Answer:
-64/5
Step-by-step explanation:
Basically, the word "quotient" means the answer to a division problem. Therefore, its a division problem, so you have to work backwards with multiplication. -8 times a number is 5/8, so the other number is going to be negative.
The number is -64/5
Answer:
Inequality Form:
2
−
√
11
<
x
<
2
+
√
11
Interval Notation:
(
2
−
√
11
,
2
+
√
11
)
Step-by-step explanation:
Solve the inequality for x by finding a
, b
, and c of the quadratic then applying the quadratic formula.
Answer:
V = 2304π units³
Step-by-step explanation:
The volume (V) of a sphere is calculated as
V = 
πr³ ( where r is the radius ) , then
V = π × 12³
= π × 1728
= 4π × 576
= 2304π units³
Answer:
x = 0
, y = 7/6
Step-by-step explanation:
Solve the following system:
{18 y - 12 x = 21
6 x - 9 = -9
In the second equation, look to solve for x:
{18 y - 12 x = 21
6 x - 9 = -9
Add 9 to both sides:
{18 y - 12 x = 21
6 x = 0
Divide both sides by 6:
{18 y - 12 x = 21
x = 0
Substitute x = 0 into the first equation:
{18 y = 21
x = 0
In the first equation, look to solve for y:
{18 y = 21
x = 0
Divide both sides by 18:
{y = 7/6
x = 0
Collect results in alphabetical order:
Answer: {x = 0
, y = 7/6
Direct Proportion functions look like this:
y=kx
'k' is the constant of proportionality and in this case its 7.5 or 15/2.
--------------------------------------------
When x=1, y=7.5
When x=2, y=15
When x=3, y=22.5
Therefore y is directly proportional to x.
--------------------------------------
DIRECT PROPORTION EXPLAINED:
Say a football costs £7.50. If you buy one football you'll have to pay out £7.50, but if you you buy two footballs you'll have to pay out £15.00. Therefore the cost of the football(s) is directly proportional to the amount of footballs you buy. C=cost, f=football(s) and C<span>∝f, therefore C=kf, but as k=7.5, C=7.5f.
INVERSE PROPORTION EXPLAINED:
If it were to take 8 hours for one bricklayer to set up a wall, how long would it take for two bricklayers to set up a wall? The answer in this case would be 4 hours.
T=time to set up a wall
b=bricklayer(s)
Therefore T</span><span>∝1/b, and T=k/b. In this case k=8 so T=8/b.
When b=1, T=8.
When b=2, T=4.
We'd say that the time it would take for bricklayers to set up a wall would be inversely proportional to the amount of bricklayers available.</span>
