Write the quadratic equation whose roots are
-1
and
6
, and whose leading coefficient is
4
.
(Use the letter
x
to represent the variable.)

The table of values for the equation xy =5 are

x       y  

5       1

10     1/2

15     1/3

20   1/4

25    1/5

The relationship between the various data points is displayed using tables of values. In scientific lesson, a table of values could be used. Tables of values are used by scientists and researchers to record their data, which is subsequently examined for patterns. Then, they can use this pattern to forecast things.

In the problem, the equation to derive the table of value is xy = 5, this is re written to be y = 5/x

The values of y are solved as follows

For x = 5, y = 5/5 = 1

For x = 10, y = 5/10 = 1/2

For x = 15, y = 5/15 = 1/3

For x = 20, y = 5/20 = 1/4

For x = 25, y = 5/25 = 1/5

Table of values

x       y  

5       1

10     1/2

15     1/3

20   1/4

25    1/5

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The correct conversion factor is B: 5280 ft / 1 mi.

Option (B) is correct.

What is unit conversion?

Unit conversion is the process of changing a measurement from one unit to another. For example, converting meters to feet, or kilometers to miles. In order to convert from one unit to another, you need to know the conversion factor between the units, which is the ratio of equivalent values in the two units.

When converting a distance in miles to feet, you need to multiply the distance in miles by the number of feet in a mile. The conversion factor that is commonly used to convert miles to feet is 1 mi = 5280 ft.

The correct conversion factor to convert a distance of 12 mi to feet is therefore:

12 mi x (5280 ft / 1 mi) = 12 x 5280 ft

Hence, the correct conversion factor is B: 5280 ft / 1 mi.

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The number of slices that Jamal eats will be 10 slices.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Let Amelia's share be x.

Jamal's share will be x + 4.

Therefore, the equation will be Illustrated as:

3/5 = x/(x + 4)

Cross multiply

5x = 3x + 12

5x - 3x = 12

2x = 12

Divide

x = 12 / 2

x = 6

Jamal's share will be

= 6 + 4.

= 10

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The Side-Angle-Side rule is the foundation for this query. The correct response is therefore option A, since ABC=DEF cannot be inferred from the additional statement that AB=EF.

According to this rule, the corresponding two angles of one triangle are congruent with the two angles of the other triangle. The side-angle-side postulate is the only congruence rule that can be applied as a result.

Here,

A=D and C=F in triangle ABC and triangle DEF.

We must choose a statement that prevents you from deducing that triangle ABC = triangle DEF.

The correct response is therefore option A, since ABC=DEF cannot be inferred from the additional statement that AB=EF.

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In given word problem the possibility for 3 non repeating digits followed by # sign is 720 ways.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here the gate code at your apartment complex is three numerical digits followed by the "#"sign.

There are 10 digits (0 to 9)

Compute the number of possible gate codes if each code contains non repeating digits as follows,

The first 3 place in the code must be filled by three non-repeating digits.

So, there are 10 possibility for first  digit and 9 possibility for second digit and 8 possibility for third digit.

Hence the 3 non repeating digits can occur un 10×9×8 ways.

The three non repeating digit followed by #. Then sign # can occur in only way, then,

Total possibility = 10×9×8×1 = 720 ways.

Hence the possibility for 3 non repeating digits followed by # sign is 720 ways.

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The area of shaded region from the given figure is 278.64 when the diameter of the circle is 36m.

What is area of circle ?

area of circle can be defined as the product of pi and square of radius

and here the value of pi is 22/7 or 3.14

Given in the figure,

a circle is within square with diameter 36m .

So, we have to find the

area of a shaded region  = area of square - area of circle .

radius = d/2

radius = 36/2

radius = 18 .

= 36*36 - 3.14 * 18*18

= 1296 - 1017.36

= 278.64

Hence, The area of shaded region from the given figure is 278.64 when the diameter of the circle is 36m.

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Answer:

1 2/3 went in each container

Step-by-step explanation:

10 divided by 6 is 1.666666666677777777777 which equals to 1 2/3 multiply it by 6 and you will get 10.

As a result, the angle's measure is 135° and its supplement is 45°.

Two angles are referred to as supplementary angles when the sum of their measures is 180 degrees.

For instance, 70 degrees and 110 degrees complement one another.

Two angles are said to be supplementary if their sums total 180 degrees.

