Which system is equivalent to StartLayout Enlarged left-brace 1st Row 5 x squared + 6 y squared = 50 2nd row 7 x squared + 2 y squared = 10 EndLayout? StartLayout Enlarged left-brace 1st Row 5 x squared + 6 y squared = 50 2nd row negative 21 x squared minus 6 y squared = 10 EndLayout StartLayout Enlarged left-brace 1st Row 5 x squared + 6 y squared = 50 2nd row negative 21 x squared minus 6 y squared = 30 EndLayout StartLayout Enlarged left-brace 1st Row 35 x squared + 42 y squared = 250 2nd row negative 35 x squared minus 10 y squared = negative 50 EndLayout StartLayout Enlarged left-brace 1st Row 35 x squared + 42 y squared = 350 2nd row negative 35 x squared minus 10 y squared = negative 50 EndLayout

Caden's speed is 10 mph and Rahquez's speed is 16 mph faster, which is 16+6 = 32 mph

Let's use the formula: distance = rate x time

Since Caden and Rahquez are traveling towards each other, their combined distance will be 208 miles. Let's call Caden's speed "x" and Rahquez's speed "x+6", since Rahquez is traveling 6 mph faster than Caden.

Using the formula above, we can set up the equation:

208 = (x + x + 6) * 8

Simplifying, we get:

208 = (2x + 6) * 8

208 = 16x + 48

160 = 16x

x = 10

Therefore, Caden's speed is 10 mph and Rahquez's speed is 32 mph.

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(NO)²

\(\huge\mathfrak\red{hope \: it \: helps}\)

Selling price of a bicycle = 2850

Profit percentage = 14%

We know that :

\(\color{plum}\tt{Cost \: \: price = \frac{Selling \: \: price \: \times \: 100}{100 \: \: + \: \: profit \: \%} }\)

Then, the cost price of this bicycle :

\( = \tt \frac{2850 \times 100}{100 + 14} \)

\( = \tt \frac{285000}{114} \)

\( =\color{plum} \tt2500\)

Thus, the cost price of this bicycle = 2500

In another scenario :

Profit percentage = 8%

Cost price of the bicycle = 2500

Then, Selling price will be equal to :

Let x be the selling price of the bicycle.

\( = \tt2500 = \frac{\: x \: \times 100}{100 + 8} \)

\( = \tt2500 = \frac{100x}{108} \)

\( =\tt 100x = 2500 \times 108\)

\( = \tt100x = 270000\)

\( =\tt x = \frac{270000}{100} \)

\( =\color{plum}\tt x = 2700\)

Therefore, the selling price with a profit of 8% will be = 2700

Based on the dimensions of the triangular flower bed, the cost of the border will be $70.

First, you need to find the total length of the triangular flower bed to find out how much thin metal border is needed.

This length is:

= 7 feet + 6 feet + 9 feet

= 22 feet

Then convert these to yards because the cost of the thin metal border wall is in yards. Every yard is about 3 feet so 3 feet is 1/3 yeards.

If you have 22 feet therefore, the number of yards is:
= 22 x 1/3

= 22 / 3

= 7.33 yards

Only whole numbers of yards can be bought so we round this up to 8 yards.

The cost of the border would be:

= Number of yards x Cost per yard

= 8 x 8.75

=  $70

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Answer:

The third expression: (2x)^3

Step-by-step explanation:

Plug in 3 for x in each expression

2x^3

2(3)^3

Use PEMDAS

2 (3 × 3 × 3)

2 (9 × 3)

2 (27)

54

2x^3 + 5

(The last expression told us 2x^3 = 54 so feel free to use this information to make life easier)

54 + 5

59

(2x)^3

(2 × 3)^3

Use PEMDAS

6^3

6 × 6 × 6

36 × 6

216

(x - 1)^3

(3 - 1)^3

Use PEMDAS

2^3

2 × 2 × 2

4 × 2

8

216 is the greatest value so the third expression is the answer

Answer:

y = -x + 9

Step-by-step explanation:

Since the line is parallel, the slope is -1.

y = -x + c

Substituting (0,9) into the above equation:

9 = 0 + c

c = 9

y = -x + 9

Feel free to mark this as brainliest! :D

Answer:

Here is one :)

x - 12  =  - 8

Using the information provided in the table, The total holding cost is  $547.50, the total setup cost is $600 and the total cost is  $1,147.50.

To develop a POQ (Periodic Order Quantity) solution use a lot-for-lot solution, which means that we will order exactly what we need for each period.

The missing values can be found on the attached table.

From the table, the total holding cost which is the sum of the holding costs for all periods is $547.50 while the total setup cost which is the sum of the setup costs for all periods is $600.

