Express each number as a quotient of two integer of 54

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Answer 1

Answer: There are many possibilities. For example 108/2, -108/-2, 162/3, -162/-3, 216/4, -216/-4, and so forth....

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a box with no top is constructed from a 10 inch x 12 inch piece of cardboard by cutting out congruent squares from each corner of the cardboard and then folding the resulting tabs. We determined the volume of that box (in cubic inches) is given by V(x) = 4x³ - 44x² + 120x where x denotes the length of the side of the square which is removed from each corner (in inches), 0 < x < 5. Solve the inequality V(x)≥80 analytically and interpret your answer in the context of that example.

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Answer:

$To solve the inequality $V(x) \geq 80$, we'll first set up the inequality and then find the values of $x$ that satisfy it.The inequality is $4x^3 - 44x^2 + 120x \geq 80$.Let's simplify it further:$4x^3 - 44x^2 + 120x - 80 \geq 0$.Now, we need to find the values of $x$ that make this inequality true.We can start by factoring the expression:$4(x^3 - 11x^2 + 30x - 20) \geq 0$.$

$Now, let's factor the cubic polynomial inside the parentheses:$x^3 - 11x^2 + 30x - 20 = (x - 2)(x - 5)(x - 2)$.Now, the inequality becomes:$4(x - 2)(x - 5)(x - 2) \geq 0$.To determine the intervals where this inequality is satisfied, we can use a sign chart. We'll consider the values of $x$ that make each factor and the whole expression positive or negative.$

$1. $x - 2$ is positive for $x > 2$ and negative for $x < 2$.\n2. $x - 5$ is positive for $x > 5$ and negative for $x < 5$.\n3. $x - 2$ is positive for $x > 2$ and negative for $x < 2$.Now, consider the overall sign of the expression $4(x - 2)(x - 5)(x - 2)$:- Positive when all three factors are positive (i.e., $x > 5$).- Negative when exactly one factor is negative (i.e., $2 < x < 5$).- Positive when all three factors are negative (i.e., $x < 2$).$

$So, the solution to the inequality $V(x) \geq 80$ is:\[x < 2 \text{ or } 2 < x < 5.\]$

Step-by-step explanation:

In the context of the example, this means that the side length of the square removed from each corner must be less than 2 inches or between 2 and 5 inches for the volume of the box to be greater than or equal to 80 cubic inches. This helps determine the range of valid values for

x to achieve the desired volume for the box.

Final Answer:

The solution to the inequality V(x) ≥ 80 is x ≥ 3.5 inches.

Explanation:

To solve the inequality V(x) ≥ 80, we set the equation 4x³ - 44x² + 120x ≥ 80 and simplify. This simplifies to x³ - 11x² + 30x - 20 ≥ 0, which can be factored as (x - 3.5)(x - 2)(x - 2.857) ≥ 0. Since x represents the side length of the squares removed from the corners, it cannot be negative, so we focus on the values of x that make the expression on the left side of the inequality greater than or equal to zero. This leads us to the solution x ≥ 3.5 inches.

In the context of the example, when the side length of the squares removed from each corner is 3.5 inches or larger, the resulting box has a volume greater than or equal to 80 cubic inches. This means that to achieve a box with a volume of at least 80 cubic inches, you need to remove squares with sides of at least 3.5 inches.

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Which linear function equation would contain the points below? (-6,-8) and (12,4)

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Answer:

Step-by-step explanation:

The equation of a linear function can be written in the form y = mx + b, where m represents the slope and b represents the y-intercept.

To find the equation of a linear function that contains the points (-6,-8) and (12,4), we first need to find the slope.

The slope (m) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Let's substitute the values from the given points into the formula:

m = (4 - (-8)) / (12 - (-6))

m = (4 + 8) / (12 + 6)

m = 12 / 18

m = 2/3

Now that we have the slope, we can use one of the given points and the slope to find the y-intercept (b).

Using the point (-6, -8), we substitute the values into the equation y = mx + b and solve for b:

-8 = (2/3)(-6) + b

-8 = -12/3 + b

-8 = -4 + b

b = -8 + 4

b = -4

Therefore, the equation of the linear function that contains the points (-6,-8) and (12,4) is y = (2/3)x - 4.

Final answer:

The equation of the linear function that contains the points (-6,-8) and (12,4) is y = (2/3)x - 4.

Explanation:

The linear function equation that contains the points (-6,-8) and (12,4) can be determined by using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. First, calculate the slope using the formula m = (y2 - y1) / (x2 - x1). Plugging in the values from the given points, we have m = (4 - (-8)) / (12 - (-6)) = 12/18 = 2/3. Next, choose one of the points to substitute into the equation to find the value of b. Using the point (-6,-8), we have -8 = (2/3)(-6) + b. Solving for b, we get b = -8 + 4 = -4. Therefore, the equation of the line is y = (2/3)x - 4.

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Find the X-intercept of the line 4x+11y=20

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Answer:

Step-by-step explanation:

To find the x-intercept of the line 4x+11y=20, we need to set y=0 and solve for x. This is because the x-intercept is the point where the line crosses the x-axis, which is the point where y=0.

First, substitute y=0 into the equation: 4x+11(0)=20

Simplify: 4x=20

Solve for x: x=5

Therefore, the x-intercept of the line 4x+11y=20 is 5.

Frank's bank charges a variable finance rate of 1.5 percent on purchases up to $100, and one percent for purchases over $100. If his unpaid balance is $354.15 this month, what is his finance charge?

Answers

Answer:

Hi there, $4.04 should be his finance charge.

Step-by-step explanation:

The Red Robins are facing off against the Aliens in fantasy football. The Red Robins scored 393939 points this week. The Aliens scored -25−25minus, 25 points this week.

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Answer:

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Step-by-step explanation:

Answer:

25 points hbn nrnrrfkkkkkllm

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A loan of 900 will be repaid in 36 installments of 30.22what is the finance charge of the loan

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The cost of renting their money is $187.92 . The interest rate is about 14%.

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