A linear pair's two angles, are always supplementary.

Let x be the angle's measurement. If so, (180x) is the size of its supplementary angle.

Now, calculate:

180 - x = 1/3x

3(180 - x) = x

4x = 540

x = 135

Supplementary angle = 180 - 135 = 45°

Therefore, as a result, the angle's measure is 135° and its supplement is 45°.

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The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles

The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles.

Always true. The opposite angles of an isosceles trapezoid are supplementary because the diagonals of an isosceles trapezoid bisect each other. Therefore, the angles formed by the intersection of the diagonals are supplementary, since the sum of two supplementary angles is 180 degrees.

The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles.

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Answer:

c. Y has a binomial distribution with n=40 observations and probability of success p=0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.

Step-by-step explanation:

if wrong pls tell

Using mathematical operations, the distance that differentiates Terry and Damon is 7 kilometers.

Mathematical operations are the computation of values using mathematical operands (÷, ×, +, -, etc), and mathematical operators like addition, subtraction, division, and multiplication.

In this situation, we use the subtraction operation to determine the difference or the distance between Terry and Damon.

The total distance between Toronto and Sudbury = 418 km

The distance covered by Terry from Sudbury to Toronto = 310 km

The length yet to be covered by Terry = 108 km (418 - 310)

The distance covered by Damon from Toronto to Sudbury = 303 km

The length remaining for Damon = 115 km (418 - 303)

The distance apart between Damon and Terry = 7 km (115 - 108)

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Answer:

x = 6

Step-by-step explanation:

Vertices of a rectangle are normally listed so that adjacent vertices are connected by edges. Therefore, the edges of rectangle HIJK are HI, IJ, JK and KH.

As the opposite sides of a rectangle are congruent:

Therefore, to find the value of x, set the given expressions for HI and JK equal to each other and solve for x:

[tex]\implies \sf HI=JK[/tex]

[tex]\implies 3x+7=6x-11[/tex]

[tex]\implies 3x+7-7=6x-11-7[/tex]

[tex]\implies 3x=6x-18[/tex]

[tex]\implies 3x-6x=6x-18-6x[/tex]

[tex]\implies -3x=-18[/tex]

[tex]\implies -3x \div -3=-18 \div -3[/tex]

[tex]\implies x=6[/tex]

Answer:

9

Step-by-step explanation:

The Total surface area of a pyramid formula = ½ pl + B, Where 'p' is the perimeter of the base and 'l' is the slant height of the pyramid and B is the area of the base.

A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=13Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.

A triangular pyramid, for instance, has a base area of 20 cm2 and a height of 9 cm. The formula V = (1/3) Bh, where "B" stands for the base area and "h" for the height of the pyramid, is used to calculate the volume of a pyramid.

We can use the formulas for the area of polygons to calculate "B" because we know that the base of a pyramid can be any polygon. A pyramid with a triangle base is referred to as a triangular pyramid. 

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The value of x is 2, when the volume of pyramid is 125 cm³ which is equal to [tex]\mathrm{5^{\tfrac{x}{6}} }[/tex].

A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=1/3Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.

We know that pyramid's volume is

[tex]\mathrm{{\textstyle V={\tfrac {1}{3}}Bh}}[/tex]

B = base area = [tex]25^{1/4} \times25^{1/4}[/tex]

= [tex]\sqrt[4]{25} \times \sqrt[4]{25}[/tex]

= [tex]\sqrt[4]{25}^2[/tex]

= [tex]\sqrt[2]{25}[/tex]

= 5 cm²

and

h = 75 cm

[tex]$\mathrm{{\textstyle V={\dfrac {1}{3}} \times5 \times 75}}[/tex]

V = 125 cm³

Now it is given that  [tex]\mathrm{5^{\tfrac{x}{6}} = 125 }[/tex]

So,

[tex]\mathrm{5^{\tfrac{x}{6}} = 125 }[/tex]

[tex]\mathrm{5^{\tfrac{x}{6}} = \sqrt[3]{5} }[/tex]

[tex]\mathrm{5^{\tfrac{x}{6}} = 5^{\tfrac{1}{3}} }[/tex]

[tex]\dfrac{x}{6} = \dfrac{1}{3}[/tex]

3x = 6

x = 6/3

x = 2

Thus, the value of x is 2, when the volume of pyramid is 125 cm³ which is equal to [tex]\mathrm{5^{\tfrac{x}{6}} }[/tex].

