When an integer is subtracted from 5 times the next consecutive odd integer, the difference is 38. Find the value of the greater integer

When 2 angles and an included side of 1 triangle are congruent to the corresponding piece of another triangle, it is said to be in ASA or AAS congruency

According to the Angle-Side-Angle Postulate (ASA), two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

And as seen in the figure to the right, we prove that triangle ABC is congruent to triangle DEF by the Angle-Side-Angle Postulate.

Contrarily, the Angle-Angle-Side Postulate (AAS) states that two triangles are congruent if their respective non-included sides are congruent with two angles from one triangle and two angles from another.

And as seen in the figure to the right, we prove that triangle ABC is congruent to triangle PQR by the Angle-Angle-Side Postulate.

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Answer:

well 700m is 2296.59 feet

and 1km is 3280.84 feet

and 300m is 984.252 feet

Step-by-step explanation:

hope this helps :)

The slope of the line y = - 4x + 10 is -4.

The slope of any line can be calculated using any two distinct points lying on the line. It is defined as the change in y coordinate with respect to the change in x coordinate of that line.

The net change in y coordinate is Δy, while the net change in the x coordinate is Δx, then the slope

                    m = Δy/Δx = dy/dx.

Here, we are given the line y = - 4x + 10

Differentiating the equation of line with respect to x, we get

                  dy/dx = - 4

⇒ slope m = dy/dx = -4.

Therefore, the slope of the line was found to be -4.

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NOTE : The question given here is not complete. The complete question is given below.

Question: What is the slope of y = - 4x + 10?.

Answer:

rate of the boat is 10.5 and the rate of the current is 1.5

Step-by-step explanation:

Distance = rate x time

Let r = rate of the boat

Let c = current

Upstream:

Rate: r -c

Time: 4 hours

Distance: 36

36 = 4(r-c)  Divide both sides of the equation by 4

9 = r - c

Downstream:

Rate: r + c

Time: 3 hours

Distance: 36

36 = 3(r+c)  Divide both sides by 3

12 = r -c

Combine the two bold equations:

9 = r - c

12 = r + c

21 = 2r  Divide both side's by 2

10.5 = r This is the rate of the boat.

Rate of the current:

4(10.5 - c) =36

42 - 4x = 36  Subtract 42 from both sides

-4x = -6  Divide both sides by -4

x = 3/2 or 1.5

The Side-Angle-Side rule is used to demonstrate the congruent theorem of a particular collection of triangles.

The two sides and included angle of ABDA are therefore equivalent to ABDC's two sides and included angle. According to the SAS Triangle Congruence Theorem, the triangles are congruent.

Knowing merely angle-angle-angle (AAA) is insufficient because it can result in triangles that are similar but not congruent. There are four shortcuts that can be used to check whether two triangles are congruent.

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Answer:

E

Step-by-step explanation:

We just need the last two clues. Since they said it is a line (4th clue) it could only be B, C, or E. But then, the last clue says the domain is -7. Now for almost all lines the domain is 'all real numbers'. All kinds of diagonal lines and also horizontal lines, the domain is all real numbers. Only vertical lines have a domain that is a single value. Graph E is a line that has the domain -7.

The solution of the equation x²-x -3 = 0 are x = (1±√13) /2.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Here we are given the equation x²-x -3 = 0 ---(i) which is a quadratic equation which we can solve using Sri Dharacharya Method.

Sri Dharacharya Formula:   For a quadratic equation ax² + bx + c = 0

The value of x is x= (-b ± [tex]\sqrt{b^{2}-4ac }[/tex]) /2a.

Using this formula in (i), we get

     x = (-(-1) ± [tex]\sqrt{(-1)^{2} -4*1*(-3)}[/tex]) /2*1

⇒  x = (1±√13) /2.

The solution of the equation are irrational which are x = (1±√13) /2.

