Answer:
20 cm
Step-by-step explanation:
5x + 32 + 6x + 4 = 80
11x + 36 = 80
11x = 44
x = 4
sides of triangle:
5(4) = 20 cm
32 cm
6(4) + 2 = 26 cm
Answer:
- 0.5 + 2.985i
- 1 + 2.828i
- 1.5 + 2.598i
- 2 + 2.236i
Explanation:
Complex numbers have the general form a + bi, where a is the real part and b is the imaginary part.
Since, the numbers are neither purely imaginary nor purely real a ≠ 0 and b ≠ 0.
The absolute value of a complex number is its distance to the origin (0,0), so you use Pythagorean theorem to calculate the absolute value. Calling it |C|, that is:
Then, the work consists in finding pairs (a,b) for which:
You can do it by setting any arbitrary value less than 3 to a or b and solving for the other:

I will use b =0.5, b = 1, b = 1.5, b = 2

Then, four distinct complex numbers that have an absolute value of 3 are:
- 0.5 + 2.985i
- 1 + 2.828i
- 1.5 + 2.598i
- 2 + 2.236i
Answer: second option.
Step-by-step explanation:
You must apply 
Then, given the right triangle and the angle D, the opposite side and the hypotenuse of the triangle are the following:

Therefore, when you substitute values, you have:

Reduce the fraction, then you obtain:

Answer:
Answer:
y = -5(x - 7)^3 - 1
Step-by-step explanation:
You kind of just plug in the numbers.
a vertical stretch by a factor of 5: y = 5x^3
a reflection across the x-axis: y = -5x^3
a vertical translation 1 unit down: -5x^3 - 1
a horizontal translation 7 units right: -5(x - 7)^3 -1
Step-by-step explanation:
An inequality which compares the changes in elevation of this hot air balloon while in flight is given by L - 83 2/5 ≤ L ≤ L + 83.7.
<h3>What is an elevation?</h3>
An elevation is also referred to as an altitude and it can be defined as the vertical distance (height) above a natural satellite or the surface of planet Earth such as land or sea level.
This ultimately implies that, an elevation (altitude) simply refers to the vertical height (elevation) of an object or physical body above a particular location or planetary reference plane such as land or sea level on planet Earth.
<h3>What is an inequality?</h3>
An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
- Less than (<).
- Greater than (>).
- Less than or equal to (≤).
- Greater than or equal to (≥).
For this exercise, let the variable L represent the initial height of this balloon. Also, since the hot air balloon decreased its elevation by 83 2/5 and increases its elevation by 83.7 meters, we have the following:
- The lower limit is equal to: L - 83 2/5.
- The upper limit is equal to: L + 83.7.
In this context, an inequality which models the changes in elevation of this hot air balloon is L - 83 2/5 ≤ L ≤ L + 83.7.
Read more on inequality here: brainly.com/question/6666926
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