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3 years ago

How many solutions does x2 - 10x = -25 have?

Mathematics

1 answer:

Nataly_w [17]3 years ago

3 0

To solve, first add 25 to both sides to get

${x}^{2} - 10x + 25 = 0$

Then factor to get

$(x - 5)(x - 5) = 0$

$x - 5 = 0$

$x = 5$

There is only one solution, x = 5.

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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

3 years ago

Solve for X rx+h=sx-k

Vlada [557]

Rx + h = sx - k
rx - sx = -k -h
x ( r -s ) = -k -h
x = -k -h / r -s Ans

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3 years ago

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If Alice would to leave her house around 6:30am and get back about 7:15am, but its a 21 mintue walk to and back. Will she make i

Naddik [55]

Before 7:15 is the answer.

6:30 + 21 minutes + 21 minutes puts the time back at 7:12.

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Can someone solve this? Number 25 only please.

V125BC [204]

0.06x0.06 = 0.0036

dont wory about the zeros just the actual numbers than add the zeros

6 0

3 years ago

Sherri saves nickels and dimes in a coin purse for her daughter. The total value of the coins in the purse is $0.95. The number

forsale [732]

I’m guessing that this is for systems of equations?
n - nickels
d - dimes

These are the equations you start off with.
n = 5d-2
0.95 = 0.10d+0.05n

Substitute the top equation for n into the variable n in the bottom equation.
0.95 = 0.10d+0.05(5d-2)

Solve for d.
0.95 = 0.10d+0.25d-0.10
1.05 = 0.35d
3 = d

Substitute d into the top equation and solve for n.
n = 5(3)-2
n = 15-3
n = 12

There are 3 dimes and 12 nickels in the coin purse! Hope this helped <3

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