Answer:
The function that represents the mass of the sample after t days is 
.
The percentage rate of change per hour is of -2.46%.
Step-by-step explanation:
Exponential amount of decay:
The exponential amount of decay for an amount of a substance after t days is given by:
In which A(0) is the initial amount, and r is the decay rate, as a decimal.
Element X is a radioactive isotope such that its mass decreases by 59% every day. The experiments starts out with 390 grams of Element X.
This means, respectively, that 
So
The function that represents the mass of the sample after t days is .
Hourly rate of change:
Decreases by 59% every day, which means that for 24 hours, the rate of change is of -59%. So
-59%/24 = -2.46%
The percentage rate of change per hour is of -2.46%.
Answer:
27.84 m² , 42.48 m²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = 
bh ( b is the base and h the perpendicular height )
Shape A
has b = 9.6 and h = 5.8, then
A = 0.5 × 9.6 × 5.8 = 27.84 m²
Shape B
has b = 11.8 and h = 7.2 , then
A = 0.5 × 11.8 × 7.2 = 42.48 m²
The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7
Step-by-step explanation:
The parallel lines have:
- Same slopes
- Different y-intercepts
The form of the linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept
∵ The equation of the given line is y = 5x + 4
∴ m = 5 and b = 4
∵ The two lines are parallel
∴ Their slopes are equal
∴ The slope of the parallel line = 5
- Substitute the value of the slope in the form of the equation
∴ y = 5x + b
- To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ The parallel line passes through point (-1 , 2)
∴ x = -1 and y = 2
∵ 2 = 5(-1) + b
∴ 2 = -5 + b
- Add 5 to both sides
∴ 7 = b
- Substitute the value of b in the equation
∴ y = 5x + 7
The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7
Learn more:
You can learn more about the equations of the parallel lines in brainly.com/question/9527422
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Answer:
Step-by-step explanation:
32. Answer: 2+5×3=17
33. Answer: 2×5+3=17
34. Answer: 2×5×3=30
35. Answer: 2×5-3=7
