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3 years ago

6. Select all the expressions that are equivalent to 12x + 10. Check all that apply.

Mathematics

1 answer:

stich3 [128]3 years ago

5 0

Answer:

B) and E)

Step-by-step explanation:

E) 12x+10=2(6x+5)

but and

B) 6x+7+3+3(2x)=6x+10+6x=12x+10

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A coin is tossed 2 times. find the probability that all 2 tosses are tails

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2 years ago

The sum of two whole numbers is 84, and their positive difference is 18.What are the two numbers? Please help

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2 years ago

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What is the answer to 4+4-(5-1)

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3 years ago

The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th

vitfil [10]

Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by $P(t)=1.394(1.006)^t$

To find the derivative you need to:

$\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t$

To find the population growing at the start of 2014 we say t = 0

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year$

To find the population growing at the start of 2015 we say t = 1

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year$

To convert billion to million you multiple by 1000

$P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year$

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3 years ago

Two identical masses are moving down a slope one masses traveling twice as fast as the other mass how does the kinetic energy of

GaryK [48]

Answer:

One mass's kinetic energy is 4 times the other.

Step-by-step explanation:

The formula for kinetic energy is $KE=\frac{1}{2}mv^2$

Where

KE is the kinetic energy

m is the mass

v is the velocity

Now, let mass of the first be m (second is identical so mass of 2nd is m as well)
Let velocity of the first one be v. Since 2nd one is travelling twice as fast, its velocity will be 2v

KE of 1st mass is:

$\frac{1}{2}mv^2$

KE of 2nd mass is:

$\frac{1}{2}m(2v)^2\\=\frac{1}{2}m(4v^2)\\=\frac{1}{2}mv^2 * 4$

Hence, the kinetic energy of the 2nd mass is 4 times the first.

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3 years ago