GIVEN THAT log81 s=1/2, what is S?
41.0
27.0
9.0
3.0
To solve the equation log81 s = 1/2 and find the value of s, we need to rewrite the equation in exponential form.
In exponential form, the equation would be: 81^s = √(81)
Since √(81) is equal to 9, the equation becomes: 81^s = 9
We can rewrite 9 as 3^2: 81^s = 3^2
Comparing the bases, we can conclude that s = 2.
Therefore, the value of s is 2.
What is the area, in square units, of ΔDEF
with D(5,−1)
, E(1,−4)
, and F(−5,4)
?
Responses
25 square units
25 square units
37.5 square units
37.5 square units
50 square units
50 square units
75 square units
To find the area of triangle ΔDEF with coordinates D(5,-1), E(1,-4), and F(-5, 4), we can use the formula for the area of a triangle given three vertices:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Substituting the coordinates of the vertices into the formula:
Area = 1/2 * |5(-4 - 4) + 1(4 - (-1)) + (-5)((-1) - (-4))|
Simplifying:
Area = 1/2 * |-20 + 5 + 12|
Area = 1/2 * |-3|
Area = 1.5 square units
Therefore, the area of triangle ΔDEF is 1.5 square units.
that is not one of the options
Apologies for the error. Let's calculate the area of the triangle again:
Using the formula for the area of a triangle given three vertices:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Substituting the coordinates of the vertices: D(5,-1), E(1,-4), and F(-5, 4):
Area = 1/2 * |5(-4 - 4) + 1(4 - (-1)) + (-5)((-1) - (-4))|
Simplifying:
Area = 1/2 * |-40 + 5 + 18|
Area = 1/2 * |-17|
Area = 8.5 square units
Therefore, the area of triangle ΔDEF is 8.5 square units.
Out of the given options, the closest one is 9.0 square units.
answer with one of these options
25 square units
37.5 square units
50 square units
75 square units
Apologies for the confusion. Let's re-calculate the area and match it with one of the given options.
Using the formula for the area of a triangle given three vertices:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Substituting the coordinates of the vertices: D(5, -1), E(1, -4), and F(-5, 4):
Area = 1/2 * |5(-4 - 4) + 1(4 - (-1)) + (-5)((-1) - (-4))|
Simplifying:
Area = 1/2 * |-40 + 5 + 18|
Area = 1/2 * |-17|
Area = 8.5 square units
Based on the given options, the closest one to 8.5 square units is 9.0 square units.