=
Quadrilateral N' is the image of quadrilateral N under a dilation.
A
B
N
OG
IN
D

The vector equation for the line of intersection of the planes x+4y-4z=-3 and x + z = 5 is r = <5, -2, 0> + t <-1, 5/4, 1>

The equations of the planes are:

x + 4y - 4z = -3                    ..............(1)

and x + z = 5                      .............(2)

Subtract equation (2) from equation (1),

( x + 4y - 4z + 3) - (x + z - 5 ) = 0

4y - 5z + 8 = 0

we can rewrite is as,

4y = 5z - 8

y = 5/4 z - 8/4

y = 5/4 z - 2                  ...............(3)

Here, we don't have enough equations to uniquely solve for either y or z. So, we set z = t, where t can be any real number.

The variable t is the free parameter for the parametrization of the line.

Substitute z = t in equation (3) we get,

y = 5/4 t - 2        

From equation (2),

x = 5 - z

For z = t,

x = 5 - t

Thus, the parametrization of the line would be,

(x, y, z) = (5 - t, -2 + 5/4 t , t)

           = <5, -2, 0> + t<-1, 5/4, 1>

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When the line passes through two points as shown, the slope is 11/3.

The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.

Here,

m=3

m=(y2-y1)/(x2-x1)

3=(y+5)/(-3+(2))

-3=y+5

y=-8

The value of slope is 11/3 when the line is passing through 2 points as given.

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The expression representing the total amount paid by Joshua at the register is 1.007x dollars.

We have,

To represent the total amount that Joshua paid at the register, we need to account for the following steps:

- Applying the 5% discount to the original price x:

Discount = 5% of x = 0.05x

Calculating the price after the discount:

Price after discount = x - Discount = x - 0.05x = 0.95 x

Adding the 6% tax to the discounted price:

Tax = 6% of the discounted price = 0.06 x (0.95x)

The expression for the total amount that Joshua paid at the register:

Total amount paid

= Price after discount + Tax

= 0.95 x + 0.06 (0.95 * x)

Simplifying the expression:

Total amount paid = 0.95x + 0.057x

Total amount paid = 1.007x

Thus,

The expression representing the total amount paid by Joshua at the register is 1.007x dollars.

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The shortest route from Ellport to Union Falls using road is 18 miles

An equation is an expression that shows the relationship between numbers and variables.

Pythagoras theorem is used to determine the measure of the sides of a right angled triangle. It is given by:

(hypotenuse side)² = (adjacent side)² + (opposite side)²

The distance from Larksville to Smithfield = 9 + 9 + 6 = 24 miles

The distance from Larksville to Union Falls = 19.5 + 6.5 = 26 miles

Let x represent the distance from Smithfield to Union falls, using Pythaoras:

26² = 24² + x²

x² = 100

x =  10 miles

the distance from Smithfield to Union falls is 10 miles.

Let y be the shortest route from Ellport to Union Falls, using Pythagoras:

y² = 10² + (9 + 6)²

y² = 10² + 15²

y² = 325

y = 18 miles

The distance from Ellport to Union Falls is 18 miles

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Answer:

yes

Step-by-step explanation:

when y equals 0, x equals 0 also

y = x will produce a straight line passing through the point of origin (0,0)

The estimated mean score is given as follows:

19.12.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

For each score, we consider it to be the mean of each interval in the frequency table, hence the sum of all scores is given as follows:

4 x 19 + 9 x 14 + 13 x 15 + 18 x 28 + 28 x 10 + 43 x 13 = 1740.

The total number of scores is of:

19 + 14 + 15 + 20 + 10 + 13 = 91.

Hence the mean score is obtained as follows:

1740/91 = 19.12.

The frequency distribution for this problem is given as follows:

1-7:19

8-10:14

11-15:15

16-20:20

21-35:10

36-50:13

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The percent of Carmela's gross pay that is her take-home pay is 75%

Carmela's gross pay is $784.25

Her total deductions is $191.17

Therefore the percent of her gross pay can be calculated as follows

The first step is to subtract the deductions from the gross pay

784.25 - 191.17

= 593.08

The percent of the gross pay that is take-home pay is

593.08/784.24 × 100

= 0.75 × 100

= 75%

Hence 75% of her gross pay is take-home pay

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A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

Because we are dealing with different units here, we first would need to know how many inches are in one foot.

1 foot = 12 inches

Now that we know how many inches are in a foot, we can convert the length and width of the room from feet to inches.

6 feet = 72 inches

10 feet = 120 inches

Taking these numbers, we now need to figure out the area of the floor.

72 × 120 = 8640

Now, find the area of each tile.

6 × 8 = 48

Taking 8640, we can now divide that by 48 to get the number of tiles needed.

