When we say two quantities 
and 
are proportional to one another, there are two ways we could mean this.
- If is *directly* proportional to , then we mean that as changes, changes in the same direction. In other words, if is in/decreased, then also in/decreases. The rate of in/decrease doesn't have to be one-to-one; for example, we could have increase by 1 unit while would proportionally increase by 5 units. In this case, we'd have 
.
- On the other hand, if is *inversely* proportional to , then a change in results in a change in that goes in the opposite direction. A common example involves taking a rectangle of constant area and adjusting the width and length . If the rectangle has an area of 5 square units, then we could have 
and 
, or we could have 
and 
, or 
and 
, or any combination of and such that 
is satisfied.
In both cases, we call 5 the "constant of proportionality".
On to your exercises:
(1a) Looks like 
stands for number of apples. Then we're told that the cost 
, which means that for every apple, the cost increases by 2.3 dollars. So the constant of proportionality is 2.3. In the language of proportionality, we could then say that the cost of apples is directly proportional to the number of apples by a factor of 2.3.
(1b) 5.4
(1c) 12.5
Answer:
It's a
Step-by-step explanation:
This is a quadratic expression with the highest power of X being 2.
The coefficient of X² = 1
Note that the general form of a quadratic equation is aX² + bX + C
In this question,
a = 1
b = 7
C = 10
First step is to multiply a and C ( a x C)
= 1 X 10 = 10
Then, find 2 factors of 10 which can both add up to give 7, the coefficient of X given in the question.
The possible factors of 10 are 5 and 2. The sum of 5 and 2 is
5 + 2
Hence, the equation can be written as;
X² + 7X + 10 = X² + 5X + 2X + 10
The next step is to group using a bracket and factorise each bracket individually
(X² + 5X) + (2X + 10) =
X( X + 5) + 2( X + 5) =
(X + 5) (X + 2)
(X + 5) (X + 2) are the factors of the quadratic equation, X² + 7X + 10
Answer:
8
16/8=2 and 24/8=3 that is the common denominator of 8
Step-by-step explanation:
Answer:
D) Square root of 48
Step-by-step explanation:
We have to split the triangle in half and then multiply that by two for the answer. Then we use a²+b²=c² because the two triangles are right triangles, and we know b=4 and c=8, so a²+(4²)=8², or a²+16=64
a² would have to equal 48. a=√48.
Good to hear.dose he have a YouTube account?
