1=6x+3=3(2x+1)

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Step-by-step explanation:

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Given segments AB and CD intersect at E.

nata0808 [166]

The length of a segment is the distance between its endpoints.

$\mathbf{AB = 3\sqrt{2}}$
AB and CD are not congruent
AB does not bisect CD
CD does not bisect AB

(a) Length of AB

We have:

$\mathbf{A = (1,2)}$

$\mathbf{B = (4,5)}$

The length of AB is calculated using the following distance formula

$\mathbf{AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

So, we have:

$\mathbf{AB = \sqrt{(1 - 4)^2 + (2 - 5)^2}}$

$\mathbf{AB = \sqrt{18}}$

Simplify

$\mathbf{AB = 3\sqrt{2}}$

(b) Are AB and CD congruent

First, we calculate the length of CD using:

$\mathbf{CD = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

Where:

$\mathbf{C = (2, 4)}$

$\mathbf{D = (2, 1)}$

So, we have:

$\mathbf{CD = \sqrt{(2 -2)^2 + (4 - 1)^2}}$

$\mathbf{CD = \sqrt{9}}$

$\mathbf{CD = 3}$

By comparison

$\mathbf{CD \ne AB}$

Hence, AB and CD are not congruent

(c) AB bisects CD or not?

If AB bisects CD, then:

$\mathbf{AB = \frac 12 \times CD}$

The above equation is not true, because:

$\mathbf{3\sqrt 2 \ne \frac 12 \times 3}$

Hence, AB does not bisect CD

(d) CD bisects AB or not?

If CD bisects AB, then:

$\mathbf{CD = \frac 12 \times AB}$

The above equation is not true, because:

$\mathbf{3 \ne \frac 12 \times 3\sqrt 2}$

Hence, CD does not bisect AB

Read more about lengths and bisections at:

brainly.com/question/20837270

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3 years ago

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Answer:

Sketch the following three graphs:

1) y = (x - 5)²

2) y = -(x - 5)²

3) y = x - 5

First two are parabolas with vertex at (5,0)

Third one is a line which intersects both the parabolas as (5,0)

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You are seeking to be emancipated from your parents. You are

FromTheMoon [43]

It will take 20 months for the cost to be same.

Step-by-step explanation:

Apartment A;

Security deposit = $1000

Each month cost = $1200

Let,

x be the number of months.

A(x) = 1000 + 1200x

Apartment B;

Security deposit = $1500

Each month cost = $1175

B(x) = 1500 + 1175x

The cost will be same when the functions are equal, therefore,

A(x) = B(x)

$1000+1200x=1500+1175x\\1200x-1175x=1500-1000\\25x=500$

Dividing both sides by 25

$\frac{25x}{25}=\frac{500}{25}\\x=20$

It will take 20 months for the cost to be same.

Keywords: function, division

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