Mathematics, 29.11.2020 19:00 cadenhuggins2

Hi. I need help with these questions.
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Answer 20 and 21

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Answer from: emmaja121003

20. The vertex is (2/3, 14/3) | p = 3, q = -2/3 and r = 14/321. 20x² + 2x - 3 = 0

Step-by-step explanation:

20.

Giveny = 3x² - 4x + 6To findThe least value of the y and the corresponding value of xConstants p, q and r such that 3x² - 4x + 6 = p(x + q)² + rSolution

The given is the parabola with positive a coefficient, so it opens up and the minimum point its vertex.

The vertex has x = -b/2a and corresponding y- coordinate is found below:

x = - (- 4)/2*3 = 2/3, and y = 3(2/3)² - 4(2/3) + 6 = 4/3 - 8/3 + 6 = 14/3So the vertex is (2/3, 14/3)

The vertex form of the line has the equation:

y = a(x - h)² + k, where (h, k) is the vertex

Plugging in the values:

y = 3(x - 2/3)² + 14/3

Comparing with p(x + q)² + r, to find out that:

p = 3, q = -2/3 and r = 14/3

21.

(i) α and β are the roots of: ax² + bx + c = 0

Show that:

α + β = -b/a and αβ = c/aSolution

Knowing the roots, put the equation as:

(x - α)(x - β) = 0x² - αx - βx + αβ = 0x² - (α+β)x + αβ = 0

Comparing this with the standard form:

ax² + bx + c = 0

Divide by a to make the constants of x² same:

x² + b/ax + c/a = 0

Now comparing the constants:

- (α+β) = b/a ⇒ α+β = - b/aαβ = c/a

(ii)

Givenα and β are the roots of: 3x² - x - 5 = 0To Find The equation with roots 1/2α and 1/2βSolution

The sum and the product of the roots:

α + β = -b/a = 1/3αβ = c/a = -5/3

The equation is:

(x - 1/2α)(x - 1/2β) = 0x² - (1/2α + 1/2β)x + 1/(2α)(2β) = 0x² - (α + β)/(2αβ)x + 1/4αβ = 0x² - (1/3)/(2(-5/3))x + 1/(4(-5/3)) = 0x² + 1/10x - 3/20 = 020x² + 2x - 3 = 0

Answer from: Quest

after 1 year: 221 deer

step-by-step explanation:

30% of 170 is 51. 170+51=221

Answer from: Quest

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.

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