Asked by DestinyBright

GIVEN THAT log81 s=1/2, what is S?
41.0
27.0
9.0
3.0
Answered by DestinyBright
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
Answered by DestinyBright
that is not one of the options
Answered by DestinyBright
answer with one of these options
25 square units

37.5 square units

50 square units

75 square units
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.