Line A is perpendicular to the line represented by the equation 5x+4y=10.line a passes through the point (5,-4).which equation can be used to represent line A
?

On solving the provided question, we got to know that - carpenter should make the diagonals 37 ft

A diagonal is a line connecting two vertices of a solid or polygon whose vertices do not share an edge in mathematics. The vertices of a shape are connected by oblique or sloping lines, which are known as diagonals. A horizontal shape with sides/edges, corners, and is called a diagonal.

We can answer this problem using Pythagoras' Theorem since the diagonal would turn the angle into a right angle.

[tex]12^2+35^2= d^2[/tex]

[tex]d^2 = 144 + 1225\\d^2 = 1369\\d = 37\\[/tex]

So, carpenter should make the diagonals 37 ft

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Answer:

Slope:  - 4/3

Point (4,1)

Step-by-step explanation:

hope this helps

To write its equation in the form y is a(xh)2+k and then determine the value of the coefficient a.

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The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total time required to finish building the transmission if Jose and Luis works together be = A

Now , the equation will be

The time required by Jose to build a transmission = 10 hours

The time required by Luis to build a transmission = 8 hours

If it takes one person 10 hours to build a transmission and another person 8 hours to build the same transmission , working together they could build the transmission even quicker

So ,

If Jose builds the transmission is 10 hours , he builds 1/10th of the transmission in one hour

If Luis builds the transmission in 8 hours , he builds 1/8th of the transmission in one hour

And ,

Together they build the transmission in

1/A = 1/10 + 1/8

where A is the total time required to finish building the transmission if Jose and Luis works together

So , the equation is

1/A = 1/10 + 1/8

1/A = 18/80

Taking reciprocals on both sides of the equation , we get

A = 80/18

A = 40/9

On simplifying the equation , we get

A = 4.44 hours

Therefore , the value of A is 4.44 hours

Hence , The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours

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x =3 and y = 4 , these two perpendicular bisectors will come together. These are the triangle's circumcenter's coordinates.

What is perpendicular in triangle?

The sides of a triangle are divided into two equal portions by the perpendicular, which is parallel to the sides drawn from the opposing vertices.

The circumcenter of a triangle is the location where the three perpendicular bisectors of the triangle meet.

A(0, 0), B(0, 8), C(6, 0)

Circumcenter , P(x,y)

AP = BP = CP

AP² = BP²

(x - 0 )² + ( y - 8 )² = ( x- 0)² + ( y - 0 )²

x² + y² + 64 - 16y = x² + y²

 64 - 16y = 0

 16y = 64

     y = 4

BP = CP

BP² = CP²

(x - 0)² + ( y- 0 )² = ( x- 6)² + ( y - 0)²

x² + y² = x² 36 - 12x + y²

       36 - 12x = 0

         12x = 36

           x = 3

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The term used to denote the process that builds a regression equation by testing one variable at a time, starting with the one which is significantly corelated and keeping only the other significant coefficients is known as stepwise regression.

Iteratively building a regression model step by step, stepwise regression entails choosing independent variables to be included in the final model. It entails successively introducing or eliminating putative explanatory factors and assessing statistical significance after each iteration.

Stepwise regression can be accomplished in one of two ways: either by including all potential independent variables in the model and removing those that are not statistically significant, or by attempting each independent variable one at a time and including it in the regression model if it is statistically significant.

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If the integer begins through being rational, multiplying by 0.5 would not change whether or not something is rational. It will continue with rational numbers.

In mathematics, a rational number is a number that can be written as the quotient or fraction p/q of two numbers, an integrand p and a non-zero denominator q.

For instance, −3/7 is a rational number, and so is every integer.

So, in that case, any even number would be 12 * 0.5 = 6.

The solution is reasonable because 12 began as rational (6).

Any odd number also is rational:

23 * 0.5 = 11.5

23 and 11.5: Both rational

1.818181818 is reasonable hence when multiplied by 0.5 the result will be rational 3.636363636.

Therefore, if we begin with an irrational number like π:

π*0.5: Not rational

Therefore, if the integer begins through being rational, multiplying by 0.5 would not change whether or not something is rational. It will continue rational.

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Correct question:
Which number produces a rational number when multiplied by 0.5?

Answer:

6

Step-by-step explanation:

all are divisible by 6 or can be added by six to get the next number

The required value of the contant of proportionality is given as 1/4.

Proportionality is described as the relationship between two or more sets of values, and whether these values are directly proportional or inversely proportionate to one other.

Here,

Let G be the number of games and T be the number of tickets,

G ∝ T

So,

G = kT

From the table,

4 = 16k

k = 4/16

k = 1/4

Thus, the required value of the contant of proportionality is given as 1/4.

