I need the steps to solve this question any help ​

The two x values that make up the equation's roots are:

x = [tex]\frac{5+\sqrt{13} }{2}[/tex]

x =[tex]\frac{5-\sqrt{13} }{2}[/tex]

These two items are the two answers to the problem.

A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

from the question:

We can use the quadratic formula to determine the roots of the equation [tex]x^2 - 5x + 3 = 0.[/tex]

x = (-b ± [tex]\frac{b^2 - 4ac}{2a}[/tex])

where the quadratic equation's coefficients are a, b, and c.

With respect to our equation, we have:

a = 1, b = -5, and c = 3

These values are entered into the quadratic formula as follows:

x = (-(-5) ± [tex]\sqrt(-5)^2}[/tex] - 4(1)(3))) / 2(1)

x = (5 ± [tex]\frac{{13}}{2}[/tex])

The two x values that make up the equation's roots are:

x = [tex]\frac{5+\sqrt{13} }{2}[/tex]

x =[tex]\frac{5-\sqrt{13} }{2}[/tex]

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Answer:

The function h(x) is defined as:

h(x) = { x + 4, if x < -3

{ 2x + 5, if x >= -3

To plot this function on the graph, you would plot the points (-4, 0) and (-3, -1) for the first part of the function, and then plot the line with slope 2 passing through the point (-3, 2) for the second part of the function.

Step-by-step explanation:

Answer:

Step-by-step explanation: 5.6 / 8 = 0.7

According to the definition of different number sets, 23 is an element of:

1) Natural number set

2) Whole number set

3) Integers set

4)Rational number set ( it can be written as 23/1)

A similar question is attached below.

What are the different number sets?

The different number sets are:

         Natural numbers are the collection of positive integers from 1 to infinity. The letter "N" stands for the set of natural numbers.

Natural numbers with a zero are another name for whole numbers. The set is made up of non-negative integers without any fractional or decimal parts. The letter "W" stands for the whole number set.

The set of all whole numbers with a negative set of natural numbers is known as an integer. The letter "Z" stands for the integer set.

Every integer that can be expressed as p/q, or as a ratio of one number to another, is referred to be a rational number. The letter "Q" can be used to signify a rational number.

The number that cannot be represented by p/q. It denotes a number as being irrational if it cannot be expressed as a ratio of one to another. The letter "P" is used to signify it.

Therefore according to the definition of different number sets, 23 is an element of:

1) Natural number set

2) Whole number set

3) Integers set

4)Rational number set ( it can be written as 23/1)

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The piecewise function graphed is given as follows:

A piece-wise function is a function that has different definitions, based on the input x of the function.

For this problem, the intervals are given as follows:

For the first interval, the interval is open due to the open circle, and the quadratic function is a translation up 4 units of y = x², hence^:

y = x² + 4, x < 2.

For the second interval, which is the closed interval, we have a decaying line with slope of -1 and x-intercept of 4, hence:

y = -x + b

0 = -4 + b

b = 4.

Hence:

y = -x + 4, x ≥ 2.

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Answer:

$13,500

Step-by-step explanation:

I = (P·r·t) / 100

I = (9,000·10·15) / 100

I = 1,350,000 / 100

I = $13,500

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Thanks.

The value of the length CE is 19.3 units

From the question, we have the following parameters that can be used in our computation:

The right triangle

Start by calculating the length AE using the following sine ratio

sin(B) = AE/AB

Substitute the known values in the above equation, so, we have the following representation

sin(40) = AE/50

So, we have

AE = 50 * sin(40)

Evaluate

AE = 32.14

From the figure, we can see that

Triangle CDE is 3/5 of triangle ABE

Using the above as a guide, we have the following:

CE = 3/5 * AE

So, we have

CE = 3/5 * 32.14

Evaluate

CE = 19.284

Approximate

CE = 19.3

Hence, the length is 19.3 units

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The probability that one client drives less than 10,000 miles a year and has an accident is 0.06.

Given is a table as shown in the image attached.

It is aske to find the probability that one client drives less than 10,000 miles a year and has an accident. Form the table, we can write the cell corresponding to driving less than 10,000 miles and having the accident as 0.06.

Therefore, the probability that one client drives less than 10,000 miles a year and has an accident is 0.06.

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The solution to the system of equations is x = 6 and y = 2.

The system of equations can also be solved using the elimination method.

We are aware that a system of linear equations is a collection of two or more equations with at least two unknown variables. Finding the answers to the unknown variables in a system of equations is the process of solving a linear equation. There are numerous ways to identify the answers to the unknown variables. These include the cross-multiplication method, elimination method, substitution method, and graphic method.

from the question:

A system of equations can be solved in a variety of methods, including substitution, elimination, and matrices. I'll apply the substitution technique here:

x = 8 - y is the result of the first equation.

