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2 years ago

A segment has the following coordinates A(6, 7), B(4, -3). Find the coordinates of the midpoint of segment AB

Mathematics

2 answers:

raketka [301]2 years ago

4 0

Answer:

i think that would be (5,2)

Tpy6a [65]2 years ago

3 0

Answer:

(5,2)

Step-by-step explanation:

A(6, 7), B(4, -3)

the mid point has the coordinates

x coordinate is ( 6+4)/2 = 10/2=5

y coordinate is (7 + -3)/2 = 4/2=2

The midpoint of the line segment AB is the point with the coordinates (5,2)

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The graphs of y = f(x) and y = g(x) are shown on the coordinate plane below. If g(x) = k* f(x), what is the value of k?

mixer [17]

Answer:

Value of k = -2

Step-by-step explanation:

Using slope intercept form:

The equation of line is given by:

y = mx+b

where, m is the slope and b is the y-intercept.

As per the statement:

The graphs of y = f(x) and y = g(x) are shown on the coordinate plane.

First find f(x):

Consider two points on y=f(x) are:

(0,-3) and (2, 1)

Formula for slope:

$\text{Slope(m)} = \frac{y_2-y_1}{x_2-x_1}$

then;

$m = \frac{1-(-3)}{2-0}=\frac{4}{2} = 2$

then;

$y = 2x+b$

Substitute the point (0, -3) to solve for b:

$-3= 2(0)+b$

⇒ $-3=b$

∴ $y=f(x)=2x-3$

Similarly for g(x):

Consider two points on y = g(x) are:

(0, 6) and (2, -2)

then;

$\text{Slope(m)} = \frac{y_2-y_1}{x_2-x_1}$

then;

$m = \frac{-2-6}{2-0}=\frac{-8}{2} =-4$

then;

$y = -4x+b$

Substitute the points (0, 6) to solve for b:

$6= -4(0)+b$

⇒ $6=b$

then we get an equation:

y = g(x) = -4x+6

It is given that: If g(x) = k* f(x)

Solve for k:

$-4x+6 = k(2x-3)$

⇒ $-4x+6 = 2kx-3k$

on comparing both sides we have;

$-2kx = -4x$

⇒ $-2k = -4$

Divide both sides by -2 we have;

$k = 2$

-3k = 6

⇒k = -2

Therefore, the value of k is, -2

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3 years ago

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Help plz

LUCKY_DIMON [66]

Answer:

h = 0.64 ft

Step-by-step explanation:

$s = \frac{14 + 12 + 6}{2} = \frac{32}{2} = 16 \: ft \\ \\ A = \sqrt{(s - 14)(s - 12)(s - 6)} \\ \\ A = \sqrt{(16 - 14)(16 - 12)(16 - 6)} \\ \\ A = \sqrt{(2)(4)(10)} \\ \\ A = \sqrt{80} \\ \\ A = 8.94427191\\ \\ A \approx 8.94 \: {ft}^{2}$

A = 14h

8.94427191 = 14h

h = 8.94/14

h = 0.638571429

h = 0.64 ft

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424 pens over the month

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Suppose two events A and B are mutually exclusive, with P(A) ≠ 0 and P(B) ≠ 0. By working through the following steps, you'll se

DanielleElmas [232]

Answer with Step-by-step explanation:

We are given that two events A and B are mutually exclusive.

$A\cap B=\phi$

$P(A\cap B)=0$

$P(A)\neq 0$

$P(B)\neq 0$

a.For mutually exclusive events,

$P(A/B)=\frac{P(A\cap B)}{P(B)}=\frac{0}{P(A)}=0$

Therefore, event A can not occurred if event B has occurred because two events can not occur together.

Answer:No, by definition mutually exclusive events cannot occur together.

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Then , $P(A\cap B)=P(A)\cdot P(B)$

$P(A/B)=\frac{P(A)\cdot P(B)}{P(B)}=P(A)$

If two events are mutually exclusive then

$P(A\cap B)=0$

Then , $P(A/B)=0$

Therefore, $P(A/B)\neq P(A)$

Hence, we can concluded that events A and B are not independent if they are mutually exclusive.

Answer:Yes, $P(A/B)\neq P(A)$

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