If <em>f(x)</em> is a linear function, then
<em>f(x)</em> = <em>ax</em> + <em>b</em>
for some constants <em>a</em> and <em>b</em>.
Given that <em>f</em> (1) = 4 and <em>f</em> (4) = 1, these constants are such that
<em>f</em> (1) = <em>a</em> + <em>b</em> = 4
<em>f</em> (4) = 4<em>a</em> + <em>b</em> = 1
Solve for <em>a</em> and <em>b</em> : eliminate <em>b</em> by subtracting the two equations,
(<em>a</em> + <em>b</em>) - (4<em>a</em> + <em>b</em>) = 4 - 1
-3<em>a</em> = 3
<em>a</em> = -1
Then
-1 + <em>b</em> = 4
<em>b</em> = 5
So we have
<em>f(x)</em> = -<em>x</em> + 5
Evaluate for x=6
(3)(6)+7
18 + 7
=25
Answer:
There are 2.22 grams of clay are in each pot.
Step-by-step explanation:
Given:
Dakota has 4/10 kg of clay. He divides the clay to make 888 equal-sized pots.
Now, to find the number of grams of clay are in each pot.
Dakota has clay =
So, by using conversion factor we convert it into grams:
Quantity of clay he has = 400 grams.
Number of equal-sized pots to make = 888.
Now, to get the quantity of grams of clay are in each pot we divide number of equal-sized pots to make by quantity of clay he has:
Therefore, there are 2.22 grams of clay are in each pot.
Answer:
36 people of them did not have a beach umbrella.
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal.
Let x represents the number of people did not have a beach umbrella.
As per the statement:
Bella saw that 7 : 11 people brought an umbrella to the beach.
Out of 11 people, only 7 people brought an Umbrella to the beach.
Remaining people did not brought an Umbrella to the beach = 11 -7 = 4 people
It is also given that there were 99 people there.
then by definition of proportion:
By cross multiply we have;
Divide both sides by 11 we get;
Simplify:
x = 36 people.
Therefore, 36 people of them did not have a beach umbrella.
Answer: 317/305 or 1 12/305
Step-by-step explanation: Reduce the expression, if possible, by cancelling the common factors.
