find the equation of the line through the point(6,7) and (2,-1). then give its x- and y- intercepts as ordered pairs

The true statements are,

[tex]\overline{WX} \perp ZY[/tex] and [tex]\overline{WX} || AB.[/tex]

[tex]\overline{UV} || \overline{AB}[/tex] and [tex]\overline{UV} || \overline{ZY}[/tex].

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We know perpendicular lines make an angle of 90° at their intersecting point.

And we also know that the distance between two parallel lines is constant.

The line segment WX ⊥ ZY and WX is parallel to AB.

The line segment UV ⊥ WX and UV is parallel to ZY.

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You will need 7.104 feet of lumber. (rounded to three decimal places)

There are four basic arithmetic operations in mathematics: addition, subtraction, multiplication, and division.

Among these four procedures, division is one of the most important in our everyday tasks. It is the division of a large group into equal smaller groups.

To find out how many feet of lumber you need, you need to add up the length of all the pieces and then divide by the number of inches in a foot (12).

First, we'll add up the length of all the pieces:

11 (1/4) + 11 (1/4) + 12 (1/2) + 12 (1/2) + 28 (1/8) + 28 (1/8)

= 85 (1/4) inches

Next, we'll convert this total length to feet by dividing by 12:

85 1/4 inches ÷ 12 inches/foot = 7.104 feet

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Answer:

3x²–2x+1=0

3x²+x–3x+1=0

(3x²+x)-(3x+1)=0

x(3x+1)-1(3x+1)=0

either (x-1) (3x+1)=0

x=1 or x=-⅓

After three steps, the average value of the displacement and the average value of the squared displacement are given by zero and two, respectively.

The average value of the displacement is calculated by summing up all the displacement values and dividing by the total number of steps. In this case, the average value will be zero because each step has an equal probability of moving forward or backward, resulting in an average net displacement of zero.

The average value of the squared displacement is calculated by summing up the squares of all the displacement values and dividing by the total number of steps. In this case, the average value will be two because each step has an equal probability of moving two units forward or two units backward, resulting in an average squared displacement of two.

These values can be used to calculate various statistical measures such as the mean squared displacement, which can provide insight into the diffusion of particles or the behavior of random walks.

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The difference quotient for the given function is given by f(x) - f(x)/x - a, which simplifies to -(x-a)/x.

The difference quotient for the given function is given by f(x) - f(x)/x - a, which simplifies to -(x-a)/x. This expression is obtained by subtracting f(x)/x - a from f(x). The numerator is the difference between x and a, while the denominator is x.

The difference quotient for the given function f(x) = 1/x can be expressed as:

f(x) - f(x)/x - a = -(x-a)/x

This expression can be further expanded as follows:

f(x) - f(x)/x - a = [1/x - 1/x] - (x - a)/x

                   = 0 - (x - a)/x

                   = -(x - a)/x

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number of tickets?

The two equations can be set equal to each other and solved for x:

30x + 20 = 20x + 50

10x = 30

x = 3

Therefore, they sold the same number of tickets after 3 days

Compare the number of times customers who saw either version of the menu ordered the item.

In order to understand if setting the menu item apart in a text box increased the likelihood the item is ordered, researchers should first compare the number of customers who saw version A of the menu to the number of customers who saw version B of the menu. This will allow the researchers to determine if there is any difference in the number of customers who saw each version of the menu. Once this comparison is made, the researchers should then compare the number of times that customers who saw version A of the menu ordered the item to the number of times that customers who saw version B of the menu ordered the item. This will allow the researchers to see if the item was ordered more frequently with version A of the menu. Lastly, the researchers should compare the percentage of times that customers who saw version A of the menu ordered the item to the percentage of times that customers who saw version B of the menu ordered the item. This will allow the researchers to determine if there was a significant difference in the likelihood of the item being ordered with the different versions of the menu.

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For the given transformation C(-2,1), D (2,2), E(-1,-2) to C'(-4,-2), D'(4,4), E'(-2,-4) the rule used is scaling, where the figure is scaled by a factor of 2.

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point.

In the given transformation the coordinated of C', D', and E' are two times the coordinate of C, D, and E.

Thus, For the given transformation C(-2,1), D (2,2), E(-1,-2) to C'(-4,-2), D'(4,4), E'(-2,-4) the rule used is scaling, where the figure is scaled by a factor of 2.

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Answer:

y-10

Step-by-step explanation:

The system of equation has no solution.

Two or more expressions with an Equal sign is called as Equation.

