What is the positive solution to the equation 0=-x^2+2x+1?

A quadrilateral has vertices at A(-5,5), B(1,8), C(4,2), and D(-2,-2). Use slope to determine if the quadrilateral is a rectangl

AysviL [449]

Answer:

The quadrilateral is not a rectangle

Step-by-step explanation:

we know that

If a quadrilateral ABCD is a rectangle

then

Opposite sides are congruent and parallel and adjacent sides are perpendicular

Remember that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

A(-5,5), B(1,8), C(4,2), and D(-2,-2)

Plot the figure to better understand the problem

see the attached figure

Find the slope of the four sides and then compare

step 1

Find slope AB

A(-5,5), B(1,8)

substitute in the formula

$m=\frac{8-5}{1+5}$

$m=\frac{3}{6}$

$m_A_B=\frac{1}{2}$

step 2

Find slope BC

B(1,8), C(4,2)

substitute in the formula

$m=\frac{2-8}{4-1}$

$m=\frac{-6}{3}$

$m_B_C=-2$

step 3

Find slope CD

C(4,2), and D(-2,-2)

substitute in the formula

$m=\frac{-2-2}{-2-4}$

$m=\frac{-4}{-6}$

$m_C_D=\frac{2}{3}$

step 4

Find slope AD

A(-5,5), D(-2,-2)

substitute in the formula

$m=\frac{-2-5}{-2+5}$

$m=\frac{-7}{3}$

$m_A_D=-\frac{7}{3}$

step 5

Verify if the opposites are parallel

Remember that

If two lines are parallel, then their slopes are the same

The opposite sides are

AB and CD

BC and AD

we have

$m_A_B=\frac{1}{2}$

$m_C_D=\frac{2}{3}$

so

$m_A_B \neq m_C_D$

It is not necessary to continue verifying, because two of the opposite sides are not parallel

therefore

The quadrilateral is not a rectangle

4 0

3 years ago

Fill in the blank to make the expression a perfect square.. . u^2-16u+?

hram777 [196]

U² - 16 u + 64 = ( u - 8 )²
because: A² - 2 A B + B² = ( A - B )²
Answer: 64

8 0

3 years ago

11. find the value of x in the kite below. E (6x + 6) F Р G

cluponka [151]

14.

Step-by-step explanation:

6x+6=90 (being a straight line)

6x=90-6

6x=84

x= 84/6

x=14.

8 0

3 years ago

a product code consists of picking a two-digit number (including 00) and 3 not necessarily distinct letters. How many codes are

Brrunno [24]

Answer:

The codes are:

N,_,_,_

Where each _ represents a possible letter, out of 26.

And N is a number of two digits.

So in total we can think that we have 5 empty slots.

_,_,_,_,_

In the first slot we can put any digit between 0 and 9, so here we have 10 options.

In the second slot we can put any digit between 0 and 9, so here we have 10 options.

In the third slot we can put any letter, so here we have 26 options (and exactly the same for the fourth and fifth slots)

The total number of different combinations is equal to the product of the number of options for each slot.

C = 10*10*26*26*26 = 1,757,600

Now, if we want to have at least one nine, we can fix it in the first slot.

Then we have:

in the first slot we have only one option (the 9)

In the second slot we can put any digit between 0 and 9, so here we have 10 options.

In the third slot we can put any letter, so here we have 26 options (and exactly the same for the fourth and fifth slots)

The number of combinations is:

C = 1*10*26*26*26 = 175,760

But we also should consider the case where we fix the 9 in the second slot, so the actual number of combinations is twice the number above.

C = 2*175,760 = 351,520

The probability that the code does not contain the number 9.

Now in the first slot we have only 9 options, all the whole numbers between 0 and 8.

The same for the second slot, 9 options.

For the third, fourth and fifth slot is the same as before.

The total number of combinations is:

C = 9*9*26*26*26 = 1,423,656

4 0

3 years ago

The question is in the screenshot

zmey [24]

Correct probability : 3/7

To find the correct probability, Noura needs to count ALL of the times she tossed the coin. To find that we just add 15 + 20, which equals 35.

Then to calculate the probability she will get heads is out the number of heads landed over the amount of times the coin was flipped.

15/35

We then simplify this fraction by dividing the top and bottom both by 5.

This leaves us with the answer of 3/7.

3 0

3 years ago