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Therefore, Gracie will earn $61600 if she waits until December 21. However, she will earn bank discount $61132.87 on November 12.

A bank discount is interest that the bank deducts beforehand in the basic discount note. The maturity value less the bank discount equals the amount owed. The total of the principle and interest due at the conclusion of the time period is the maturity value.

Date of note = 14th July

Face value = $60000

Length of note = 160 days,

Interest rate = 6%

Calculating the interest and maturity value:

Interest  = Principal × interest × time

= 60000 × 0.06 × 160/360

= 1600

So the maturity value MV = Face value + interest

= 60000 + 1600

= 61600

2. Calculating discount period:

Note discounted on 12th November

Time till 12th November = 315 days

Time till 14th July = 194 days

So days before note is discount = 315 - 194= 121 days

Length of note = 160 days,

So the discount period = 160 - 121 = 39 days

3 - Bank discount:

Bank discount = MV × Bank discount rate × number of days bank waits till due date

= 61600 × 0.07 × 39/360

= 467.133

4 - Proceeds from bank: Proceeds = MV - Bank discount

= 61600 - 467.133

= 61132.87

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c)  It will have less variation.

Decreasing the sample size will generally result in more variation in the distribution of sample means. This is because with a smaller sample size, there is less information available to estimate the population mean, which means that the sample mean will be less precise and will vary more from one sample to the next.

For example, if you take a sample of 10 individuals from a population and calculate the mean of their heights, the sample mean will likely be a good estimate of the population mean height. However, if you take a sample of just 2 individuals and calculate the mean of their heights, the sample mean will be less precise and will be a less reliable estimate of the population mean height. This is because the sample of 2 individuals may not be representative of the overall population, and the sample mean will be more influenced by extreme values or outliers.

In general, as the sample size decreases, the distribution of sample means will become more spread out and will have more variation. This is because with a smaller sample size, there is more uncertainty about the population mean, and the sample means will be more likely to deviate from the true population mean.

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Answer:

62.625

Step-by-step explanation:

First, we divide 33.4 by 4 to see what ONE gallon weighs.
33.4/4=8.35

8.35*7=58.45+(8.35*(1/2))= 62.625

Therefore, your answer is 62.625

I hope you understand my explanation. I pride myself on making my answers, short, descriptive, yet easy to read.

please give brainliest! Thanks! Hope this helped.

Answer:

62.625 lb

Step-by-step explanation:

Define the variable:

Set up a ratio of weight to number of gallons:

[tex]\implies x:7.5=33.4 :4[/tex]

Solve for x:

[tex]\implies \dfrac{x}{7.5 }=\dfrac{33.4}{4}[/tex]

Cross multiply:

[tex]\implies 4x=33.4 \cdot 7.5[/tex]

[tex]\implies 4x=250.5[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4x}{4}=\dfrac{250.5}{4}[/tex]

[tex]\implies x=62.625[/tex]

Therefore, the weight of 7.5 gallons of water is 62.625 lb.

The formula for the entries of [tex]M^{n}[/tex], where n is a positive integer is [tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex]  for M = [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] .

Let us find the formula for entries of [tex]M^{n}[/tex], where n is a positive integer.

Let M be a 2 x 2 matrix  [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex]

we get the eigenvalues and their associated eigenvectors as follows-

Eigenvalue : 9λ , multiplicity : 1λ, eigenvector : [ 1, 1]

Eigenvalue : 7λ , multiplicity : 1λ, eigenvector : [ 0.5, 1]

now, we have

[tex]{\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right] }[/tex] = [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]^{-1}[/tex] [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex]

              = [tex]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex]

hence, [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] = [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}9 & 0 \\0 & 7\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]

So,

[tex]{\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]^n } & =\left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right]^n\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]

                    [tex]= \left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{cc}9^n & 0 \\0 & 7^n\end{array}\right]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]

                    [tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex]

Thus, the formula for the entries of [tex]M^{n}[/tex], where n is a positive integer is [tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex] for M = [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] .

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Using Pythagoras theorem If sin tetha = x/4, then cos tetha = √(16-x²)/4

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

The sides of this triangle have been named Perpendicular, adjascent and Hypotenuse. If sin (tetha) = x/4, this means

x = opposite and

4 = hypotenuse

From hypotenuse² = opposite² + adjacent²

4² = x²+y²

y² = 16-x²

y = √ ( 16-x²)

cos (tetha) = adjacent/ hypotenuse

cos (tetha) = √(16-x²)/4

Therefore the value of cos (tetha) = √(16-x²)/4

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discount= 27.5

S.P= 522.5

Step-by-step explanation:

Marked price of dress(m.p)= 550

Discount % = 5%

Discount amount = 5% of MP

=5÷100×550

=27.5

S.P of the dress = ?

we know,

S.P = MP- discount

= 550-27.5

=522.5

Therefore, the slope of the line of best fit is 1.4.