The system of solution is

y=2x+6...(1)

2y=4x-2...(2)

Multiply equation 1 with 2

2y=4x+12...(3)

Subtract equation 2 and 3

2y-2y=4x-2-4x-12

0=-14

Hence, the system of equation has no solution.

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The value of a 10% stake is given as $88.

The formula for the Gordon growth model is:

Stock Price = Dividend / (Required Yield - Growth Rate)

Substituting the given values gives:

Stock price = 1.76 / (0.10 - 0.08) = 1.76 / 0.02 = $88 

Stocks are documents that prove that someone owns a share of the capital of a company. A person who owns shares has the right to some of the company's assets. For example, if a company issues 1000 shares of stock and a person owns 200 shares in that company, that person actually owns 20% of the assets in that company. Majority shareholders will have control rights over a company.

Shareholders also have the right to receive dividends according to the number of shares they own. The acquisition of these dividends usually depends on the profits of the company and has been regulated in accordance with the company's articles of association.

Issuing shares is one way for companies to get fresh funds or capital for long-term business development. Shares themselves can be traded through the Stock Exchange at prices that change according to company conditions and economic conditions.

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Option B is correct, WX is perpendicular to ZY and WX is parallel to AB.

Coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

To find the solution of this problem.

Firstly let us understand the parallel and perpendicular lines.

Parallel lines are the lines that do not intersect or meet each other at any point in a plane.

Two geometric objects are perpendicular if they intersect at a right angle. The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂.

As we check all the options, WX is perpendicular to ZY and WX is parallel to AB.

Hence, Option B is correct, WX is perpendicular to ZY and WX is parallel to AB.

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Answer: 43516

Step-by-step explanation:

C =(Current Salary). C x .012( 12%)=516

C + 516 = 43516

Answer: 3 13/24

Step-by-step explanation:

When the term "evaluate" is in a question you are being asked to perform the operation, in this case subtraction of fractions.

Note that these are mixed number fractions, meaning there is a whole number with a fraction.

7 1/6 - 3 5/8

Step 1: Convert the mixed fractions to improper fractions.

For 7 1/6 take 7 x 6 = 42. Take 42 + 1 = 43

7 1/6 becomes 43/6

For 3 5/8 take 3 x 8 = 24. Take 24 + 5 = 29

3 5/8 becomes 29/8

Step 2: Arrange the improper fractions into the subtraction problem.

43/6 - 29/8

Step 3: Find the least common denominator for 6 and 8, which is 24.

43/6 (4/4) - 29/8 (3/3) =

172/24 - 87/24 = 85/24

Step 4: Turn the improper fraction into a mixed fraction.

Divide 85 by 24, which equals 3 13/24.

The value of x that makes ABC~ ADEF is 4

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

AABC~ ADEF.

So, we have the following equovalent ratio

6 : 2x = 24 : 32

So, we have

2x/6 = 32/24

Make x the subject

So, we have the following representation

x = 6 * 32/(24 * 2)

Evaluate the expression

x = 4

Hence, the value is 4

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The probability that X will be between 21 and 25 is increased.

The probability that a continuous random variable with a uniform distribution takes on a value between two specific points (a, b) is given by:

P(a X b) = (b - a) / (max - min)

where X is the random variable, max and min are the distribution's upper and lower bounds, and (b - a) is the length of the interval between two specific points.

In this case, the uniform distribution of X is from 20 to 28, so:

max = 28 min = 20

And we want to know how likely it is that X will have a value between 21 and 25:

P(21 < X < 25) = (25 - 21) / (28 - 20) = 4 / 8 = 0.5

As a result, the probability that X will be between 21 and 25 is increased.

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There is no significant difference in interaction means.

The ANOVA table is used to test the null hypothesis that the means of two or more groups are equal. In this case, we are testing the means of four levels of Factor A and three levels of Factor B. The table shows the Sum of Squares (SS) for each source, the Mean Squares (MS), and the F-value for each source.

To determine if there is a significant difference in Factor A and Factor B means, we must calculate the critical values to test for equal means. We can do this by dividing the Mean Square (MS) of each factor by the Error Mean Square (MS Error). For Factor A, we have MS Factor A/MS Error = 60/400 = 0.15. For Factor B, we have MS Factor B/MS Error = 40/400 = 0.1. We can then compare these values to the critical value for a 0.05 significance level, which is 3.89. Since both of our values are below this critical value, we can conclude that there is no significant difference in Factor A and Factor B means.