8640 ÷ 48 = 180

Therefore, 180 tiles are needed to cover the floor.

By using the equation of the line of best fit, the​ number of minutes Nikki would need to listen to the radio is equal to 63.275 minutes.

In order to determine the​ number of minutes Nikki would need to listen to the radio, we would have to substitute the value representing the number of commercials (y) into the linear equation and then evaluate as follows;

y = 0.338x − 1.387

When the value of y = 20 commercials, the number of minutes (x) in feet is given by;

20 = 0.338x − 1.387

By rearranging and collecting like terms, we have the following:

0.338x = 20 + 1.387

0.338x = 21.387

Number of minutes (x) = 21.387/0.338

Number of minutes (x) = 63.275 minutes.

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Complete Question:

Nikki gathered data about the length of time she spent listening to the radio and the number of commercials she heard. She organized the data in a scatter plot, where x represents the minutes spent listening and y represents the number of commercials. Then she used the graphing tool to find the equation of the line of best fit: y = 0.338x − 1.387. Based on the line of best fit, for approximately how many minutes will Nikki need to listen to the radio to hear 20 commercials?

The linear function that describes the relationship is y = -2x + 3

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

x f(x)

−1 5

0 3

1 1

A linear function is represented as

y = mx + c

Where

c = y when x = 0

This means thar

c = 3

So, we have

y = mx + 3

From the table, we can see that

As x increases by 1, y decrease by 2

This means that

m = -2

So, we have

y = -2x + 3

Hence, the equation is y = -2x + 3

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Answer: I'm sorry, but the information provided is not enough to determine the value of x. The statement "mA = 3x°" does not provide enough context to understand what "mA" and "x" represent, and what the relationship between them is. Additionally, the statement "m" does not provide any information that can help determine the value of x. Can you please provide more information or context?

Step-by-step explanation:

By factoring the preceding quadratic equation and then inserting the values of "x," which are -3, -2, -1, 0, 1, 2, 3, 4, 5, the values of "y," which are 12, 5, 0, -3, -4, 3, 0, 5, 12, may be found.

First, factorize the given quadratic equation before completing the table.

Now, the values of "x" according to the given table are:

x = -3, -2, -1, 0, 1, 2, 3, 4, 5

Add the expression x=-3 to the equation (1).

y = (-3-3)(-3+1)

y = 12

Add the expression x=-2 to the equation (1).

y = (-2-3)(-2+1)

y = 5

Put x=-1 as a value in the equation (1).

y = (-1-3)(-1+1)

y = 0

Put x=0 as the value in the equation (1).

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

y = -3

Put x=1 as the value in the equation (1).

y = (1-3)(1+1)

y = -4

Put x=2 as a value in the equation (1).

y = (2-3)(2+1)

y = -3

Add the expression x=3 to the equation (1).

y = (3-3)(3+1)

y = 0

Add the expression x=4 to the equation (1).

y = (4-3)(4+1)

y = 5

Add the expression x=5 to the equation (1).

y = (5-3)(5+1) y = 12

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Answer:

4 or 3

Step-by-step explanation:

X³+12X=7X²

X³-7X²+12X=0

X(X²-7X+12)=0

SOLVING THE QUADRATIC EQUATION

you have X=3 or X=4

The surface area of the triangular prism is 120[tex]cm^2[/tex]

Now, According to the question:

A triangular prism is a polyhedron with a triangle for a base, thus it is a three-sided prism. Given that the triangle has three sides and a height of h, the surface area would be A = Ph + ab where P is the perimeter of the triangle.

We have :

A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters.

Now,

Hypotenuse  = 13

a = 5 cm

b = 12 cm

h = 2 cm

The perimeter of the triangle is the sum of all the sides or:

P = 13 + 5 + 12

P = 30 cm

To get the surface area, substitute the values in the formula below:

A = Ph + ab

A = (30)(2) + (5)(12)

A = 60 + 60

A = 120

Hence, The surface area of the triangular prism is 120[tex]cm^2[/tex]

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If you invest $10000 in a bank , then the better investment plan is (a) 9% compounded monthly .

The amount to be invested in bank is = $10000  ;

the formula to calculate the final amount by compounding is given as :

A = P(1 + r/n)^(nt)   ;

Where: (A) = final amount , (P) = initial amount ,

⇒ r is interest rate (in decimal form) , n is number of times the interest is compounded per year and

⇒ t is number of years investment is made

(a) the rate of interest is 9% compounded monthly ;

in this case n = 12  , because there are 12 months in 1 year ;

So , Amount = 10000(1 + 0.09/12)^(12×t)

Amount = 10000 × (1.0075)^(12×t)  

Suppose t = 1 ;

we get , Amount = 10000 × (1.0075)¹² ≈  10938 .