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Answer:

c

Step-by-step explanation:

because y = 0 when x = 2 and y = -4 when x =0

The area of R can be calculated using the definite integral of the function y = 2x^2 -6x +4 and  between g(x ) = cos1/4 and x = 4.

The integral expression is ∫(2x^2)-6x+4dx = ∫e^u du = e^u + C = e^(2x-x^2) + C. Evaluating the integral between x = 0 and x = 1 gives the area of R as e^2 - 1.

(b) The area of S can be calculated using the definite integral of the function y = e^(2x-x^2) between x = 0 and x = 1, minus the integral of the function y = 1 between x = 0 and x = 1. The integral expression for S is ∫e^(2x-x^2)dx - ∫1dx = ∫e^u du - x = e^u + C - x = e^(2x-x^2) + C - x. Evaluating the integral between x = 0 and x = 1 gives the area of S as e^2 - 1 - 1.

(c) The volume of the solid generated when R is rotated about the horizontal line y = 1 can be found using the integral expression ∫2πx(e^(2x-x^2) - 1)dx. This expression represents the area of the circular cross-sections of the solid multiplied by 2πx, which is the circumference of the circle. When evaluated between x = 0 and x = 1, this integral gives the volume of the solid generated when R is rotated about the horizontal line y = 1.

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the difference of of equations in the system 1. Equation (1) for system 1 is similar to the equation (4) of the system 2.

Lx + My = N ---------(1)

Ax + By = C ---------(2)

System 2 :

(L - A)x + (M - B)y = N - C -------(3)

Lx + My = N ---------(4)

If we subtract equation (2) from equation (1),

(Lx + My) - (Ax + By) = N - C

Lx - Ax + My - By = N - C

(L - A)x + (M - B)y = N - C

Which is similar to equation (3) of the system 2.

And equation (1) of the system (1) is similar to the equation (4) of the system (2)

Therefore, equation (3) of the system 2 is the difference of of equations in the system 1. Equation (1) for system 1 is similar to the equation (4) of the system 2.

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Answer:

Step-by-step explanation:

Given that 79 balcony and 27 general admission tickets sell for $5550, and 79 balcony and 36 general admission tickets sell for $5820, you want the cost of each kind of ticket.

The equations representing the sales are ...

  79b +27g = 5550

  79b +36g = 5820

Subtracting the first equation from the second, we have ...

  (79b +36g) -(79b +27g) = (5820) -(5550)

  9g = 270 . . . . . . . . . simplify

  g = 30 . . . . . . . divide by 9

  79b +27(30) = 5550 . . . . . . substitute into the first equation

  79b = 4740 . . . . . . . . . . subtract 810 & simplify

  b = 60 . . . . . . . divide by 79

A balcony seat ticket costs $60; a general admission floor ticket costs $30.

Reason:

The like terms 2n and -5n combine to -3n. In other words, 2n-5n = -3n

The other pair of like terms 3 and 6 combine to 3+6 = 9

R13 fiberglass batt insulation, typically used in walls and floors, is 3 5/8 inches thick, according to Energy.gov.

To determine the number of insulation batts required, first determine the area to be insulated in square meters (m2). Calculating the square metre (m2) area of your walls is actually fairly simple; simply multiply the length by the breadth.

To assess the cost of cellulose insulation for your project, first decide how much insulation you would require. To do so, divide the square footage of the space by the depth or the desired R-value. R-25 EcoTouch insulation is designed to fit snugly between outside wall wood studs. After installing cover material on one side of the cavity, friction-fit unfaced insulation between studs.

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Answer: C - 5 cups

Step-by-step explanation:

Hello! The art teacher mixes 3 cups of blue paint with 2 cups of red paint.  Since the art teacher combines the two, you have to add the two.  3 + 2 = 5, which should be your answer.  Hope this helps!

The temperature on the Fahrenheit scale is 107.6°F and Kelvin scale is 315.15K. The solution has been obtained by unit conversion.

What is unit conversion?

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, instead of using hours to represent time, you might use minutes, or you could use feet instead of miles to express distance. Measurements are frequently offered in one set of units, like feet, but are required in another set, like chains.

We are given the melting point of an unknown solid to be 42.0°C.

