Paul works for a company that deals in paints and dyes. He is paid a fixed monthly salary plus 15 percent commission on monthly sales over $20,000.

Answer:

a = 3

Step-by-step explanation:

f(x) = a(bˣ)

At x = 0

f(0) = a(b⁰)

f(0) = a(1)

f(0) = a

From the graph

f(0) = 3

Therefor

a = 3

Answer:

The range would include all real numbers.

Step-by-step explanation:

Consider the provided information.

Range of a function is the set of output values which a function can produce.

Let say we created a function to represent the balance on a credit card each month. Then the range will be the balance amount.

The balance amount can be a negative number as we are talking about credit card, also the balance can be zero or a positive number.

The credit card balance can be in decimals.

Thus, the balance can be any real number.

Hence, the range would include all real numbers.

Answer: Arturo is 14 years

Benny is 17 years

Carlos is 10 years

Step-by-step explanation:

Let x represent the age of Arturo.

Let y represent the age of Benny.

Let z represent the age of Carlos.

The sum of the ages of Arturo, Benny, and Carlos is 41 years. It means that

x + y + z = 41- - - - - - - - - - - - -1

Twice Arturo's age exceeds the sum of Benny and Carlos's ages by one year. It means that

2x = y + z + 1- - - - - - - - - 2

Five years ago, Benny was 2 years more than twice as old as Carlos. It means that

y - 5 = 2(z - 5) + 2

y - 5 = 2z - 10 + 2

y = 2z - 8 + 5

y = 2z - 3

Substituting y = 2z - 3 into equation 2, it becomes

2x = 2z - 3 + z + 1

2x = 2z + z - 3 + 1

2x = 3z - 2

x = 3z/2 - 1

Substituting y = 2z - 3 and

x = 3z/2 - 1 into equation 1, it becomes

3z/2 - 1 + 2z - 3 + z = 41

Multiplying through by 2, it becomes

3z - 2 + 4z - 6 + 2z = 82

3z + 4z + 2z - 2 - 6 = 82

9z - 8 = 82

9z = 82 + 8 = 90

z = 90/9

z = 10

x = 3z/2 - 1 = (3 × 10)/2 - 1

x = 14

y = 2z - 3 = 2 × 10 - 3

y = 17

Answer:

dx/dt= 0.2608 at  h= 3.1 m

Step-by-step explanation:

a is the length of the ladder. a=5

by pythagorus theorem

differentiating with respect to t we get

......1

The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom

At h= 3.1

x^2= 6^2-3.1^2 = 9.1×2.9

x= 5.1371 m

given

putting values in 1 to get dx/dt

.

dx/dt= 0.2608 at  h= 3.1 m

Answer:

= 0.3

Step-by-step explanation:

The given situation forms a right triangle. We have to use the Pythagorean theorem's statement to solve this problem.

The theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse.

Here Hypotenuse = length of the ladder (a)

Legs are h and x.

So, using the Pythagorean theorem, we get

-------------(1)

We are given a = 5 meters, = 0.4

Now plug in a = 5 in the above equation, we get

25 = -----(2)

To find the . Differentiate the above equation with respective to the time t, we get

-------(3)

We know that h = 3.1 and = 0.4.

We can find x, by plug in h = 3.1 from the equation (2)

25 =

x = 3.9

Now plug h = 3.1, x = 3.9 and = -0.4 in the derivative (3) and find dx/dt

Here we represents   = -0.4 because it is sliding down

2(3.1)(-0.4) + 2(3.9) = 0

-2.48 + 7.8    = 0

7.8  = -2.48

 = -2.48 ÷ -7.8

= 0.3179

When we rounding off to the nearest tenths place, we get

= 0.3