To rationalize the expression -1/2, you can multiply the numerator and denominator by -2 to eliminate the negative sign and simplify the fraction:
(-1/2) * (-2/-2) = 2/(-2) = -1.
Therefore, -1/2 rationalizes to -1.
-1/2
6 answers
Find the distance between point
�
(
3
,
8
)
A(3, 8) and
�
(
16
,
11
)
B(16, 11). Round your answer to the nearest tenth.
�
(
3
,
8
)
A(3, 8) and
�
(
16
,
11
)
B(16, 11). Round your answer to the nearest tenth.
To find the distance between two points (x1, y1) and (x2, y2), you can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point A are (3, 8) and the coordinates of point B are (16, 11). Substituting these values into the formula:
Distance = √((16 - 3)^2 + (11 - 8)^2)
= √(13^2 + 3^2)
= √(169 + 9)
= √178
≈ 13.34
Therefore, the distance between points A(3, 8) and B(16, 11) is approximately 13.34 units.
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point A are (3, 8) and the coordinates of point B are (16, 11). Substituting these values into the formula:
Distance = √((16 - 3)^2 + (11 - 8)^2)
= √(13^2 + 3^2)
= √(169 + 9)
= √178
≈ 13.34
Therefore, the distance between points A(3, 8) and B(16, 11) is approximately 13.34 units.
(2×10
9
) ÷
(
8
×
1
0
3
)
(8×10
3
)
9
) ÷
(
8
×
1
0
3
)
(8×10
3
)
To simplify the expression (2×10^9) ÷ (8×10^3), we can simplify the numerator and denominator separately.
The numerator is 2 times 10 raised to the power of 9, which can be written as 2×10^9.
The denominator is 8 times 10 raised to the power of 3, which can be written as 8×10^3.
When we divide both of these numbers, we subtract the exponents of 10 in the numerator and denominator:
2×10^9 ÷ (8×10^3) = 2 ÷ 8 × 10^(9 - 3).
The division of 2 by 8 is 0.25:
0.25 × 10^(9 - 3) = 0.25 × 10^6.
10 raised to the power of 6 is 1,000,000:
0.25 × 1,000,000 = 250,000.
Therefore, the simplified expression is 250,000.
The numerator is 2 times 10 raised to the power of 9, which can be written as 2×10^9.
The denominator is 8 times 10 raised to the power of 3, which can be written as 8×10^3.
When we divide both of these numbers, we subtract the exponents of 10 in the numerator and denominator:
2×10^9 ÷ (8×10^3) = 2 ÷ 8 × 10^(9 - 3).
The division of 2 by 8 is 0.25:
0.25 × 10^(9 - 3) = 0.25 × 10^6.
10 raised to the power of 6 is 1,000,000:
0.25 × 1,000,000 = 250,000.
Therefore, the simplified expression is 250,000.
multiplication