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1. F v (D → T)

2.  V F

3. D

∴ T

4. D → T (Disjunctive syllogism 1,2)

5. T          ( Modus Ponens 3,4)

2. P → (cu → T)

2. Q → (T → E)

3. P

4. Q

∴ Cu → E

5. Cu → T  (modus ponens 1,3)

6. T → E  ( modus ponens 2,4)

7. Cu → E (Hypothetical syllogism 5,6)

3. 1. ~ X → [~X → (y → X)]

   2. ~ X

   ∴ ~ y

  3. ~X → (y → X)   (modus ponens 1,2)

  4.  y → X              ( modus ponens 2,3)

  5. ~ y                     ( modus tollens 2,4)

4. 1. k → (L→m)

    2. m v k

    3. ~m

    ∴ ~L

    4. K   (disjunctive syllogism 2,3)

    5. L → m  (modus ponens 1,4)

    6. ~ L    (modus tollens 3,5)

5. 1. ~S → D

   2. ~S v (~D→K)

   3. ~ D

∴ K

  4. ~(~S)   (Modulas tollens 1,3)

  5. S          ( Double nojection 4)

  6. ~D→K (Disjunctive syllogism 2,5)

  7. K         (Modus ponenes 3,6)

Hence we get the required answer.

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The expected value of the number of bids and profit are 0.2 and $220000

The possible question is added as an attachment

From the complete question, we have the following table of values

X (Number of bids)    0            1                   2

M = Profit               -$10000    $40000    $90000

Probability               0.81           0.18         0.01

Expected value of the number of bids

This is calculated as

E(x) = Sum of the products of the number of bids and the probability

This is represented as

E(x) = 0. * 0.81+1 * 0.18 + 2 * 0.01

Evaluate the products

E(x) = 0 + 0.18 + 0.02

Evaluate the sum

E(x) = 0.2

Expected value of the profit

This is calculated as

E(x) = Sum of the products of the number of profits and the probability

This is represented as

E(x) = 0 * -10000 + 1 * 40000 + 2 * 90000

Evaluate the products

E(x) = 0 + 40000 + 180000

Evaluate the sum

E(x) = 220000

Hence, the expected profit is $220000

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To make a volume of 320mL mixture that contains 8% vinegar, use 64mL of the first brand and 256mL of the second brand.

Let F be the volume of the first brand and let S be the volume of the second brand.

Now, we want the total mixture to be 320mL so: F + S = 310

Also, you want the total mixture to contain 12% vinegar so:

0.08F + 0.13S = 0.12(320)

Now, we can solve the system of equations using substitution method.

F + S = 320   -----(1)

0.08F + 0.13S = 0.12(320)   -----(2)

F = 320 - S      [solve 1st equation for F]

0.08(320 - S) + 0.13S = 0.12(320)     [substitute into 2nd equation]

25.6 - 0.08S + 0.13S = 38.4

0.05S = 12.8

S = 256 mL

F + 256 = 320     [substitute answer for S back into original equation]

F = 320 - 256

F = 64 mL

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After plotting all the three points, we get the parabolic equation in the form is 2(x - 1)²-34.

Any point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line.

General equation of the quadratic equation,

Y = ax² + bx +c

Given points,

(-2, 0),

(-1, -10),

(4, 0).

Putting the points in the general equation,

Putting (-2, 0), we get

0 = 4a - 2b + c

Putting (-1, -10), we get

-10 = a - b +c

Putting (4, 0), we get

0 = 16a + 4b +c

Solving all equations we get,

a = 2 , b = -4 , c = -16

After putting the values,

Y = 2x²- 4x- 16

2(x² - 2x - 8)

2(x²- 2x + 1 - 1 - 16)

=2(x - 1)²-34

Hence we get the required equation in the parabolic form.

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Number of ways 5 gymnasts participate including exactly two from Lia , Bella , Priscilla is equal to 252.

As given in the question,

Total number of gymnasts = 12

Number of gymnasts to be participates = 5

Condition:

Exactly two gymnasts from Lia , Bella , Priscilla

Number of ways 5 gymnasts participates

= ⁹C₃ × ³C₂

= ( 9!)/ ( 9 - 3)! 3! × 3!/ ( 3-2)! 2!

