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3 years ago

Which equation is y = 2x2 – 8x + 9 rewritten in vertex form?

Mathematics

1 answer:

-BARSIC- [3]3 years ago

8 0

Answer:

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Given

y = 2x² - 8x + 9

The coefficient of the x² term must be 1, so factor out 2 from 2x² - 8x

y = 2(x² - 4x) + 9

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² - 4x

y = 2(x² + (- 2)x + 4 - 4) + 9

= 2(x - 2)² - 8 + 9

= 2(x - 2)² + 1 → C

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A rectangular lawn, 100 feet long by 50 feet wide, is to have two sidewalks installed that will cut the lawn in half both ways,

Damm [24]

Answer:

3.41 feet

Step-by-step explanation:

Area = Length × Breath

Area of the rectangular lawn = 100 × 50

= 5000 feet²

The sidewalk must occupy an area no more than 10% of the total lawn area.

So, the area of the sidewalk would be not more than = 10% × 5000

= 0.10 × 5000

= 500 feet²

Let the width of the sidewalk = x feet

area of the side walk = (L×W of the long way) + ((L-x)×W of the short way)

(100 × x) + ((50 - x) × x) < 500

100x + (50-x)(x) < 500

-x² + 150x < 500

-x² + 150x = 500

-x² + 150x - 500 = 0

By using quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

$x=\frac{(-150)\pm\sqrt{(150)^2-4(-1)(-500)} }{2(-1)}$

$x=\frac{-150\pm \sqrt{20500} }{-2}$

$x=75-5\sqrt{205}$ or $x=75+5\sqrt{205}$

x = 3.41089 ≈ 3.41 feet or x = 146.58

Therefore, width of the sidewalk would be 3.41 feet.

5 0

3 years ago

How to Become a Millionaire Upon graduating from col- lege, Donna has no initial capital. However, during each year she makes de

lesantik [10]

Answer:

amount is 1000 × $e^{0.08t}$

$40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years

rate 14.97 % when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500

Step-by-step explanation:

principal = $1000

rate = 8 % = 0.08

to find out

the future value, S(t)

principal when Donna's account will be 1 million dollars when she retires in 40 year

at what rate Donna's account will have a balance of 1 million dollars in 40 years

solution

we know compounded continuously formula i.e.

amount = principal × $e^{rt}$ ..................1

put the value principal and rate in equation 1 to find amount any time

amount = principal × $e^{rt}$

amount = 1000 × $e^{0.08t}$

in 2nd part we have time 40 year and amount 1 million so put rate amount and time in equation 1 to find principal

rt = 0.08 × 40 = 3.2

amount = principal × $e^{rt}$

1000000 = principal × $e^{3.2}$

principal = 1000000 / $e^{3.2}$

principal = 1000000 / 24.5325302

principal = 40762.20397

so $40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years

in 3rd part we have amount 1 million and principal $2500 and time 40 year put all these in equation 1 to find rate

amount = principal × $e^{rt}$

1000000 = 2500 × $e^{40r}$

take ln both side

ln $e^{40r}$ = ln (1000000 / 2500 )

40 r = ln 400

r = ln (400) / 40

r = 0.149787

so rate 14.97 % when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500

5 0

3 years ago

Ethan Purchased A new cell phone for $75.00. The cost of the phone is included in his first months bill. His cell phone plan cha

Kaylis [27]

Answer:

he had $90

he bought a phone for $75

90-75=15

he has $15 now

15÷0.06=1500÷6=250 minutes

7 0

3 years ago

What is the least common multiple of 8 and 12?

MArishka [77]

8:8,16,24,32,40,48,56,64,
12:12,24,36,48
Least common multiple is 24 because it's less then the other common multiples such as 48

4 0

3 years ago

3 days to 1 week. Type as a ratio in the form of a fraction

Vadim26 [7]

3 days : 1 week

1 week = 7 days

therefore 3 days : 1 week = 3 days : 7 days = 3 : 7

8 0

3 years ago