Answer:
{-7, 2, 8}
Step-by-step explanation:
We see that the domain is limited to three x-values: -3, 0 and 2. To find the range (which is the set of all y-values) we just need to plug-in these x-values and find the corresponding y-values.
So our equation is:
y = 3x + 2
Then we substitute for the x-values:
y = 3(-3) + 2
y = -9 + 2
y = -7
y = 3(0) + 2
y = 0 + 2
y = 2
y = 3(2) + 2
y = 6 + 2
y = 8
So our range would be {-7, 2, 8}.
Answer:
The half-life of the radioactive substance is of 3.25 days.
Step-by-step explanation:
The amount of radioactive substance is proportional to the number of counts per minute:
This means that the amount is given by the following differential equation:
In which k is the decay rate.
The solution is:
In which Q(0) is the initial amount:
8000 counts per minute on a Geiger counter at a certain time
This means that 
500 counts per minute 13 days later.
This means that 
. We use this to find k.
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 of 3.25 days.
Answer:
x = -2
Step-by-step explanation:
-6x + 5 = 17
First, combine the constants by subtracting 5 from each side.
-6x = 17 - 5
-6x = 12
Now you want x by itself, so divide both sides by -6.
x = -2
Check your answer by plugging x = -2 into the original equation.
-6(-2) + 5 = 17
12 + 5 = 17
17 = 17
Your answer is correct.
Answer:
A. By SAS only
Step-by-step explanation:
Side Side Side postulate (SSS) states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.
Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
In triangles ABC and AED:
- sides ACand AD are congruent (from the diagram);
- angles BCA and EDA are congruent (given);
- sides BC and ED are congruent (from the diagram).
So, SAS postulate can be applied.
SSS postulate cannot be applied, because it is not given that sides AB and AE are conruent.
Answer:
7/8 or 0.875 units^3
Step-by-step explanation:
The volume for a rectangular prism is l*w*h. What you must remember is that l*w can be rewritten as the base of the prism. Thusly, the volume formula can be reduced to B*h, where B is the area of the base. You are given the area of the base as 1/2, so just multiply 1/2 by 1&3/4 (I rewrote it as 7/4) to get 7/8.
