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3 years ago

The function f(x) = x^2 - 12x + 5 written in vertex form is f(x)=(x-6)^2 - 31. What are the coordinates of the vertex?

Mathematics

2 answers:

boyakko [2]3 years ago

4 0

The coordinates for the vertex is (6,-31)

soldier1979 [14.2K]3 years ago

3 0

Answer:

(6, - 31)

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

f(x) = (x - 6)² - 31 ← is in vertex form

with vertex = (6, - 31 )

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Your engineering firm is asked to specify the maximum load for the elevators in a new building: Each elevator has mass 490 kg wh

steposvetlana [31]

Answer:

a) m =589.734kg

b) n = 8 people (rounded down)

Step-by-step explanation:

The first step is to calculate the maximum load after safety considerations ( $T_{max}$

Since we know that the maximum tension the cables can withstand is 19500N (or 19.5kN). To calculate ( $T_{max}$ we multiply this value by $\frac{2}{3}$ (as per the given safety consideration.

Hence

$T_{max} = \frac{2}{3} (19500) \\ T_{max} = 13000N$

a) Now to find the maximum load in kgs, we use the following formula

$(m_{0} + m)(g + a) = T_{max}$

Where

$m_{0}$ = mass of elevator

$m$ = maximum load

$g$ = acceleration due to gravity

$a$ = maximum acceleration of elevator

Inputting the values and solving

$m_{0} + m)(g + a) = T_{max}\\ (490 + m)(9.8 + 2.24) = 13000\\ 12.04m = 7100.4\\ m = 589.734kg$

Hence the maximum load is m =589.734kg

b) To find the number of people (n) we divide the value of m by 70kg

n = 589.734 / 70

n = 8.42 or 8 people

7 0

3 years ago

Which is a better deal: 10 pounds of hamburger for $4.99 or 5 pounds of hamburger for $2.69? PLEASE HELP ME QUICKLY ILL LOVE YOU

JulijaS [17]

Answer:

10 pounds for $4.99

Step-by-step explanation:

If you multiply the 5 pounds for 2.69 by 2, you would get 10 pounds of hamburger for 5.38 which is more than 4.99

7 0

3 years ago

Read 2 more answers

A bag has 4 red marbles, 5 white marbles, and 6 blue marbles. three marbles are drawn from the bag (without replacement). what i

diamong [38]

It was 1/3 because all colour could be same

3 0

4 years ago

X/2 If x = 16, what is the solution? A 8 B 9 C 14 D 32

stich3 [128]

$\huge\textsf{Hey there!}$

$\rm{YOUR\ EQUATION: \dfrac{x}{2}}$

$\large\text{If x = 16, then substitute it where the x-value is in the given equation}$

$\rm{NEW\ EQUATION: \dfrac{16}{2}}$

$\rm{\dfrac{\bold{16}}{{2}}$

$\rm{= \underline{\bf 8}}$

$\large\text{Because, 8}\times\large\text{2 gives you 16}$

$\boxed{\boxed{\large\text{Answer: \huge \bf Option A. 8}}}\huge\checkmark$

$\large\textsf{Good luck on your assignment and enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

4 0

3 years ago

It takes Audrey 3/5 hour to paint 2/5 square yards of wood to be used for making shelves. How many square yards can she paint in

ivanzaharov [21]

This is how I would do it;

Convert to minutes 3/5 *60 = 36
Convert this to decimal 2/5 = 0.4

Then;

if it takes 36 mnts to paint 0.4yd^
in 60 mnts x yd^
___________________

60 x 0.4 / 36 = 0.66666667

convert back to fraction = 2/3 yd^ in 1hr

5 0

3 years ago