(b) the rate of interest is 9% compounded annually ;

in this case n = 1  , because compounded annually ;

So , Amount = 10000 × (1 + 0.09)^(1×t)

Amount = 10000 × (1.09)^t  

Suppose t = 1 ; we get , Amount = 10000 × (1.09)¹ ≈ 10900 ;

On comparing both the interest value we observe that ,

the monthly compounding returns more value than compounding annually  .

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Answer:

9.87 Gallons

Step-by-step explanation:

Start by finding how far mr. keith here can drive with one gallon of gas.

to do this you will:

360 ÷ 12 = 30

For one gallon of gas, he can drive 30 miles.

Now that we know the rate for 1 gallon of gas, you just apply that rate to the new mileage:

296 (new distance) ÷ 30 (how many he can do in one mile) = 9.87 (how many times that 30 miles goes into 296 (recall that this is the rate))

To drive 296 miles, keith will use 9.87 gallons of gasoline.

hope this helped :)

√5 is the minimum distance between the line AB and CD.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given Two lines AB and CD,

Since, The minimum distance between two lines is the distance between B and C As we can see in the graph

Since, coordinates of B and C are, (1, 2) and (3, 1)

From the formula of distance between two coordinates:

Distance = √((x₂ -x₁)² + (y₂ -y₁)²)

in our case,

Distance = √((3 - 1)²  + (1-2)²)

Distance = √4 + 1)

Distance = √5

Therefore, the minimum distance between the line AB and CD is √5.

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The number of terms in the algebraic expressions are:

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

6y + 14 and 3x³ + 7x² + x - 5

Consider an expression given as

ax + b

The number of terms in the expression is 2 and the terms are ax and b

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

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Complete question

Identify the number of terms and then the resend themselves for each algebraic expression

6y + 14 and 3x³ + 7x² + x - 5

The range would be; [75,212] and the greatest one is around 212.5. .5] a domain and a range.

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

Recall this by saying "DoLaR RiBiT," where "DoLaR" stands for "domain," "L" and "R" stand for "left to right," "R" stands for "range," and "B" and "T" stand for "bottom to top," and "R" stands for "range."

Since we can see that the function doesn't approach 250,  in the graph, 250 is not inside the range.

Between the minimum and greatest value are the numbers that make up the range. The range would be; [75,212] because the lowest Y value is 75 and the greatest one is around 212.5. .5] a domain and a range.

The collection of values that can be substitute into a function's domain are called its parameters.

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The system of linear equations is y = 800x + 5445, and y = 900x + 4995. The solution is 4.50. This states that the number of steps taken by Danna and Lucia will be equal after 4.50 hours.

The set of two or more linear equations containing the same variables is known as a system of linear equations in mathematics. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation.

Let us suppose the number of hours = x.

Let us suppose the total number of steps = y.

Given that, Lucia has 5445 steps and Lucia averages 800 steps per hour.

For Lucia the linear equation is:

y = 800x + 5445

For Danna, Danna has 4995 steps and Danna averages 900 steps per hour.

For Danna the linear equation is:

y = 900x + 4995

The system of linear equations is:

y = 800x + 5445 (equation 1)

y = 900x + 4995 (equation 2)

Substitute the value of y of equation 1 in equation 2:

800x + 5445 = 900x + 4995

5445 - 4995 = 900x - 800x

450 = 100x

x= 4.50

B. The solution of the linear equation is 4.50. This states that the number of steps taken by Danna and Lucia will be equal after 4.50 hours.

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The slope is 2, which equals the distance travelled each hour. The total distance hiked at the start of the second day is represented by the y-intercept, which is 4, which is also the y-value. intercept's

We locate the rise/run before calculating the slope. Since the line increases by 2 between each point, the rise is 2. It travels over 1 between the points, hence the run is 1. The slope is now 2/1, or 2.

Given that it is rise/run, this gives us miles/hours, which indicates the number of miles she treks per hour.

The line's crossing of the y-axis is known as the y-intercept. At four, this is.

The fact that the y-value at this time is 4 and the x-value at this point is 0 tells us that she has trekked 4 miles in the 0 hours since the start of the second day, which is the distance she has covered so far.

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Answer:

a₈ = 44

Step-by-step explanation:

to find a₈, substitute n = 8 into the explicit formula

a₈ = 6(8) - 4 = 48 - 4 = 44

The degree measure of the sector is θ = 180°

We know that the area of a sector is nothing but the area inside the section of the circle created by two radii and an arc.

