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3 years ago

9

Find the midpoint of the line segment with the given endpoints. (14, -6), (13, 14)

2 answers:

Cloud [144]3 years ago

3 0

Answer:

Step-by-step explanation:

23

Flura [38]3 years ago

3 0

Answer:

( $\frac{27}{2}$ , 4 )

Step-by-step explanation:

Use the midpoint formula

midpoint = [ $\frac{1}{2}$ (x₁ + x₂), $\frac{1}{2}$ (y₁ + y₂ ) ]

with (x₁, y₁ ) = (14, - 6) and (x₂, y₂ ) = (13, 14), hence

[ $\frac{1}{2}$ (14 + 13), $\frac{1}{2}$ (- 6 + 14) ]

= ( $\frac{27}{2}$ , 4)

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Suppose that p is the probability that a randomly selected person is left handed. The value (1-p) is the probability that the pe

solmaris [256]

Answer:

a) 1/2

b) 250

Step-by-step explanation:

The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for $p$ such that $1000p(1-p)$ is maximized. Once we have that $p$ , we can easily find the answer to part b.

Finding the value that maximizes $1000p(1-p)$ is the same as finding the value that maximizes $p(1-p)$ , just on a smaller scale. So, we really want to maximize $p(1-p)$ . To do this, we will do a trick called completing the square.

$p(1-p)=p-p^2=-p^2+p=-(p^2-p)=-(p^2-p+1/4)-(-1/4)=-(p-1/2)^2+1/4$ .

Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of $p$ such that the inner part of the square term is equal to $0$ .

$p-1/2=0\\p=1/2$ .

So, the answer to part a is $\boxed{1/2}$ .

We can then plug $1/2$ into the equation for p to find the answer to part b.

$1000(1/2)(1-1/2)=1000(1/2)(1/2)=1000*1/4=250$ .

So, the answer to part b is $\boxed{250}$ .

And we're done!

3 0

2 years ago

Solvex2<br> - 4x=21 <br> using the zero product property.

Ierofanga [76]

Answer:

The answer is (x + 3) (x - 7) = 0

Step-by-step explanation:

x² - 4x = 21

x² - 4x - 21 = 0

x² - 7x + 3x - 21 = 0

x(x - 7) + 3(x - 7) = 0

(x + 3) (x - 7) = 0

Thus, The answer is (x + 3) (x - 7) = 0

<em><u>-TheUnknownScientist</u></em>

5 0

2 years ago

Solving an Absolute Value Equation

Andre45 [30]

Answer:

Solution set = {-12, 12}

Step-by-step explanation:

Start by dividing both sides of the given equation by negative one, to get rid of the negative signs on both sides:

$-\,|-x|=-\,12\\|-x|=12$

Now we consider the two possible cases:

1) The expression inside the absolute value symbol is a positive number, then :

$|-x|=-x\\$

and replacing it in the equation, this becomes:

$|-x|=12\\-x=12\\x=-12$

which is our first answer.

2) The expression inside the absolute value symbol is a negative number, then :

$|-x|=x\\$

and replacing it in the equation, this becomes:

$|-x|=12\\x=12$

which is our second possible answer.

Then the set of solutions is: {-12, 12}

8 0

2 years ago

Fill in the missing value for Y,<br> then click DONE.<br> y = 2x + 3

BARSIC [14]

Answer:

x = 2 so y = 7

x = 4 so y = 11

Step-by-step explanation:

y = 2x + 3

x = 0 so y = 2(0) + 3 | y = 3

x = 2 so y = 2(2) + 3 | y = 7

x = 4 so y = 2(4) + 3 | y = 11

x = 6 so y = 2(6) + 3 | y = 15

6 0

2 years ago

if one m&m is randomly selected from a dish containing 7 green, 4 red, 5 blue and 8 yellow m&ms, find the probability th

Bad White [126]

Answer:

1/6 = 16.67%

Step-by-step explanation:

There are a total of 24 m&ms. The probability of picking an m&m that has a quantity of 4 is 4/24 = 1/6 = 16.67%

6 0

3 years ago