9514 1404 393
Answer:
ASA
Step-by-step explanation:
The shared angle, the marked angle, and the marked sides between those angles are congruent. That is, you have congruent Angle, Side, Angle, so the ASA postulate applies.
Answer:
36 units²
Step-by-step explanation:
rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
we use the inverse formula
12 * 3 =<em> </em>
<em>36 units²</em>
<em>-----------------------</em>
check
36 : 12 = 3
the answer is good
Two angles are said to be supplement when their measure add up to 180 degrees.
Assume that the angle we are looking for is a and its supplement is s (I used s instead of x).
a + s = 180
a = 180 - s ......> equation I
We know that <span>the measure of the angle is eight times greater than its supplement.
This means that:
a = 8s ......> equation II
Substitute by equation II in equation I to get s as follows:
180 - s = 8s
180 = 9s
s = 20 degrees
Substitute in equation I to get the measure of the angle as follows:
a = 180 - s = 180 - 20 = 160 degrees
Based on these calculations:
The measure of the angle is 160 degrees
The measure of its supplement is 20 degrees</span>
Answer:
144
Step-by-step explanation:
54+90=144
144-90=54
90+54=144
144-54=90
Answer:
The half-life of the radioactive substance is 135.9 hours.
Step-by-step explanation:
The rate of decay is proportional to the amount of the substance present at time t
This means that the amount of the substance can be modeled by the following differential equation:
Which has the following solution:
In which Q(t) is the amount after t hours, Q(0) is the initial amount and r is the decay rate.
After 6 hours the mass had decreased by 3%.
This means that 
. We use this to find r.
So
Determine the half-life of the radioactive substance.
This is t for which Q(t) = 0.5Q(0). So
The half-life of the radioactive substance is 135.9 hours.
