Suppose that the functions g and h are defined for all real numbers x as follows. gx = x − 3xhx = 5x + 2Write the expressions for (g - h)(x) and (g * h)(x) and evaluate (g + h)(−2).

Step-by-step explanation:

Given the functions g(x) = x − 3x  and h(x) = 5x + 2, we are to calculatae for the expression;

a) (g - h)(x)  an (g * h)(x)

(g - h)(x)  = g(x) - h(x)

(g - h)(x)  = x − 3x -(5x+2)

(g-h)(x) = x-3x-5x-2

(g-h)(x) =-7x-2

b)  (g * h)(x) =  g(x) * h(x)

(g * h)(x)  = (x − 3x)(5x+2)

(g * h)(x) = 5x²+2x-15x²-6x

(g * h)(x) = 5x²-15x²+2x-6x

(g * h)(x) = -10x²-4x

c) To get (g + h)(−2), we need to first calculate (g + h)(x) as shown;

(g + h)(x)  an (g * h)(x)

(g + h)(x)  = g(x) +h(x)

(g + h)(x)  = x − 3x + (5x+2)

(g+h)(x) = x-3x+5x+2

(g+h)(x) =3x+2

Substituting x = -2 into the resulting function;

(g+h)(-2) = 3(-2)+2

(g+h)(-2) = -6+2

(g+h)(-2) = -4

Related Questions

y = 64°

Step-by-step explanation:

From the picture attached,

m(∠E) = 90°

m(∠E) = m(∠D)

m(∠B) + 67° = 180° [pair of linear angles]

m(∠B) = 113°

m(∠C) + 75° = 180°

m(∠C) = 180° - 75°

= 105°

Since, sum of interior angles of a polygon = (n - 2) × 180°

Here, n = number of sides

For n = 5,

Sum of interior angles = (5 - 2) × 180°

= 540°

m(∠A) + m(∠B) + m(∠C) + m(∠D) + m(∠E) = 540°

m(∠A) + 113° + 105° + m(∠D) + 90° = 540°

(m∠D) + m(∠D) = 540 - 308 [Since, m(∠A) = m(∠D)]

2(m∠D) = 232

m(∠D) = 116°

m(∠D) + y° = 180° [Linear pair of angles]

116 + y = 180

y = 64°

13. B

14. A

both declining slopes

If a sphere fits snugly inside a cube with 34-in edges. What’s is the approximate volume of the space between the sphere and cube

The volume of the space between the sphere and cube is equal to the volume of the sphere subtracted from the volume of the cube:

The volume of a cube is:

s is the length of each edge in the cube

The volume of a sphere is:

The diameter of the sphere is equal to the edge of the cube, then, its radiusr is:

Then, the volume of the space between the sphere and cube is:

s is 34 in

Then, the approximate volume of the space between the sphere and cube is 18724,47 cubic inches

Explanation:

The question is asking for an equation that relates the total cost (C) to the number of gallons of gas purchased (g). Since the cost of gas is $2.75 per gallon, you multiply the number of gallons by$2.75 to find the total cost. Therefore, the equation that represents this relationship is C = 2.75g.

This equation states that the total cost (C) is equal to the cost per gallon ($2.75) multiplied by the number of gallons of gas (g). For instance, if you buy 10 gallons of gas, you would plug in 10 for g in the equation like this: C = 2.75 * 10, which will give you$27.50.

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Step-by-step explanation:

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