Solve the quadratic equation by using either a numeric or a graphic approach.
x squared minus 14 x minus 49 = 0
a.
x = -11.1 or x = -12
c.
x = 16.9 or x = -2.9
b.
x = 12.3 or x = -10.82
d.
x = 1 or x = -3

Answer:

\(\frac{x+4}{3(x-1)}\)

\(x^2/x-1/3x^2/x+4\)

This can be written as a/b * d/c using the KCF method, which stands for keep, change, flip when dividing fractions. You keep the first fraction, change the sign from divide to multiply, and flip the last fraction.

For example:

4/5 / 6/7 =

4/5 * 7/6

28/30

14/15

\(\frac{x^2}{x-1} * \frac{x+4}{3x^2}\)

Next, multiply top and bottom to combine the fractions.

\(\frac{x^3+4x^2}{3x^3-3x^2}\)

Factor \(x^2\) out of \(x^3 + 4x^2\).

\(\frac{x^2(x+4)}{3x^3-3x^2}\)

Factor  \(3x^2\)  out of \(3x^3-3x^2\).

\(\frac{x^2(x+4)}{3x^2(x-1)}\)

Cancel out \(x^2\) from top and bottom.

\(\frac{x+4}{3(x-1)}\)

Answer:

angle k and n are adjacent to angle j

Time series analysis is a statistical technique used to analyze time series data, which is data that is collected over time. Time series data can be used to make forecasts, identify trends, and detect patterns in the data.

When the relationship between the independent and dependent variables is not expected to remain constant, an appropriate method of analysis is time series analysis.
Time series analysis is useful when the relationship between the independent and dependent variables is not expected to remain constant over time. This can occur for a variety of reasons, such as changes in consumer behavior, changes in market conditions, or changes in the economy.
Time series analysis involves the use of statistical techniques such as trend analysis, seasonal analysis, and cyclical analysis. These techniques are used to identify patterns in the data and to make predictions about future trends.
Trend analysis is used to identify long-term trends in the data. Seasonal analysis is used to identify seasonal trends in the data, such as fluctuations in sales during the holiday season. Cyclical analysis is used to identify cyclical patterns in the data, such as the business cycle.
Time series analysis is a powerful tool that can be used to make forecasts and to identify trends in the data. It is particularly useful when the relationship between the independent and dependent variables is not expected to remain constant over time. By identifying patterns in the data, time series analysis can help businesses and individuals make more informed decisions.

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3x - 8y = 19

3x + 5y = -46

As you can see in the image below the solution of the system of equations is (-7,-5).

Answer:

8x+5005073

Step-by-step explanation:

Answer:

Step-by-step explanation:

L = 3x

w = 2x

Area = 294 ft^2

Formula

Area = L * w

Solution

Area = L * w                   Substitute into formula

294 - 3x  *   2x              Combine the right and switch

6x^2 = 294                    Divide by 6

x^2 = 294/6

x^2 = 49                         Take the square root of both sides

√x^2 = √49

x = 7

w = 2*7 = 2x = 14

L  = 3*7 = 3x  =21

Answer:B

Step-by-step explanation:

Answer:

\(x^2-10x+8=0\)

Step-by-step explanation:

\(\frac{1}{x} +\frac{1}{x-2}=\frac{1}{4} \\\\\frac{x-2+x}{x(x-2)} = \frac{1}{4} \\\\\frac{2x-2}{x(x-2)}=\frac{1}{4} \\\\4(2x-2)=x(x-2)\\8x-8=x^2-2x\\0=x^2-2x-8x+8\\0=x^2-10x+8\\x^2-10x+8=0\\\)

Using the least common denominator in simplifying the rational equation, the result of in standard form is: \(\mathbf{x^2 -10x + 8 = 0}\)

Given:

\(\frac{1}{x} + \frac{1}{x - 2} = \frac{1}{4}\)

The least common denominator of the two fractions on the left side of the equation is x(x - 2).

Thus:

\(\frac{1(x - 2) + x(1)}{x(x - 2)} = \frac{1}{4}\\\\\frac{x - 2 + x}{x(x - 2)} = \frac{1}{4}\\\\\frac{2x - 2}{x^2 - 2x)} = \frac{1}{4}\)

\(4(2x + 2) = 1(x^2 - 2x)\\\\8x + 8 = x^2 - 2x\\\\\)

\(0 = x^2 - 2x - 8x + 8\\\\0 = x^2 -10x + 8\\\\\mathbf{x^2 -10x + 8 = 0}\)

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Answer: use subtraction

Step-by-step explanation:   u welcome

Answer:

no solution.

Step-by-step explanation:

Lines are parallel ,so they do not cut at any point.Hence no solution.

