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Black_prince [1.1K]
3 years ago
14

F(x)=square root of x^2+24x+144. g(x) = square root of x^3 -216

Mathematics
2 answers:
Triss [41]3 years ago
6 0

Answer:

Step-by-step explanation:

x^2 + 24x + 144 is a perfect square:  (x + 12)².  The square root of this is

±(x + 12).

g(x) = square root of x^3 -216 = √(x^3 - 216), or

√(x³ - 6³).   x³ - 6³ is not a perfect square, altho' it can be factored.

KiRa [710]3 years ago
5 0

Answer:

x^3 + x - 204

Step-by-step explanation:

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A rectangular region is removed from another rectangular region to create the shaded region shown below. Find the area of the sh
Alexus [3.1K]

Answer:

57m^2

Step-by-step explanation:

First we need to find the area of both shaded and not shaded regions. Since we are solving area for 2-D images we will use the equation Area=length(with)

Shaded Region: 11(9)=99

Unshaded Region: 8(6)=42

Now we subtract the shaded region with the unshaded region to get an area of 57 Meters. Therefore the area of the shaded region is 57m^2

5 0
3 years ago
How long does it take to travel 240 km at a constant speed of 12 km/h?
tankabanditka [31]

Answer:

It will take 12 hours

Step-by-step explanation:

Distance equals rate times time

d = rt

We know the distance and the rate

240 = 12 * t

Divide each side by 12

240/12 = 12t/12

20 = t

It will take 12 hours

5 0
3 years ago
A plane can fly 540 miles with the wind in one hour less than it can fly 480 miles against the wind. The average wind speed is 3
Bess [88]

Answer:

The speed of the plane in still air = 150 mph

Step-by-step explanation:

This is a relative velocity question

Let the velocity of the plane in still air be v

And let the time the plane can fly 480 miles against the wind be t

(Velocity of the plane relative to the wind) = (velocity of plane) - (velocity of wind)

Flying against the wind

(Velocity of plane relative to the wind) = (480/t)

(Velocity of the plane) = v

(Velocity of the wind) = 30 mph

(480/t) = v - 30

t = 480/(v-30) (eqn 1)

Flying with the wind

(Velocity of plane relative to the wind) = 540/(t-1)

(Velocity of the plane) = v

(Velocity of the wind) = -30 mph

540/(t - 1) = v + 30

t - 1 = 540/(v+30) (eqn 2)

Since t is equal in both cases, substitute the value of t in eqn 1 into eqn 2.

[480/(v-30)] - 1 = [540/(v+30)]

Multiply through by (v+30)(v-30)

480(v+30) - [(v+30)(v-30)] = 540(v-30)

480v + 14400 - (v² - 900) = 540v - 16200

480v + 14400 - v² + 900 = 540v - 16200

v² + 540v - 480v - 16200 - 14400 - 900 = 0

v² + 60v - 31500 = 0

Solving the quadratic equation,

v = 150 mph or v = -210 mph

We'll pick the positive answer because of the directions we have established.

Therefore, the speed of the plane in still air = 150 mph

Hope this Helps!!!

3 0
2 years ago
For the straight line defined by the points (4,57) and (6,91) , determine the slope ( m ) and y-intercept ( ???? ). Do not round
Ksivusya [100]

\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{57})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{91}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{91}-\stackrel{y1}{57}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{4}}}\implies \cfrac{34}{2}\implies 17 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{57}=\stackrel{m}{17}(x-\stackrel{x_1}{4})\implies y-57=17x-68

\bf y=17x-11\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad \begin{cases} \stackrel{slope}{17}\\\\ \stackrel{y-intercept}{(0,-11)} \end{cases}

4 0
2 years ago
Leap years are years in which February has 29 days instead of 28. The device of leap year was invented to keep the calendar in s
goldenfox [79]

Answer:

As you know, a year has around 365 + 1/4 days.

This means that in two years, we have:

365 + 356 + 1/4 + 1/4 = 730 + 1/2

and so on.

adding this up, when we have 4 years we have a full day extra, this is:

1460 + 1

When we divide 1461 by 4, we have 365 with a surpass of 1.

The rule used to keep the calendar in sync with this extra day is adding an extra day to each fourth year.

So each fourth year, we have an extra day in Februray (the Februray 29th), this is called a bisiest year.

The "math rule" used to know if a year is leap or not is:

if a year is not divisible by 4, then it is a common year

else if the year is not divisible by 100 then it is a leap year,

else if the year is not divisible by 400, then it is a common year

if not, the year is a leap year.

Where "year" represents the number of the year.

8 0
2 years ago
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