Let the first integer be x. Then the next consecutive integer is x+1.
Translating the word problem into symbols, x(x+1)-20(x+1) = 442.
Then x^2 + x - 20x - 20 = 442
or x^2 - 19x - 462 = 0
Solve by completing the square:
x^2 - 19x + 90.25 - 90.25 - 462 = 0
(x-9.5)^2 - 552.25 = 0
Taking the positive square root of both sides, we get x-9.5 = 23.5, or
x = 33
The two consecutive integers are 33 and 34.
Check: (33)(34)-20(34) = 442 (as expected).
Answer:
Joint variation says that:
if
and 
then the equation is in the form of:
, where, k is the constant of variation.
As per the statement:
If x varies jointly as y and z
then by definition we have;
......[1]
Solve for k;
when x = 8 , y=4 and z=9
then
Substitute these in [1] we have;

⇒
Divide both sides by 36 we have;

Simplify:

⇒
to find z when x = 16 and y = 6
Substitute these value we have;

⇒
Multiply both sides by 9 we have;

Divide both sides by 12 we have;
12 = z
or
z = 12
Therefore, the value of z is, 12
To solve the problem shown above, you must apply the proccedure shown below:
1. You must use tthe formula for calculate the volume of a sphere, which is:
V=4πr³/3
V is the volume of the sphere.
r is the radius of the sphere (r=3.5 inches)
2. When you susbstitute these values into the formula shown above, you obtain the volume of the sphere. Therefore, you have:
V=4πr³/3
V=4π(3.5 inches)³/3
3. Therefore, the answer is:
V=179.5 inches³
<u>Part 1) which angle is congruent to Angle 1?</u>
we know that
When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called <u>corresponding angles</u>
m∠5=m∠1 ----------> by corresponding angles postulate
therefore
<u>the answer Part 1) is </u>
Angle 
Part 2) Which can be used to directly prove that Angle 1 =~ Angle 8?
we know that
<u>Alternate exterior angles</u> are defined as two exterior angles on opposite sides of a transversal which lie on different parallel lines.
in this problem
m∠1=m∠8 -------> by alternate exterior angles theorem
therefore
<u>the answer part 2) is the option </u>
Alternate Exterior Angles Theorem
<u>Part 3) If m Angle 5 = 42 degrees, what is m Angle 4?</u>
we know that
<u> Alternate interior angles</u> are two interior angles which lie on different parallel lines and on opposite sides of a transversal
m∠4=m∠5 --------> by alternate interior angles theorem
so
m∠4=
therefore
<u>the answer Part 3) is</u>
