Answer:
X=65°
Step-by-step explanation:
Both angles combined is a right angle as indicated by the small square drawn on it, a right angle is always 90° therefore
(x-15°)+40°=90°
combine like terms
x+25°=90°
subtract 25° from each side
x=65°
Answer:
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Answer:
Hi there!
Your answer is:
Based off the problem we can tell that the slope is -2/3 and the y intercept is 2. This means we must start our line at the point (0,2). Since slope is in the form rise/run, we know that we must go UP 2 units for every 3 units we go LEFT! We know to go left (As x goes to positive infinity, y goes to negative infinity. ) because the slope is negative!
Hope this helps
Assuming that the base of the prism is a regular pentagon, the area of a regular polygon is given by the formula A = 0.5pa; where p is the perimeter and a is the apothem. An apothem is a line that connects the center of the polygon to the midpoint of a side and is also perpendicular to the said side. For this example, the assumed apothem here is k.
Area of base = 2 (0.5 x 20" x k) = 20k
The sides of the prism are rectangles, with width 6" and length (20"/5) = 4".
Area of sides of prism = 5 (6" x 4") = 120
Total Area T.A. = 120 + 20k
Answer:
a)
We know that:
a, b > 0
a < b
With this, we want to prove that a^2 < b^2
Well, we start with:
a < b
If we multiply both sides by a, we get:
a*a < b*a
a^2 < b*a
now let's go back to the initial inequality.
a < b
if we now multiply both sides by b, we get:
a*b < b*b
a*b < b^2
Then we have the two inequalities:
a^2 < b*a
a*b < b^2
a*b = b*a
Then we can rewrite this as:
a^2 < b*a < b^2
This means that:
a^2 < b^2
b) Now we know that a.b > 0, and a^2 < b^2
With this, we want to prove that a < b
So let's start with:
a^2 < b^2
only with this, we can know that a*b will be between these two numbers.
Then:
a^2 < a*b < b^2
Now just divide all the sides by a or b.
if we divide all of them by a, we get:
a^2/a < a*b/a < b^2/a
a < b < b^2/a
In the first part, we have a < b, this is what we wanted to get.
Another way can be:
a^2 < b^2
divide both sides by a^2
1 < b^2/a^2
Let's apply the square root in both sides:
√1 < √( b^2/a^2)
1 < b/a
Now we multiply both sides by a:
a < b
