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This is easy, Manuel

If   a,b  are integer zeroes....we just need to expand this ( x -a)  ( x - b)

So....since  7, -4 are zeroes....we have

(x  - 7 )  (  x  -   -4)   =

( x - 7 )  ( x + 4)   =

x^2 - 7x + 4x  - 28  =

x^2 - 3x  - 28

Pretty easy, huh  ??

Area of a sector   =   pi * radius^2  *  (central angle measure of the sector / 360) ....so we have..

72 pi  = pi (r^2)  (180/ 360)  divide out pi

72  = (1/2) r^2       multiply both sides by 2

144  = r^2       take the positive root

12 in  =   r

Thanks, adore....and good luck to you  !!!!

a) Current population =P(c)

Future population =P(f)

P(f) =P(c) x e^(rt), where r= Rate of growth, t =Number of years.

70,000,000 = 35,000,000 x e(0.082t)  Divide both sides by 35,000,000

2 = e^0.082t     Take the natural log of both sides

t = ln(2) / 0.082

t =~ 8.45 - years for the population of the country to double.

b) e^.082 =1.0854558..... - 1 x 100 =~8.55% - the equivalent yearly rate of growth.

(Since there is no right angle, there is no hypotenuse )
 

A = 40°, B = 60°, c = 20

Let  a  be the length of the side opposite angle A.

Let  b  be the length of the side opposite angle B.

Let  C  be the measure of the angle opposite side c .

The sum of the angle measures in a triangle is  180°  , so...

A + B + C  =  180°

C  =  180° - A - B

C  =  180° - 40° - 60°

C  =  80°

Using the Law of Sines...

\(\begin{array}\ \frac{b}{\sin B}&=&\frac{c}{\sin C} \\ \frac{b}{\sin 60°}&=&\frac{20}{\sin 80°} \\ \quad b&=&\frac{20\sin60°}{\sin 80°} \\ \quad {\color{purple}b}&{\color{purple}\approx}&{\color{purple}17.6} \\~\\ \frac{a}{\sin A}&=&\frac{c}{\sin C} \\ \frac{a}{\sin 40°}&=&\frac{20}{\sin 80°} \\ \quad a&=&\frac{20\sin40°}{\sin 80°} \\ \quad {\color{purple}a}&{\color{purple}\approx}&{\color{purple}13.1 } \end{array}\)

(Also...this is not the ambiguous case...the ambiguous case is SSA)

Is it the bear that has no teeth or me ?

How big is it, and does it still have nasty sharp claws ?

i dont know

thanks

It is a linear equation.

At the points where the curve crosses the x axis we have:

(x-1)(x-5)=0

x²-6x+5=0

multiply by -1

-x²+6x-5=0

So b = 6

.

Just ' follow your nose '.

You know angles A and B, so work out angle C.

You can now work out angles CAH and CBE.

That allows you to work out angles HAB and HBA.

Knowing those allows you to work out AHB.

Job done.

Appreciate it.

117 ^°

Alas as this is not a right triangle the basic trig ratios won't give you the correct answer. Here you need to employ the sin rule ie a/sinA = b/sinB = c/sinC

Picture time! :D:D (I filled in B since \(180-(40+60) = 80\))

To solve for other sides, we can do the sine of the angles and add "x" whenever we need to solve for a variable.

\(sin(x)=\frac{opposite}{hypotenuse}\)

We have 20 units for c, so let's find a, since that's the opposite of A.

\(sin(A)=\frac{a}{c}\)

\(sin(40)=\frac{x}{20}\)

\(x = 20sin(40)\)

\(x = 14.90226320958​\)

\(x = 15\) \(units\)

Now that I solved for c, try and find b with the same method.

The distance from a point (x, y) to the origin is given by \(\displaystyle D = \sqrt{x^{2}+y^{2}}.\)

So, if

 \(\displaystyle y=x^{2}-5,\text{ then}\\D=\sqrt{x^{2}+(x^{2}-5)^{2}}=\sqrt{x^{4}-9x^{2}+25}.\)

Now complete the square, (add and subtract (9/2)^2),

\(\displaystyle D = \sqrt{x^{4}-9x^{2}+(81/4)+(100/4)-(81/4)}\\=\sqrt{\{x^{2}-(9/2)\}^{2}+(19/4)}.\)

This will take its smallest value 

\(\displaystyle \sqrt{19/4}=\sqrt{19}/2, \text{ when }x^{2}=9/2.\)

Tiggsy

Since the graph is a line, it's easy to solve for two points on a graph, draw a line, and figure out what the equation is. You've already got one point, so now you need a second one. I'm going to use t=1 just so I can get points that are right next to each other.

\((2t+3, 3-3t)\)

\((2+3, 3-3)\)

\((5, 0)\)

Now we need to put these two points on a graph.

Connect the lines and extend out until you hit the edges of the graph.

After this, you need to figure out \(y = ax+b\), where a is \(\frac{rise}{run}\) and b is where the point crosses the y-axis.

For x, if we zoom in, we can see that it goes down 3 and to the right 2 every time it tries to get to a new point.

If we follow \(\frac{rise}{run}\) , a should be \(\frac{-3}{2}\) . 

B is the y-intercent (or where the line crosses the y-axis). That number is 7.5, so b is 7.5.

The final answer for the graph should be \(y=-\frac{3}{2}t+7.5\).

Hi F

i can only help with 2 and 3. I can't see the diagrams of the others.

using the chord intercept theorem in both you get OP = sqrt48 and RX = 2

regards

Zero.

It will take an even number of steps to get back to the starting point so after 15 steps you can't be at the starting point.

Translation: stick your d i c k in the whatcha macallit and see what happens.

This is Mr. BB. Gingerale trolls this f u c k face because he is so stu.pid and dum.b he is actually contagious.

A long time ago, Mr. BB stuck his d ic k ina whatcha macallit that was actually a dirtdevil vacuum. These have the fan blade in the front. Now Mr. BB has to sit when he takes a p i ss

Wish you the best of luck in whatever you decide to do next.