Answer:
-4/27
Step-by-step explanation:
first write -4 1/2 as a fraction, which is -9/2. Then you divide by 1/3:
-9/2 / 2/3=
-2/9 * 2/3 =
-4/27
Good luck on your report card!
The Pyth. Thm. applies here:
(√x + 1)^2 + (2√x)^2 = (2√x + 1 )^2
Expanding the squares:
x + 2sqrt(x) + 1 + 4x = 4x + 4sqrt(x) + 1
Let's subtract x + 2sqrt(x) + 1 + 4x from both sides:
4x + 4sqrt(x) + 1
-(x + 2sqrt(x) + 1 + 4x)
-------------------------------
3x + 2sqrt(x) - 4x = 0
Then 2sqrt(x) = x
Squaring both sides, 4x = x^2, or x^2 - 4x = 0. Then (x-4)x = 0, and the two possible solutions are 0 and 4.
Check these results by substitution. Does the Pyth. Thm. hold true for x=4?
Answer:
RS = 32
Step-by-step explanation:
M is the bisector of RS , then
RM = MS , that is
6x - 2 = 3x + 7 ( subtract 3x from both sides )
3x - 2 = 7 ( add 2 to both sides )
3x = 9 ( divide both sides by 3 )
x = 3
Then
RS = 6x - 2 + 3x + 7 = 9x + 5 = 9(3) + 5 = 27 + 5 = 32
There is a solution for f(x) = g(x) between x = 1 and x = 2.
The second choice is correct. Given that angle 2 and angle 6 are congruent, the largest in each of the corresponding triangles are vertical angles meaning that two known angles are known in each triangle (and they are equal) which means that the last "unknown" (angles 3 and 7) are congruent. The lines DC and AB correspond with these defined, congruent triangles meaning they are parallel.