Average By adding a collection of numbers and then dividing by their count, the arithmetic mean—also known as the median—is determined. For instance, 30 divided by 6 equals 5, which is the https://brainly.com/question/24057012of 2, 3, 4, 5, 7, and 10.

To find the slope of the line of best fit, you will need to use the formula:

slope = (mean(x) * mean(y) - mean(x*y)) / (mean(x)^2 - mean(x^2))

where x represents the average daily temperature and y represents the total ice cream sales.

First, you will need to calculate the mean of x, the mean of y, the mean of x*y, and the mean of x^2.

The mean of x is (56.1 + 60.3 + 64.2 + 66.4 + 71.3 + 73.9 + 74.2 + 75.2 + 80.1 + 84.8) / 10 = 71.54

The mean of y is (107 + 116 + 120 + 122 + 125 + 130 + 132 + 135 + 141 + 152) / 10 = 128.6

The mean of xy is (56.1107 + 60.3116 + 64.2120 + 66.4122 + 71.3125 + 73.9130 + 74.2132 + 75.2135 + 80.1141 + 84.8*152) / 10 = 8707.7

The mean of x^2 is (56.1^2 + 60.3^2 + 64.2^2 + 66.4^2 + 71.3^2 + 73.9^2 + 74.2^2 + 75.2^2 + 80.1^2 + 84.8^2) / 10 = 6043.17

Plugging these values into the formula for the slope, we get:

slope = (71.54 * 128.6 - 8707.7) / (71.54^2 - 6043.17) = 1.4

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The value of x is [tex]\frac{37 - b}{a}[/tex] by taking a and b as non-zero constant . It is solved by using simple arithmetic calculations .

What are arithmetic calculations?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.,

Addition : (+)

The addition is the process of taking two or more numbers and adding them together. In other words, it is the total sum of all the numbers.

Subtraction : (-)

Subtraction is the process in which we remove objects from the original group.

Multiplication : (×)

Multiplication is adding the same number to itself a certain number of times.

Division : (÷)

The division is breaking a large object or group into smaller parts or groups.

Here ,

given equation: ax + b = 37

To calculate value of x :

ax  = 37 - b

As, it is given that a is non-zero constant then,

x = (37 - b)/a

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Answer:

(-41, 30)

Step-by-step explanation:

The midpoint of a segment lies on the segment.

x: (-88 + 6)/2 = -41

y: (61 + (-1)) = 30

Answer: (-41, 30)

Answer:

1.1 hectares

Step-by-step explanation:

6.93/6.3 = 1.1

He can plant 1.1 hectares of land.

The required coordinate pair for W" is (2,-3)

When a point is reflected over axes, its position changes and sign of coordinates also change.

Given that, Point W is located at (-2, 3) on a coordinate plane. Point W is reflected over the x-axis to create point W'. Point W' is then reflected over the y-axis to create point W".

When a point is reflected over the x-axis, then we know,

(x, y) = (x,-y)

W(-2,3) = W (−2,−3)

And,

When a point is reflected over the y-axis, then we know,

(x, y) = (-x, y)

Therefore, W'(-2,-3) = W" (2,-3)

Hence, the coordinates of the point W" are (2,-3)

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The 3 combinations of coins with the value of 30% of a dollar are 2 dimes + 1 Nickel + 5 Pennies, 1 dime + 2 Nickels + 10 Pennies, 3 Nickels + 1 dime + 5 Pennies.

How many types of coins are there?

There are 4 types of coins. They are Quarter, Nickel, dime, and Penny.

1 Quarter = 25 cent

1 dime = 10 cents

1 Nickel = 5 cents

1 penny = 1 cent

Now calculate 30 percentage of a dollar.

1 dollar = 100 cents.

30% of 100 cents = (30/100) × 100 = 30 cents.

2 dimes + 1 Nickel + 5 Pennies = 20 cents + 5 cents + 5 cents = 30 cents

1 dime + 2 Nickels + 10 Pennies = 10 cents + 10 cents + 10 cents = 30 cents

3 Nickels + 1 dime + 5 Pennies = 15 cents + 10 cents + 5 cents = 30 cents

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The percentage of respondents who said the magazine is useful is referred to as the population parameter of interest.