Therefore, the total cost is the sum of the holding cost and the setup cost and it is calculated as $1,147.50.

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Answer:

b. x = 1

Step-by-step explanation:

(1^2+3x)=(1^2+1+2) is equal to 4

Answer:

D. 10

Step-by-step explanation:

\({ \sf{(12x + 12) \degree = 79\degree + (5x + 3)\degree}} \\ { \sf{ \{outer \: angle \: is \: equal \: to \: sum \: of \: inner \: angles \}}} \\ { \sf{12x - 5x = 79 + 3 - 12}} \\ { \sf{7x = 70}} \\ { \sf{x = 10}}\)

The substitution method is used in elimination to find the solution to the equation.

A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.

The given equation in the problem is;

Equation P: a - b = 9

Equation Q: a+b=5

The value obtained from the equation P is;

a - b = 9

a=b+9

Substitute the value in the equation Q;

a+b=5

b+9+b=5

2b=9-5

b=2

The value of a is;

a-b=9

a-2=9

a=9+2

a=11

Hence the value of a and b will be 11 and 2.

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Answer:

16

Step-by-step explanation:

Pemdas is the order of operations

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

16

Step-by-step explanation:

3 x 6 - 12 / 6.

18 - 2

  16

Answer:

5+7*x

Step by step explanation.....

Using a system of equations, the number of children who swam at the public pool that day was 268 while adults were 92.

A system of equations involves two or more equations solved simultaneously.

It is known as a system of equations or simultaneous equations.

The total number of people who used the public swimming pool = 360

Children's ticket = $1.50

Adult's ticket = $2.25

Total receipts on that day = $609

Let's form the following equations:

Let the number of children = x

Let the number of adults = y

x + y = 360 ... equation 1

1.50x + 2.25y = 609  ... equation 2

From equation 1, y = 360 - x ... equation 3

In equation 2, replace y = 360 - x and solve:

1.5x + 2.25(360 - x) = 609

1.5x + 810 - 2.25x = 609

-0.75x = -201

x = 268

In equation 3, replace x = 268 to find y:

y = 360 - 268

y = 92

Check:

Equation 2:

1.50x + 2.25y = 609

1.50(268) + 2.25(92) = 609

402 + 207 = 609

609 = 609

Thus, with our simultaneous equations, we can conclude that 268 children and 92 adults graced the swimming on that hot summer's day.

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The admission receipts totaled $609.

Answer: here u go

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

\(\frac{1}{8}*3200=\frac{3200}{8}=400\)

3200 ÷ 8 = 400

The summary of the calculations for the given data set is as follows: The median is 48, the mean is approximately 46.42, the variance is approximately 120.52, the standard deviation is approximately 10.98, and the quartiles are Q₁ = 42, Q₂ = 48, and Q₃ = 52.

1. Median:

Arrange the data in ascending order: 21, 27, 28, 29, 32, 35, 35, 36, 41, 41, 42, 42, 43, 44, 44, 45, 46, 46, 46, 47, 47, 48, 48, 48, 49, 49, 50, 50, 51, 51, 52, 52, 53, 53, 54, 54, 56, 56, 56, 58, 64.

The median is the middle value, which is 48.

2. Mean:

Sum all the values: 45 + 52 + 48 + 41 + 56 + 46 + 44 + 42 + 48 + 53 + 51 + 53 + 51 + 32 + 56 + 21 + 49 + 56 + 28 + 35 + 64 + 48 + 46 + 43 + 52 + 50 + 54 + 47 + 44 + 47 + 50 + 49 + 52 + 28 + 36 + 54 + 41 + 29 + 35 + 58 + 42 + 46 + 27 = 1998.

Divide the sum by the number of data points (43): 1998 / 43 = approximately 46.42.

3. Variance:

Calculate the mean: 46.42 (from the previous step).

For each data point, subtract the mean, square the result, and sum all the squares.

Sum of squares: (45 - 46.42)² + (52 - 46.42)² + ... + (27 - 46.42)² = 52680.34.

Divide the sum by the number of data points (43): 52680.34 / 43 = approximately 1225.12.

4. Standard Deviation:

Take the square root of the variance: √1225.12 = approximately 35.00.

5. Quartiles:

Q₁: The median of the lower half of the data set is the 22nd value, which is 42.

Q₂: The overall median is the 22nd value, which is 48.

Q₃: The median of the upper half of the data set is the 32nd value, which is 52.

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S cannot be a basis for \(R^{n }\)

What is Matrix ?

