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

Answers

Answer 1
Answer:

Answer:

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


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Consider the polygon shown. Determine the value of y. PLEASE HELP​

Answers

Answer:

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°

PLEASE ANSWER I NEED ITTY

Answers

Answer:

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

Answers

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:

V_{}=V_(cube)-V_(sphere)

The volume of a cube is:

V=s^3

s is the length of each edge in the cube

The volume of a sphere is:

V=(4)/(3)\pi\cdot r^3

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

r=(s)/(2)

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

V=s^3-(4)/(3)\pi\cdot((s)/(2))^3

s is 34 in

\begin{gathered} V=(34in)^3-(4)/(3)\pi\cdot((34in)/(2))^3 \n \n V=39304in^3-(4)/(3)\pi\cdot(17in)^3 \n \n V=39304in^3-(4)/(3)\pi\cdot4913in^3 \n \n V=39304in^3-(19652\pi)/(3)in^3 \n \n V\approx18724.47in^3 \end{gathered}Then, the approximate volume of the space between the sphere and cube is 18724,47 cubic inches

At one gas station, gas costs $2.75 per gallon. Write an equation that relates the total cost, C , to the number of gallons of gas purchased, g.

Answers

Answer:

C = 2.75g

Step-by-step explanation:

The total cost of the gas purchased is the product of the price per gallon and the number of gallons.

Hope this helps. :)

Final answer:

The equation that relates the total cost (C) to the number of gallons of gas (g) is C = 2.75g. This equation indicates that to find the total cost, you multiply the number of gallons by $2.75.

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.

Learn more about Equation Creation here:

brainly.com/question/33813291

#SPJ3

I WILL GIVE 100 POINTS IF YOU ANSWER THE QUESTIONS BELOW

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Answer:

BRO I HAVE THE SAME QUESTION I NEEEED HELP

Step-by-step explanation:

(Functions and Relations) Answer getting brainliest!!

Answers

Answer:

D

Step-by-step explanation:

Have a nice day