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3 years ago

Please help me figure out this problem

Mathematics

1 answer:

tiny-mole [99]3 years ago

5 0

Answer:

$f(g(x))=f\left(-\dfrac{3x+21}{5}\right)=x\\\\g(f(x))=g\left(-\dfrac{5}{3}x-7\right)=x$

Step-by-step explanation:

Fill in the given expressions and simplify.

$f(g(x))=f\left(-\dfrac{3x+21}{5}\right)=-\dfrac{5}{3}\left(-\dfrac{3x+21}{5}\right)-7\\\\=\left(-\dfrac{5}{3}\right)\left(-\dfrac{3x}{5}\right)-\left(\dfrac{5}{3}\right)\left(-\dfrac{21}{5}\right)-7\\\\=\dfrac{15x}{15}+\dfrac{5\cdot 21}{3\cdot 5}-7=x+7-7=x$

Going the other way, we have ...

$g(f(x))=\displaystyle -\frac{3\left(-\frac{5}{3}x-7\right)+21}{5}=-\frac{-5x-21+21}{5}=x$

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X^2 +6x+30 in vertex form

Elina [12.6K]

Answer:

Step-by-step explanation:

Factoring x2-6x-30

The first term is, x2 its coefficient is 1 .

The middle term is, -6x its coefficient is -6 .

The last term, "the constant", is -30

Step-1 : Multiply the coefficient of the first term by the constant 1 • -30 = -30

Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -6 .

-30 + 1 = -29

-15 + 2 = -13

-10 + 3 = -7

-6 + 5 = -1

-5 + 6 = 1

-3 + 10 = 7

-2 + 15 = 13

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7 0

3 years ago

Read 2 more answers

PLEASE HELP ME!!!! I NEED THIS QUICKLY!!

zloy xaker [14]

Part A: $y=-\frac{5}{4} x+\frac{35}{2}$ is the equation of the line.

Part B: Anika worked 17.5 hours on day 0.

Part C: The setup time decreases with 1 hour and 15 min per day.

Explanation:

Part A: Let us find the equation of the line using the points (2,15) and (6,10)

The equation of the line is given by,

$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \cdot\left(x-x_{1}\right)$

Substituting, we get,

$y-15=\frac{10-15}{6-2} (x-2)$

Simplifying, we have,

$y-15=-\frac{5}{4} (x-2)$

$y-15=-\frac{5}{4} x+\frac{5}{2}$

Subtracting both sides by 15, we get,

$y=-\frac{5}{4} x+\frac{35}{2}$

Hence, the equation of the line is $y=-\frac{5}{4} x+\frac{35}{2}$

Part B: To determine the number of hours Anika worked on day 0, let us substitute x = 0 in the equation of the line.

Thus, we get,

$y=\frac{35}{2}\\y=17.5$

Hence, Anika worked 17.5 hours on day 0.

Part C: The setup time decrease per day can be determined using the slope.

The formula for slope is given by

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting , we have,

$m=\frac{10-15}{6-2}=-\frac{5}{4}$

Converting the fraction into hours and minutes, we get,

$-\frac{5}{4}\times60=-75 min$

Since, 1 hour = 60 min

Subtracting 60 and 75 = 15 min

Thus, the setup time decreases with 1 hour and 15 min per day.

6 0

3 years ago

The zoo feeds the tortoise, rhinoceros, and zebra a total of 23 pounds of vegetables a day. How many pounds does the zoo feed th

vekshin1

If I understand your question correctly, you want to know how many pounds of vegetables the zoo feeds the animals a month if its a 30 day month?

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Is that what your asking for?

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2 years ago

Mr and mrs Lim took their 2 children to the bird park.An adult ticket cost 4 times as much as a child’s ticket.Mr Lim paid a tot

Vinil7 [7]

c = unknown

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3 years ago

Read 2 more answers

write two equations that when graphed look like this *see image*. please help its due soon and i will give ya 75 points for answ

myrzilka [38]

Answer:

the graph is at 4 1/2 and 0 is that what you were looking for

Step-by-step explanation:

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2 years ago