Answer:
The passenger train traveled at a speed of 25 miles/hour
Step-by-step explanation:
In this question, we are asked to calculate the rate at which a particular passenger train is traveling.
We use the information in the question to answer as follows;
Firstly, we identify that they traveled at the same time but their distances are different. This means that their speed must be different also.
Mathematically, we know that time can be calculated as distance/ time.
Let us say the speed at which the passenger train traveled is x miles per hour. This means that the speed of the freight train which was 5 miles per hour slower would be (x-5) miles per hour.
We know their times are equal;
Hence;
100/x = 80/(x-5)
We cross multiply
100(x-5) = 80x
100x -500 = 80x
100x-80x = 500
20x = 500
x = 500/20
x = 25 miles per hour
The correct question is;
Layla wants to build a wooden box with a volume of 45 cubic centimeters. She started with a width of 3 cm and a height of 3 cm. How long should Layla make the box?
Answer:
Box is 5 cm long.
Step-by-step explanation:
We are given;
Volume; V = 45 cm³
Width; w = 3 cm
Height;h = 3 cm
Now, this box has the shape of a cuboid and the volume of a cuboid is given as;
V = l × w × h
Where;
L is length
w is width
h is height
Making L the subject, we have;
V/wh = L
Plugging in the relevant values to obtain;
L = 45/(3 × 3)
L = 45/9
L = 5 cm
Solution:
Given equation: h = -0.5x² + x + 12
h = 0.5
-0.5x² + x + 12 = 0.5
-0.5x² + x + 11.5 = 0
Find the roots of quadratic equation.
x = ((-b )+- √(b² - 4ac))/2a
= ((-1 )+- √(1² - 4*(-0.5)*(11.5)))/2(1)
= -3.9, 5.9
The distance will not be negative.
Hence, the distance is 5.9.
