What’s 14/15 divided by 7

The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

What is the discriminant of a polynomial?

The discriminant of a polynomial is a function of its coefficients and is represented by the capital ‘D’ or Delta symbol (Δ). It shows the nature of the roots of any quadratic equations where a, b, and c are real numbers.

It is represented as ‘D’

D = b² - 4ac

Where,

a is the coefficient of x²

b is the coefficient of x

c is a constant term

x² + 5x + 4 = 0

We have given:

x² + 5x + 4 = 0

Comparing the equation with the standard form.

a = 1, b = 5 and c = 4

Substituting it in the formula

D = 5² - 4 × 1 + 4

By further calculation

D = 25 - 16

D = 9,

The quadratic roots are real and distinct

Therefore, the value of b² - 4ac is 9.

Hence, The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

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Step-by-step explanation:

\(2 + 8(x + 2) = 52 \)

\(2 + 8x + 16 = 52\)

\(8x + 18 = 52\)

\(8x = 52 - 18\)

\(8x = 32\)

\(x = \frac{34}{8} \)

\(x = 4.25\)

Hope it helps u

Answer?

Step-by-step explanation:

The solution to the IVP is: y(t) = 2e^t - 2e^(t/2). The critical point of the differential equation where the maximum value occurs is y(6) = 2e^6 - 2e^(3).  The point where the solution y(t) is zero is t = 4.

The given problem involves solving the initial value problem (IVP) for the second-order linear homogeneous differential equation 2y" - 3y' + y = 0 with initial conditions y(0) = 2 and y'(0) = 12.

(a) By solving the differential equation using the characteristic equation method, we find the general solution y(t) = c1e^t + c2e^(t/2).

Applying the initial conditions, we determine the specific values of c1 and c2 to obtain the particular solution y(t) = 2e^t - 2e^(t/2).

(b) To find the maximum value of the solution in exact form, we take the derivative of y(t) with respect to t, set it equal to zero, and solve for t.

Substituting the value of t obtained into the equation y(t), we determine the maximum value to be y(6) = 2e^6 - 2e^(3).

(c) To find the point where the solution is zero, we set y(t) equal to zero and solve for t. Substituting y(t) = 0 into the equation y(t), we determine the point to be t = 4.

We find the particular solution to the given second-order differential equation with the provided initial conditions.

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Answer:

45

Step-by-step explanation:

Answer: x can equal 9 or -1

Step-by-step explanation:

\(\\ \sf\longmapsto \dfrac{21.5}{5}-\dfrac{1}{5}\times (20.5-5.5)+5.5(8)\)

\(\\ \sf\longmapsto 4.3-0.2\times 15+44\)

\(\\ \sf\longmapsto 1.3+44\)

\(\\ \sf\longmapsto 45.3\)

Probability refers to the measure of the likelihood or chance of an event occurring, expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty.

To find the probability that the driver will find the second traffic light green, we need to make an assumption that the probability of each traffic light being green is independent of the other traffic lights. This means that the probability of finding the second traffic light green is the same as the probability of finding the first traffic light green.

Since the probability of finding the first green light is given as 0.56, the probability of finding the second green light is also 0.56.

Therefore, the probability that the driver will find the second traffic light green is 0.56.

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Step-by-step explanation:

Each of the printing companies have their own advantages. APlus Printing has a lower setup fee and PrintMore has a lower cost for each poster printed. We can find out at what number of posters are the 2 costs the same.

Let x be the number of posters.

We have $20 + $0.1x = $55 + $0.05x.

=> $0.05x = $35

=> x = 700

Hence we can give a conclusion:

c) 84%

hope this helps :)

85% of take-home pay is spent on expenses option (D)85% is correct.

It is given that in the chart there are various expenses.

It is required to find the percentage of take-home pay is spent on expenses.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

We have a total take-home salary = $5388

Total expenses = $4558

In percentage it can be expressed as follows:

\(=\frac{4558}{5388}\times100\)

\(=0.84595\times100\\\\= 84.595 \ \%\)

or ≈ 85%  (round to nearest whole)

Thus, 85% of take-home pay is spent on expenses.

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The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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Answer:

Step-by-step explanation:

its the 3rd option

Answer:

c

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

They are not equivalent fractions

Answer:

No, they are not equivalent

Step-by-step explanation:

Answer:

a) Slave labor was needed for the economy.

Step-by-step explanation:

Slave labor was needed for the economy of the southern states during the early 1800’s. Hence, the option (a) is correct.

Answers:

Each answer has 7 as the base and a fraction as an exponent.

