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miss Akunina [59]
3 years ago
14

Which number line represents the solution to 5x ≥ 30?

Mathematics
1 answer:
Westkost [7]3 years ago
5 0
I believe that the answer is B
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The graphs of the function f (given in blue) and g (given in red) are plotted above. Suppose that u(x)=f(x)g(x) and v(x)=f(x)/g(
Rus_ich [418]
U(x) = f(x).(gx)
v(x) = f(x) /  g(x)

Use chain rule to find u(x) and v(x).

u '(x) = f '(x) g(x) + f(x) g'(x)

v ' (x) = [f '(x) g(x) - f(x) g(x)] / [g(x)]^2

The functions given are piecewise.

You need to use the pieces that include the point x = 1.

You can calculate f '(x) and g '(x) at x =1, as the slopes of the lines that define each function.

And the slopes can be calculated graphycally as run / rise of each graph, around the given point.

f '(x) = slope of f (x); at x = 1, f '(1) = run / rise = 1/1 = 1

g '(x) = slope of g(x); at x = 1, g '(1) = run / rise = 1.5/ 1 = 1.5

You also need f (1) = 1 and g(1) = 2

Then:

u '(1) =  f '(1) g(1) + f(1) g'(1) = 1*2 + 1*1.5 = 2 + 1.5 = 3.5

v ' (x) = [f '(1) g(1) - f(1) g(1)] / [g(1)]^2 = [1*2 -  1*1.5] / (2)^2 = [2-1.5]/4 =

= 0.5/4 = 0.125

Answers:
u '(1) = 3.5
v '(1) = 0.125

 


 

3 0
3 years ago
#
fiasKO [112]

4. The point Z is the orthocenter of the triangle.

5. The length of GZ is of 9 units.

6. The length of OT is of 9.6 units.

<h3>What is the orthocenter of a triangle?</h3>

The orthocenter of a triangle is the point of intersection of the three altitude lines of the triangle.

Hence, from the triangle given in the end of the answer, point Z is the orthocenter of the triangle.

For the midpoints connected through the orthocenter, the orthocenter is the midpoint of these segments, hence:

  • The length of segment GZ is obtained as follows: GZ = 0.5 GU = 9 units. -> As z is the midpoint of the segment.
  • The length of segment OT is obtained as follows: OT = 2ZT = 2 x 4.8 = 9.6 units.

<h3>Missing Information</h3>

The complete problem is given by the image at the end of the answer.

More can be learned about the orthocenter of a triangle at brainly.com/question/1597286

#SPJ1

8 0
1 year ago
A graph, titled a Car, on a coordinate plane. Horizontal axis measures gasoline in gallons. Vertical axis measures distance in m
borishaifa [10]

its 1200 i think i work it out but i could have done it wrong


4 0
3 years ago
There are 59 people going on a field trip.
Maru [420]

You first multiply 6 and 8 to see how many people are put in the vans without rented a van. This would equal 48. You then subtract 48 from 59 to see how many people still need to be in a van. This would leave you with 11 people. Then you divide 8 from 11 to get 1 3/8. This means you need 2 vans to fit everyone.

3 0
3 years ago
Find the volume of a sphere with a surface area of 2916 squared pi
Svet_ta [14]

Answer:

it would be somewhere around 29161231

Step-by-step explanation:

it is m8

6 0
3 years ago
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