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3 years ago

−1.5(4−n)+2.8−1.5(4−n)+2.8 simplified is

1 answer:

5 0

-1.5(4-n) + 2.8 - 1.5(4-n) + 2.8
Two ways of solving this, you can just expand and solve, or combine like terms then solve. I will combine like terms.

-1.5(4-n) + 2.8 - 1.5(4-n) + 2.8
(2*-1.5)(4-n) + (2*2.8)
-3(4-n) + 5.6
-3*4 + 3n + 5.6
-12 + 3n + 5.6
3n - 6.4

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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

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

6 0

3 years ago

Which description best compares the graphs given by the equations:

nexus9112 [7]

x - 5y = -5, -5x - 25y = 25

First, you'll need to get the x variable by itself.

x - 5y = -5
 +5 +5
 x = 0
So x is plotted on the 0.

For the second part of the first equation, you'll be looking for what the y variable represents.

x - 5y = -5
-x -x
 -5y = -5
 5 5
 y = 1
So y is plotted on the 1 on the vertical line above the 0.

For the first part of the second equation, you'll do the same thing as in the first equation.

-5x - 25y = 25
 +25 +25
 -5x = 50
 5 5
x = 10
So the x for this equation is plotted on 10 on the horizontal line.

For the second part of the second equation, you will do the same thing as in the first equation.

-5x - 25y = 25
+5 +5
 -25y = 30
 25 25
y = 1.2
So the y for the second half of the second question is plotted on 1.2 on the vertical line.

<h2>Answer: B) Perpendicular</h2>

Perpendicular means the lines may or may not be of equal length and they will not be perfectly in line with each other.

Parallel means the lines may or may not be of equal length but will be perfectly in line with each other.

Intersecting means the lines may or may not be of equal length but will touch each other.

6 0

2 years ago

The speed limit is 25 miles per hour, but it seems that many of the cars are going faster. The city places 2 counter strips 360

klio [65]

You figure out how long it would take a car traveling at 25 mph
to cover 360 ft. Any driver who does it in less time is speeding.

   (25 mi/hr) · (5,280 ft/mile) · (1 hr / 3,600 sec)

   = (25 · 5280 / 3600) ft/sec = (36 and 2/3) feet per second.

To cover 360 ft at 25 mph, it would take

360 ft / (36 and 2/3 ft/sec) = 9.82 seconds .

Anybody who covers the 360 feet in less than 9.82 seconds
is moving faster than 25 mph.
_________________________________

If you're interested, here's how to do it in the other direction:

Let's say a car covers the 360 feet in ' S ' seconds.
What's the speed of the car ?

   (360 ft / S sec) · (1 mile / 5280 feet) · (3600 sec/hour)

   = (360 · 3600) / (S · 5280) mile/hour

   = 245.5 / S miles per hour .

The teacher timed one car crossing both strips in 7.0 seconds.
How fast was that car traveling ?

   245.5 / 7.0 = 35.1 miles per hour

Another teacher timed another car that took 9.82 seconds to cross
both strips. How fast was this car traveling ?

245.5 / 9.82 = 25 miles per hour

7 0

3 years ago

What type of function does this equation represent? 2 Y = 4 (1)

Sphinxa [80]

Answer:

2y=4 is a linear function

Step-by-step explanation:

Since 2y=4 is the same as 2y¹=4, then a degree of 1 makes the function linear, aka. a straight line.

4 0

3 years ago

Can I get help please with all 20 questions I have 156points

motikmotik

Answer:

It’s the third ans

Step-by-step explanation:

7 0

3 years ago