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Mathematics

1 answer:

Pavel [41]4 years ago

6 0

A cycle in the graph below is HDGH.

A cycle is where a vertices, or corner, can be traced back to itself. HDGH starts with H and traces back to H on the same line.

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Find the slope of the line through the points (4, 4) and (-1, 5).

Phoenix [80]

We write pattern linear function
f(x) = ax + b

Both points must be in one straight line so they can be used to lay the system of equations .
Points A=(4,4), B = (-1,5)
x y x y

 $\left \{ {{f(x)=ax + b (Point A)} \atop {f(x) = ax +b (PointB)}} \right. \\ \\ \left \{ {{4 =a*4 + b} \atop {5=a*(-1)+b}} \right. \\ \\ \left \{ {{b= 4 -4a} \atop {5 = -a + (4 - 4a)}} \right. \\ \\ \left \{ {{b = 4 - 4a} \atop {5 - 4 = - 5a }} \right. \\ \\ \left \{ {{b = 4 - 4a} \atop {a = - \frac{1}{5} }} \right. \\ \\ \left \{ {{ b = 4 - 4*(- \frac{1}{5} )= 4 + \frac{4}{5} = 4,8} \atop {a = - \frac{1}{5} }} \right.$

We insert the calculated a and b in the equation f(x) = ax + b

 $y = - \frac{1}{5} x + 4,8$

Since a> 0, the function is decreasing

4 0

3 years ago

If you drive 208 miles and use 8 gallons of gas what is your rate of gas consumption

Natasha_Volkova [10]

26 miles per gallon is your answer you divide 208 miles by 8 finding out how many miles per gallon you drive. To check your answer you can multiply 26 times 8 and you get 208 miles.

3 0

3 years ago

Hey can you please help me posted picture of question

ruslelena [56]

Answer:
Two

Explanation:
The solution of a system of equations is defined as the values which satisfies both equations.

Graphically, the solutions are represented by the points of intersection between the two equtaions.

In the given graph, we have a circle and a line, we can note that these two intersect in two points.

This means that the system has two solutions

Hope this helps :)

5 0

3 years ago

Read 2 more answers

If f(2) = 13 and f '(x) ≥ 2 for 2 ≤ x ≤ 7, how small can f(7) possibly be?

timofeeve [1]

Answer:

Step-by-step explanation:

We are given that

f(2)=13

$f'(x)\geq 2$