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babymother [125]
2 years ago
9

Please I’m giving away Brainly ASAP

Mathematics
1 answer:
AnnyKZ [126]2 years ago
7 0

Answer:

g and f are inverse functions because g(f(x)) = f(g(x)) = x

Step-by-step explanation:

Let's start by finding f(g(x)) and g(f(x)). As we discussed in another question, to find a composite function, apply the outer function to whatever the inner function evaluates to. We can start with f(g(x)):

f(g(x))=f(\frac{x+6}{7})=7(\frac{x+6}{7} )-6=x+6-6=x

Now, let's find g(f(x)):

g(f(x))=g(7x-6)=\frac{(7x-6)+6}{7} =\frac{7x}{7}=x

There is a property that says that if f(g(x)) = g(f(x)) = x, the two functions are inverse. This suggests that g and f are inverse functions. We can verify this by taking one function, switching y and x, and then solving for y. If we complete this process and find that we get the OTHER function, it means the two functions are inverse. Let's try that:

f(x)=y=7x-6

Swap x and y:

x=7y-6

Solve for y:

x+6=7y\\y=\frac{x+6}{7}

Notice that we got g, which means f and g are inverse.

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bobby pays a $25 membership free to join YMCA gym. This gym allows members to attend any exercise class for only $4. The linear
blagie [28]

Answer:

Step-by-step explanation:

T = 4c + 25....where c = # of classes and T = total cost

2 classes...so sub in 2 for c and solve for T

T = 4(2) + 25

T = 8 + 25

T = 33 <==== with 2 classes ,its $ 33

4 classes....so sub in 4 for c and solve for T

T = 4(4) + 25

T = 16 + 25

T = 41 <==== with 4 classes, its $ 41

8 classes....sub in 8 for c

T = 4(8) + 25

T = 32 + 25

T = $ 57 <==== with 8 classes, its $ 57

10 classes...sub in 10 for c

T = 4(10) + 25

T = 40 + 25

T = 65 <===== with 10 classes, its $ 65

7 0
3 years ago
Nina used plastic rectangles to make 6 rectangular prisms. How many rectangles did she use?
Reil [10]

Answer:

36

Step-by-step explanation:

6 X 6 = 36

7 0
3 years ago
Suppose brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt.
Oliga [24]

Answer:

(a) 0.288 kg/liter

(b) 0.061408 kg/liter

Step-by-step explanation:

(a) The mass of salt entering the tank per minute, x = 0.2 kg/L × 5 L/minute = 1 kg/minute

The mass of salt exiting the tank per minute = 5 × (5 + x)/500

The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;

Δ/dt = x - 5 × (5 + x)/500

The increase, in mass, Δ, after an increase in time, dt, is therefore;

Δ = (x - 5 × (5 + x)/500)·dt

Integrating with a graphing calculator, with limits 0, 10, gives;

Δ = (99·x - 5)/10

Substituting x = 1 gives

(99 × 1 - 5)/10 = 9.4 kg

The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank)

∴ The concentration of the salt and water in the tank after 10 minutes =  (5 + 9.4)/500 = (14.4)/500 = 0.288

The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter

(b) With the added leak, we now have;

Δ/dt = x - 6 × (14.4 + x)/500

Δ = x - 6 × (14.4 + x)/500·dt

Integrating with a graphing calculator, with limits 0, 20, gives;

Δ = 19.76·x -3.456 = 16.304

Where x = 1

The increase in mass after an increase in = 16.304 kg

The total mass = 16.304 + 14.4 = 30.704 kg

The concentration of the salt in the tank then becomes;

Concentration = 30.704/500 = 0.061408 kg/liter.

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3 years ago
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