Answer:
The pizza heats up an average of 7.50 degrees per minute
Step-by-step explanation:
The table shown
Time (minutes) Temperature (degrees Celsius)
1 2.52
7 47.547
13 92.592
Since the pizza was heated at a constant rate, we can model the experiment as a line, where the slope represents how fast the pizza was heated
Slope
m = (y2 - y1)/(x2 - x1)
Let
(x1,y1) = (7, 47.547)
(x2,y2) = (13, 92.592)
m = (92.592 - 47.547)/(13-7)
m = 7.5075
The pizza heats up an average of 7.50 degrees per minute
Answer:
The faster computer can do the job in 20 mins on it own.
Step-by-step explanation:
Given:
Time taken by slower computer to do job on its own =30 minutes.
Time taken by both the computers to do the job = 12 mins.
We need to find the Time taken by faster computer to do job on its own.
Solution:
Let the the Time taken by faster computer to do job on its own be 'x'.
Now we know that;
Rate to complete the job is equal to number of jobs divided by time taken to complete the job.
Rate of faster computer = 
Rate of slower computer = 
Rate of both the computers = 
Now we can say that;
Rate of both the computers is equal to sum of Rate of faster computer and Rate of slower computer.
framing in equation form we get;
Now we will take the LCM to make the denominator common we get;
Now denominator are same so we will solve the numerator.
Hence The faster computer can do the job in 20 mins on it own.
The equation to represent the area of the triangle would be:
y = 1/2(x²) - (7/2)x
The equation to represent the perimeter of the triangle would be:
y = 3x - 6
The solutions to the system would be (12, 30) or (1, -3). The only viable solution is (12, 30).
Explanation
The area of a triangle is found using the formula
A = 1/2bh
For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x
We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x
The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)
Combining like terms we get:
P = 3x - 6
We will replace P with y, so we have:
y = 3x - 6
Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:
3x - 6 = 1/2(x²) - (7/2)x
It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x
We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x
When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12
This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)
Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.
Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)
We cannot have a negative perimeter, so the only viable solution is (12, 30).
Answer:
Whether a net force acts on the object.
Step-by-step explanation:
Newtons first law states that an object will remain at rest unless it is acted upon by an imbalanced force.
Answer:
Rhombus
Step-by-step explanation:
