21 trucks, each with a 2.5-ton payload, are needed to unload a freight train. How many trucks, each with a 3.5-ton payload, would be needed to do the same job? What is the constant of variation?

Option D:

Difference between g(x) and f(x) is 44.

Solution:

Let us first write the function of f(x).

Take any two points on the line (0, -1) and (-2, 0).

Here,

Equation of a line:

Do cross multiplication.

-2(y + 1) = x

-2y - 2 = x

Add 2 on both sides.

-2y = x + 2

Divide by -2 on both sides.

y = -0.5x - 1

f(x) = -0.5x - 1

At x = 20,

f(20) = -0.5(20) - 1 = -11

g(x) = 1.5x + 3

g(20) = 1.5(20) + 3 = 33

Difference between g(x) and f(x)

            = g(20) - f(20)

            = 33 - (-11)

            = 33 + 11

            = 44

Difference between g(x) and f(x) is 44.

Option D is the correct answer.

The expression equivalent to (7x-5)-(3x-2) is 4x-3

What is an expression?

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is an expression (7x-5)-(3x-2), we need to find an expression equivalent to it,

= (7x-5)-(3x-2)

Opening the brackets and multiply by - sign,

= 7x-5-3x+2

Combine the like terms,

= 4x-3

Hence, the expression equivalent to (7x-5)-(3x-2) is 4x-3

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Answer:

x = - 3, x =

Step-by-step explanation:

Given

f(x) = 4x² + 5x - 21

To obtain the zeros, equate f(x) to zero, that is

4x² + 5x - 21 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 4 × - 21 = - 84 and sum = + 5

The factors are + 12 and - 7

Use these factors to split the x- term

4x² + 12x - 7x - 21 = 0 ( factor the first/second and third/fourth terms )

4x(x + 3) - 7(x + 3) = 0 ← factor out (x + 3) from each term

(x + 3)(4x - 7) = 0

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

4x - 7 = 0 ⇒ 4x = 7 ⇒ x =

Final answer:

You can find the zeros of the function f(x) = 4x² + 5x - 21 by setting the function equal to zero and solving for x using the quadratic formula. Upon solving, you get the zeros as -7/4 and 3.

Explanation:

To find the zeros of the quadratic function f(x) = 4x² + 5x - 21, you need to set the function equal to zero and solve for x. This means solving the equation 4x2 + 5x - 21 = 0. This is a quadratic equation that can be solved using the quadratic formula, x = [-b ± √(b² - 4ac)] / (2a).

Here, a = 4, b = 5, and c = -21. Substituting these values into the quadratic formula gives us x = [-5 ± √((5)² - 4*4*(-21))] / (2*4). Simplifying yields x = {-7/4, 3}.

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Answer:

600

Step-by-step explanation:

You would do 36,000 divided by 60 because there are 60 minutes in an hour, and it would be 600.

Answer:

600

Step-by-step explanation:

if it prints 36000 comics per hour divide that by 60 (for 60 minutes in a hour) to get how many comics it prints in a minute

Answer:

240; 24

Step-by-step explanation:

Given that:

Sum of two numbers = 264

One number ends with '0'

Second number = first number without '0'

Let the first number be 'a'

Since the second number is the first number with '0' erased, then,

Second number = (a ÷ 10)

Therefore, the expression becomes :

a + a/10 = 264

Multiply the equation by 10

10a + a = 2640

11a = 2640

a = 2640/11

a = 240

Therefore ;

a = 240 ;

a/10 = 240/10 = 24

The numbers are 240 and 24