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andriy [413]
3 years ago
10

Find the midpoint of the line segment whose endpoints are given (3/5 , -6/7),(2/5,5/7)

Mathematics
1 answer:
snow_lady [41]3 years ago
3 0

The formula of a midpoint between E and F:

M_{EF}\left(\dfrac{x_E+x_F}{2};\ \dfrac{y_E+y_F}{2}\right)

We have the points \left(\dfrac{3}{5},\ -\dfrac{6}{7}\right) and \left(\dfrac{2}{5},\ \dfrac{5}{7}\right). Substitute:

\dfrac{\frac{3}{5}+\frac{2}{5}}{2}=\dfrac{\frac{5}{5}}{2}=\dfrac{1}{2}\\\\\dfrac{-\frac{6}{7}+\frac{5}{7}}{2}=\dfrac{-\frac{1}{7}}{2}=-\dfrac{1}{7}\cdot\dfrac{1}{2}=-\dfrac{1}{14}

Answer: \boxed{\left(\dfrac{1}{2},\ -\dfrac{1}{14}\right)}

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4. Identify the zeros and the graph of the function y = x(x − 2)(x + 5).
Natalka [10]

The zeros of

y = x(x + 2)(x + 5)y=x(x+2)(x+5)

are

x=0,x=-2,x=-5x=0,x=−2,x=−5

EXPLANATION

The given function is

y = x(x + 2)(x + 5)y=x(x+2)(x+5)

To find the zeros of the above function, we just have to equate the function to zero and solve for x.

x(x + 2)(x + 5) = 0x(x+2)(x+5)=0

This implies that,

x = 0 \: \: or \: x + 2 = 0 \:or \: x + 5 = 0x=0orx+2=0orx+5=0

x = 0 \: \: or \: x = - 2\:or \: x = - 5x=0orx=−2orx=−5

To graph the above function, we need to consider the multiplicity.

We can see that the multiplicity of the roots are odd. This means that, the graph crosses the x-axis at each x-intercept.

We also need to consider the position of the graph on the following intervals,

x < - 5x<−5

When

x = - 10x=−10

y = - 10( - 8)( - 5) \: < \: 0y=−10(−8)(−5)<0

The graph is below the x-axis.

- 5 \: < \: x \: < \: - 2−5<x<−2

When

x = - 3x=−3

y = - 3(2)( - 1) \: > 0y=−3(2)(−1)>0

The graph is above the x-axis.

- 2 \: < \: x < \: 0−2<x<0

when

x = - 1x=−1

y = -1(1)(4) \: < \: 0y=−1(1)(4)<0

The graph is below the x-axis.

Finally the interval,

x \: > \: 0x>0

when

x = 1x=1

y = 1(3)(6) \: > \: 0y=1(3)(6)>0

The graph is above the x-axis.

We can now use the above information to sketch graph as shown in the diagram above

3 0
2 years ago
Find the percent of the number 60% of 20
In-s [12.5K]

Step-by-step explanation:

60% of 20 = 12

5 0
3 years ago
Read 2 more answers
What is the sum of?<br><br> A. S=1.5<br> B.S=2<br> C.S=4.5<br> D.=8
sweet [91]
8.  You can graph this or use the summation function on the TI computer. 
5 0
2 years ago
Read 2 more answers
The sum of 3 fifteens and 4 twos
iogann1982 [59]
The sum of 3 fifteens and 4 twos will be 45 +8 = 53

3 0
3 years ago
Whats 2/3 times negative 6/10
Fed [463]
The answer is
-  \frac{2}{5}
5 0
2 years ago
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