Answer:
B. The relative lengths of the corresponding sides in two triangles.
Step-by-step explanation:
We know that, Hinge theorem states that if two sides of one triangle is congruent to two sides of another triangle and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.
Or we can also say it as, if two triangles have two congruent sides (sides of equal length), then the triangle with the larger angle between those sides will have a longer third side.
So basically,Hinge theorem compares the relative lengths of the corresponding sides in two triangles.
Answer:
A). Options (C) and (E)
B). 4.8 times
Step-by-step explanation:
Part A
Volume of cylinder (1) = πr²h
= π(6)²(5)
= 565.5 cubic inches
Volume of cone (1) = 
= 
= 188.5 cubic inches
Volume of cylinder (2) = πr²h
= π(6)²(15)
= 1696.5 cubic inches
Volume of cone (2) =
= 
= 565.5 cubic inches
Volume of sphere = 
= 
= 904.8 cubic inches
Figure having volume greater than 600 cubic inches are cylinder (2) and sphere.
Options (C) and (E) are the correct options.
Part (B)
= 
Therefore, volume of sphere is 4.8 times the volume of cone (1).
Answer:
14in approx
Step-by-step explanation:
Given data
number of rotations= 10
Distance travelled= 879.2 inches
Hence if in 10 rotations the distance covered is 879.2 inches
in 1 rotation the distance covered will be x inches
cross multiply
10x= 879.2
x= 879.2/10
x= 87.92 inches
This means that the circumference of the tire is 87.92 in
From
C= 2πr
Let us solve for r
87.92=2*3.142*r
87.92=6.284r
r= 87.92/6.284
r= 13.9
Hence the radius is 14in approx
Answer:
Option C
Step-by-step explanation:
We are given two matrices A and B and we have to calculate the value of the expression -4A + 8B. Each element of matrix A will be multiplied by -4 and each element of matrix B will be multiplied by 8. The corresponding elements of the resulting matrices will be added.
![-4A+8B=-4\times\left[\begin{array}{ccc}-4&-4&1\\1&4&7\\2&3&3\end{array}\right] +8\times\left[\begin{array}{ccc}2&9&-9\\8&8&-2\\4&10&1\end{array}\right] \\\\\\ -4A+8B=\left[\begin{array}{ccc}16&16&-4\\-4&-16&-28\\-8&-12&-12\end{array}\right] +\left[\begin{array}{ccc}16&72&-72\\64&64&-16\\32&80&8\end{array}\right]\\\\ \\ -4A+8B=\left[\begin{array}{ccc}32&88&-76\\60&48&-44\\24&68&-4\end{array}\right]](https://tex.z-dn.net/?f=-4A%2B8B%3D-4%5Ctimes%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%26-4%261%5C%5C1%264%267%5C%5C2%263%263%5Cend%7Barray%7D%5Cright%5D%20%2B8%5Ctimes%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%269%26-9%5C%5C8%268%26-2%5C%5C4%2610%261%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%20-4A%2B8B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D16%2616%26-4%5C%5C-4%26-16%26-28%5C%5C-8%26-12%26-12%5Cend%7Barray%7D%5Cright%5D%20%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D16%2672%26-72%5C%5C64%2664%26-16%5C%5C32%2680%268%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%20%5C%5C%20-4A%2B8B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D32%2688%26-76%5C%5C60%2648%26-44%5C%5C24%2668%26-4%5Cend%7Barray%7D%5Cright%5D)
Therefore, option C gives the correct answer.
Integer for the first ship: - 40 feet
integer for the second ship: -100 feet
inequality: -40 > -100
hope I could help. good luck
