Use a factor tree to find the prime factorization of 164

Answers

Answer 1
Answer:   On the first hand, 164 is not a prime number. Prime numbers are numbers that can only be divided by 1 or itself which is also greater than 1 thus;
Prime divisor of 164= 2,2,41 or 2^2 x 41
Here is the factor tree of 164:
164
/     \
2     82

 /       \
2      41
 
Prime factorization of a number determines the set of prime integers multiplied together to make the original number. 
 


Answer 2
Answer:

Answer:

2 * 2 * 41

Step-by-step explanation:


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Given that the following statement is true"If a shape is a polygon, then it is a closed figure."
Which of the following statements must also be true?
A. If a shape is a closed figure, then it is a polygon.
B. If a shape is not a polygon, then it is not a closed figure
C. If a shape is not a closed figure, then it is not a polygon
D. If the shape is not a polygon, then it is a closed figure.

Answers

Answer:

C IS THE ANS COS ALL POLYGONS ARE CLOSED AND IF IT NOT CLOSED IT NOT A POLYGON

Help me with this!!!

Answers

Answer:

3.5 would be halfway of 3 and 4.

Answer:3.5

Step-by-step explanation:

3.5 is half of 3 and 4

the price of gravel is $24 for every 3/8 ton. Kate wants to know the price of 2 tons of gravel. at that rate, what is the price of 2 tons of gravel

Answers

Answer:

$128

Step-by-step explanation:

This problem is on rate.

firstly we have to find the rate at which 1 ton is sold

given that 3/8 ton is sold for $24

hence 1 ton will be sold for X

cross multiply

X = 24/3/8

inverse the denominator and multiply the result with the numerator we have

X= 24*8/3

X= $64

Now having found out that 1 ton cost $64

2 tons will cost =64*2

                         = $128

Therefore at this rate two tons will cost $128

Answer:128

Step-by-step explanation:

Water coming out from a fountain is modeled by the function: f(x)=−x2+6x+6
Where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change of f(x) from x = 2 to x = 5 represent?

a.The water travels an average distance of 4 feet from 2 seconds to 5 seconds.

b.The water travels an average distance of 1 foot from 2 seconds to 5 seconds.

c.The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds.

d. The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

Answers

Average rate of change from x = 2 to x = 5 is (f(5) - f(2))/(5 - 2) = ((-(5)^2+6(5)+6) - (-(2)^2+6(2)+6))/3 = ((-25+30+6) - (-4+12+6))/3 = (11 - 14)/3 = -3/3 = -1

Therefore, the water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.
Average speed = change in position / change in time.
m = (f( b ) - f ( a )) / ( b - a )
a = 2,  b = 5
f ( a ) = f ( 2 ) = - 4 + 12 + 6 = 14
f ( b ) = f ( 5 ) = - 25 + 30 + 6 = 11
m = (11-14) / (5-2) = -3/3 = -1
Answer: D ) The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds. 

The area of a rectangular bathroom floor is 53 square feet. The bathroom is 6 feet wide. What is the length?

Answers

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If cosx=1/12 and sinx>0 find tan2x

Answers

cosx=(1)/(12)\n\nsin^2x+cos^2x=1\n\nsin^2x+\left((1)/(12)\right)^2=1\n\nsin^2x+(1)/(144)=1\n\nsin^2x=1-(1)/(144)\n\nsin^2x=(144)/(144)-(1)/(144)\n\nsin^2x=(143)/(144)\n\nsinx=\sqrt(143)/(144)\n\nsinx=(√(143))/(12)


tan2x=(sin2x)/(cos2x)\n\nsin2x=2sinxcosx;\ cos2x=cos^2x-sin^2x\n\nsin2x=2\cdot(√(143))/(12)\cdot(1)/(12)=(2√(143))/(144)\n\ncos2x=\left((1)/(12)\right)^2-\left((√(143))/(12)\right)^2=(1)/(144)-(143)/(144)=-(142)/(144)\n\ntan2x=(2√(143))/(144):\left(-(142)/(144)\right)=-(2√(143))/(144)\cdot(144)/(142)=-(√(143))/(71)