Finally, to determine if there is a significant difference in interaction means, we must calculate the F-value for the Interaction source. This is done by dividing the Mean Square of the Interaction source (MS Interaction) by the Error Mean Square (MS Error). In this case, we have MS Interaction/MS Error = 110/400 = 0.275. We can then compare this value to the critical value for a 0.05 significance level, which is 3.89. Since our value is below this critical value, we can conclude that there is no significant difference in interaction means.

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Answer:

Step-by-step explanation:

slope= y2-y1/x2-x1 ---->  3-2/1-3 ----> 1/-2 ----> slope=-1/2

slope intercept form is y=mx+b. (b is the y-intercept, and m is the slope.)

y=-1/2x+b

we need to find b so you plug in one of the points and isolate b.

3=-1/2(1)+b

+1/2 on both sides to move it over.

3.5=b

FULL EQN: y=-1.2x+3.5

The circuit starts at the final AND gate. It has two inputs, one from an OR gate and one from a NOT gate.

The OR gate has two inputs, p and q. If either p or q is high (1), the OR gate will output a high signal. If both p and q are low (0), the OR gate will output a low signal. In this case, we only have the value of p, which is high, so the output from the OR gate is also high.

The NOT gate has one input, q. It inverts the signal, so if q is high (1), the NOT gate will output a low signal (0), and if q is low (0), the NOT gate will output a high signal (1). We don't know the value of q, so we don't know the output from the NOT gate.

Finally, the AND gate takes the outputs from the OR gate and the NOT gate as its inputs. If both inputs are high (1), the AND gate will output a high signal (1). If either input is low (0), the AND gate will output a low signal (0). Since we don't know the output from the NOT gate, we can't determine the output from the AND gate.

So, to summarize, without knowing the value of q, we can't determine the output from the final AND gate.

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If the slope of the line is 4, then the value of r is 17.

Remember that the slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know that the slope is 4 and the points are  (-5, -7) and (1, r), then we can write:

4 = (r + 7)/(1 + 5)

And now solve that for r:

4 = (r + 7)/6

4*6 - 7 = r

17 = r

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The equation that represents the distance traveled by the second car is 60(t + 1.33).

Let t = travel time of the 2nd car when it overtakes the 1st

:

Find the travel time of the 1st car to go 80 mi; time = dist/speed

time = 80%2F60

time = 1.33 hrs for the 1st car to go 80 mi

therefore

(t+1.33) = travel time of the 1st car when it is overtaken

:

When the 2nd overtakes the 1st, they will have traveled the same distance

Write a distance equation, dist = speed * time

:

2nd car dist = 1st car dist

70t = 60(t+1.33)

70t = 60t + 80

70t - 60t = 80

10t = 80

t = 8 hrs travel time of the 2nd car to overtake the 1st

:

;

Confirm this by finding the actual distances, should be equal

70*8 = 560 mi

60*9.33 ~ 560 mi

Hence , the equation that represents the distance traveled by the second car is 60(t + 1.33).

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The equation of the line that passes through the points (1,9) and (−4,8) is y= 1/5 x+45.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given coordinate points are (1, 9) and (-4, 8).

Here, slope (m)= (8-9)/(-4-1)

m= 1/5

Substitute m=1/5 and (x, y)=(1, 9) in y=mx+c, we get

9=1/5 (1)+c

c=45

Substitute m=1/5 and c=45 in y=mx+c, we get

y= 1/5 x+45

Therefore, the equation of the line that passes through the points (1,9) and (−4,8) is y= 1/5 x+45.

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Answer:

[tex]y=\dfrac{1}{5}x+\dfrac{44}{5}[/tex]

Step-by-step explanation:

To write the equation of the line that passes through the points (1, 9) and (-4, 8), first find its slope.

To do this, substitute the given points into the slope formula:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{8-9}{-4-1}=\dfrac{-1}{-5}=\dfrac{1}{5}[/tex]

To write the equation of the line, we can use the point-slope form of a linear equation.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope m = 1/5 and point (1, 9) into the formula:

[tex]y-9=\dfrac{1}{5}(x-1)[/tex]

Simplify:

     [tex]y-9=\dfrac{1}{5}x-\dfrac{1}{5}[/tex]

[tex]y-9+9=\dfrac{1}{5}x-\dfrac{1}{5}+9[/tex]

           [tex]y=\dfrac{1}{5}x+\dfrac{44}{5}[/tex]

Therefore, the equation of the line that passes through the points (1, 9) and (-4, 8) is:

[tex]\boxed{y=\dfrac{1}{5}x+\dfrac{44}{5}}[/tex]

