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sveticcg [70]
3 years ago
15

Y = x —6x+8 The equation above represents a parabola in the xy-plane. Which of the following equivalent forms of the equation di

splays the x-intercepts of the parabola as constants or coefficients?
Mathematics
1 answer:
forsale [732]3 years ago
3 0

Answer:

y=(x-4)(x-2)

Step-by-step explanation:

Consider the given equation

y=x^2-6x+8

Factor form of a parabola: It displays the x-intercepts.

y=a(x-p)(x-q)          .... (1)

where, a is a constant and, p and q are x-intercepts.

So, we need to find the factored form of the given equation.

Splinting the middle term we get

y=x^2-4x-2x+8

y=x(x-4)-2(x-4)

y=(x-4)(x-2)         .... (2)

On comparing (1) and (2) we get

p=4,q=2

It means x-intercepts of the given parabola are 4 and 2.

Therefore, equivalent forms of the equation is y=(x-4)(x-2).

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DJ Titus is making a playlist for a radio show; he is trying to decide what 10 songs to play and in what order they should be pl
Dominik [7]

Answer:

Different playlists possible = 18287141644800

Step-by-step explanation:

Given - DJ Titus is making a playlist for a radio show; he is trying to

            decide what 10 songs to play and in what order they should be

            played.

            Step 1 of 2 : If he has his choices narrowed down to 7 blues,

                                 7 disco, 5 pop, and 7 reggae songs.

To find - He wants to play no more than 4 reggae songs.

              How many different playlists are possible ?

Proof -

Given that he wants to play no more that 4 reggae songs.

So the possibility of choice of reggae song is 0, 1, 2, 3, 4

Now,

Case I -

If 0 reggae song is selected

⇒All 10 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₁₀ ₓ ⁷C₀ = 92,378

Case II -

If 1 reggae song is selected

⇒All 9 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₉ ₓ ⁷C₁ = 646,646

Case III -

If 2 reggae song is selected

⇒All 8 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₈ ₓ ⁷C₂ = 1,587,222

Case IV -

If 3 reggae song is selected

⇒All 7 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₇ ₓ ⁷C₃ = 1,763,580

Case V -

If 4 reggae song is selected

⇒All 6 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₆ ₓ ⁷C₄ = 949,620

So,

Total possible ways = 92,378+ 646,646+ 1,587,222+ 1,763,580+ 949,620

                               = 5,039,446

⇒Total possible ways = 5,039,446

Now,

Also the 10 songs selected can arranged themselves in 10! ways. ( because order of song played does not matter )

∴ we get

Different playlists possible = 10! × 5,039,446

                                          = 18287141644800

⇒Different playlists possible = 18287141644800

6 0
3 years ago
Solve s=2(lw+lh+wh) for w
Scilla [17]

                                                                   s = 2(lw + lh + wh)

Divide each side by  2 :                            s/2 = lw + lh + wh

Subtract 'lh' from each side:                s/2 - lh = lw + wh

Combine the 'w' terms:                        s/2 - lh = w(l + h)

Divide each side by (l + h):  (s/2 - lh) / (l + h) = w

7 0
3 years ago
There are two functions that can be used to describe the percent of people 25 years and older who have completed at least high s
Korvikt [17]

Answer:

g(15)=93.8\%

see the explanation

Step-by-step explanation:

Let

x ----> the number of years since 2008,

g(x) ----> the percent of people 25 years and older who have completed at least high school

we know that

g(x)=0.008x^2+0.42x+87.5

so

For x=15 years since 2008

substitute

g(15)=0.008(15)^2+0.42(15)+87.5=93.8\%

That means

In the year 2023 (2008+15) the percent of people 25 and older completing at least high school will be 93.8%

5 0
3 years ago
Solve the system of equations -2x+y=5 x-3y=-30
EastWind [94]
-2x+y=5
x-3y=-30 so you can multiply the bottom equation by 2 you'll get 2x-6y=-60

-2x+y=5
2x-6y=-60 And subtract the equations. You'll get -5y=-55 y=11. Plug it in to one of the original equations. -2x+(11)=5 
-2x=-6 so x=3 

y=11 and x=3 
5 0
3 years ago
Teri goes shopping for some new clothes and then out to lunch with a friend. She spends $32.94 on some shirts, $15.89 for a belt
Alexus [3.1K]

Answer:

Step-by-step explanation:

Its B

6 0
3 years ago
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