==========================================================

Explanation:

One useful rule here is that \(\sqrt[n]{x^m} = x^{m/n}\). The fraction m/n is the exponent for the base x. Note how the index of the root (n) becomes the denominator of the fraction m/n. So for example if we had n = 3, then we'd be dealing with a cube root.

For part a), we have x = 7, m = 1 and n = 5 to get

\(\sqrt[n]{x^m}=x^{m/n}\\\\\sqrt[5]{7^1}=7^{1/5}\\\\\sqrt[5]{7}=7^{1/5}\\\\\)

-----------------

Part b) is the same idea

We would find that

\(\sqrt[n]{x^m}=x^{m/n}\\\\\sqrt[7]{7^1}=7^{1/7}\\\\\sqrt[7]{7}=7^{1/7}\\\\\)

Then apply the reciprocal to both sides. This is the same as raising both sides to the exponent -1

\(\sqrt[7]{7}=7^{1/7}\\\\\left(\sqrt[7]{7}\right)^{-1}=\left(7^{1/7}\right)^{-1}\\\\\frac{1}{\sqrt[7]{7}}=7^{1/7*(-1)}\\\\\frac{1}{\sqrt[7]{7}}=7^{-1/7}\\\\\)

You could also use the rule that x^(-y) = 1/(x^y) when dealing with negative exponents.

In the second to last step shown above, I used the rule (x^y)^z = x^(y*z) on the right hand side.

The inverse of (- 2 . 3 ) is (1 / - 2.3 ).

In mathematics, the inverse of a number refers to the concept of taking its reciprocal; for instance (2 . w ) results in its reciprocal as ( 1/ 2. w ). When a number is multiplied by its inverse the result yields 1, meaning that the product of the number and its inverse, i.e. reciprocal always equals 1.

As per the given number which is (-2.3) and its inverse is ( 1 / -2.3 ), when these two numbers are multiplied together they result in 1. Such as:

(-2.3) x ( 1 / -2.3 ) = 1

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Creative objectives for therapy with troubled middle school children can include fostering self-expression, promoting emotional regulation, and building social skills.

Self-Expression: Encouraging self-expression through creative activities like art, music, or creative writing can be a therapeutic objective. Providing a safe space for children to express their thoughts, emotions, and experiences can help them develop a better understanding of themselves and their feelings. Emotional Regulation: Using creative outlets to teach and practice emotional regulation skills can be beneficial. Incorporating activities like mindfulness exercises, guided imagery, or drama therapy can help children learn to identify and manage their emotions in a healthy way. Engaging in creative activities allows them to explore and process their feelings in a non-threatening and enjoyable manner.

Social Skills Development: Creative objectives can also focus on improving social skills and interpersonal interactions. Group activities like improvisation, role-playing, or collaborative art projects provide opportunities for children to practice communication, empathy, teamwork, and conflict resolution. Engaging in these activities within a therapeutic context allows children to learn and apply social skills in a supportive environment.

By incorporating creative objectives into therapy for troubled middle school children, therapists can provide a platform for self-expression, emotional regulation, and social skills development. These objectives help children develop coping strategies, enhance self-awareness, and improve their overall emotional well-being. Moreover, creative therapy allows for a more engaging and enjoyable therapeutic experience, making it easier for children to open up, explore their inner world, and develop resilience.

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Answer:the third one

Step-by-step explanation:

Answer: x5/6+2x7/3

Step-by-step explanation:

I took the test

If there is no difference between sample and population values, then you have no sampling error. This is because sampling error refers to the difference between the sample value and the population value. Alternative a. is correct.

Population refers to a complete set of elements or individuals that share a common characteristic and are to be studied. On the other hand, a sample is a selected subset of the population, which is used to make a statistical inference about the population.

If there is no difference between the two, then there is no sampling error. This means that the sample accurately represents the population and there is no need for further sampling or adjustment. Consequently, alternative a. is correct.

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Answer:

(h, k). (2,0)

Triangle LRG is similar to triangle CNP. Therefore, the following ratios apply;

Hence, for triangle LRG to be dilated to become CNP,

Therefore, the scale factor needed to dilate triangle LRG so that its image is congruent to triangle CNP is 1.5 (that is the decimal equivalent of 3/2)

This means triangle LRG would be multiplied by 1.5 in order to have an image congruent to triangle CNP

Using proportions, it is found that the total cost for beverages will be of $552.00.

A proportion is a fraction of a total amount.

In this problem, there will be a total of 46 people, and each will spend $12.00 on beer and wine, hence:

46 x $12.00 = $552.00.

The total cost for beverages will be of $552.00.

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The probability that no one enters between 12:00 and 12:05 is 0.082.

