Answer:
114
Step-by-step explanation:
Since DE and EF are equal, DEF is an isosceles triangles.
In isosceles triangle, two angles are equal.
So,
∠F = ∠D = 33
Sum of interior angles in a triangles is 180,
∠D + ∠F + ∠E = 180
33 + 33 + ∠E = 180
∠E = 180 - 33 - 33
∠E = 114
The absolute value inequality can be decomposed into two simpler ones.
x < 0
x > -8
<h3>
</h3><h3>
Which two inequalities can be used?</h3>
Here we start with the inequality:
3|x + 4| - 5 < 7
First we need to isolate the absolute value part:
3|x + 4| < 7 + 5
|x + 4| < (7 + 5)/3
|x + 4| < 12/3
|x + 4| < 4
The absolute value inequality can now be decomposed into two simpler ones:
x + 4 < 4
x + 4 > - 4
Solving both of these we get:
x < 4 - 4
x > -4 - 4
x < 0
x > -8
These are the two inequalities.
Learn more about inequalities:
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Answer:
Randall: 44, Amy: 35
Step-by-step explanation:
Four years ago, their age added up to 71. Since four years have passed and they've each grown four years older since then, their ages added up together is 79. Here is the equation for Amy: x + (x + 9) = 79. We can simplify to get 35. Now we add 9 to 35 to get Randall's age. So, Amy's age is 35 and Randall's age is 44, and 35 + 44 = 79.
F(1) = (1)^3 + 2(1)^2 - 5(1) - 6 = 1 + 2 - 5 - 6 = -8; x = 1 is not a solution to the polynomial.
f(-1) = (-1)^3 + 2(-1)^2 - 5(-1) - 6 = -1 + 2 + 5 - 6 = 0; x = -1 is a solution to polynomial.
From the options, a or c has x = -1, both has x = , so lets check for x = 3
f(3) = (3)^3 + 2(3)^2 - 5(3) - 6 = 27 + 18 - 15 - 6 = 24; x = 3 is not a solution to the polynomial.
Therefore the solutions to the polynomial are x = -3, x = -1, x = 2
Answer:
option a 75°
Step-by-step explanation:
45°+60°+third angle=180°[by angle sum property]
105°+third angle=180°
third angle =180°-105°
third angle=75°
