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3 years ago

How do i do these using the following functions

Mathematics

1 answer:

attashe74 [19]3 years ago

6 0

Step-by-step explanation:

(f+g)(x) means f(x) + g(x).

(f−g)(x) means f(x) − g(x).

So all you have to do is add them and subtract them.

1. (f+g)(x) = f(x) + g(x)

(f+g)(x) = (3x − 7) + (2x − 4)

(f+g)(x) = 5x − 11

2. (f−g)(x) = f(x) − g(x)

(f−g)(x) = (3x − 7) − (2x − 4)

(f−g)(x) = 3x − 7 − 2x + 4

(f−g)(x) = x − 3

3. (f+g)(x) = f(x) + g(x)

(f+g)(x) = (2x + 3) + (x² + ½ x − 7)

(f+g)(x) = x² + 2½ x − 4

4. (f−g)(x) = f(x) − g(x)

(f−g)(x) = (2x + 3) − (x² + ½ x − 7)

(f−g)(x) = 2x + 3 − x² − ½ x + 7

(f−g)(x) = -x² + 1½ x + 10

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Given and which statement is correct? AB = FD AB < FD AB > FD AB ≤ FD

mojhsa [17]

Side AB is longer than side FD. Option (b) is correct.

Further explanation:

Given:

The options area as follows,

(a). $\overline {{\text{AB}}}$ and $\overline {{\text{FD}}}$ are the same length.

(b). $\overline {{\text{AB}}}$ is longer than $\overline {{\text{FD}}}.$

(c). $\overline {{\text{AB}}}$ is shorter than $\overline {{\text{FD}}}.$

(d). ${\text{AB}} \leqslant {\text{FD}}$

Explanation:

The sides opposite to equal angles are equal.

The side opposite to greater angle is greater than the other one.

The measure of $\angle {\text{DEC}}$ is ${65^ \circ }.$

The measure of $\angle {\text{BCA}}$ is ${72^ \circ }.$

$\angle {\text{BCA}}$ is greater than $\angle {\text{DEC}}$ . Therefore, the side opposite to greater angle is greater.

Side AB is longer than side FD. Option (b) is correct.

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

Learn more:

Learn more about inverse of the function brainly.com/question/1632445.
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Answer details:

Grade: High School

Subject: Mathematics

Chapter:Triangles

Keywords: relations, functions, all relation are functions, all functions are relations, no relations are functions, no functions are relation, one-to-one, onto, graph representation, paired, y-value, x-values, origin.

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3 years ago

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Nady [450]

Answer:

(1,3) is inside the triangle

Step-by-step explanation:

Orthocenter is the intersection of altitudes.

We'll calculate the slopes of the two sides and their altitudes ad find the intersection.

m = (3 - 5)/(4 - (-1)) = -2/5

<u>Perpendicular slope:</u>

-1/m = 5/2

<u>Perpendicular line passes through S(-1, -2):</u>

y - (-2) = 5/2(x - (-1)) ⇒ y = 5/2x + 1/2

m = (-2 - 3)/(-1 -4) = -5/-5 = 1

<u>Perpendicular slope:</u>

-1/m = -1/1 = -1

<u>Perpendicular line passes through Q(-1, 5):</u>

y - 5 = -(x - (-1)) ⇒ y = -x + 4

The intersection of the two lines is the orthocenter.

<u>Solve the system of equations to get the coordinates of the orthocenter:</u>

5/2x + 1/2 = x + 4
5x + 1 = -2x + 8
7x = 7
x = 1

<u>Find y-coordinate:</u>

y = -1 + 4 = 3

The orthocenter is (1, 3)

If we plot the points, we'll see it is inside the triangle

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