What transformation is represented by the rule (x, y)→(−y, x)?

Let f(x)=3x2−5x+13 and g(x)=2x−7 . What is g(f(x)) ?

grigory [225]

Option B: $6x^2-10x+19$ is the correct answer

Step-by-step explanation:

Given functions are:

$f(x) = 3x^2-5x+13\\g(x) = 2x-7$

We have to find g(f(x))

So,

$g(f(x)) = 2(f(x))-7\\= 2(3x^2-5x+13)-7\\=6x^2-10x+26-7\\= 6x^2-10x+19$

Hence,

Option B: $6x^2-10x+19$ is the correct answer

Keywords: Functions, Composition

Learn more about functions at:

#LearnwithBrainly

7 0

3 years ago

Jamie and Stella are saving money to sign up for a school trip to Washington, D.C. In order to sign up for the trip, they must p

rusak2 [61]

The answer is incomplete. Here is the complete question:

Jamie and Stella are saving money to sign up for a school trip to Washington, D.C. In order to sign up for the trip, they must pay $600 upfront. Jamie earns his money by washing cars for $25 each. Stella earns her money by making pecan pies for $15 each. Jamie earns more money than Stella does because Stella only has enough supplies to make 40 pies. let x represent the number of cars Jamie washes. Let y represent the number of pies Stella makes.

Part 1: Write a constraint (an inequality) to represent how much money Jamie needs for his trip.

Part 2: Write a constraint (an inequality) to represent how much money Stella needs for her trip.

Part 3: Write a constraint (an inequality) to represent the limitations of Stella's supplies.

Part 4: Can Stella afford to sign up for the trip with the money she earns? Explain your answer and show any work that might support your answer.

Answer:

Part 1: $25x\geq 600$

Part 2: $15y\geq 600$

Part 3: $y\leq 40$

Part 4: Yes, she makes exactly 600 dollars by making 40 pies.

Step-by-step explanation:

Given:

Total money needed for the trip is 600 dollars.

Money earnt by Jamie for washing one car is $25.

Money earnt by Stella for making one pie is $15.

Let $x$ represent the number of cars Jamie washes. Let $y$ represent the number of pies Stella makes.

Part 1:

Since the cost for washing one car is $25

Therefore, the cost of washing $x$ cars is $25x$ .

Now, in order to sign up for the trip, money obtained from car washing must be greater than or equal to $600.

Therefore, $25x\geq 600$

Part 2:

Since the cost for making one pie is $15

Therefore, the cost of making $y$ pies is $15y$ .

Now, in order to sign up for the trip, money obtained from pie making must be greater than or equal to $600.

Therefore, $15y\geq 600$

Part 3:

As per the question, the maximum number of pies that Stella can make is 40. So, the value of $y$ can't exceed 40 and must be less than or equal to 40. Therefore,

$y\leq 40$

Part 4:

Now, in order to sign up for the trip, Stella's total earning must be at least $600. So, $15y=600$ is the minimum condition for signing up for the trip. Now, let us solve the above equation for $y$ . This gives,

$15y=600\\y=\frac{600}{15}=40$

Therefore, minimum number of pies required for signing up for the trip is 40 and luckily that's the maximum supply Stella has for pies. Therefore, she can sign up for the trip by making all the 40 pies and earning a total of 600 dollars.

8 0

3 years ago

On Venus how can you overcome extreme temperature and microgravity

matrenka [14]

Mercury is very different than Earth. I think Mercury is a very hot planet, and because of the gravity and other conditions - look these up online - Humans and other life on Earth cannot live on Mercury, much less visit without being fully protected. Temperature on Mercury 426 degrees Celsius, about 800 degrees fahrenheit - very hot. You would want your space craft to completely protected from these temperatures, think of some materials you could use, and how thick you would need them? What material protects from heat? As far as vacuum conditions, and gravity, you will need to have that included as well.Maybe you would just wear a type of clothing to protect against bumping around in your space craft since you will not have gravity, you will also want to think about food!

8 0

3 years ago

What is the distance between -3 and 2 on the number line?<br> O-5<br> O-1<br> O- 1<br> 05

snow_lady [41]

Its the last answer, 5

6 0

3 years ago

PLEASE HELP!!! WILL GIVE BRANLIEST

Setler79 [48]

Answer:

A

Step-by-step explanation:

becuase you its A

6 0

3 years ago