After manipulating above equation we get, 2x^2 - 7x - 8= 0. Discriminant= b^2 - 4ac = (-7)^2 - 4(2)(-8) = 113>0. So there are 2 real roots :)
The volume of a cuboid is given by length × width × height
We have:
Volume = 7.6 ft³
Height = 3x - 1
Length = x + 5
Width = x
Substituting these into the formula, we have:
7.6 = (3x - 1) (x + 5) (x)
7.6 = [3x² + 15x - x - 5] (x)
7.6 = [3x² + 14x - 5](x)
7.6 = 3x³ + 14x² - 5x
0 = 3x³ + 14x² - 5x - 7.6
Drawing the graph is one way of finding the solution (refer to the graph below):
We have three solutions (where the curve crosses the x-axis):
x = -4.9
x = -0.6
x = 0.8
Putting these solutions back into the context, since we are looking for the value of x which is part of measurement of length, we cannot have negative value, so we will take the value of x = 0.8 ft
Converting 0.8 ft into inches = 0.8 × 12 inches = 9.6 inches
Answer: x = 9.6 inches
Answer:
True
Step-by-step explanation:
In my opinion the following statement would be true. In order to become good at anything you need to practice, (also could mean hard work) and determination the drive to get good at the act you are working on. Some believe discipline would often be a good way to get good at something.
Hope this helps.
To find the area of the full shape, we can find the areas of individual smaller shapes and add them together. Lets break this up into a rectangle and a triangle.
The rectangle is easy to calculate as we already have its measurements. The area of a rectangle is h*w=A.
25*36=A
900=A
Next the triangle, and we need to do some logic work with the measurements to find the necessary measurements to take the area.
We know the base of the triangle is some part of 36 feet. We also know from the image that the part of the 36 that is not part of the base of the triangle is 12. Therefore, the base of the triangle is 36 - 12 = 24.
Now we need the height of the triangle. We know the height of the triangle is some part of 39, and the part that is not part of the triangle is 25. Therefore, the height of the triangle is 39 - 25 = 14.
We now have the height and base of the triangle and can find its area. The area of a triangle is 0.5wh=A.
0.5(24)(14)=A
168=A
Finally, we just need to add the two results together to find the total area.
168 + 900 = A
1068 = A
The total area of the shape is 1068.