Answer:
<h2>33</h2>
Step-by-step explanation:
Given the average low temperature by month in Nashville is represented by the function f(x)=-1.4x² + 19x +1.7, where x is the month, the average rate of change is expressed as d[f(x)]/dx = 2(1.4x) + 19
d[f(x)]/dx = 2.8x + 19
Since the number of months between March and August is 5 months and x is in months, hence we will substitute x = 5 into the resulting function to get the average rate of change from March to August as shown;
d[f(x)]/dx at x = 5
= 2.8(5)+ 19
= 14 + 19
= 33
<em>Hence the average rate of change from March to August is 33</em>
Answer:
(8,9)
Step-by-step explanation:
Given
Required
Determine the 4th point
The coordinate point of a horizontal or a vertical rectangle is given as:
(x1,y1), (x2,y2), (x3,y3), (x4,y4)
Where:
So, we have:
--- 
---- 
---- 
Using the above equations:
Hence, the coordinate of the 4th point is:
A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The missing value in the table below is 343. The correct option is A.
<h3>What is geometrical series?</h3>
A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.
The given table if closely observed forms a geometric progression, this is because the value of the dependent variable, y is increasing by a common ratio. The common ratio in the table is,
Common ratio = y₂/y₁ = 1/(1/7) = 7
Now, for any geometric progression, the value of the nth term is given as,
Tₙ = a₁ (r)⁽ⁿ⁻¹⁾
where a₁ is the first term of the geometric progression and r is the common ratio. Therefore, the nth term of the series is,
T = a₁ (r)⁽ⁿ⁻¹⁾
Tₙ = (1/7) (7)⁽ⁿ⁻¹⁾
y = (1/7)(7)⁽ˣ⁻¹⁾
Now, the value of the y when the value of x is 5 is,
y = (1/7)(7)⁽ˣ⁻¹⁾
y = (1/7)(7)⁽⁵⁻¹⁾
y = (1/7)(7)⁴
y = (1/7) × 2401
y = 343
Hence, the missing value in the table below is 343.
Learn more about Geometrical Series here:
brainly.com/question/4617980
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Answer:
y + 4 = 5(x - 3)
Step-by-step explanation:
In the Point-Slope Formula, <em>y</em><em> </em><em>-</em><em> </em><em>y</em><em>₁</em><em> </em><em>=</em><em> </em><em>m</em><em>(</em><em>x</em><em> </em><em>-</em><em> </em><em>x</em><em>₁</em><em>)</em><em>,</em><em> </em>all the negative symbols give the OPPOSITE terms of what they really are.
Answer:
70 m
Step-by-step explanation:
AB makes a 30-60-90 triangle with the wall.
AC makes a 45-45-90 triangle with the wall.
In a 30-60-90 triangle, the short leg (opposite of the 30° angle) is half the hypotenuse.
In a 45-45-90 triangle, the legs are the same length.
So the distance between the left wall and the laser is 60/2 = 30 m.
The distance between the right wall and the laser is 40 m.
The total distance is therefore 70 m.