The probability that at least 4 people enter the casino during that time is 0.242

Given that people enter the casino at the rate of 1 every 2 minutes. A random variable X is defined as the number of people entering the casino between the time period of 12:00 and 12:05. Since we are given in the question that people enter the casino at the rate of 1 every minute, hence in the given time period they enter at the rate of 2.5.

P(X=0) = \(e^{-2.5}\) = 0.082

Hence the probability that no one enters between 12:00 and 12:05 is 0.082.

The required probability is simply

P(X≥4) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3)

= 1 - \(e^{-2.5}\) - 2.5\(e^{-2.5}\) - (((2.5)² / 2)\(e^{-2.5}\) ) - (((2.5³)/3!)\(e^{-2.5}\))

= 0.242

Hence, the probability that at least 4 people enter the casino during that time is 0.242

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The value of x for the length A'E' of the similar shape A'B'C'D'E' is equal to 6⅔.

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other.

The side A'E' corresponds to the side A'E' and also E'D' corresponds to the side ED so;

(7). A'E'/AE = E'D'/ED

x/10 = 6/9

x = (10 × 6)/9 {cross multiplication}

x = 20/3

x = 6⅔

Therefore, the value of x for the length A'E' of the similar shape A'B'C'D'E' is equal to 6⅔

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Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

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Answer:

Calculate the x distance from A to B and the x distance from A to X and verify that the x distance from A to X is 1/3 of the x distance from A to B.

Calculate the y distance from A to B and the y distance from A to X and verify that the y distance from A to X is 1/3 of the y distance from A to B.

Step-by-step explanation:

The correct answer is: B) cos 2t

We can use the double angle identity for cosine, which states that:

cos(2t) = \(cos^2(t) - sin^2(t)\)

Rearranging and substituting 1 - cos^2(t) for sin^2(t), we get:

cos(2t) =\(cos^2(t) - (1 - cos^2(t)) = 2cos^2(t) - 1\)

Therefore, we can rearrange 2cos(2t) - 1 in terms of cos(2t) as:

\(2cos(2t) - 1 = 2cos^2(t) - 1\) = cos(2t)

This means that the expression 2cos(2t) - 1 is equal to the cosine of twice the angle t, which is option B.

Note that the other options involve the sine function or the negative of cosine, so they are not equal to 2cos(2t) - 1 for all values of t.(option-b)

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The expression 2cos2t-1 is equal to -4sin^2(t) + 1.

The expression 2cos2t-1 can be simplified using the double angle formula for cosine, which states that cos(2t) = cos^2(t) - sin^2(t). By substituting this equation into the expression, we get:

2cos2t-1 = 2(cos^2(t) - sin^2(t)) - 1 = 2cos^2(t) - 2sin^2(t) - 1.

We can further simplify by using the Pythagorean identity, which states that sin^2(t) + cos^2(t) = 1. By rearranging this equation, we get cos^2(t) = 1 - sin^2(t). Substituting this into the expression, we have:

2cos2t-1 = 2(1 - sin^2(t)) - 2sin^2(t) - 1 = 2 - 2sin^2(t) - 2sin^2(t) - 1 = -4sin^2(t) + 1.

Therefore, the expression 2cos2t-1 is equal to -4sin^2(t) + 1.

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The value of the quantity d is 0.0462 m^2/s.

Here,

The quantities a=3.7m, b=3.7s, c=80m/s.

We have to find the value of d = a^3/cb^2

What is quantity?

A quantity is an amount, number, or measurement that answers the question 'how much?' Quantities can be expressed in numbers or non-standard units.

Now,

The quantities a=3.7m, b=3.7s, c=80m/s.

The value of d;

\(d = \frac{a^{3} }{cb^{2} }\)

\(d = \frac{3.7*3.7*3.7 }{80 * 3.7^{2} }\)

\(d = \frac{3.7}{80}\)

\(d = 0.0462\)

Hence, The value of the quantity d is 0.0462 m^2/s.

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An observation that causes the values of the slope and the intercept in the line of best fit to be considerably different from what they would be if the observation were removed from the data set is said to be an outlier.

An outlier is an observation that is significantly different from other observations in a dataset. It is a data point that is located far away from the other data points, and it may have a disproportionate influence on the analysis and conclusions drawn from the data.

what is slope?

Slope is a measure of the steepness of a line. It is calculated as the change in the y-coordinate (vertical change) divided by the change in the x-coordinate (horizontal change) between two points on the line. The slope represents the rate at which the line is rising or falling.

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Answer:

When you fold the number line ( vertically through the point zero on the number line ) you have successfully divided the number line into 2 equal halves.

Step-by-step explanation:

When you fold the number line ( vertically through the point zero on the number line ) you have successfully divided the number line into 2 equal halves. and this causes the points labelled on either side of the number line  to match up with with the points on the opposite side