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3 years ago

What’s the axis of symmetry and the vertex of x^2-4x-32

1 answer:

6 0

<span>x^2 -4x -32
</span>a =1b= -4c= -32
The x,y points of the vertex are usually referred to as Vertex = (h, k)where h = -b / (2 * a)
h = --4 / (2 * 1)h = 4 / 2h = 2
k = ah^2 +bh + ck =1*4 -4*2 -32k = 4 -8 -32k = -36
vertex = (2, -36)axis of symmetry = x position = 2
Source:http://www.1728.org/quadr3.htm

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A deck of 52 cards is shuffled. The first five cards of the deck are red. What is the probability that the last card in the deck

saveliy_v [14]

Answer:

The answer is " $\frac{1}{47}$ ".

Step-by-step explanation:

Although the five first players are red, the very first five cards are not spaded as the spad is a black card.

Its chance of the final card mostly on deck being the ace of spades is therefore determined as:

$= \frac{1}{\text{Number of remaining cards with the initial 5 cards}} \\\\= \frac{1}{47}$

Thus, $\frac{1}{47}$ here is the necessary chance.

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3 years ago

Lydia graphed ADEF at the coordinates D (-2,-1), E (-2, 2), and F (0,0). She thinks ADEF is a right triangle. Is Lydia's asserti

Setler79 [48]

The true statement is (c) No; the slopes of segment EF and segment DF are not opposite reciprocals.

<h3>Right triangles </h3>

Right triangles have a pair of perpendicular lines

Coordinates

The coordinates are given as:

D = (-2,-1)
E = (-2,2)
F = (0,0)

<h3>Slopes</h3>

Start by calculating the slopes of lines DF and EF using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m_{DF} = \frac{0 + 1}{0 +2}$

$m_{DF} = \frac{1}{2}$

Also, we have:

$m_{EF} = \frac{0 -2 }{0+2}$

$m_{EF} = \frac{-2 }{2}$

$m_{EF} = -1$

For the triangle to be a right triangle, then the calculated slopes must be opposite reciprocals.

i.e.

$m_1 = -\frac{1}{m_2}$

By comparison, the slopes of both lines are not opposite reciprocals.

Hence, the true statement is (c)

Read more about right triangles at:

brainly.com/question/17972372

7 0

2 years ago

Read 2 more answers

Part B

Elanso [62]

Answer:

22 1/2

Step-by-step explanation:

2 1/4 x 10 = c

2 1/4 x 10 = 22.5

22.5 = 22 1/2

3 0

3 years ago

It take Sophia 1/5 weeks to read one book and Sophia reads for 1/6 weeks how many books where she read

ladessa [460]

Sophia has not even completed 1 book. She has managed to complete 83% of the book.

<u>Explanation:</u>

Given:

Time taken to read one book = 1/5

Total weeks for which sophia read = 1/6

Number of books, z = ?

Total weeks = z X time taken to read one book

$\frac{1}{6} = z X \frac{1}{5} \\\\z = \frac{5}{6} \\\\z = 0.83$

Therefore, sophia has not even completed 1 book. She has managed to complete 83% of the book.

3 0

3 years ago

Amanda and jamie are standing 25 feet apart and spot a bird in the sky between them the angle of elevation from Amanda is 25 fee

finlep [7]

Answer:

25.2294 feet

Step-by-step explanation:

We can solve this question drawing a triangle using the values given and then using the law of sines. (See image attached to know how to draw the triangle and use the values).

First we need to find the third angle of the triangle, that is, the angle in the vertix where the bird is:

y + 55 + 63 = 180

y = 62°

The relation between the angles and the distances are:

25 / sin(y) = x / sin(63)

25 / 0.8829 = x / 0.8910

x = 25 * 0.8910 / 0.8829 = 25.2294 feet

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3 years ago