Based on the graphs of f (x) and g(x), what must the domain of (f ⋅ g)(x)be?

A building makes a 90° angle with the ground. A ladder leans against the building, making a 110° exterior angle with the ground.

liberstina [14]

<u>Answer:</u>

A building makes a $90^{\circ}$ angle with the ground .The two interior angles are $70^{\circ}$ and $20^{\circ}$

<u>Solution: </u>

Given, a ladder which is against the building wall makes an exterior angle of $110^{\circ}$

And building makes a $90^{\circ}$ angle with the ground.

So, altogether it makes a right angle triangle with ladder as hypotenuse and ground as base leg and building as another leg.

Now, we know that, sum of exterior angles and interior angles equals to $180^{\circ}$

Here, in the case of ground and ladder, exterior angle is $110^{\circ}$ and interior angle is unknown.

Exterior angle + interior angle = 180

110 + interior angle = 180

Interior angle = 180 – 110

Interior angle = $70^{\circ}$

We have found one of the two interior angles of right angle triangle.

We know that, sum of angles in a triangle is 180 degree

Known Interior angle + unknown interior angle + right angle = 180

70 + unknown interior angle + 90 = 180

Unknown interior angle + 160 = 180

Unknown interior angle = 180 - 160

Unknown interior angle = $20^{\circ}$

Hence the two interior angles are $70^{\circ}$ and $20^{\circ}$

7 0

4 years ago

Please answer these last four questions.

Crank

Answer:

numbwer 8 is 44.04

Step-by-step explanation:

plz put brainliest

4 0

3 years ago

Identify the effect on the graph of replacing f(x) by f(x - h)

Tresset [83]

Given:

Replace f(x) by f(x - h).

To find:

The effect on the graph of replacing f(x) by f(x - h).

Solution:

Horizontal shift is defined as:

If the graph f(x) shifts h units left, then f(x+h).

If the graph f(x) shifts h units right, then f(x-h).

Where, h is a constant that represents the horizontal shift.

In the given problem f(x) is replaced by f(x - h) and we need to find the effect on the graph.

Here, we have x-h in place of x.

Therefore, the graph of f(x) shifts h units right to get the graph of f(x-h).

4 0

3 years ago

The graph of the step function g(x) = –⌊x⌋ + 3 is shown. On a coordinate plane, a step graph has horizontal segments that are ea

AleksAgata [21]

Answer:

{x| –2 ≤ x < 5}

Step-by-step explanation:

There is a box function plotted on the graph.

The function is g(x) = –⌊x⌋ + 3.

Now, we know that a box function represents a step graph having horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle.

It is given that the left-most segment of the given graph goes from (-2,5) to (-1,5) and the rightmost segment goes from (4,-1) to (5,-1).

So, for the left most segment the domain is -2 ≤ x < -1

And for the right most segment the domain is 4 ≤ x < 5

Therefore, the total domain of g(x) will be {x| –2 ≤ x < 5} (Answer)

8 0

3 years ago

Read 2 more answers

A triangle has a perimeter of 10a + 3b + 12 and has sides of length 3a + 8 and 5a + b what is the length of the third side ?

RideAnS [48]

Answer:

2a +2b +4

Step-by-step explanation:

The perimeter is the sum of the lengths of the three sides. If x represents the length of the third side, then ...

(3a +8) +(5a +b) +x = (10a +3b +12)

Subtracting from the equation everything on the left side that is not x, we get ...

x = (10a +3b +12) -(3a +8) -(5a +b)

= a(10 -3 -5) +b(3 -1) +(12 -8)

= 2a +2b +4

The length of the third side is 2a +2b +4.

5 0

3 years ago