For converting the given temperature in Fahrenheit, we use the given formula:

⇒(Temperature in Celsius × 9/5) + 32 = Temperature in Fahrenheit

So,

⇒(42°C × 9/5) + 32 = x°F

⇒(42°C × 9/5) + 32 = 107.6°F

Now, for converting the given temperature in Kelvin, we use the given formula:

⇒Temperature in Celsius  +  273.15 = Temperature in Kelvin

This is because 0°C = 273.15 K

So, 42°C + 273.15 = 315.15K

Hence, the temperature on the Fahrenheit scale is 107.6°F and Kelvin scale is 315.15K.

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Answer:

wouldnt it just be 1/9

Step-by-step explanation:

Answer:

$195,345.60

Step-by-step explanation:

We can calculate the amount of money remaining in the fund after 6 years by multiplying the initial amount by (1 - 0.2)^6. In this case,

(1 - 0.2)^6 = 0.32768

So the fund will have $597,000 * 0.32768 = $195,345.60 after 6 years.

Line segment AB is congruent to line segment CD, ∠A ≡ ∠C, BE is congruent to DE and AE is congruent to CE in triangle ABE and triangle CDE. So all the first four options are corresponding parts of the two congruent triangles.

Therefore, the answer is e. None of the above.

Corresponding parts of congruent triangles are any pair of matching or identical elements in two congruent triangles. These can include:

Sides, such as line segment AB being congruent to line segment CD

Angles, such as ∠A being congruent to ∠C

Vertices, such as point E being the intersection of segments BD and AC in both triangles

Any other element that is identical in both triangles, like height, medians, circumcenters, etc.

In triangle ABE ≡ triangle CDE, congruent sides are

AB ≡ CD

BE ≡ DE

AE ≡ CE

Congruent angles are

∠A and ∠C

∠B and ∠D

∠BEA and ∠DEC

--The question is not readable, answering to the question below--

"Which of the following are not corresponding parts of the congruent triangles, triangle ABE and triangle CDE? Segments BD and AC intersect at point E to form one vertex and two sides of each triangle.

a. line segment AB is congruent to line segment CD

b. ∠A ≡ ∠C

c. BE is congruent to DE

d. AE is congruent to CE

e. None of the above"

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The value of the expression 84.7 divided by 14 will be 6.05.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value of the expression 84.7 divided by 14 will be:

= 84.7 / 14

= 6.05

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16 is  Median a sample with data values .

What is the mathematical median?

The middle number, or median, is obtained by sorting all of the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers).

                                 Example: Because the number 4 is in the middle when the numbers are ordered (1, 4, 7), it is the median of 4, 1, and 7.

Mean = Total of values/ Total number of observations

Total of values = 10+20+12+17+16 = 75

Total number of observations = 5

Mean = 75/5 = 15

Median:

Arrange in ascending order = 10, 12,16,17,20

Median = [n+1] / 2

N = number of observation = 5

Median = [5+1]/2 = 3rd observation

Median = 16

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a) The average price of a house today is $341,700.

b) The average price of a house next year is $325,865.

What is the average price?

The average price is a measure of the central tendency of a set of data points. It is defined as the sum of all the data points divided by the number of data points.

(a) To find the average price of a house today, we can use the formula:

New price = Original price x (1 + percentage increase)

New price = 260000 x (1 + 0.295) = 3417000

So, the average price of a house today is $341,700

(b) To find the average price of a house next year, we can use the formula:

New price = Original price x (1 - percentage decrease)

New price = 341700 x (1 - 0.05) = $325,865

So, the average price of a house next year is $325,865

Hence,

a) The average price of a house today is $341,700.

b) The average price of a house next year is $325,865.

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Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)

What is mean value theorem ?

The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].

The property of derivative  : r'(t) is the rate of change of water flow.

Justification :

r(s) - r(4) = r'(3) (5-4)

        - 5 = r(3)

In (4,5) , r(t) decreasing , so there are value of 3 and r'(3) > 0 , r'(3) = -5.

r(6) - r(5) = r'(3) (6-5)

          4  = r'(3)

In (5,6), r(t) increasing , so there are values of 3 and r'(3) > 0, r'(3) = 4.

∴ Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)

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The complete question is :

Water is flowing into a tank at a rate of r(t) where t is measured in seconds. Is there ever a time where the r'(t) = 0? If so, what time interval does t occur in? Justify your answer using the Mean Value Theorem.