= [( 9× 8 ×7 × 6!)/ 6! ( 3× 2× 1)] × ( 3 × 2!)/ 2!

= [( 9× 8 ×7)/ ( 3× 2× 1)] × 3

= 252

Therefore, the number of ways 5 gymnast can participate out of 12 with the given condition is 252.

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The true statement for the relation is, the order of rows is unimportant.

What is row and column?

A row is an arrangement of items that are put next to or horizontally. A vertical split of items based on category is known as a column. The arrangement is in a left to right direction. The set-up is vertical, from top to bottom.

A table's rows are individual groups of connected data. Rows and columns are found in tables in relational databases (also known as records and fields, respectively).

Consider the given statements,

Entities in a column vary as to kind.

The order of the columns is important.

The order of the rows is unimportant.

More than one column can use the same name.

From the given statements, the true statement for the relation is, the order of rows is unimportant.

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The number of goals scored by one team is 56 and the other team scored 79 goals.

What are the linear equations in two variables?

A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.

Let the number of goals scored by one team be 'x' and the number of goals scored by the other team be 'y'

One team scored 23 goals more than another team

                        y = x + 23 --------(I)

And both teams scored 135 goals in total, so

                        x + y = 135 ------(II)

ut the value of y = x + 23 in equation (II), we get

                    x + x + 23 = 135

                   2x = 135 - 23

                    x = 112/2

                    x = 56

then y = 79.

Hence, the number of goals scored by one team is 56 and the other team scored 79 goals.

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The graph will cross the x-axis if the multiplicity of the real root is odd.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)

(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)

(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)

(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.

The graphs: (a) black, (b) red, (c) green

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Step-by-step explanation:

the standard form is (x - h)² = 4p(y - k), where the focus is (h, k + p) and the directrix is y = k - p.

the vertex is exactly in the middle between focus and directrix, and is therefore (h, k) = (0, 0).

therefore, p = 9.

(x - 0)² = 4×9×(y - 0)

x² = 36y

y = 1/36 x²

Answer: less than 4 days

Step-by-step explanation:

415 - 25 = 390

if ur spending 100 each day then

day 1 = 290

day 2 = 190

day 3 = 90

he needs to spend less than 4 days

The lower bound of the area of the rectangle is  7062.75 [tex]mm^{2}[/tex].

What is the Lower bound and Upper bound?

Lower Bounds - The lowest value that would be utilized to round a number to the previously estimated value is known as the lower bound.

Upper Bounds - The lower value that would be used to round a number to the next expected value is known as the upper bound.

Given, length = 370 mm

           width = 19.4 mm

First, we consider length = 370 mm, then

The upper bound for length = 375 mm

And, the lower bound = 365 mm

Second, we consider  width = 19.4 mm, then

The upper bound for width = 19.45 mm

And, the lower bound = 19.35 mm

So, the area of the given rectangle is:

Area =  length * width

Using lower bounds dimensions for both length and width, then

Area = 365*19.35 [tex]mm^{2}[/tex]

        = 7062.75 [tex]mm^{2}[/tex]

Therefore, the lower bound of the area of the rectangle is  7062.75 [tex]mm^{2}[/tex]

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Factoring the expression [tex]x^{6} - y^{6}[/tex] is[tex](x^{3} +y^{3})(x^{3}-y^{3})(x^{2}+y^{2}+xy)(x^{2}+y^{2}-xy)[/tex]

Given expression = [tex]x^{6}-y^{6}[/tex]

= [tex](x^{3})^{2} - (y^{3})^{2}[/tex]

Now, using the formula [tex]a^{2}-b^{2} = (a+b) (a-b)[/tex]

= [tex](x^{3}-y^{3})(x^{3}+y^{3})[/tex]

Here, using the formulas

[tex]x^{3}-b^{3} = (a-b)(a^{2}+b^{2}+ab)[/tex] and [tex]a^{3} + b^{3} = (a+b)(a^{2}+b^{2} -ab)[/tex]

Therefore, [tex](x^{3} +y^{3})(x^{3}-y^{3})(x^{2}+y^{2}+xy)(x^{2}+y^{2}-xy)[/tex]

When a number or other mathematical object is expressed as the sum of several factors, usually smaller or easier versions of the same kind, this is referred to as factorization. When an expression has been fully factorized, it must be enclosed in brackets by removing the factors with the highest common denominator. The simplest method of factorization is to find the phrase's highest common factor among all of its terms. The highest common factor (HCF) should be placed in front of any brackets.