Answer:

B

Step-by-step explanation:

calculate the distance between A and B using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = A (1, 6 ) and (x₂, y₂ ) = B (x, - 2 )

d = \(\sqrt{(x-1)^2+(-2-6)^2}\)

   = \(\sqrt{(x-1)^2+(-8)^2}\)

   = \(\sqrt{(x-1)^2+64}\)

given AB = 10, then equating gives

\(\sqrt{(x-1)^2+64}\) = 10 ( square both sides to clear the radical )

(x - 1)² + 64 = 10² = 100 ( subtract 64 from both sides )

(x - 1)² = 36 ← take square root of both sides

x - 1 = ± \(\sqrt{36}\) = ± 6 ( add 1 to both sides )

x = 1 ± 6

then

x = 1 - 6 = - 5

x = 1 + 6 = 7

from the list then x = - 5 is a possible value

Note that the Absolute Values of the above numbers will be:

5,4,3,2,1,0,1,2,3,4,5. Since positive values cannot be represented on the Negative spectrum of the Coordinate system, we are left with 0,1,2,3,4,5 which means is represented by 0 ≤ x ≤ 5. See the attached Number Line.

A number line is a graphical representation of numbers on a line, where each point corresponds to a unique real number. It is important for understanding numerical concepts and operations visually.

The absolute value of a number is the distance of the number from zero, regardless of its sign. It is represented as a positive number and is important for understanding the magnitude of a quantity or a distance between two points on a number line.

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The standard error of estimate in a simple linear regression is equal to: a) the square root of the mean squared error.

Standard error of estimate simply refers to the amount of mistake that can be seen when the estimate from the regression analysis is utilized instead of the actual data, and a small estimate error is not necessarily a bad thing.

A. The assumption about errors at different levels is that the variance between two errors is the same as the variance between two other errors. The variance basically refers to the residual. The standard error is computed assuming homoskedasticity, that is, the constant variance of the error terms.

B. The standard error of the estimate is a way to measure the accuracy of the predictions made by a regression model.

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The correct answer is: 4.75; a puppy who is just born is predicted to weigh 4.75 ounces.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The equation of the line of fit is w = 4.75 + 0.5d, where w is the weight of the puppy in ounces and d is the age of the puppy in days.

The w-intercept of the line of fit is the value of w when d = 0, that is, the predicted weight of a puppy when it is just born.

From the equation, we see that when d = 0, we have:

w = 4.75 + 0.5(0) = 4.75

Therefore, the w-intercept of the line of fit is 4.75 ounces, and its meaning in terms of the scenario is that a puppy who is just born is predicted to weigh 4.75 ounces.

So, the correct answer is: 4.75; a puppy who is just born is predicted to weigh 4.75 ounces.

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The area of the figure can be obtained by splitting the figure into smaller components

The area of the irregular figure = Area of A + Area of B + Area of C

Area of A = L X B = 12 x 7 = 84 sq meters

Area of B = L X B = 5 X 8 = 40 sq meters

Area of C = L X B = 5 x 8 = 40 sq meters

Total area = 84 + 40 + 40 = 164 sq meters

For the given equation, we will find the value of (a) to find the equivalent equations.

First equation:

Second equation:

Third equation:

Fourth equation:

As shown all the equations given the same value of a = 3

So, the answer will be Y

Answer:

4 and 5

Hope this helps!-xoxo

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Answer:

It equal

Step-by-step explanation:

Answer:

x = 50 minutes

Step-by-step explanation:

GIven:

Container A contain = 800 mL

Container B contain = 1,000 mL

Container A leak = 6 mL per min

Container B leak = 10 mL per min

Computation:

Assume; in x minute

So,

800 - 6x = 1,000 - 10x

4x = 200

x = 50 minutes

The number of men living in the village is 260.

A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:

                                           \(ax + by = c\)

Given:

Total inhabitants in the village: 817

Number of children: 241

There are 56 more women than men in the village

Total adults = Total inhabitants - Number of children

Total adults = 817 - 241

Total adults = 576

Let number of men in the village be 'x' and number of women in the village be 'y',

∴ y=x+56 (given) ..................(1)

Also, x+y=576 .................(2)

From equation (1) and (2),

x + (x + 56) = 576

2x + 56 = 576

2x = 576 - 56

2x = 520

x = 520 / 2

x = 260

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Answer:

63

Step-by-step explanation:

C=diameterxpi

or C=radius x 2 x pi

the radius is half of diameter so simplify to C=diamerter x pi

C=20x3.14

C=62.8

Answer:

c?.... 23 is the closest to 20...

Step-by-step explanation:

~one variable linear equation

4t = -10

t = -10 ÷ 4

t = -2,5 ✔️

So, the answer is -2,5 no 2,5

~ nice to help you ^^

The pair (52,20) is the one that can be expected to represent the inverse relationship between the functions.The correct answer is option B.

When verifying whether a function represented in another table is the inverse of a given cost function, we need to check if the ordered pairs in the second table correspond to the inverse relationship with the cost function. In this case, we have the options (20,20), (52,20), (20,52), and (52,52).

