Answer:
See Below.
Step-by-step explanation:
<u>Statements</u> <u>Reasons: </u>
<u />
Given
Given
Vertical Angles are Congruent
AAS Congruence
CPCTC
Answer:
Step-by-step explanation:
Given the volume of the cylindrical soup expressed as V = πr³+ 7πr²
From V = πr³ + 7πr²;
factor out the common variable
V = πr³ + 7πr²
V = πr²(r+7) ... 1
The original volume of a cylinder V = πr²h .... 2 where;
r is the radius of the cylinder
h is the height of the cylinder
Equating equation 1 and 2, we will have;
πr²(r+7) = πr²h
Divide both sides by πr²
πr²(r+7)/ πr² = πr²h/ πr²
r+7 = h
h = r+7
<em>Hence the factor in the context given is equivalent to the height of the cylinder written as a function of its radius r</em>.<em> The statement means that the height of the cylindrical soup is 7 more than its radius.</em>
<em></em>
We know that the perimeter of a rectangle is twice the length, plus twice the width.
P = 2L + 2W
We also know that the perimeter is 156.
P = 156
Finally, we know that the width is 12 less than the length.
W = L - 12.
The next thing that we do is substitute the information that we have into the original equation:
P = 2L + 2W
156 = 2L + 2(L - 12)
From this point we start to solve
156 = 2L + 2L - 24 <---we multiplied the '2' through the parenthesis
156 + 24 = 2L + 2L - 24 + 24
180 = 2L + 2L <--- getting like terms on same sides
180 = 4L <---combining like terms
180/4 = 4L/4 <--- getting like terms on same sides
45 = L <---now we have a value for L
Now we take the known value for L and substitute it in to our equation for W
W = L - 12
W = 45 - 12
W = 33
So now we have Length = 45 and Width = 33.
Answer:
4√34
Step-by-step explanation:
Let the unknown side be y
y^2 = 20^2 + 12^2
y^2 = 400 + 144
y^2 = 544
Take the square root of both side
y = √544
y = √(16x34)
y = √16 x √34
y = 4√34
