Determine the discriminant for the quadratic equation 0 = –2x2 + 3. Based on the discriminant value, how many real number solutions does the equation have?

Discriminant = b2 – 4ac


real number solutions

The inequality representing '15 is no more than a number T divided by 5' is written as 15 <= T/5, which means T divided by 5 should be greater than or equal to 15.

The phrase '15 is no more than a number T divided by 5' can be translated into an inequality. When we interpret 'no more than', it means 'less than or equal to'. Therefore, the statement can be translated into the inequality 15 <= T/5. This expresses that when you divide the number T by 5, the result should be at least 15 or any value less than 15. The interpretation of "no more than" as "less than or equal to" clarifies the inequality's meaning, emphasizing that the resulting quotient from dividing T by 5 should not exceed 15. Thus, the inequality encapsulates the relationship between the number 15 and T when considering their division by 5.

Answer:

5 weeks 2 days

Step-by-step explanation:

A certain plant grows every week = [tex]1\frac{1}{6}[/tex] = [tex]\frac{7}{6}[/tex] inches

1 week = 7 days

Therefore in 1 day the plant grows = [tex]\frac{\frac{7}{6}}{7}[/tex]

                                                         = [tex]\frac{1}{6}[/tex] inch

Now we have to calculate number of days in which the plant grows  [tex]6\frac{1}{6}[/tex] inches ≈ [tex]\frac{37}{6}[/tex] inch

Number of days = [tex]\frac{\text{Total growth}}{\text{Growth in one day}}[/tex]

                           = [tex]\frac{37}{6}[/tex] ÷ [tex]\frac{1}{6}[/tex]

                           =  [tex]\frac{37}{6}[/tex] × 6

                           = 37 days ≈ 5 weeks and 2 days

It will take the plant 5 weeks 2 days to grow [tex]6\frac{1}{6}[/tex] inches.

Answer:

The rate of the area increasing for square is 24cm²/ s

            Rate of increasing side ?

    Changing the length of side with respect to time is the rate of increasing side .

    Given each side of square is increasing at a rate 3cm/s.

          Area of square = sides²

           Side length = a

       (dA/dt) = (dA/da)×(da/dt) { chain rule of differentiation}

             Differentiation of area w.r.t. t is

                dA/da= 2a (da/dt)

                dA/dt = 2a *(da/dt)

                 da/dt = 3 cm/s

              When A=16 cm²

                      16 = a²

                         a= 4

                (dA/dt) = 2x4 x 3

                           = 24 cm²/ s

Hence, the rate of the area increasing for square is 24cm²/s

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The solution after divide is,

⇒ 0.893

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

To divide the numbers,

⇒ 25 divided by 28

Now, We can divide the numbers as;

⇒ 25 divided by 28

⇒ 25 ÷ 28

⇒ 25 / 28

⇒ 0.893

Thus, The solution after divide of the numbers is,

⇒ 0.893

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[tex]\boxed{{\mathbf{40\% }}}[/tex] of the first 10 natural numbers are prime numbers.

Further explanation:  

The prime numbers are the numbers that is only divisible by 1 and itself and greater than 1.

Natural numbers are the numbers that is easily countable as their successors can be defined and its starts from 1.

The natural number can be expressed as,

[tex]1,2,3,4,5,6,7,8,9,10 \ldots[/tex]  

Step by step explanation:

Step 1:

First determine the first ten natural numbers.

[tex]1,2,3,4,5,6,7,8,9,10[/tex]  

Step 2:

Now determine the prime numbers among the first ten natural numbers.

The prime numbers among the first ten natural number are [tex]2,3,5,7[/tex].

Therefore, there are 4 prime numbers.

Step 3:

Now, find the percentage of the first 10 natural numbers are prime numbers.

In general the percentage of any number can be calculated as,

[tex]{\text{percent of  }}x = \dfrac{x}{{{\text{total number}}}} \times 100[/tex]  

The percentage of the prime numbers can be calculated as,

[tex]\begin{aligned}{\text{percent of  prime number}}& = \frac{4}{{{\text{10}}}} \times 100\\ &= 40\% \\\end{aligned}[/tex]  

Therefore, [tex]40\%[/tex] of the first 10 natural numbers are prime numbers.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Percentage

Keywords: Integers, expression, natural numbers, prime numbers, percentage, denominator, numerator, fractions, divisible, total number, the required number

xm-2m

x=-2, m = -3

xm = -2 *-3 = 6

2m = 2*-3 = -6

6- -6 = 6+6 = 12

The proportion form of Newton’s second law is when finding the acceleration of a problem as this is the equation suitable of finding the acceleration and to be able to compute the missing answer to the problem. In the form of the equation, it is ‘a + f / m’.

Decimals can be found in various sources including the internet, and they are used in everyday activities like shopping online. The word problem involves a book sale where a discount is given in decimal form.

Decimals are usually found in various sources such as newspapers, magazines, television, and predominantly on the internet. For example, when we read about the latest international currency exchange rates or the percentage rates in the stock market, we encounter decimals.

Let's create a real-world problem involving decimals: Sam is browsing a popular online bookstore. He found a book he wanted to buy for $5.49. However, there is a pop-up stating that for today only, all books are discounted by 0.15 (or 15%). How much would the book cost after the discount?

To find the solution, subtract the discount from the original price in decimal form i.e., $5.49 * 0.15 = $0.82 (approx). Then subtract this amount from the original price, $5.49 - $0.82 = $4.67. So, Sam will pay $4.67 for the book after discount.

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Final answer:

The donations in 2012 had a more dispersed distribution than in 2013, as indicated by a higher coefficient of variation of 20% compared to 15% in 2013.

Explanation:

To determine which year had a more dispersed contribution distribution, we examine the coefficient of variation (CV), which is calculated by dividing the standard deviation by the mean and then multiplying by 100 to express it as a percentage. A higher CV indicates a more dispersed distribution.

For 2012:

For 2013:

Comparing the coefficients of variation, we can conclude that the donations in 2012 had a more dispersed distribution than in 2013 since the CV in 2012 was higher.

The mean travel distance for the sample of 100 customers surveyed by the manager at First City Bank is considered a statistic.

The mean travel distance for the sample of 100 customers surveyed by the manager at First City Bank is considered a statistic.

In statistics, a parameter is a numerical characteristic of the whole population that can be estimated by a statistic. Since the manager is surveying only a sample of customers, the mean travel distance calculated from this sample is a statistic, not a parameter.

For example, if the manager had surveyed all customers of First City Bank, then the mean travel distance calculated from that data would be a parameter.

Infinite is the answer

To find out how many DVDs you can buy for the same price at both stores, you create a formula incorporating the cost per DVD and the shipping cost at the online store. Solving this equation will give you the number of DVDs where the cost will be equal at both stores. However, this might not always result in a whole number, indicating that there is no exact count of DVDs resulting in the same cost.

To determine how many DVDs you can buy for the same amount at both stores, you can set up a mathematical equation accounting for the cost of each DVD and the shipping cost in the online store. The equation would look like this:

15.49 x = 13.99 y + 6

where x and y represent the number of DVDs bought from the local and online store respectively. By solving this equation we're finding out for which number of DVDs the total costs at both stores are equal.

To find the exact number of DVDs where the total cost will be the same, the equation needs to be solved for a whole number. This may result in no exact integer solution, showing that there's no exact number of DVDs for which the cost will be the same at both stores.

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