To determine the inverse of a function, we need to swap the x and y values of the original function. If we evaluate the cost function at the x-value of the original function and get the y-value of the original function, it indicates that we have found the inverse.

Looking at the options, the only pair that meets this criterion is (52,20). If we evaluate the cost function at x=52 and obtain y=20, and if the original function evaluates to x=20 when y=52, then it suggests an inverse relationship.

Therefore, the pair (52,20) is the one that can be expected to represent the inverse relationship between the functions. The other options do not satisfy the condition for an inverse relationship between the given cost function and the represented function in the table.

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The probable question may be:

When verifying that a function represented in another table is the inverse of the given cost function, which ordered pair can be expected?

A. (20,20)

B. (52,20)

C. (20,52)

D. (52,52)

Answer:

The tip will be $3.05.

The bill will cost $18.28 with the tip and tax.

Step-by-step explanation:

14.50 + 5% (or 0.73) = 15.23

15.23 + 20% (or 3.05) = 18.28

a) Approximately 25.78% of students should have grades less than 511.  b) Approximately 99.99% of students should have grades between 410 and 597.

A normal table, also known as a standard normal table or a z-table, is a mathematical table that provides values of the cumulative distribution function (CDF) of the standard normal distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1, and is a common distribution used in statistics and probability theory. A normal table is used to calculate probabilities for a normal distribution by looking up values in the table based on the standard deviation and mean of the distribution. The values in the table represent the area under the curve of the normal distribution to the left of a given z-score, and can be used to find probabilities and percentiles for specific z-scores or ranges of z-scores.

a) To find the percentage of students who scored less than 511, we need to standardize the score using the formula:

z = (x - μ) / σ

where x is the score obtained, μ is the mean, and σ is the standard deviation.

Substituting the given values, we get:

z = (511 - 518) / 10.77 = -0.65 (\(\sqrt{116} = 10.77\))

Using the normal table, we can find the area to the left of z = -0.65, which is 0.2578 or 25.78%. Therefore, approximately 25.78% of students should have grades less than 511.

b) To find the percentage of students who scored between 410 and 597, we need to standardize both scores and find the area between the two z-scores.

For x = 410:

z₁ = (410 - 518) / 10.77 = -10.04

For x = 597:

z₂ = (597 - 518) / 10.77 = 7.34

Using the normal table, we can find the area to the left of z1 and z2, which are both very close to 0. We can then subtract the smaller area from the larger area to find the area between the two z-scores.

Area to the left of the z₁ = 0.0001

Area to the left of the z₂ = 0.9999

Area between z₁ and z₂ = 0.9999 - 0.0001 = 0.9998

Therefore, approximately 99.99% of students should have grades between 410 and 597.

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Answer:

-1

Step-by-step explanation:

what you would start by doing is subtract x from 5 which gives it -6x. then, you would add the 2 to the 4 which cancels out the negative 2. so it should look like 6=-6x, then you would divide 6 by -6 which gives your answer as -1

Using the permutation formula, the number of different options for the top three finishers is given as follows:

\(P_{14,3} = \frac{14!}{11!} = 2184\)

The order in which the players are chosen is important, as A, B, C is a different outcome than C,B,A for example, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

\(P_{(n,x)} = \frac{n!}{(n-x)!}\)

In this problem, 3 students will be chosen from a set of 14, hence the number of ways is:

\(P_{14,3} = \frac{14!}{11!} = 2184\)

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15 liquids that can be found in a kitchen include:

15 solids in a kitchen are:

When it comes to solids in the kitchen, we can mostly find either food ingredients, such as salt, flour, and spices, or actual food that can be prepared such as meat, vegetables, and bread.

As for liquids, these can be anything from drinks such as juice, water and wine, to liquids used for cooking such as oil, soy sauce and vinegar.

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The formula to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

The formula presented derived from the formula for the circumference of a circle, which is C = 2πr. By rearranging the equation and isolating the radius (r) on one side, we get r = C/(2π).

So, if the circumference (C) of a circle is 18 centimeters, you can use the formula r = C/(2π) to find the radius (r). Plugging in the given value for the circumference (C), we get:

r = 18/(2π)

Simplifying the equation gives:

r = 9/π

Therefore, the radius (r) of the circle is 9/π centimeters.

In conclusion, the formula you can use to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

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Answer:

C. 39/48 = 81%

Step-by-step explanation:

To determine the percentage of females who only said they like cats using the given two-way table, we need to find the number of females who selected "cats" only and divide it by the total number of females surveyed. We can then multiply the result by 100 to get the percentage.

According to the provided two-way table:

Number of females who only said they like cats = 39

Total number of females surveyed = 48

To calculate the percentage:

Percentage of females who only said they like cats = (Number of females who only like cats / Total number of females surveyed) * 100

Percentage of females who only said they like cats = (39 / 48) * 100 ≈ 81.25%

Therefore, the correct option is:

C. 39/48 = 81%