which numbers are rational:
square root of 23
-3/13
square root of 4
0.232323....
pi
12
93
13 answers
-3/13, square root of 4, 0.232323...., 12, 93 are rational numbers.
write this as a fraction. you dont need to simplify.
0.66...
0.66...
To express 0.66... as a fraction, let's call it x:
x = 0.666...
Next, we multiply both sides of the equation by 10 to move the decimal point two places to the right:
10x = 6.666...
Now, we subtract the original equation from the new equation to eliminate the repeating decimal:
10x - x = 6.666... - 0.666...
9x = 6
Finally, we divide both sides of the equation by 9 to solve for x:
x = 6/9
Therefore, 0.66... can be written as the fraction 6/9.
x = 0.666...
Next, we multiply both sides of the equation by 10 to move the decimal point two places to the right:
10x = 6.666...
Now, we subtract the original equation from the new equation to eliminate the repeating decimal:
10x - x = 6.666... - 0.666...
9x = 6
Finally, we divide both sides of the equation by 9 to solve for x:
x = 6/9
Therefore, 0.66... can be written as the fraction 6/9.
7^-7 x 7^? = 7^12
?=
?=
To solve for the unknown exponent, we can use the rule of exponents that states when multiplying exponential expressions with the same base, we can add their exponents.
In this case, we have 7^-7 x 7^? = 7^12.
Using the rule of exponents, we can simplify the left side of the equation to:
7^(-7 + ?) = 7^12.
To make the bases equal, we need the exponents to be equal as well.
Therefore, -7 + ? = 12.
Adding 7 to both sides of the equation:
? = 12 + 7.
Therefore, ? = 19.
In this case, we have 7^-7 x 7^? = 7^12.
Using the rule of exponents, we can simplify the left side of the equation to:
7^(-7 + ?) = 7^12.
To make the bases equal, we need the exponents to be equal as well.
Therefore, -7 + ? = 12.
Adding 7 to both sides of the equation:
? = 12 + 7.
Therefore, ? = 19.
2^-2 x 2^9
To simplify this expression, we can use the rule of exponents that states when multiplying exponential expressions with the same base, we can add their exponents.
In this case, we have 2^-2 x 2^9.
Using the rule of exponents, we can simplify the expression as:
2^(-2 + 9).
Adding -2 and 9, we get:
2^7.
Therefore, 2^-2 x 2^9 simplifies to 2^7.
In this case, we have 2^-2 x 2^9.
Using the rule of exponents, we can simplify the expression as:
2^(-2 + 9).
Adding -2 and 9, we get:
2^7.
Therefore, 2^-2 x 2^9 simplifies to 2^7.
Diana went on a trip over spring break. She traveled 484.5 miles and used 17 gallons of gas. At what unit rate did Diana use gasoline?
A.
30.28 miles per gallon
B.
28.5 miles per gallon
C.
467.5 miles per gallon
D.
45.5 miles per gallon
A.
30.28 miles per gallon
B.
28.5 miles per gallon
C.
467.5 miles per gallon
D.
45.5 miles per gallon
To find the unit rate at which Diana used gasoline, we divide the total distance traveled by the total amount of gas used.
The unit rate can be calculated as:
484.5 miles / 17 gallons = 28.5 miles per gallon
Therefore, the correct answer is B. 28.5 miles per gallon.
The unit rate can be calculated as:
484.5 miles / 17 gallons = 28.5 miles per gallon
Therefore, the correct answer is B. 28.5 miles per gallon.
Richard can read 1/4 of a book in 3/5 of an hour. At this rate, how much can Richard read in one hour?
A.
5/12 of a book
B.
2 2/5 books
C.
3/20 of a book
D.
4/9 of a book
A.
5/12 of a book
B.
2 2/5 books
C.
3/20 of a book
D.
4/9 of a book
To find out how much Richard can read in one hour, we need to determine the reciprocal of 3/5 (which represents the rate at which he reads a fraction of a book per hour).
The reciprocal of 3/5 is 5/3.
Now, we multiply the reciprocal by 1/4 (which is the fraction of the book Richard can read in that amount of time):
(5/3) * (1/4) = 5/12
Therefore, Richard can read 5/12 of a book in one hour.
Hence, the correct answer is A. 5/12 of a book.
The reciprocal of 3/5 is 5/3.
Now, we multiply the reciprocal by 1/4 (which is the fraction of the book Richard can read in that amount of time):
(5/3) * (1/4) = 5/12
Therefore, Richard can read 5/12 of a book in one hour.
Hence, the correct answer is A. 5/12 of a book.
Francis ran 2 4/5 miles in 7/12 of an hour. How many miles can Francis run in one hour?
A.
5/24
B.
3 19/35
C.
4 4/5
D.
24
A.
5/24
B.
3 19/35
C.
4 4/5
D.
24
To find out how many miles Francis can run in one hour, we need to determine the reciprocal of 7/12 (which represents the rate at which he runs a fraction of a mile per hour).
The reciprocal of 7/12 is 12/7.
Now, we multiply the reciprocal by 2 4/5 (which is the distance Francis runs in that amount of time):
(12/7) * (2 4/5) = (12/7) * (14/5) = 168/35 = 4 4/5
Therefore, Francis can run 4 4/5 miles in one hour.
Hence, the correct answer is C. 4 4/5 miles.
The reciprocal of 7/12 is 12/7.
Now, we multiply the reciprocal by 2 4/5 (which is the distance Francis runs in that amount of time):
(12/7) * (2 4/5) = (12/7) * (14/5) = 168/35 = 4 4/5
Therefore, Francis can run 4 4/5 miles in one hour.
Hence, the correct answer is C. 4 4/5 miles.
1 answer