Answer:
<em>The total percentage discount was 19%</em>
Step-by-step explanation:
<u>Percentages</u>
Suppose the original price of the shirt was x.
A discount of 10% reduces the price by:
10*x/100 = 0.1x
Thus, the discounted price is:
x - 0.1x = 0.9x
The second discount reduces the price by:
10*0.9x/100 = 0.09x
The new discounted price is:
0.9x - 0.09x = 0.81x
With respect to the original price, the last discounted price has been discounted by:
x - 0.81x = 0.19x
This means the total percentage discount was 0.19*100 = 19%.
The total percentage discount was 19%
Answer:
The third score must be larger than or equal to 72, and smaller than or equal 87
Step-by-step explanation:
Let's name "x" the third quiz score for which we need to find the values to get the desired average.
Recalling that average grade for three quizzes is the addition of the values on each, divided by the number of quizzes (3), we have the following expression for the average:
SInce we want this average to be in between 80 and 85, we write the following double inequality using the symbols that include equal sign since we are requested the average to be between 80 and 85 inclusive:
Now we can proceed to solve for the unknown "x" treating each inaquality at a time:
This inequality tells us that the score in the third quiz must be larger than or equal to 72.
Now we study the second inequality to find the other restriction on "x":
This ine
quality tells us that the score in the third test must be smaller than or equal to 87 to reach the goal.
Therefore to obtained the requested condition for the average, the third score must be larger than or equal to 72, and smaller than or equal 87:
Answer:
b is 15.
Step-by-step explanation:
Trust me on this, The answer could only be 15 when solving for b. Hopefully that helps.
Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.
