If 5 beads weigh 30 grams, how many beads weigh 48 grams?

Answer:

Part 1) The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.

Part 2)

Step-by-step explanation:

Part 1)

Let

x-----> the number of pounds of regular coffee

we know that

The inequality that represent the situation is

Solve for x

Divide by 2 both sides

The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.

The solution of the inequality is the interval ------> (-∞,7.5]

but the number of pounds cannot be a negative number

therefore

The solution is the interval -----> [0,7.5]

see the attached figure

Part 2) we have

Adds m and n

Group terms that contain the same variable

Combine like terms

The solution is, A) 5, 2  are the coefficients in the polynomial 5x^2 + 2x - 4.

What are Polynomials?

Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.

here, we have,

given that,

the polynomial is : 5x^2 + 2x - 4

now, we have to find the coefficients in the polynomial 5x^2 + 2x - 4

we know that,

a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression. When the coefficients are themselves variables, they may also be called parameters.

and. we have,

a variable is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.

so, we get,

a coefficient is the number in front of the variable,

here, 5, 2  are the coefficients.

and the variable is x.

Hence, The solution is, A) 5, 2  are the coefficients in the polynomial 5x^2 + 2x - 4.

Know more about Polynomials here:

brainly.com/question/2833285

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I can help you with graphing quadratics in intercept form. Here's a step-by-step guide:

Step 1: Identify the intercepts

The intercepts are the points where the parabola crosses the x-axis and y-axis. In intercept form, the x-intercepts are given by the factors of the quadratic expression. For example, in the equation f(x) = 2(x+4)(x+6), the x-intercepts are -4 and -6. To find the y-intercept, set x = 0 and solve for y.

Step 2: Find the vertex

The vertex is the point where the parabola reaches its maximum or minimum value. The x-coordinate of the vertex is the average of the x-intercepts. In the equation f(x) = 2(x+4)(x+6), the x-intercepts are -4 and -6, so the x-coordinate of the vertex is (-4 + -6)/2 = -5. To find the y-coordinate of the vertex, substitute the x-coordinate into the equation and solve for y.

Step 3: Plot the intercepts and vertex

Mark the intercepts and vertex on the coordinate plane.

Step 4: Sketch the parabola

Draw a smooth curve that passes through the intercepts and vertex. The parabola should be symmetric about the vertical line passing through the vertex.

Example:

Let's graph the equation f(x) = 2(x+4)(x+6).

Step 1: Identify the intercepts

The x-intercepts are -4 and -6. To find the y-intercept, set x = 0 and solve for y:

f(0) = 2(0+4)(0+6) = 48

So the y-intercept is (0, 48).

Step 2: Find the vertex

The x-coordinate of the vertex is (-4 + -6)/2 = -5. To find the y-coordinate of the vertex, substitute x = -5 into the equation:

f(-5) = 2(-5+4)(-5+6) = 2

So the vertex is (-5, 2).

Step 3: Plot the intercepts and vertex

Plot the intercepts (-4, 0), (-6, 0), and (0, 48), and the vertex (-5, 2) on the coordinate plane.

Step 4: Sketch the parabola

Draw a smooth curve that passes through the intercepts and vertex. The parabola should be symmetric about the vertical line passing through the vertex.

The graph of the equation f(x) = 2(x+4)(x+6) is a parabola that opens upwards and has intercepts at (-4, 0), (-6, 0), and (0, 48). The vertex of the parabola is at (-5, 2).

Answer:

x>13

Step-by-step explanation:

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