A matrix is a rectangular array of numbers or symbols arranged in rows and columns. Matrices are commonly used in mathematics, physics, engineering, computer science, and other fields to represent systems of linear equations, transformations, and other mathematical objects and operations.

The statement "For each b in  \(R^{m }\), the equation Ax - b has a solution" is equivalent to the following statements:

A. The columns of A span \(R^{m }\)

B. Each b in \(R^{m }\) is a linear combination of the columns of A.

E. The matrix A has a pivot position in each column.

To explain why S cannot be a basis for  \(R^{n }\) , we can use the fact that a set of vectors S = {v1, ..., vk} is a basis for  \(R^{n }\) if and only if the matrix whose columns are the vectors in S is invertible. In this case, since k < n, the matrix whose columns are the vectors in S cannot be invertible because it has more columns than rows.

Therefore, S cannot be a basis for \(R^{n }\).

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Confidence level feature of the poll was ​ omitted

To find the what important feature of the poll was ​ omitted?.

The illustration showed that​ 26% of applicants said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company.

The margin of error was given as plus or minus 3 percentage points.

The important feature of the poll that was​ omitted was - confidence level.

The percent of all samples that are included in the true population parameter is given by a confidence level.

Confidence interval defines the probability that the given population parameter will fall within a specific range of values.

Mathematically we can express the scenario as :

Sample size is given as 1910​ professionals

Point estimate is 26%

Confidence level is not given.

Confidence interval is plus or minus 3 percent around 26%.

Hence, Confidence level feature of the poll was ​ omitted.

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Karnaugh maps or K-maps are pictorial methods used to minimize Boolean expressions without having to use Boolean algebra theorems and equation manipulations. Option Q is the correct answer.

They provide a visual aid for determining the optimal grouping of terms. Karnaugh maps reduce logic functions more quickly and easily than Boolean algebra simplification. It is a practical tool to use for problems that require minimizing Boolean expressions. There are two common versions of Karnaugh maps: 2-D Karnaugh maps and 3-D Karnaugh maps. A Karnaugh map consists of squares in which each square represents a product term or minterm.

In a two-variable Karnaugh map, there are four squares, whereas in a three-variable Karnaugh map, there are eight squares. Karnaugh maps are read and interpreted from left to right and top to bottom. Terms that are adjacent or touching in the map can be combined to produce a simplified expression. K-maps can minimize up to 4 variables in a 2-D map and up to 6 variables in a 3-D map. Karnaugh maps help reduce the complexity of Boolean expressions and make it easier to implement logic circuits.

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Answer: \(12\ ft\)

Step-by-step explanation:

Given

Total height of utility pole is 18 ft

After breakage, only 5 foot tall portion is standing

The fallen part is \(18-5=13\ ft\) in length

From the figure, apply the Pythagoras theorem

\(\Rightarrow 13^2=x^2+5^2\\\Rightarrow x^2=169-25\\\Rightarrow x=\sqrt{169-25}\\\Rightarrow x=\sqrt{144}\\\Rightarrow x=12\ ft\)

Thus, the fallen part is \(12\ ft\) away from the base of the pole.

The second is a Uniform distribution with a minimum value of 50 and a maximum value of 100, where all values have equal frequencies.

Frequency distribution is a statistical representation of the number of occurrences of each value in a set of data. Let's consider the given set of values and describe two types of distributions for it.

Distribution Type 1: Normal Distribution with mean = 75 and standard deviation = 25.

This distribution follows a bell-shaped curve that is symmetric around the mean value of 75. The standard deviation of 25 indicates that the data is spread out with a moderate amount of variability. The highest frequency occurs at the mean value of 75, and as we move away from the mean in either direction, the frequency gradually decreases. The distribution provides information about how the values are distributed around the mean.

Distribution Type 2: Uniform Distribution U[50, 100].

This distribution is characterized by a rectangular shape, where all values have the same frequency. In this case, the minimum value is 50, and the maximum value is 100, resulting in a range of 50. The frequencies are uniform throughout the distribution, meaning that each value has the same frequency. In this case, since there are seven values in the set, each value has a frequency of 1/7.

To summarize, the given set of values can be represented by two different distributions. The first is a Normal distribution with a mean of 75 and a standard deviation of 25, which shows the overall pattern and spread of the data.

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Answer:

200

Step-by-step explanation:

I mean this one is pretty simple. all you do is 8*25 because she has 8 acres and each acre is divided into 25

Answer:

I think you meant "Jess owns 8 acres of land. She wants to divide it into lots of 2/5 of an acre." so the answer is 8 times 5/2 = 20

Step-by-step explanation:

pls like!!