We can solve for y by substituting this expression for x in the second equation:

-x + 4y = 2

-(8 - y) + 4y = 2 (substituting x = 8 - y)

-8 + 5y = 2 (simplifying)

5y = 10 (adding 8 to both sides)

y = 2 (dividing by 5)

Knowing y, we can now use this quantity to solve one of the initial equations to determine x:

x + y = 8

x + 2 = 8 (substituting y = 2)

x = 6 (subtracting 2 from both sides)

Hence, x = 6 and y = 2 are the answers to the system of equations.

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According to the calculation D(5) = 100, the price of 5 mangoes at the fresh market will be $1.00, or 100 cents.

Your example is an equation because a calculation is any formula with an equals symbol. Due to scientists' adoration of equal signs, equations are commonly used in mathematical expressions. A recipe is a collection of guidelines for producing a specific outcome.

The equation D(5) = 100 means that if you buy 5 mangoes at the fresh market, the cost will be 100 cents, or $1.00.

In general, the function D gives the cost (in cents) of buying M mangoes at the fresh market, so D(M) represents the cost of buying M mangoes. Therefore, D(5) means that we are evaluating the function D when M = 5, or when we buy 5 mangoes. The value of D(5) is 100 cents, or $1.00, which represents the cost of buying 5 mangoes at the fresh market.

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Answer: 81.75

Make 7 an improper fraction:

[tex]\frac{109}{12}[/tex] = [tex]\frac{k}{9}[/tex]

(9)(109) = 12k

981 = 12k

k = 81.75

 [tex]\frac{2}{5+\sqrt{3}}[/tex]  fraction can be simplified to [tex](10 - \sqrt{23}) / (22)[/tex] .

What are fractions?

A fraction is a number that represents a part of a whole. It consists of two numbers, a numerator and a denominator, separated by a horizontal or diagonal line. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts in the whole.

For example, 1/2 represents one part out of two equal parts, or one-half of the whole. Fractions can also represent values less than one, greater than one, or even negative values.

To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is 5 - 3^(1/2):

[tex]\frac{2}{5+\sqrt{3}}[/tex] * [tex]\frac{(5-\sqrt{3})}{(5-\sqrt{3})}[/tex]

=       [tex]\frac{2*(5-\sqrt{3})} {(5+\sqrt{3}) (5-\sqrt{3})}[/tex]

= [tex](10 - \sqrt{23}) / (25 - 3)[/tex]

= [tex](10 - \sqrt{23}) / (22)[/tex]

Therefore, [tex]\frac{2}{5+\sqrt{3}}[/tex] can be simplified to [tex](10 - \sqrt{23}) / (22)[/tex]

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Complete question:

simplify the given fraction [tex]\frac{2}{5+\sqrt{3}}[/tex]

Answer:

Below

Step-by-step explanation:

Where the graphs cross or touch each other is a solution.....see graph below   ....how many solutions do YOU see ?

Given that 17.5 is the bottom end of the box, the lower quartile's value equation (Q1) must fall between 17.5 and 30. Hence, the appropriate response is 17.5

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

25% of the data fall inside the lower quartile (Q1), which is represented by that number. Q1 is situated near the bottom of the box in the box plot.

According to the description, the box's boundary is at 30, and its size ranges from 17.5 to 40.5 on the number line. As a result, the median value of the middle 50% of the data is 30, with a range of 17.5 to 40.5.

There are some data points outside the middle 50% since the lines outside the box finish at 10 and 42.

Given that 17.5 is the bottom end of the box, the lower quartile's value (Q1) must fall between 17.5 and 30. Hence, the appropriate response is

17.5

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Answer:

To compute the probability that a person who tests positive actually has the disease, we need to use Bayes' theorem:

P(D|P) = P(P|D) * P(D) / P(P)

where:

P(D|P) is the probability of having the disease given a positive test result

P(P|D) is the probability of testing positive given that the person has the disease (also known as sensitivity), which is 1 - false negative rate = 0.92 in this case

P(D) is the incidence rate of the disease, which is 0.4% = 0.004

P(P) is the probability of testing positive, which can be computed using the false positive rate as 1 - specificity = 1 - 0.98 = 0.02

Plugging in the values, we get:

P(D|P) = 0.92 * 0.004 / 0.02 = 0.184

Therefore, the probability that a person who tests positive actually has the disease is 0.184, or about 18.4%.

The general format of the exponential expression is given as follows:

[tex]a^{\frac{n}{m}}[/tex]

In which:

The radical form is given as follows:

[tex]\sqrt[m]{a^n}[/tex]

Meaning that the equivalence relation is given as follows:

[tex]\sqrt[m]{a^n} = a^{\frac{n}{m}}[/tex]

That is:

Hence the relation for the cube root of 21 is given as follows:

[tex]\sqrt[3]{21} = 21^{\frac{1}{3}}[/tex]

(applying the conversion of the fractional exponent to a radical expression).