The formula for the area of a sector of the circle is:

area of a sector = [tex]\frac{\theta}{360} \times \pi \times r^2[/tex]

where θ is the central angle measure in degrees

And πr² is the area of the circle

Here, the area of a sector of the circle A = 32π cm²

and the area of a circle (πr²) =  64π cm²

Using above formula of the area of a sector of the circle,

[tex]A=\frac{\theta}{360} \times \pi \times r^2\\\\32\pi=\frac{\theta}{360} \times \pi \times r^2\\\\32\pi=\frac{\theta}{360} \times 64\times \pi\\\\\theta=\frac{360}{2}\\\\ \theta=180^{\circ}[/tex]

Therefore, the central angle associated to that sector is 180°

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The operation of 1 * (-1) * 2 equals option D. 2.

Binary operations are the operations which are performed on a specific set.

If the operation is defined on a set X, then binary operation can be defined as,

* : X * X → X.

Addition, subtraction, ... are some of the binary operations.

The given binary operation is defined as,

a * b * c = [tex]a^b-b^c+c^a[/tex]

We have to find the value of 1 * (-1) * 2.

By the definition,

1 * (-1) * 2 = [tex]1^{-1}-(-1)^{2}+2^1[/tex]

              = 1 - 1 + 2

              = 2

Hence the correct option is D.

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The new value = 340 + (19% × 340)

The actual change = The new value - 340

"Information available from the question"

340 increased by 19%

To write in mathematically:

The value of the percentage increase = 19% × 340

The new value = 340 + The value of the percentage increase

The new value = 340 + The value of the percentage increase

= 340 + (19% × 340)

= 340 + 19% × 340

= (1 + 19%) × 340

= (100% + 19%) × 340

= 119% × 340

= 119 ÷ 100 × 340

= 119 × 340 ÷ 100

= 40,460 ÷ 100

= 404.6

The actual change = The new value - 340

                              = 404.6 - 340

                              =  64.6

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Jill ride 43.39 meters farther than Jessica.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.

Given, Jill and Jessica are bike riding at the park. Jill rides her bike around the two edges of the rectangular park while Jessica takes the shortcut

Given the length of the Rectangular park = 100m

The width of the park =  60m

Thus jill ride total = 60 + 100

Jill ride total = 160m

Jessica took a shortcut since she rides diagonally.

From the Pythagorean theorem:

hypotaneus² = base² + height²

Thus,

total distance Jessica covers = √(60² + 100²)

total distance Jessica covers = √3600 + 10000

total distance Jessica covers = √13600

total distance Jessica covers = 116.61

Difference between their distances = 160 - 116.61

Difference between their distances = 43.39

therefore, 43.39 m farther does Jill ride than Jessica.

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Complete question:

Answer:

3

Step-by-step explanation:

15 is divisible by 3, 3 × 5 = 15. Then of course 1 and 15 no other ones. 1,3,5,15

39 is divisible by 3, 3× 13 = 39, then 1 and 39. 1,3,13,39

The only common factors are 1 and 3, and since 3 is greater that is the greatest common factor.

Hope that helps! Let me know if you have any further questions.

The greatest common factor shared by numbers 39 and 15 is 3.

Given two numbers, 39 and 15.

The greatest common factor can be defined as the factor which is common to both 39 and 15 and is the greatest of all those common factors of 39 and 15.

First, list out the factors of 39 and 15.

Factors of 39 = 1, 3, 13, 39

Factors of 15 = 1, 3, 5, 15

The only factor which is common to both 39 and 15 is 3.

So, the greatest common factor of both is 3.

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The length of side AB rounded to two decimal places is 16.25.

In a right angle triangle, the side on the base of the angle in question is divided by the hypotenuse. In this case, we can use the cosine ratio to find the length of AB.

We are provided with the following information,

C is the right angle, C= 90°

A= 52°

AC = 10. 01

sin 52° = 0. 788

cos 52° = 0. 616

tan 52° = 1. 280

Now,

since angle C is the right angle, AB is the hypotenuse.

Therefore, with respect to Angle A, AC will be the base and BC will be the perpendicular.

We know, cos x= base/hypotenuse

In this case, cos A = AC / AB

cos 52° = 10. 01/ AB

AB = 10. 01 / 0. 616

AB = 16.25

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The distribution of the mean, median, and mode values will depend on how skewed the distribution is. As a result, mean or mode may be larger than or less than mode.

correct answer is D.

Different measures of the center in a set of numerical data include mean, median, and mode. They each attempt to condense a dataset into a single number that may be used to represent a "typical" data point.

The "mean" value is obtained by summing all the data points and dividing the result by the total number of data points.

The middle number, or median, is obtained by placing all data points in order and choosing the middle one (or, if there are two middle numbers, the mean of those two figures).

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