We are given the triangle
△ABC, with m∠A=60° and m∠C=45°, and AB=8.
To start, we will calculate all angles and sides.
Finding angle B:
The total of all angles in a triangle equals 180.
m∠A + m∠B + m∠C = 180.
Substituting the known values,
60° + m∠B + 45° = 180.
This gives us m∠B = 75°.
Calculating BC:
Using the law of sines,
We can substitute in the values.
Finding AC:
Now we'll input the values.
Calculating Perimeter:
We substitute values here as well.
Calculating Area:
Using the area formula,
we can then insert values.
...............Answer
Answer:
a) The first inequality is 100 + 55x > 150 + 51x;
b) The final inequality results in x > 12.5
c) Sal's mother will need to use the second phone for at least 13 months.
Step-by-step explanation:
a) Let x represent the number of months.
1. The first phone is priced at $100, with a monthly fee of $55 for unlimited use, leading to a total cost of $(100 + 55x) for x months.
2. The second phone costs $150 with a monthly fee of $51 for unlimited use, resulting in a total of $(150 + 51x) for x months.
3. For the second phone to be cheaper, we set up the inequality:
150 + 51x < 100 + 55x
which simplifies to
100 + 55x > 150 + 51x
b) Now solve this:
55x - 51x > 150 - 100
4x > 50
so x > 12.5
c) This means Sal's mother has to retain the second phone for at least 13 months (since x > 12.5).
Answer:
The formula representing the penny's height as a function of time is:
After 7 seconds, the height of the penny will reach 667 feet.
Step-by-step explanation:
The penny experiences free fall.
With an initial velocity of zero and an initial height of h(0)=1,451.
Gravity acts as the acceleration, measured as g=32 ft/s^2.
The model can be initiated by analyzing speed:
Then, the height is expressed as:
The height of the penny at approximately 7 seconds can be calculated as:
After 7 seconds, the penny will stand at a height of 667 feet.
Jacob's lunch account will deplete in 16 days while Samantha's will run out in just 2 days. Step-by-step explanation:
