If f(x)=1/2x+2, find f^-1(20)

Angela and Michelle shared some money in the ratio 4: 9 then Angela gave Daniel half her share.Michelle gave Daniel a third of h

SVEN [57.7K]

Using a system of equations, it is found that £52 was originally shared.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

Variable x: Angela's share.

Variable y: Michelle's share.

Variable z: Daniel's share.

Angela and Michelle shared some money in the ratio 4: 9, hence, considering t as the total:

$x = \frac{4t}{13}$ .

$y = \frac{9t}{13}$

Angela gave Daniel half her share.Michelle gave Daniel a third of her share. Daniel was given a total of £20, hence:

$\frac{x}{2} + \frac{y}{3} = 20$

$\frac{4t}{26} + \frac{9t}{39} = 20$

$\frac{12t + 18t}{78} = 20$

30t = 20 x 78

t = 20 x 78/30

t = £52.

More can be learned about a system of equations at brainly.com/question/24342899

#SPJ1

5 0

2 years ago

Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and foci (0, -5) and (0, 5).

andre [41]

Check the picture below. So, more or less looks like so.

notice, the center is clearly at the origin, and notice how long the "a" component is, also, bear in mind that, is opening towards the y-axis, that means the fraction with the "y" variable is the positive one.

Also notice, the "c" distance from the center to either foci, is just 5 units.

$\bf \textit{hyperbolas, vertical traverse axis }\\\\
\cfrac{(y-{{ k}})^2}{{{ a}}^2}-\cfrac{(x-{{ h}})^2}{{{ b}}^2}=1
\qquad 
\begin{cases}
center\ ({{ h}},{{ k}})\\
vertices\ ({{ h}}, {{ k}}\pm a)\\
c=\textit{distance from}\\
\qquad \textit{center to foci}\\
\qquad \sqrt{{{ a }}^2+{{ b }}^2}
\end{cases}\\\\
-------------------------------\\\\$

$\bf \begin{cases}
h=0\\
k=0\\
a=4\\
c=5
\end{cases}\implies \cfrac{(y-{{ 0}})^2}{{{ 4}}^2}-\cfrac{(x-{{ 0}})^2}{{{ b}}^2}=1\implies \cfrac{y^2}{16}-\cfrac{x^2}{b^2}=1
\\\\\\
c=\sqrt{a^2+b^2}\implies c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b
\\\\\\
\sqrt{5^2-4^2}=b\implies \boxed{3=b}
\\\\\\
\cfrac{y^2}{16}-\cfrac{x^2}{3^2}=1\implies \boxed{\cfrac{y^2}{16}-\cfrac{x^2}{9}=1}$

7 0

3 years ago

An NFL coach sometimes uses a defense that utilizes 3 defensive linemen, 4 linebackers, and 4 defensive backs. His roster (the p

Alexandra [31]

Answer:

68,600

Step-by-step explanation:

The order of the players is not important. For example, a defensive line of Shaq Lawson, Ed Oliver and Jerry Hughes is the same as a defensive line of Ed Oliver, Shaq Lawson and Jerry Hughes. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Defensive Lineman:

3 from a set of 8. So

$C_{8,3} = \frac{8!}{3!5!} = 56$

56 combinations of defensive lineman

Linebackers:

4 from a set of 7. So

$C_{7,4} = \frac{7!}{4!3!} = 35$

35 combinations of linebackers

Defensive backs:

4 from a set of 7. So

$C_{7,4} = \frac{7!}{4!3!} = 35$

35 combinations of defensive backs

How many different ways can the coach pick the 11 players to implement this particular defense?

56*35*35 = 68,600

68,600 different ways can the coach pick the 11 players to implement this particular defense

7 0

3 years ago

calculate E, the amount of euros that has the same value as D U.S. dollars, using the equation E=17/20D=

Aleksandr [31]

<em>The given equation is: E=17/20 D , where E=amount of Euros and D= amount of U.S dollar. </em>

<em>Now for 1 U.S dollar, we need to plug D=1 into the above equation. So, we will get......... </em>

<em>0.85 Euros have the same amount as 1 U.S dollar. </em>

<h2><em>HOPE IT HELPS (◕‿◕✿) SMILE!!</em></h2>

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8 0

3 years ago

- The table shows how many pages Andy reads. Does Andy read at a<br> constant rate? Explain.

spayn [35]

Answer:

no because it is not linear

Step-by-step explanation:

5 0

3 years ago