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3 years ago

Which of the following is an irrational number A.3\14 B.3.8 C.√38 D.√64

1 answer:

6 0

It is
$\sqrt{38}$
because an irrational number cannot be written as a simple fraction ( because there is not a finite number of numbers when written as a decimal ).

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Select the correct answer from each drop-down menu. A parabola is given by the equation y = x2 − 2x − 3. The directrix of the pa

choli [55]

Answer:

Part 1) The directrix of the parabola is y=-4.25

Part 2) The focus of the parabola is F(1,-3.75)

Step-by-step explanation:

we have

$y=x^{2}-2x-3$

This is a vertical parabola open upward

we know that

If a parabola has a vertical axis, the standard form of the equation of the parabola is

$(x - h)^{2}=4p(y - k)$

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h, k + p).

The directrix is the line y = k - p.

The axis is the line x = h.

step 1

Convert the equation of the parabola in standard form

$y=x^{2}-2x-3$

$y+3=x^{2}-2x$

$y+3+1=x^{2}-2x+1$

$y+4=x^{2}-2x+1$

$y+4=(x-1)^{2}$

$(x-1)^{2}=(y+4)$ ----> equation in standard form

The vertex is the point (1,-4)

4p=1 ------> p=1/4

step 2

Find the directrix of the parabola

The directrix is the line y = k - p

we have

k=-4

p=1/4

substitute the values

y = k - p

y=-4-(1/4)=-17/4

y=-4.25

step 3

Find the focus of the parabola

we know that

The focus is at (h, k + p).

we have

h=1

k=-4

p=1/4

substitute

F(1,-4+1/4)

F(1,-3.75)

4 0

3 years ago

Type the correct answer in each box. If necessary, use / for the fraction bar. A bag contains 5 blue marbles, 2 black marbles, a

serg [7]

Answer:

P (not drawing a black marble) = 4/5

P (red marble) = 3/10

Step-by-step explanation:

The total number of marbles is

5 blue marbles +2 black marbles+ 3 red marbles = 10 marbles

P (not drawing a black marble) =

The marbles that are not black/ total marbles

(blue + red)/ total

(5+3)/10

8/10

4/5

P (red marble) = red marble/ total

= 3/10

7 0

3 years ago

Does anyone know how to solve |4x+3|-9<5

elixir [45]

Answer in fraction form: -17/4 < x < 11/4

Answer in decimal form: -4.25 < x < 2.75

=======================================================

Work Shown:

|4x+3| - 9 < 5

|4x+3| < 5+9 .... adding 9 to both sides

|4x+3| < 14

-14 < 4x+3 < 14 .... see note at the bottom

-14-3 < 4x < 14-3 .... subtracting 3 from all sides

-17 < 4x < 11

-17/4 < x < 11/4 .... divide all sides by 4

-4.25 < x < 2.75

This says that x is between -4.25 and 2.75, but x is not equal to either endpoint.

Note: I used the rule that |x| < k becomes -k < x < k where k is a positive real number.

6 0

3 years ago

Graph this rational equation. Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asy

irakobra [83]

Step-by-step explanation:

We have given,

A rational function : f(x) = $\frac{x-2}{x-4}$

W need to find :

Point of discontinuity : - At x = 4, f(x) tends to reach infinity, So we get discontinuity point at x =4.

For no values of x, we get indetermined form (i.e $\frac{0}{0}$ ), Hence there is no holes

Vertical Asymptotes:

Plug y=f(x) = ∞ in f(x) to get vertical asymptote {We can us writing ∞ = $\frac{1}{0}$ }

i.e ∞ = $\frac{x-2}{x-4}$

or $\frac{1}{0}=\frac{x-2}{x-4}$

or x-4 =0

or x=4, Hence at x = 4, f(x) has a vertical asymptote

X -intercept :

Plug f(x)=0 , to get x intercept.

i.e 0 = $\frac{x-2}{x-4}$

or x - 2 =0

or x = 2

Hence at x=2, f(x) has an x intercept

Horizontal asymptote:

Plug x = ∞ in f(x) to get horizontal asymptote.

i.e f(x) = $\frac{x-2}{x-4}$ = $\frac{x(1-\frac{2}{x} )}{x(1-\frac{4}{x} )}$

or f(x) = $\frac{(1-\frac{2}{∞} )}{(1-\frac{4}{∞} )}$

or f(x) = 1 = y

hence at y =f(x) = 1, we get horizontal asymptote

4 0

3 years ago

Samantha is training for a race. The distances of her training runs form an arithmetic sequence. She runs 1 mi the first day and

Nezavi [6.7K]

B Because how far does she runs on day 19

5 0

3 years ago