Which equation has the same solution for x as x−12=40
?(1 point)
Responses
12−x=40
12 minus x is equal to 40
x4=13
x over 4 is equal to 13
x+12=−40
x plus 12 is equal to negative 40
x2=14
17 answers
x + 12 = -40
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The diagonal of a square equals √2 times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side?
To solve this problem, we can use the formula for the diagonal of a square, which states that the diagonal is equal to the side length of the square multiplied by the square root of 2.
Given:
Side length of the square park = 700 feet
Approximate value of square root of 2 = 1.4
We can plug these values into the formula to find the approximate length of the diagonal:
Diagonal = side length * square root of 2
Diagonal = 700 * 1.4
Diagonal = 980 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 980 feet.
Given:
Side length of the square park = 700 feet
Approximate value of square root of 2 = 1.4
We can plug these values into the formula to find the approximate length of the diagonal:
Diagonal = side length * square root of 2
Diagonal = 700 * 1.4
Diagonal = 980 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 980 feet.
Using a number line, what whole number and rational number to the nearest half is √40 between?
√40 is between ___and___.
.
√40 is between ___and___.
.
To determine the whole number and rational number to the nearest half that √40 is between, we can find the two consecutive whole numbers whose squares are closest to 40.
The square root of 40 is approximately 6.32.
The square of 6 is 36, and the square of 7 is 49. Since 40 is closer to 36 than to 49, we can conclude that √40 is between the whole numbers 6 and 7.
To find the rational number to the nearest half, we can divide the distance between 6 and 7 into two equal parts and determine where √40 falls within this subdivision.
The midpoint between 6 and 7 is 6.5.
Therefore, √40 is between 6 and 6.5.
The square root of 40 is approximately 6.32.
The square of 6 is 36, and the square of 7 is 49. Since 40 is closer to 36 than to 49, we can conclude that √40 is between the whole numbers 6 and 7.
To find the rational number to the nearest half, we can divide the distance between 6 and 7 into two equal parts and determine where √40 falls within this subdivision.
The midpoint between 6 and 7 is 6.5.
Therefore, √40 is between 6 and 6.5.
Using a number line, what whole number and rational number to the nearest half is √58 between?
A. between 8 and 8.5
B. between 7.5 and 8
C. between 8.5 and 9
D. between 7 and 7.5
A. between 8 and 8.5
B. between 7.5 and 8
C. between 8.5 and 9
D. between 7 and 7.5
To find the whole number and rational number to the nearest half that √58 is between, we need to determine the consecutive whole numbers whose squares are closest to 58.
The square root of 58 is approximately 7.62.
The square of 7 is 49, and the square of 8 is 64. Since 58 is closer to 64 than to 49, we can conclude that √58 is between the whole numbers 7 and 8 on the number line.
To find the rational number to the nearest half, we can divide the distance between 7 and 8 into two equal parts and determine where √58 falls within this subdivision.
The midpoint between 7 and 8 is 7.5.
Therefore, √58 is between 7 and 7.5 on the number line.
The answer is D. between 7 and 7.5.
The square root of 58 is approximately 7.62.
The square of 7 is 49, and the square of 8 is 64. Since 58 is closer to 64 than to 49, we can conclude that √58 is between the whole numbers 7 and 8 on the number line.
To find the rational number to the nearest half, we can divide the distance between 7 and 8 into two equal parts and determine where √58 falls within this subdivision.
The midpoint between 7 and 8 is 7.5.
Therefore, √58 is between 7 and 7.5 on the number line.
The answer is D. between 7 and 7.5.
Using rational approximations, what is an inequality statement comparing √81 and √88? Enter <, >, or =.
To compare √81 and √88 using rational approximations, we need to find their nearest rational approximations.
√81 is an exact value and equals 9.
To find the rational approximation of √88, we can check the square roots of nearby perfect squares.
√81 = 9, √100 = 10
Since 88 is between 81 and 100, we can estimate that √88 is between 9 and 10.
Therefore, the inequality statement is:
√81 < √88
√81 is an exact value and equals 9.
To find the rational approximation of √88, we can check the square roots of nearby perfect squares.
√81 = 9, √100 = 10
Since 88 is between 81 and 100, we can estimate that √88 is between 9 and 10.
Therefore, the inequality statement is:
√81 < √88
Write 6,739 in expanded form.
6,739 in expanded form is written as:
6,000 + 700 + 30 + 9.
6,000 + 700 + 30 + 9.
Express 8/11 as a repeating decimal
To express 8/11 as a repeating decimal, we can use long division.
When we divide 8 by 11, we get a quotient of 0 and a remainder of 8. We can bring down the next digit (0) and divide it by 11 again.
0.72
____________
11 | 8.00
-7.92
________
80
-77
______
30
-22
_______
80
-77
______
30
-22
_______
80
-77
______
30
As we can see, the division repeats with a remainder of 30 each time. Therefore, the decimal representation of 8/11 is 0.72, with the "72" part repeating indefinitely.
When we divide 8 by 11, we get a quotient of 0 and a remainder of 8. We can bring down the next digit (0) and divide it by 11 again.
0.72
____________
11 | 8.00
-7.92
________
80
-77
______
30
-22
_______
80
-77
______
30
-22
_______
80
-77
______
30
As we can see, the division repeats with a remainder of 30 each time. Therefore, the decimal representation of 8/11 is 0.72, with the "72" part repeating indefinitely.
Convert 0.72 to a rational number in simplest form
To convert 0.72 to a rational number in simplest form, we can express it as a fraction.
Let's assign a variable to the decimal, say x: x = 0.72
We know that the decimal part represents the numerator and the place value represents the denominator. Since 0.72 has two decimal places, the denominator will be 100 (because there are 2 digits after the decimal point).
Now, we can substitute the value of x into the fraction:
x = 0.72
x = 72/100
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 8:
72/8 ÷ 100/8
9/1 ÷ 12.5/1
9/1 * 1/12.5
9/12.5
Therefore, 0.72 as a rational number in simplest form is 9/12.5, which can also be expressed as 18/25 by multiplying both the numerator and denominator by 2:
0.72 = 9/12.5 = 18/25
Let's assign a variable to the decimal, say x: x = 0.72
We know that the decimal part represents the numerator and the place value represents the denominator. Since 0.72 has two decimal places, the denominator will be 100 (because there are 2 digits after the decimal point).
Now, we can substitute the value of x into the fraction:
x = 0.72
x = 72/100
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 8:
72/8 ÷ 100/8
9/1 ÷ 12.5/1
9/1 * 1/12.5
9/12.5
Therefore, 0.72 as a rational number in simplest form is 9/12.5, which can also be expressed as 18/25 by multiplying both the numerator and denominator by 2:
0.72 = 9/12.5 = 18/25
1 answer