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Answer:

Below

Step-by-step explanation:

angle 1 + 120 = straight line = 180    so angle 1 = 60°

angles 1  3  4  7   are all equal

angle 2 = 120° = angles 5 and 6

The rug has a dimension of 6 by 9 yards.

What is a dimension?

In everyday language, a dimension is a measurement of an object's length, width, and height, such as a box. The concept of dimension in mathematics is a continuation of the ideas that a line is one dimension, a plane is two dimensions, and space is three dimensions.

Dimensions include things like width, depth, and height. Three geometric objects have one dimension each: a line, a square, and a cube.

Solution Explained:

Given in question

Area of the room = 9*12=108 yards^2

Area of 1/2 the room = 180/2 = 90 yards^2

So according to the question, the rug covers half the room so we form the equation and we simplify,

(9-2X)(12-2X)=54

108-24X-18X+4X^2=54

4X^2-42X+108-54=0

4X^2-42X+54=0

(2X-18)(2X-3)=0

2X-3=0

2X=3

X=3/2

X=1.5

(9-2*1.5)(12-2*1.5)=54

(9-3)(12-3)=54

6*9=54

54=54

The rug has dimensions of 6 by 9 yards.

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The concept and examples of congruence are described below.

The word 'congruent' signifies 'precisely equivalent' concerning shape and size. In any event, when we turn, flip, or pivot the shapes, they stay equivalent. For instance, draw two circles of similar range, then cut them out and put them on each other.

congruent angles have a similar point measure. For instance, an ordinary pentagon has five sides and five points, and each point is 108 degrees. No matter what the size or size of a customary polygon, the points will constantly be compatible.

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The equation of parabola that open upwards with focus 6 units is x²=24y.

A parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. A parabola is a curve where any point at an equal distance from a fixed point  (the focus) and a fixed straight line (the directrix).

A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface is also Parabola.

The general equation of Parabola is given by

y = a(x-h)²+ k

where (h,k) is the vertex of parabola.

And the equation of parabola open upward is,

(x-h)² = 4a(y-k)

where (h,k) is vertex and a is focus unit.

⇒ (x-0)² = 4(6)(y-0)

⇒ x² = 24y

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The linear functions of the tables are y = 6x - 2 and y = 2.5x - 1

Table 1

From the table, we have the following points that can be used in our computation:

(x, y) = (1, 4)  and (2, 10)

The equation of the line is then calculated using the following equation

y = m(x - x₁) + y₁

Where

m = slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation, so, we have the following representation

So, we have

m = (10 - 4)/(2 - 1)

Evaluate

m = 6

Recall that

y = m(x - x₁) + y₁

So, we have

y = 6(x - 1) + 4

So, we have

y = 6x - 6 + 4

Evaluate

y = 6x - 2

Table 2

From the table, we have the following points that can be used in our computation:

(x, y) = (1, 1.5)  and (2, 4)

The equation of the line is then calculated using the following equation

y = m(x - x₁) + y₁

Where

m = slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation, so, we have the following representation

So, we have

m = (4 - 1.5)/(2 - 1)

Evaluate

m = 2.5

Recall that

y = m(x - x₁) + y₁

So, we have

y = 2.5(x - 1) + 1.5

So, we have

y = 2.5x - 2.5+ 1.5

Evaluate

y = 2.5x - 1

Hence, the linear function is y = 2.5x - 1

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Answer:

A. Both the domain and range of the transformed function are the same as those of the parent function.

Step-by-step explanation:

Parent absolute value function:

[tex]f(x)=|x|[/tex]

Graph of the parent absolute value function:

Therefore:

If function f(x) is reflected across the y-axis:

[tex]\implies f(-x)=|-x|[/tex]

The reflection does not change the graph as the parent function is symmetric about the y-axis.

