Answer:
Hence, only one triangle is possible.
Step-by-step explanation:
Let, ABC is a triangle.
Given that,
first side of a ΔABC is 4, second side of a ΔABC is 3 and ∠B is °.
Diagram of the ΔABC is shown below.
Now,
(Law of sines)
⇒
⇒ =
⇒
⇒ ∠A = 61°
Now, ∠A + ∠B+ ∠C = 180° (angle sum property)
⇒ 61° + 41° + ∠C = 180°
⇒ ∠C = 78°
⇒
⇒
⇒
Therefore, ∠A = 61°, ∠B = 41°, ∠C = 78°,
Hence, only one triangle is possible.
Answer:
The initial mass of the sample was 16 mg.
The mass after 5 weeks will be about 0.0372 mg.
Step-by-step explanation:
We can write an exponential function to model the situation.
Let the initial amount be A. The standard exponential function is given by:
Where r is the rate of growth/decay.
Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:
After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.
Therefore, when x = 12, P(x) = 2. By substitution:
Solve for A. Simplify:
Simplify:
Thus, the initial mass of the sample was:
5 weeks is equivalent to 35 days. Therefore, we can find P(35):
About 0.0372 mg will be left of the original 16 mg sample after 5 weeks.
<span>Choices were: A.5 B.7
C.12 D.15</span>
k(x,9) = (-10,-6)
k*x = -10
k*9 = -6 Distributive property of multiplication
k*9 = -6
k = -6/9
k = -2/3 Get the value of k to solve for the value of x.
k*x = -10
-2/3 * x = -10
x = -10 ÷ -2/3
x = -10 * -3/2
x = (-10 * -3)/2
x = 30/2
x = 15 Choice D.
In order to make this equation true you would have to add to it if you want w to equal 12. As it stands the equation would work out as follows...
7w = 87
w = 87/7
w = 12 3/7
As you can see 12 3/7 does not equal 12. The answer is 12 with 3 left over, so to make the equation true with w remaining 12, we have to take those 3 extras away by changing the problem...
7w + 3 = 87
7w = 87 - 3
7w = 84
w = 84/7 = 12
Answer:
4.5 miles per hour
Step-by-step explanation:
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is 3/4 of a mile long. On Monday, Selma ran the loop in 1/6 of an hour. What is Selma's unit rate in miles per hour for Monday's run?
Distance = 3/4 of a mile
Time taken on Monday = 1/6 of an hour.
What is Selma's unit rate in miles per hour for Monday's run?
Unit rate in miles per hour for Monday's run = distance ÷ time taken
= 3/4 ÷ 1/6
= 3/4 × 6/1
= (3 * 6) / (4 * 1)
= 18/4
= 4.5 miles per hour
Unit rate in miles per hour for Monday's run = 4.5 miles per hour