Divide 5 by 4. Is your answer a rational number? explain

Answers

Answer 1

Answer: Yes because a rational number is a number that can be written as a fraction. 5 divided by 4= 1.25, which is equal to 1 and one fourth. So yes, it is a rational number

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Find all solutions for a triangle with B=36 degrees, b=19, and c=36. Round to the nearest tenth.
At the beginning of the fall, the water level of a lake is 7 feet below normal level. After a drought, the lake's water level dropped 2 1/3 feet. Where is the lake's current water level in relation to its normal water level?
Please help on this question ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Please explain your answer, too!

Find the angular velocity in radians per second of a wheel turning at 25 revolutions per minute.

Answers

(25 rev/minute) x (2 pi radian/rev) x ( minute / 60 sec) = 2.618 rad/sec (rounded)

1 revolution= 2π radians= 6,28 radian
1 minute= 60 s
25 rev=50π=157 radian

$(25)/(1)* (6,28)/(60)=2,62 (rad)/(s)$

Which describes the transformation from the original to the image, and tells wether the two fugures are similar or congruent

Answers

Answer:

translation similar

Step-by-step explanation:

How would you solve (4k+5)(k+1)=0?

Answers

$(4k+5)(k+1)=0\iff4k+5=0\ or\ k+1=0\n\n4k=-5\ or\ k=-1\n\n\boxed{k=-(5)/(4)\ or\ k=-1}$

(4k + 5) (k + 1) = 0

Before you rush off and start trying to do complicated things with that equation,
put your pencil down, fold your hands in your lap, and sit and look at it for a while.
Keep looking at it until a little voice yells out "Hey ! That's a true statement if
either (4k + 5) is zero or (k+1) is zero. THEN go to work on it.

(4k + 5 = 0)
4k = -5
k = -5/4

(k + 1 = 0)
k = -1

And there are the two solutions to that equation.

there are 13 animals in a barn. some are ducks and some are pigs. there are 40 legs in all. how many of each animal are there?

Answers

Let X be chickens
Let Y be pigs,
then x+y=13
the animals have 2x+4y legs,
so 2x+4y=40
The system of the equations
[X+y=13
[2x+4y=40
Divide the second equation by 2
[x+y=13
[x+2y=20
subtract the first equation from the second one
y=20-13
y-7 pigs
substitute y=7 into the first equation
x+7=13
x=13-7
x=6 chickens

Please help!!Write an exponential function (in terms of x) to model the following situation.
A population of 110,000 grows 5% per year for 16 years.
How much will the popluation be after 16 years?

Answers

Answer:

The population will be 240,116

Step-by-step explanation:

Exponential growth can be represented by the expression:

$P(t) = P_i\,(1+r)^t$

where:

$P(t)$ is the population at time (t)

$P_i$ is the initial value of the population

"r" is the annual rate of growth (written in decimal form)

and "t" is the time in years.

Therefore in this situation, P(16) is what we want to find [the population after 16 years]

the initial population $P_i$ is 110,000

the rate of growth is 0.05 [decimal form of 5%]

and t is 16 years.

Replacing all these in the given functional form gives:

$P(t) = P_i\,(1+r)^t\nP(16)=110000\,(1+0.05)^16\nP(16)=240116$

What are the solutions to the equation x2 + 6 = 87? A. –9 and 9 B. –10 and 10 C. –6 and 6 D. The equation has no solutions.

Answers

$x^2 + 6 = 87 \ \ | -87\n \nx^2 + 6 -87 = 0 \n \n x^2 -81 = 0 \n \n(x+9)(x-9)=0 \n \n x+9 =0 \ \ \vee \ \ x-9 =0 \n \n x= -9 \ \ \vee \ \ x= 9 \n \n\nAnswer : \ A.) \ \ -9 \ \ and \ \ 9$

$a^2 - b^ 2 =(a-b)(a+b)$

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