What is the area of the triangle whose vertices are (0,0), (3,0) and (0,4)?

The correct answer is:

A=4

B=5

hopes this helps you and future people!

Answer:

a = 4 and b = 5

Step-by-step explanation:

The simplest form of square root of eighty can be written as:

[tex]\sqrt{80}=\sqrt{2\times2\times2\times2\times5}[/tex]

Now as it is a square root function, we will pair up the four 2's in two pairs.

And will take out [tex]2\times2[/tex] outside the square root.

Making the answer = [tex]2\times2\sqrt{5}[/tex]

or [tex]4\sqrt{5}[/tex]

So, a = 4

and b = 5

In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator zero, as division by zero is undefined. Graphically, these are represented as vertical asymptotes or holes. They can be accounted for by noting the x-values where the denominator equals zero.

In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator of the expression equal to zero, as division by zero is undefined. A rational expression is a ratio of two polynomials, typically written in the form P(x)/Q(x), where P(x) and Q(x) are polynomial expressions and x is a variable.

For example, in the rational expression (x+2)/(x-3), x-3 is the denominator. The restriction is determined by setting the denominator equal to zero. If x-3 equals zero, then the value of x that makes this true is 3. Therefore, x cannot be 3 as this would make the denominator zero, creating a discontinuity in the rational expression.

Graphically, discontinuities in rational expressions are represented as vertical asymptotes or holes. A vertical asymptote occurs when the denominator of the fraction is zero but the numerator is not. A hole occurs when both the numerator and the denominator are zero at the same point. These can be accounted for by noting the x-values where the denominator equals zero.

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Answer:

The land should be recorded in the purchaser's books at : $153,000.

Step-by-step explanation:

Since the parcel of land is purchased by the company for $153,000, hence the land should be recorded in the purchaser's books at : $153,000.

ok so original perimeter = 12 +12 + 17 +17 = 58 mm

if dimensions are multiplied by 12:

12*12 = 144 and 17*12 = 204

 new perimeter = 144 +144 +204 +204 = 696 mm

696 / 58 = 12

so the perimeter increased by a factor of 12, answer is A

Answer:

The perimeter is increased by a factor of 12.

Option (a) is correct .

Step-by-step explanation:

Formula

Perimeter of a rectangle = 2 (Length + Breadth)

As given

A rectangle has a length of 12 millimeters and a width of 17 millimeters.

Perimeter of a rectangle = 2 × (12 + 17)

                                         = 2 × 29

                                         = 58 millimeters ²

As given

when the dimensions are multiplied by 12 .

New Length = 12 × 12

                    = 144 millimeter

New Breadth = 17 × 12

                      = 204 millimeter

Thus

New Perimeter of a rectangle = 2 × (144 + 204)

                                         =  2 × 348

                                         = 696 millimeter²

[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = \frac{696}{58}[/tex]

[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = 12[/tex]

Therefore the perimeter is increased by a factor of 12.

Option (a) is correct .

Final Answer:

The point (0,0) does not satisfy the inequality [tex]y ≥ x^2[/tex] + x - 4, as 0 is not greater than or equal to -4. Additionally, it does not satisfy [tex]y > x^2 + 2x + 1[/tex], as 0 is not greater than 1. Therefore, (0,0) does not meet the conditions of the system of inequalities.

Step-by-step explanation:

The point (0,0) is not a solution to the given system of inequalities. First, considering the inequality [tex]y ≥ x^2 + x - 4[/tex], when substituting x=0 and y=0 into the equation, we find that 0 is not greater than or equal to -4. Therefore, (0,0) does not satisfy the conditions of the first inequality. Moving on to the second inequality, [tex]y > x^2 + 2x + 1[/tex], substituting x=0 and y=0 results in 0 not being greater than 1.

Consequently, (0,0) fails to meet the requirements of the second inequality as well. In summary, the point (0,0) does not simultaneously satisfy both inequalities, rendering it unsuitable as a solution to the system.

Analyzing solutions to systems of inequalities involves evaluating each inequality independently to ensure the chosen point satisfies all conditions. In this instance, the failure of (0,0) to satisfy either inequality demonstrates that it does not conform to the system's criteria. When dealing with systems of inequalities, it is essential to carefully assess each component to accurately determine the solution set.

No, (0,0) is not a solution to the given system.

The system consists of two inequalities: y ≥ x^2 + x - 4 and y > x^2 + 2x + 1. To check whether (0,0) is a solution, substitute x = 0 and y = 0 into both inequalities. For the first inequality, x^2 + x - 4 becomes -4, and 0 is not greater than or equal to -4. Therefore, (0,0) does not satisfy the first inequality. Moving on to the second inequality, x^2 + 2x + 1 becomes 1, and 0 is not greater than 1. Hence, (0,0) fails to satisfy the second inequality as well. As a result, (0,0) is not a solution to the system of inequalities.

