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3 years ago

10

12x(x+2)−5(2x−1) find the equation

2 answers:

ankoles [38]3 years ago

7 0

Perform the indicated multiplications...

12x*x+12x*2-5*2x-5*(-1)

12x^2+24x-10x+5 combine like terms

12x^2+14x+5

Talja [164]3 years ago

6 0

12x^2+24x-10x-5
12x^2+14x-5

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Solve for x if log 9 base x + log 3 base x^2 = 2.5

Y_Kistochka [10]

Not sure if the equation is

$\log_9x+\log_3(x^2)=\dfrac52$

or

$\log_x9+\log_{x^2}3=\dfrac52$

If it's the first one:

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot9^{\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot(3^2)^{\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{2\log_3(x^2)}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{\log_3(x^2)^2}$

$9^{\log_9x+\log_3(x^2)}=9^{\log_9x}\cdot3^{\log_3(x^4)}$

$9^{\log_9x+\log_3(x^2)}=x\cdot x^4$

$9^{\log_9x+\log_3(x^2)}=x^5$

On the other side of the equation, we'd get

$9^{5/2}=(3^2)^{5/2}=3^{2\cdot(5/2)}=3^5$

Then

$x^5=3^5\implies\boxed{x=3}$

If it's the second one instead, you can use the same strategy as above:

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot x^{\log_{x^2}3}$

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot\left((x^2)^{1/2}\right)^{\log_{x^2}3}$

(Note that this step assume $x>0$ )

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot(x^2)^{(1/2)\log_{x^2}3}$

$x^{\log_x9+\log_{x^2}3}=x^{\log_x9}\cdot(x^2)^{\log_{x^2}\sqrt3}$

$x^{\log_x9+\log_{x^2}3}=9\sqrt3$

Then we get

$9\sqrt3=x^{5/2}\implies x=(9\sqrt3)^{2/5}\implies\boxed{x=3}$

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3 years ago

Rachel types 85 words each minute. She has typed 1000000 words. If she types for 6 hours each day, for about how many days has s

denpristay [2]

If she types 85 words in a minute then
60 mins in 1 hour
85 times 60= words per hour=5100
5100 times 6=word in a day=30600
so we see how many 1,000,000 go into 30600 so
1,000,000/30600= (divide top and bottom by 100) 10,000/306=32.6 or aprox 33 days

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3 years ago

What is 10000000000000000000000000000000000000 plus 1000000000000000000000000000000000000000000-235

Alchen [17]

Answer:

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Step-by-step explanation:

i think this is right

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3 years ago

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Karolina [17]

ΔThe Answer to your question is D).<span>109.2%</span>Δ

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3 years ago

Solve the system by graphing.<br> y = x+2<br> 2x-y=-1

N76 [4]

Answer:

The intersection is at (1,3) and the answer is in the graph. (see image below)

Step-by-step explanation:

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2 years ago