Option a. calculate a correlation coefficient is the right response because a correlation coefficient measures the strength and direction of the relationship between two interval level variables.

This is because a correlation coefficient measures the strength and direction of the relationship between two interval level variables. It provides a numerical value that ranges from -1 to 1, where -1 indicates a strong negative correlation, 0 indicates no correlation, and 1 indicates a strong positive correlation.

A scatter plot is also useful in visualizing the relationship between two variables, but it does not provide a numerical value like the correlation coefficient. A test of significance and variance calculation are not typically used as first steps in assessing the relationship between two variables.

Hence, option a. calculate a correlation coefficient is the correct answer.

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In this question, we are given a subset "c" of a set "v" with a specific property.

The property states that if both "u" and "v" belong to "c", then the point "1" that lies between "u" and "v" also belongs to "c".

Now, let's assume that "w" is an element of "v". We need to show that there can be at most one point "u" in "c" that is closest to "w".

To prove this, we can use proof by contradiction. Let's assume that there are two points "u1" and "u2" in "c" that are closest to "w".

Since "u1" is closest to "w", the distance between "w" and "u1" must be less than the distance between "w" and any other point "v" in "c". Similarly, the distance between "w" and "u2" must also be less than the distance between "w" and any other point "v" in "c".

Now, consider the point "1" that lies between "u1" and "u2". By the given property of "c", since both "u1" and "u2" belong to "c", the point "1" also belongs to "c".

But this contradicts our assumption that "u1" and "u2" are the closest points to "w". If "1" belongs to "c", then the distance between "w" and "1" would be smaller than the distances between "w" and "u1" and between "w" and "u2". This contradicts our initial assumption.

Therefore, we can conclude that there can be at most one point "u" in "c" that is closest to "w".

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Answer:

  (b)  21.4

Step-by-step explanation:

There are a couple of interesting relations regarding chords and secants and tangents of a circle. With the right point of view, they can be viewed as variations of the same relation, possibly making them easier to remember.

When chords cross inside a circle (as here), each divides the other into two parts. The product of the lengths of the two parts of one chord is the same as the product of the lengths of the two parts of the other chord.

Here, that means ...

  7x = 10·15

  x = 150/7 = 21 3/7 ≈ 21.4

_____

Additional comment

A secant is a line that intersects a circle in two places. (A tangent is a special case of secant where the two points of intersection are the same point.) When two secants meet outside the circle, there is a special relation between the lengths of the various line segments.

Consider the line segment from the point where the secants meet each other to the far intersection point with the circle. The product of that length and the length to the near intersection point with the circle is the same for both secants.

Here's the viewpoint that merges these two relations:

The product of the lengths from the point of intersection of the lines with each other to the two points of intersection with the circle is the same for each line.

(Note that when the "secant" is a tangent, that product is the square of the distance from the tangent point to the point of intersection with the other line--the distance to the circle multiplied by itself.)

According to the Question,

\( \rm7x = 10 \times 15\)

\( \rm x = \frac{150}{7} \)

\( \bf x = 21.4\)

The desired 3x3 matrix A is:

[ 6,  5,  3],
[ 1,  0,  0],
[ 0,  1, -1]

To find a 3x3 matrix A with the given eigenspaces, we'll first determine eigenvectors for each eigenspace and then construct matrix A using these eigenvectors as columns.

For the -2-eigenspace with equation -2x + 12y - 2z = 0, we can rewrite it as x = 6y - z. Let y = 1 and z = 0, we have the eigenvector v1 = (6, 1, 0). Similarly, let y = 0 and z = 1, we get the eigenvector v2 = (5, 0, 1).

For the 2-eigenspace, we are given w = span{[3, 0, -1]}. This vector is already an eigenvector for the 2-eigenspace, so v3 = (3, 0, -1).

Now, we construct the matrix A using these eigenvectors as columns:

A = [v1 v2 v3] = [(6, 1, 0), (5, 0, 1), (3, 0, -1)]
A = [
    [ 6,  5,  3],
    [ 1,  0,  0],
    [ 0,  1, -1]
]

So, the desired 3x3 matrix A is:

[
[ 6,  5,  3],
[ 1,  0,  0],
[ 0,  1, -1]
]

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Answer:

(no solutions)

Step-by-step explanation:

Solve for x:

5 x - 9 = 5 x + 6

Hint: | Isolate x to the left hand side.

Subtract 5 x - 9 from both sides:

0 = 15

Hint: | Look for a false statement.

0 = 15 is trivially false:

Answer: (no solutions)

Answer:

I believe it would be B

Step-by-step explanation:

im not good at explaining, but basically that would make the most sense, forgive me if im wrong, im not good at math TwT