Choose the correct method to factor the following completely.<br> rx − sx + r − s

200% of 15 is what number

Stells [14]

Answer:

30

Step-by-step explanation:

100% of 15 is 15

200% is 15 + another 100% (15)

15+15 = 30

5 0

3 years ago

1. Find the angle for insurance and taxes

Naddika [18.5K]

Answer:

3+3+5+16+28+22=77

100-77=23% for insurance and taxes

23/100 x 360= 82.8 degrees

If clothing is 3%, do that % over 100 x $40,000 to get how much spent.

3/100 x 40000= $1200 on clothes

6 0

2 years ago

The height of a projectile launched upward at a speed of 32 feet/second from a height of 128 feet is given by the function h(t)

Phoenix [80]

Answer:

It takes 4 seconds for the projectile to hit the ground

Step-by-step explanation:

The height of the projectile after t seconds is given by the following equation:

$h(t) = -16t^{2} + 32t + 128$

How long will it take the projectile to hit the ground?

It happens when $h(t) = 0$

So

$h(t) = -16t^{2} + 32t + 128$

$-16t^{2} + 32t + 128 = 0$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$-16t^{2} + 32t + 128 = 0$

So $a = -16, b = 32, c = 128$

$\bigtriangleup = 32^{2} - 4*(-16)*(128) = 9216$

$t_{1} = \frac{-32 + \sqrt{9216}}{2*(-16)} = -2$

$t_{2} = \frac{-32 - \sqrt{9216}}{2*(-16)} = 4$

Time is a positive measure, so:

It takes 4 seconds for the projectile to hit the ground

7 0

4 years ago

A sample of bacteria is being eradicated by an experimental procedure. The population is following a pattern of exponential deca

77julia77 [94]

Answer:

There will be 50 bacteria remaining after 28 minutes.

Step-by-step explanation:

The exponential decay equation is

$N=N_0e^{-rt}$

N= Number of bacteria after t minutes.

$N_0$ = Initial number of bacteria when t=0.

r= Rate of decay per minute

t= time is in minute.

The sample begins with 500 bacteria and after 11 minutes there are 200 bacteria.

N=200

$N_0$ = 500

t=11 minutes

r=?

$N=N_0e^{-rt}$

$\therefore 200=500e^{-11r}$

$\Rightarrow e^{-11r}=\frac{200}{500}$

Taking ln both sides

$\Rightarrow ln| e^{-11r}|=ln|\frac{2}{5}|$

$\Rightarrow {-11r}=ln|\frac{2}{5}|$

$\Rightarrow r}=\frac{ln|\frac{2}{5}|}{-11}$

To find the time when there will be 50 bacteria remaining, we plug N=50, $N_0$ = 500 and $r}=\frac{ln|\frac{2}{5}|}{-11}$ in exponential decay equation.

$50=500e^{-\frac{ln|\frac25|}{-11}.t}$

$\Rightarrow \frac{50}{500}=e^{\frac{ln|\frac25|}{11}.t}$

Taking ln both sides

$\Rightarrow ln|\frac{50}{500}|=ln|e^{\frac{ln|\frac25|}{11}.t}|$

$\Rightarrow ln|\frac{1}{10}|={\frac{ln|\frac25|}{11}.t}$

$\Rightarrow t= \frac{ln|\frac{1}{10}|}{\frac{ln|\frac25|}{11}.}$

$\Rightarrow t= \frac{11\times ln|\frac{1}{10}|}{{ln|\frac25|}}$

$\Rightarrow t\approx 28$ minutes

There will be 50 bacteria remaining after 28 minutes.

3 0

4 years ago

Slope intercept form of 12x-y=4

Nata [24]

Hey there! :)

Please keep in mind that slope-intercept form is : y=mx+b ; where m=slope, b=y-intercept

Using this, we can isolate y in our original given equation.

12x - y = 4

Start off by subtracting 12x from both sides.

-y = -12x + 4

Divide both sides by -1.

-y ÷ -1 = (-12x + 4) ÷ -1

Simplify!

y = 12x - 4

Therefore, using the slope-intercept form, we can come to the conclusion that because 12 is located in the "m" slot and "m=slope" then 12 is our slope. In addition, -4 is our y-intercept because it is located on the y position.

Slope = 12

Y-intercept = -4

<em>Hope I helped! :) </em>

8 0

3 years ago

Choose the correct method to factor the following completely. rx − sx + r − s