The value of the given exponent numerical expression will be negative 32.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

[tex]\rightarrow \left ( -128 \right )^{\frac{5}{7}}[/tex]

We know that 128 can be written as,

128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

128 = 2⁷

Then the value of the expression is given as,

[tex]\rightarrow \left ( (-2)^7\right )^{\frac{5}{7}}\\\\\rightarrow \left ( -2\right )^{\frac{7 \times 5}{7}}\\\\\rightarrow \left ( -2 \right )^5[/tex]

Simplify the expression, then we have

⇒ (-2)⁵

⇒ - (2)⁵

⇒ - 32

The value of the given exponent numerical expression will be negative 32.

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The variable type for the type of flooring in a room is Qualitative Discrete. This type of variable takes on unmistakable classes and can't be estimated on a mathematical scale.

Let us consider that the type of flooring in a room may be rug, tile, or hardwood, and there is no way to quantify the type of flooring on a mathematical scale.

The variable type for the type of cooking served in a café is likewise Qualitative Discrete. This variable takes on unmistakable classes like Italian, Chinese, and Mexican, and it is basically impossible to gauge the type of food on a mathematical scale.

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The annual interest is $22.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Given;

Amount invested= $550

Annual interest= 4%

SI= 550*4*1/100

=5.5*4

=22

Therefore, the simple interest will be $22.

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8. The length VX is not equal to the length WY. Then the incorrect option is A.

9. The measure of the angle ∠DEG will be 33°.

One of the first areas of mathematics is geometry, along with maths. It is preoccupied with spatial characteristics including the separation, form, size, and relative placement of objects. A geometer is a mathematician who specializes in shape.

8. The base of the pyramid is a square. Then we have

WX = XY = YZ = ZW

VW = VX = VY = VZ

The length VX is not equal to the length WY. Then the incorrect option is A.

9. The measure of the angle ∠HBC = 33°. Then the measure of the angle ∠DEG is given as,

∠HBC = ∠DEG (Because they are alternate extiroir angles)

∠DEG = 33°

The measure of the angle ∠DEG will be 33°.

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To force the output to show the decimal point and trailing zeros of a decimal number use the showpoint, manipulator.

The showpoint function is a manipulator that sets the show point flag, which instructs an output stream to write a decimal point for floating-point output, even if the point is superfluous. This is done by setting the showpoint flag, which is done by setting the show point flag (only zeros appear after the decimal point). More specifically, the calls to the functions.

The distinction between a whole number and the fractional component of a number is denoted by the use of a symbol known as a "decimal point," which can be either a point or a dot. A different name for it is the Decimal Mark. The representation of the decimal point is the (.). In addition to using whole numbers, we frequently work with decimals.

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A. The total value of the loan with quarterly compounded interest is $52,400.

B. The total value of the loan with monthly compounded interest is $52,010.04

Part A: Total value of the loan with the quarterly compounded interest

To find the total value of the loan, we'll use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount (loan + interest)

P = principal amount (initial loan) = $20,000

r = interest rate = 7% = 0.07

n = number of times compounded per year = 4 (quarterly)

t = number of years = 10

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/4)^(4 * 10)

A = $20,000 * (1.0175)^40

A = $20,000 * 2.620075

A = $52,401.51

Rounding to the nearest hundred, the total value of the loan with quarterly compounded interest is $52,400.

Part B: Total value of the loan with the monthly compounded interest

To find the total value of the loan with monthly compounded interest, we'll use the same formula with a different value of n:

A = P * (1 + r/n)^(nt)

Where:

n = number of times compounded per year = 12 (monthly)

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/12)^(12 * 10)

A = $20,000 * (1.005833)^120

A = $20,000 * 2.600502

A = $52,010.04

Rounding to the nearest hundredth, the total value of the loan with monthly compounded interest is $52,010.04

The difference between the two loans is $52,401.51 - $52,010.04 = $391.47

The difference between the two loans is due to the higher frequency of compounding in the monthly compounded interest loan. The interest is compounded more times per year, so the interest is accumulating on the interest more quickly, leading to a higher overall interest charge.

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Sarah can pour 1 gallon from one batch of Green Team juice .

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that Sarah mixes 6 quarts of green apple juice with 3 quarts of kiwi juice and 3 quarts of spinach juice.

6 quarts apple juice and 8 cups cranberry juice.

3 quarts = 0.5 gallons

8 cups = 0.5 gallons.

Total juice got here is 0.5 + 0.5 = 1 gallon.

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