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4 years ago

PLEASE HELP!!! CONVERT TO STANDARD FORM (y=ax^2+bx+c f(x)=2(x-3)^2+7

Mathematics

1 answer:

dolphi86 [110]4 years ago

5 0

Answer:

y = 2x^2 - 12x + 25

Step-by-step explanation:

<u>Given function</u>

f(x)=2(x-3)^2+7

<u>Converting to standard form</u>

y = 2(x - 3)^2 + 7
y = 2(x^2 - 6x + 9) + 7
y = 2x^2 - 12x + 18 + 7
y = 2x^2 - 12x + 25

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serg [7]

Answer:

Step-by-step explanation:

The second card is influenced by the first only in that you have not replaced the first card. That makes a difference.

1/52 is the probability for the first card.

1/51 is the probability for the second card.

They are independent events. Drawing the 7 of diamonds does not make the chances of drawing the Ace of Spades other than the 7 came first and the probability of getting the Ace is slightly larger.

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3 years ago

Given: circle k(O), m LM = 164°, m WK = 68°, m∠MLK = 65°. Find: m∠LMW

Musya8 [376]

Answer:

The measure of angle LMW is $m\angle LMW=67\°$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc MW

we know that

The inscribed angle measures half that of the arc comprising

$m\angle MLK=\frac{1}{2}[arc\ MW+arc\ WK]$

substitute the given values

$65\°=\frac{1}{2}[arc\ MW+68\°]$

$130\°=[arc\ MW+68\°]$

$arc\ MW=130\°-68\°=62\°$

step 2

Find the measure of arc LK

we know that

$arc\ LM+arc\ MW+arc\ WK+arc\ LK=360\°$ -----> by complete circle

substitute the given values

$164\°+62\°+68\°+arc\ LK=360\°$

$294\°+arc\ LK=360\°$

$arc\ LK=360\°-294\°=66\°$

step 3

Find the measure of angle LMW

we know that

The inscribed angle measures half that of the arc comprising

$m\angle LMW=\frac{1}{2}[arc\ LK+arc\ WK]$

substitute the given values

$m\angle LMW=\frac{1}{2}[66\°+68\°]=67\°$

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3 years ago

Peyton bought a pair of shoes online for $46. She used a coupon code to get a 40% discount. The website also applied a 20% proce

photoshop1234 [79]

Answer:

28%

Step-by-step explanation:

start with $46 = 100% of starting price

coupon = 40% off starting price

40% off of 100% = 100% - 40% = 60% of starting price = price after coupon

60% = 0.6

60% of starting price = price after coupon = 0.6 * $46 = $27.6

then, a 20% processing fee is applied to the price after the discount

new price = $27.6 = 100% of new price

fee = 20% added to new price

20% added to new price = 100% + 20% = 120% of new price

120% = 1.2

final price = price after fee = 120% of new price = 1.2 * $27.6 = $33.12

change in percentange = (original price - new price) / original price * 100

= ($46 - $33.12) / $46 * 100 = 28%

3 0

2 years ago

You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 475 cm3. The material fo

zepelin [54]

Answer:

The dimensions of the box are:

x = 8,93 cm and h = 5,95 cm

C(min) = 850,69 cents

Step-by-step explanation:

The volume of the box is:

V = x²*h where x is the side of the square base and h the height

then h = V/ x² ⇒ h = 475 / x²

The total cost of box C is:

C = C₁ + 4*C₂ Where C₁ and C₂ are the costs of the base and one lateral side respectevily

Then cost C = 8*x² + 4* 6*h*x

The cost C as a function of x is

C(x) = 8*x² + (24* 475 /x² )*x

C(x) = 8*x² + 11400/x

Tacking derivatives on both sides of the equation

C´(x) = 16*x - 11400/x²

C´(x) = 0 ⇒ 16*x - 11400/x² = 0

16*x³ = 11400 ⇒ x³ = 11400/16

x³ = 712,5

x = 8,93 cm

and h = 475 / (8,93)² ⇒ h = 5,95 cm

C(min) = 8*79,77 + 4* ( 8,93)*5,95

C(min) = 638,16 + 212,53

C(min) = 850,69 cents

To check if value x = 8,93 would make C(x) minimum we go to the second derivatives

C´´(x) = 16 + 22800/x³ > 0

Then we have a minimum of C at x = 8,93

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago