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3 years ago

What is the inverse of the function f(x) = 2x - 10?

Mathematics

1 answer:

aliya0001 [1]3 years ago

5 0

Answer:

$h(x) = \frac{1}{2} x+ 5$

Step-by-step explanation:

To find the inverse of a function, simply switch the 'x' and 'y' variables. Substitute in 'y' in the place of f(x) for this purpose:

y = 2x - 10

Switch positions:

x = 2y - 10

Add '10' to both sides to begin simplifying:

x + 10 = 2y

Divide both sides by 2:

$y= \frac{x+10}{2}$

This can be rewritten as:

$y = \frac{1}{2} x+ 5$

Therefore, the inverse of the function is:

$h(x) = \frac{1}{2} x+ 5$

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3 years ago

There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4. There are 180 students at Winthrop Midd

zavuch27 [327]

Given:

Total number of students at Colfax Middle School = 270

Ratio of boys to girls is 5:4.

Total number of students at Winthrop Middle School = 180

Ratio of boys to girls is 4:5.

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To find:

The fraction of the students at the dance are girls

Solution:

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Number of boys $=270\times \dfrac{5}{9}=150$

Number of girls $=270\times \dfrac{4}{9}=120$

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$4+5=9$

Number of boys $=180\times \dfrac{4}{9}=80$

Number of girls $=180\times \dfrac{5}{9}=100$

Now,

Total number of students in both schools $= 270+180$

$= 450$

Total number of girls in both schools $= 120+100$

$= 220$

The fraction of the students at the dance are girls is

$\text{Required fraction}=\dfrac{\text{Total number of girls in both schools}}{\text{Total number of students in both schools}}$

$\text{Required fraction}=\dfrac{220}{450}$

$\text{Required fraction}=\dfrac{22}{45}$

Therefore, the required fraction is $\dfrac{22}{45}$ .

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Step-by-step explanation:

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