In summary, by substituting the coordinates of (0,0) into both inequalities, we find that the point does not meet the conditions set by either inequality. Therefore, (0,0) is not a solution to the system. This conclusion is based on the specific values obtained through substitution, demonstrating that the coordinates do not satisfy the given inequalities.

Final answer:

Ben incorrectly assumed that ¼ of two pizzas combined would still be ¼; however, the correct sum is ¼ + ¼ which equals ½ of a pizza. To add fractions, only the numerators are added when denominators match. Mastery of fractions is critical in both academics and day-to-day life.

Explanation:

Ben's error lies in the misunderstanding of fractions and how they add up. If Ben has two pizzas and each has ¼ left, combining the two portions does not result in having ½ of a pizza, but instead, he would have ¼ + ¼ which equals ½. This is because when adding fractions, you only add the numerators (the top numbers) if the denominators (the bottom numbers) are the same. Therefore, ¼ of one pizza plus ¼ of another pizza would equal ½ of a pizza. It's important to understand that fractions represent parts of a whole and that these parts must be added correctly to find the total amount.

Being comfortable with fractions is important not only for academic success but also for everyday life, such as understanding discounts, following recipes, or splitting bills. Utilizing real-life examples like these can help strengthen one's intuitive sense of fractions and make mathematical concepts more relatable.

Final answer:

The nonpermissible value for y in the expression (Y+7)/(Y-3) is 3, because it would make the denominator zero, resulting in an undefined expression.

Explanation:

The question is asking to find the nonpermissible value for y in the expression (Y+7)/(Y-3). In algebra, nonpermissible values are values for the variable that would make the denominator of a fraction equal to zero. We set the denominator of our expression equal to zero and solve for y.

Steps to find the nonpermissible value:

Identify the denominator of the expression, which is (Y-3).

Set the denominator equal to zero: Y - 3 = 0.

Solve for y: Y = 3.

Therefore, the nonpermissible replacement for y is 3, as substituting this value into the denominator would create a division by zero, which is undefined in mathematics.

Jason will take 6 weeks to pay off the home theater system on layaway after making an initial down payment of $25 and weekly payments of $54.

The student's question is about how long it will take Jason to pay for a home theater system using a layaway plan. Jason has made an initial down payment of $25 and will make weekly payments of $54.

To calculate the time it will take to pay off the remaining balance, we subtract the down payment from the total cost: $349 - $25 = $324. Then, we divide the remaining balance by the weekly payment amount: $324 / $54 = 6. This means it will take Jason 6 weeks to pay off the home theater system on layaway.

The probability that at least one of the three children gets the disease from their mother is 97.3%.

To find the probability that at least one child gets the disease from their mother when a female carrier of the gene has three children, we can follow these steps:

1. Define the probabilities:

  - Probability that a child gets the disease from their mother (given): [tex]\( P(D) = 0.70 \)[/tex].

  - Probability that a child does not get the disease from their mother: [tex]\( P(D^c) = 1 - P(D) = 0.30 \)[/tex].

2. Identify the total number of children:

  - Number of children: [tex]\( n = 3 \)[/tex].

3. Calculate the probability that none of the children get the disease:

  - For all three children to not get the disease, the probability is [tex]\( (P(D^c))^n = (0.30)^3 \)[/tex].

4. Find the probability that at least one child gets the disease:

  - The probability that at least one child gets the disease is the complement of the probability that none of the children get the disease.

  - Thus, [tex]\( P(\text{at least one child gets the disease}) = 1 - P(\text{none of the children get the disease}) \)[/tex].

Let's do the calculations step by step.

Step-by-Step Calculations:

1. Calculate the probability that none of the children get the disease:

  [tex]\[ P(\text{none of the children get the disease}) = (P(D^c))^3 = (0.30)^3 \][/tex]

2. Perform the exponentiation:

  [tex]\[ (0.30)^3 = 0.30 \times 0.30 \times 0.30 = 0.027 \][/tex]

3. Calculate the probability that at least one child gets the disease:

  [tex]\[ P(\text{at least one child gets the disease}) = 1 - P(\text{none of the children get the disease}) = 1 - 0.027 = 0.973 \][/tex]

Conclusion:

The probability that at least one child gets the disease from their mother is [tex]\( 0.973 \)[/tex], or 97.3%.

Is there a viable solution when time is 30 minutes? Answer: No, the tub will be empty by then. 

A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute.

Let w be the quarts of water left in the tub.

Let t be the time in minutes.

So, the equation to model this situation is :

Modelling equation: [tex]w=50-2.5t[/tex]

This equation is viable only up to when t is 20 minutes. That will give w = 0. More than 20 minutes is not possible.