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Answer:

20

Step-by-step explanation:

h=hypotenuse. s1=side 1. s2=side 2

h^2 = (s1)^2 + (s2)^2  ==> hypotenuse formula

h^2 = 12^2 + 16^2  => plug in known values

h^2 = 144 + 256  

h^2 = 400  ==> simplify

[tex]\sqrt{h^2 = 400}[/tex]  ==> take the square root on both sides to remove the power

[tex]\sqrt{h^2}[/tex] = [tex]\sqrt{400}[/tex]

h = 20

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Answer:

Step-by-step explanation:

Hello...

y=x-8

2x+y=-5 -> y=-2x-5

subsitution

-2x-5=x-8

3x=3

x=1

y=x-8

y=1-8

y=-7

(1,-7)

From the quadrilateral proof seen below we can prove that;

∠C + ∠D = 2∠AOB

The bisection of an angle simply means to divide an angle into two equal parts.

The sum of the interior angles of a quadrilateral is 360 degrees. Thus;

∠A + ∠B + ∠C + ∠D = 360°     ------(1)

In △AOB,

∠AOB + ∠A/2 + ∠B/2 = 180°

Multiply through by 2 to get;

2∠AOB + ∠A + ∠B = 360°

Thus;

∠A + ∠B = 360° - 2∠AOB

Put 360° - 2∠AOB for ∠A + ∠B in eq 1 to get;

360° - 2∠AOB + ∠C + ∠D = 360°

This simplifies to;

∠C + ∠D = 2∠AOB

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Complete question is;

Bisectors of two adjacent angles of angles A and B of quadrilateral ABCD intersect at a point O. Prove that 2∠AOB = ∠C + ∠D

Aggregates is distorts the effectiveness of charting data points. So the option d is correct.

In the given question, we have to select which of the following, when included, distorts the effectiveness of charting data points.

Charts are a quick and efficient way to communicate information to your audience. If the charts are properly created, that is.

A lot goes into creating the ideal visual material, and it's simple to let some components slip. Charts that are hurriedly created are frequently more detrimental than beneficial.

We've compiled a list of useful do's and don'ts to bear in mind while building your own data representations, whether they take the shape of straightforward bar charts and graphs or more intricate interactive visualizations, in order to help you prevent this.

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Prior to performing the clustering analysis, we select the value for k, the statement regarding k-means clustering is accurate and the minimum distance between the clusters should be used.

Data is divided into groups (clusters) using cluster analysis that is relevant, practical, or both. If creating meaningful groups is the goal, the clusters should reflect the data's inherent structure. However, cluster analysis can occasionally merely serve as a valuable starting point for other tasks, including data summarization. In a wide range of disciplines, including biology, statistics, pattern recognition, information retrieval, machine learning, and data mining, cluster analysis has long been crucial, whether for understanding or usefulness. Cluster analysis has been used to solve numerous practical issues.

Hartigan (1975, pp 90-91) provides the following general guideline when determining the number of clusters. When (sum(k$withinss)/sum(kplus1$withinss)-1)*(nrow(x)-k-1) is more than 10, it is justified to add the extra group if k is the result of k-means with k groups and kplus1 is the result with k+1 groups.

As a result, choice B is the appropriate response.

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Step-by-step explanation:

Answer:

Area = 600

Step-by-step explanation:

The area formula for rectangles is length x width. In this equation, the length is 20 and the width is 30, multiplying them together gets us the area of 600.

Answer: The solution of this system of equations is the point of cut of these line.

Point of cut is when x is close to -1, and y is close to 0; therefore the best estimate of the solution would be:

A) (-1,0)

We can check it out our answer solving the system of equations:

-3x+y=2

-4x+7y=1

We solve this system by substitution method.

-3x+y=2   ⇒  y=2+3x

-4x+7(2+3x)=1

-4x+14+21x=1

-4x+21x=1-14

17x=-13

x=-13/17=-0.764....≈-1

y=2+3x

y=2+3(-0.764)

y=2-2.292

y=-0.292≈0

The approximate solution will be (-1,0)

The boat's distance and bearing from the port regions are as follows;

The boat is located around 157.15 kilometers from the harbor on a bearing of 150°.

In mathematics, a bearing is an angle measured clockwise from the north or y-axis direction.

The Coast Guard cutter travels at a speed of 30 kno

Angelica, a Coast Guard cutter, has a bearing of 95 degrees.

The coast guard goes for 2 hours in the first direction.

The shift in direction of the Coast Guard cutter = 185°

Travel time in the new direction = 2 hours

30 knots equals 55.56 km/hr

The distance traveled in the first direction = 55.56 km/hr = 111.12 km in 2 hours

Distance traveled in the other direction = 55.56 km/hr 2 hours = 111.12 km

According to the accompanying graphic, the figure produced by the Coast Guard cutter's course is an isosceles triangle.

The Pythagorean theorem gives the distance from the port to the position of the boat as l = √(111.122^2 + 111.122^2) ≈ 157.15.

The boat is roughly 157.15 kilometers away from the port.

An isosceles right triangle has 45° base angles.

As a result, the bearing is 95° + 45° = 150°.

The angle between the port and the boat is 150°.

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