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Cοmparing the medians fοund using the given bοx plοt, we fοund that the median οf eighth graders is greater than the median οf the seventh graders.

A bοx and whisker plοt, οften knοwn as a bοx plοt, shοws a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary.

A bοx is drawn frοm the first quartile tο the third quartile in a bοx plοt.

At the median, a vertical line passes thrοugh the bοx. It is generally used tο shοw whether a distributiοn is skewed οr nοt and whether there are any pοtential οutliers, οr οdd οbservatiοns, in the data set.

When cοmparing οr invοlving numerοus data sets, bοxplοts are alsο highly helpful. Graphs can be used tο determine hοw widely the data values vary οr are spread οut.

Frοm the bοx plοt given, we can summarize the fοllοwing,

Fοr seventh graders,

The first quartile Q1 = 3

The third quartile Q3 = 4

Interquartile range = Q3 - Q1 = 4-3 = 1

The median = 3.5

Fοr eighth graders,

The first quartile Q1 = 3.5

The third quartile Q3 = 4.5

Interquartile range = Q3 - Q1 = 4.5 -3.5 = 1

The median = 4

Therefοre cοmparing the medians fοund using the given bοx plοt, we fοund that the median οf eighth graders is greater than the median οf the seventh graders.

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C. The diameter of a circle is two times the radius.

Answer: algebraic expression, coefficient

Step-by-step explanation:

The domain of the function shown on the graph is {-3, -2, 2, 3 }.

The domain of a function is the set of all possible input values (also known as the independent variable or x-values ) for which the function produces a valid output (also known as the dependent variable or y-values).

In other words, it is the set of values that can be plugged into the function to produce a meaningful result.

In this case, there are four (4) points on the graph.

The coordinates of the points are;

Since the domain are the set of the x-values, the domain of the function of the graph will be;

Domain : {-3, -2, 2, 3 }

Therefore, option B) {-3, -2, 2, 3 } is the correct answer.

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7 cm

im pretty sure u need to add more information to this question, but imma assume an answer

so if it's a square

21cm = 3xcm

7cm = xcm

so x = 7

The areas of triangles ABC are

12. The area is 4.8 cm²

13. The area is 61.4 m²

14.  The area is 9.0 ft²

The area of a triangle is the region occupied by the triangle.

12. Area of triangle ABC

Given that

Area of triangle ABC is A = 1/2bcsinA

= 1/2 × 7 cm × 4 cm × sin20°

= 7 cm × 2 cm × sin20°

= 14 cm² × sin20°

= 14 cm² × 0.3420

= 4.788 cm²

≅ 4.8 cm²

The area is 4.8 cm²

13. Area of triangle ABC

Given that

Area of triangle ABC is A = 1/2absinC

= 1/2 × 10 m × 15 m × sin55°

= 5 m × 15 m × sin55°

= 75 cm² × sin55°

= 75 cm² × 0.8192

= 61.436 cm²

≅ 61.4 cm²

The area is 61.4 cm²

14. Area of triangle ABC

Given that

Area of triangle ABC is A = 1/2acsinB

= 1/2 × 3 ft  × 9 ft × sin42°

= 1/2 × 27 ft² × sin42°

= 13.5 ft² × sin42°

= 13.5 ft² × 0.6691

= 9.033 ft²

≅ 9.0 ft²

The area is 9.0 ft²

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Answer:

  π/4, 7π/4

Step-by-step explanation:

You want the values of θ in the range 0 ≤ θ ≤ 2π such that cos(θ) = √2/2.

The cosine function has the value √2/2 for angles ±45° = ±π/4 radians and those angles added to an integer multiple of 2π. In the domain of interest, the angles are ...

  θ = π/4 and 7π/4

The possible values of b are 1/10, 1/2, 9/12, here we have to learn graph of a function. Diagram of question given below.

The graph of a function f in mathematics is the collection of ordered pairs where display style f(x)=y. These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the typical situation when x and f(x) are real integers.

Subset, If every element of a set P is also an element of a set Q, then set Q is a superset of set P and set A is a subset of set Q. P and Q might be equal; if not, then P is a legitimate subset of Q.

Here, when [tex]b=0,\ f(x) = a*0^{x} = 0[/tex]

[tex]b=1,\ f(x)=a*1^{x} = a[/tex]

[tex]b > 1,\ f(x)=a*b^{x}[/tex]

[tex]a < b < 1,\ f(x) = a*b^{x}[/tex]

[tex]So, b\in(0,1)=b=\frac{1}{10} ,\frac{1}{2} ,\frac{9}{10}.[/tex]

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Answer:

(-3,0), (1,0)

Step-by-step explanation:

The x-intercept is when the y = 0

In the graph, we see the line cross through the x-axis located at (-3,0), (1,0)

So, the x-intercepts are located at (-3,0) and (1,0)

Answer:

x intercepts are 1 and -3

Step-by-step explanation:

X intercepts are obtained by looking at a point where the parabola touches the x axis

The measure of data that must represent a number in the set that is greater than 2 of the numbers in the set and less than 2 of the numbers is the median.