If function f(x) is translated to the left 5 units:

[tex]\implies f(x+4)=|x+4|[/tex]

The domain remains unrestricted and the range remains [0, ∞).

Therefore, both the domain and range of the transformed function are the same as those of the parent function.

The airline might choose cluster random sampling in this case.

Cluster Sampling:

It is a sampling method where the entire population under study is divided into homogeneous groups called clusters. The clusters are externally homogeneous and internally heterogeneous.

Simple Random Sampling:

It is a sampling technique where every unit in the population has an equal chance of being selected in the sample and the samples are selected at random. The airline wants to survey 500 passengers on this flight about their overall satisfaction. The passengers will be selected using a cluster random sample where each flight is a cluster.

Cluster sampling involves fewer resources for sampling compared to simple random sampling.

Here, the population under study is people travelling the flight which is externally homogeneous.

The people travelling in the flight are classified into three groups namely first class (most expensive), business class, and economy class (least expensive) which is internally heterogeneous. More number of persons can be included in the survey which acts as a good representative of the entire population. Thus, cluster sampling is suitable for this study. Simple random sampling may result in an unequal number of persons in each class if the persons are surveyed at random. So, cluster sampling better suits the scenario than simple random sampling.

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If a single card is drawn from a standard deck of 52 cards, the probability it will be a card with a number less than 5 is 4/13.

Probability measures how likely an event occurs. The probability of an event A is defined as:

P(A) = number of ways A can occur / total possible outcomes

In the given problem, let an ace card is considered as 1. Then, for each suit of cards, the card numbers which are less than 5 are cards number: 1, 2, 3, 4.

There are 4 suits, hence:

number of ways the event can occur = 4 x 4 = 16

total possible outcomes = 52

Therefore,

P(<5) = 16/52 = 4/13

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Answer:14/52

Step-by-step explanation:

Given the function h(x) = x² - 7x - 8. The extremum of the function is the minimum one and its value is h(x) = -32.5

The relation between symmetry of the graph and the extremum point is:

Suppose x = p is the line equation of the graph's symmetry, then f(p) is the extremum value.

The given function is:

h(x) = x² - 7x - 8

Find the x-intercepts:

h(x) = 0

x² - 7x - 8 = 0

(x + 1) (x - 8) = 0

x = -1 or x = 8

The symmetry lies in the middle of x-intercepts. Hence, the symmetry occurs at:

x = (-1 + 8) / 2

x = 3.5

The extremum point is:

h(3.5) = 3.5² - 7 x 3.5 - 8 = -32.5

Since the quadratic term x²  has a positive coefficient, the graph is open downward, hence the extremum point is the minimum one.

Complete question:

Find the extremum of each function using the symmetry of its graph. classify the extremum of the function as a maximum or a minimum and state the value of x at which it occurs. h(x) = x² - 7x - 8

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Answer:

Step-by-step explanation:

Yes it is possible you start with one side worth 4 cm and the other two move on to the next

[tex]20\pi in^{2}[/tex] is the area of the shaded region of the radius of the big circle is 6 inches long and the diameter of the small circle is 8 inches long.

The circle is a closed, two-dimensional object in which all points inside the plane are equally spaced out from the center. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is rotationally symmetric about the center for all angles.

The shaded area is the portion of the bigger circle that is not included in the smaller circle, assuming that the 8-inch diameter circle is entirely contained inside the 6-inch radius circle.

Therefore, the shaded area equals the large circle's area less the small circle's area.

The little circle has a radius of 4 inches since its diameter is 8 inches, so

[tex]A_{Shaded} = A_{l} - A_{s} \\A_{Shaded} = \pi 6^{2} - \pi 4^{2} \\A_{Shaded} = 36\pi - 16\pi \\A_{Shaded} = 20\pi in^{2}[/tex]

So, Area = [tex]20\pi in^{2}[/tex]

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