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3 years ago

Which situation can be modeled by the inequality 50 - 12x > 8?

Mathematics

1 answer:

eduard3 years ago

7 0

Answer:

Option D.

Step-by-step explanation:

Borrowed $50 from your cousin. You pay him $8 and must pay him back within 12 weeks.

Let x be the amount paid on each week.

$50-8\leq 12x$

$50-12x\leq 8$

You can buy bags of pretzels in packages of 12. You $50 to spend, but want to have at least $8 left.

Let x be the amount of each package.

$50-12x\geq 8$

You owe your sister $50. You plan to pay her $12 a week till you owe her less than $8.

Let x be the amount paid on each week.

$50-12x$

You have $50 to spend on clothes, but you need to save at least $8 for bus fare. You plan to spend the rest on shirts that cost $12 each (including tax).

Let x be the number of shirts

$50-12x>8$

Therefore, the correct option is D.

You might be interested in

The graph of a linear relationship is shown. Which equation best represents the relationship between x and y in the graph

Finger [1]

Answer:

B. y = -3/4x + 5/2

Step-by-step explanation:

Take two points from the graph, let's use (-2, 4) and (2, 1):

Find slope:

m = (y₂ - y₁) / (x₂ - x₁)

= (1 - 4) / (2 - (-2))

= -3/4

Find y-intercept using slope above and anyone point:

y = mx + b

(1) = -3/4(2) + b

1 = -3/2 + b

b = 1 + 3/2

b = 5/2

Equation of line using m and b above:

y = mx + b

y = -3/4x + 5/2

8 0

2 years ago

I don’t understand :(

viktelen [127]

Answer:

The quotient when $x^3-4x^2-8x+8$ is divided by $x+2$ is $x^2-6x+4$ with no remainder, so x+2 is a factor of p(x).

Step-by-step explanation:

As the question suggests, there are two ways to solve this problem: long division (which can always be used to divide polynomials), and synthetic division (which can only be used when you are dividing by something of the form $(x-a)$ . In this case, we may use synthetic division, since $x+2$ is equal to $x-(-2)$ . I will use synthetic division here as it is slightly faster than long division.

The -2 on the left represents that we are dividing by x-(-2), and the rest of the numbers in the top row are the coefficients of p(x): 1, -4, -8, and 8.

The first step in synthetic division is to being down the leading coefficient of the polynomial: in this case, the 1 (as indicated in red). Now, we multiply the 1 by -2. We get -2, which we place directly below the -4.

Next, we add directly down the column, (-4 + (-2) is equal to -6), and this answer is placed in the box below. We can continue this process, getting the coefficients 1, -6, 4, and 0 in the bottom row.

This is the answer: the quotient is $x^2-6x+4$ , and the remainder is zero (which indicates that x+2 is a factor of p(x)).

Edit: long division

We may also solve this problem using long division (see the second image). The first step is to look at the leading coefficients: since $x \times x^2$ is equal to $x^3$ , the first term in the quotient will be $x^2$ . Since $x^2 \times (x+2)$ is equal to $x^3+2x^2$ , we must now subtract that from $x^3-4x^2-8x+8$ .

We repeat the same process, as shown in the image. Since we eventually get to zero, the remainder is zero, and the polynomial at the top (x^2-6x+4) is the quotient.

<em>I know this might be difficult to follow, so please comment if you have any questions.</em>