The median is the middle value in a set of data when the values are listed in order from least to greatest (or greatest to least). If there are an odd number of values in the set, the median is the middle value. If there are an even number of values in the set, the median is the average of the two middle values.

If a number in the set is greater than 2 of the numbers and less than 2 of the numbers, then it falls between the first and last quartile of the data set. Therefore, the median, which represents the middle value in the data set, must also fall between the first and last quartile, and thus it must represent a number in the set that is greater than 2 of the numbers and less than 2 of the numbers.

A geometric series is an expression that results from adding all the elements in a geometric order. The right answer is B.

A geometric series is an expression that results from adding all the elements in a geometric order.

The given series is a geometric series in the form , where

Now, the geometry series' total can be expressed as,

[tex]\begin{aligned}\text { Sum } & =\mathrm{a}_1 \frac{\left(1-\mathrm{r}^{\mathrm{n}}\right)}{(1-\mathrm{r})} \\& =6 \frac{\left(1-0.6^5\right)}{(1-0.6)}\end{aligned}[/tex]

Hence, the correct option is C.

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Answer:

Plot the temperature on the x-axis and the water consumption on the y-axis.

For each day, plot a point on the scatter plot with the temperature and water consumption values.

Use a regression tool or calculate the slope and intercept of the line of best fit manually.

Draw a straight line through the data points that represents the trend in the data.

The equation for the line of best fit can be used to make predictions about water consumption given a certain temperature.

Step-by-step explanation:

The scatter plot shows that there is a positive relationship between temperature and water consumption.

Here is the scatter plot of the data:

Temperature (°F) | Water Consumption (fl. oz.)

------- | --------

75 | 12

80 | 15

85 | 18

90 | 21

95 | 24

100 | 27

The line that is closest to all of the data points is a line with a positive slope. This means that as the temperature increases, the water consumption also increases. The line does not perfectly fit all of the data points, but it does a good job of capturing the general trend.

Here is an explanation of how to interpret the scatter plot:

The points that are closer to the line indicate that the relationship between temperature and water consumption is stronger for those points.

The points that are further away from the line indicate that the relationship between temperature and water consumption is weaker for those points.

The line itself indicates the general trend of the data.

In this case, the line indicates that as the temperature increases, the water consumption also increases. However, there are some points that do not follow this trend. For example, the point at 95°F has a water consumption of 24 fl. oz., which is lower than the water consumption for the points at 90°F and 100°F. This suggests that there may be other factors that affect water consumption, such as the humidity or the activity level of the person.

Overall, the scatter plot shows that there is a positive relationship between temperature and water consumption. However, there are some points that do not follow this trend, which suggests that there may be other factors that also affect water consumption.

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Answer:

Step-by-step explanation:

[tex]C=\pi d[/tex]

   [tex]=\pi \times 35[/tex]

   [tex]\approx 109.96 feet[/tex]

Answer:

110. feet approximately

Step-by-step explanation:

circumference means a closed boundary of a curved shape. Mainly known as a circle. To find circumference, use the formula c= π (pie) times diameter.

35 × π ≈ 110

Hope this helps :)

The likelihood that someone with symptoms and a positive test has hepatitis is therefore 0.994, or almost 99.4%.

We need to apply Bayes' theorem to determine the likelihood that a person with symptoms and a positive test actually has hepatitis. Let H stand for the occurrence that the person has hepatitis and T stand for the occurrence that the test is positive. Next, we have:

P(T | H) * P(H) / P(T | H) = P(H | T) (T)

where P(H) is the prior probability of the individual having hepatitis (which is 0.8), P(H) is the likelihood of the individual testing positive, and P(T) is the probability of testing positive given that the individual has hepatitis.

We must apply the law of total probability to determine P(T):

P(T) is equal to P(T | H)* P(H) plus P(T | not H)* P. (not H)

P(T | not H) is the complement of P(H), and P(not H) is the probability of testing positive if the person does not have hepatitis (0.05). (i.e., the probability of not having hepatitis, which is 0.2).

Now that the values have been inputted, we can calculate:

P(T) = (0.94 * 0.8) + (0.05 * 0.2) = 0.752 P(H | T) = (0.94 * 0.8) / 0.752 = 0.994

Although there is a strong likelihood that this is the case, it's crucial to remember that no medical test is error-free, and false positives and false negatives can still happen.

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