Y = a(x + 2)(x - 3) : equation of the parabola in factored form 10 = a(5 + 2)(5 - 2) : (5 , 10) is a point on the graph of the parabola and therefore satisfies the equation of the parabola. a = 5/7: solve the above equation for a.

4 0

3 years ago

!!!!!!!!!!!!!!!!!!!!

Andru [333]

Answer:

$f^{-1}(x)=4x+20$

Step-by-step explanation:

Given

$f(x)=\frac{x}{4}-5\\ \\y=\frac{x}{4}-5$

Swap x and y and solve for y

$y=\frac{x}{4}-5\\ \\x=\frac{y}{4}-5\\ \\x+5=\frac{y}{4}\\ \\4(x+5)=y\\\\y=4x+20$

Final answer

$f^{-1}(x)=4x+20$

Keep in mind that we need to swap the variables because a function and its inverse are symmetrical about the line y=x. See the graph below.

3 0

3 years ago

Having some trouble with these questions, how do I work them out?

matrenka [14]

Let x be the age of the father and y be the age of the son. As of today, he's 3 times older, so we have $x=3y$

10 years ago their ages were, respectively, x-10 and y-10, and the father was 5 times older: $x-10 = 5(y-10)$

So, we have the system

$\begin{cases} x=3y\\x-10=5(y-10)\end{cases}$

Using the first equation, we can substitute every occurrence of "x" with "3y" in the second equation:

$3y-10=5(y-10) \iff 3y-10=5y-50 \iff 2y = 40 \iff y=20$

So, the son is 20 years old, which means that the father is 60 years old.

Indeed, 10 years ago they were 10 and 50 years old, so the father was 5 times older.

Let x be the age of the grandfather and y the age of the granddaughter. We know that the grandfather is 10 times older: $x=10y$

He also is 54 years older: $x=y+54$

Again, if we substitute x=10y in the second equation we have

$10y=y+54 \iff 9y=54 \iff y=6$

7 0

3 years ago

a total of 408 tickets were sold for the school play. They were either adult tickets or student tickets. The number of students

Mama L [17]

Given Situation:
=> There are 408 total of ticket sold for a school play
=> 3 times of the tickets are sold to students compare to the adults
=> So the ratio of the given situation is 1 : 3
=> Now, 1 + 3 = 4
Since, we need 4 parts, let’s divide 408 by 4
=> 408 / 4 = 102 – the number of tickets for adults
=> 102 x 3 = 306 – the number of tickets for students
=> 102 : 306

4 0

3 years ago