Area of a rectangle = length x width
For this postcard:
length = 4 in
width = (3+b) in
area = 24 in^2
Substitute into the area formula:
24 = 4 x (3+b)
24 = 12 + 4b
24 - 12 = 4b
12 = 4b
b = 3 in
Therefore:
the length of the postcard = 4 inch
the width of the postcard = b+3 = 3 + 3 = 6 inch
The equation is:
f(x) = 2x² - 44x + 185
f(x) = 2(x² - 22x + 121 - 121) + 185 =
= 2(x² - 22x + 121) - 242 + 185 =
= 2(x - 11)² - 57
Conclusion:
The vertex is located at (11, -57) and the vertex form is: f(x) = 2(x - 11)² - 57
Answer:
No solution
Step-by-step explanation:
Given: 
and 
Handle each inequality separately.
Utilizing the subtraction property of inequalities
and
Utilizing the addition property of inequalities
Thus, the solution to the combined inequality is the overlap of both solutions.
Refer to the attached image for the number line representation.
No solution
Carly possesses 2 dimes and 4 nickels.
Since a dime is worth 10 cents, with 1 dime and 3 nickels you would have 20 cents; with 2 dimes and 4 nickels, the total would be 40 cents. It is required to have two additional nickels compared to the number of dimes.
The bus's speed is calculated as: velocity (bus) = 36 miles / 40 min, which simplifies to velocity (bus) = 0.9 miles / min. Given that the car's speed is 1.5 times that of the bus, we find: velocity (car) = 1.5 * 0.9 miles / min, leading to velocity (car) = 1.35 miles / min. At the point where they meet, the total distance covered equals 36 miles. Hence: 1.35 t + 0.9 t = 36, and thus 2.25 t = 36 resulting in t = 16 min. They will converge after 16 minutes.
