XYZW is a parallelogram with diagonals XZ and YW that intersect at point A. If XA=3x, ZA=5x-4, and YW = 10x, find the value of x and the length of Wa

Criteria for congruence of triangles are SSS, SAS, ASA, AAS, RHS.

As per the given data we have to determine the criteria for the congruence of triangles.

The criteria is SSS, SAS, ASA, AAS, RHS.

SSS- Two triangles are congruent if all the 3 corresponding sides of the given triangles are equal.

SAS- Two triangles are congruent if 2 corresponding sides of the given triangles and the angle included between those sides are equal to each other.

ASA- Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding angles and sides of another triangle.

AAS- if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then two triangles are congruent with each other.

RHS- If the hypotenuse and a side of a right angled triangle are congruent with the hypotenuse and the corresponding side of another right angled triangle, then the two triangles are congruent with each other.

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The vector A is (49.9m) x and vector B is (1.5m) x.

In the given question, A − B = (−51.4m)x, C =(62.2m)x, and A +B +C =(13.8m)x.

Find the vector A. Find the vector B.

We may disregard the vector x and treat the issue as an arithmetic one since all of the measurements are in the same direction (simultaneous equations).

A − B = −51.4.............................(1)

C = 62.2.............................(2)

A + B + C = 13.8.............................(3)

Now putting the value of C from Equation (2) in Equation (3)

A + B + C = 13.8

A + B + 62.2 = 13.8

Subtract 62.2 on both side, we get

A + B = 13.8 - 62.2

A + B = - 48.4.....................(4)

Adding the equation (1) and (4), we get

2A = - 99.8

Divide by 2 on both side, we get

A = - 49.9

Now subtracting the equation (1) and (4), we get

2B = -48.4 - ( -51.4)

2B = 3

Divide by 2 on both side, we get

B = 1.5

Since all of the calculations are done in terms of the unit vector x.

So the answer is vector B = (1.5m) x and vector A = (49.9m) x.

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The rule of reflection for the points (x, y) for the graph is (y, - x).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

The preimage of the given line has points(x, y), B(2, 3) and C(1, 6).

Now, The graph has been translated down 2 units and reflected 180° along the x-axis so the image of the graph has points(y, - x) B'(3, - 2) and C'(6, - 1).

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10.5 is the mean of 20 .

What are the mean, median, and example?

A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently. The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

 x = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + ................. + 20/20

  x = 210/20

  x = 10.5

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The complete question is -

How do you find the mean of 20 natural numbers?

Answer:

Step-by-step explanation:

hfhgfvbbkgb 56789+7567t+2345

y-mx+b

y=-3/2x+4

m- -3/2

b-4

y=-3/2x+4

The roots of the quadratic equation 5x² 4x 3 0 are two complex conjugates, which cannot be expression in terms of real numbers. The roots are irrational numbers and can only be approximated.

The roots of the quadratic equation 5x² 4x 3 0 are two complex conjugates, which cannot be expression in terms of real numbers. To find the roots, the quadratic formula can be used. The formula requires the coefficients of the equation, which in this case are a=5, b=4, and c=3. When the quadratic formula is applied, the results are two complex roots, which are expressed as x1 = -1/5 + (√16)/5i and x2 = -1/5 - (√16)/5i. These roots are irrational numbers and can only be approximated. Complex roots are often found when the discriminant, which is b²-4ac, is negative. In this case, the discriminant is -64, which is negative, indicating that the equation has complex roots.

Discriminant = b²-4ac = 4²-4(5)(3) = -64

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E(z),the expected value of z in which at least one member has a birthday in 12 months is (11/12)^10

Define the random variable Zi’s as

[tex]Z_{i}[/tex]= 1 : if no member of the club has a birthday in the month

   = 0: otherwise   for, i =1,2, ......,12 .

Now, we have,

= P ([tex]Z_{i}[/tex] =1) .

=p( no member of the club has a birthday in month i).

= p, say.

Now, there are a total of 10 members in the club and their birthdays are assumed to be independently and uniformly distributed over the 12 months of the year. So, there are 12 possible choices of months for each of the 10 members for their birthday. Thus, the total no. of exhaustive mutually exclusive and equally likely no. of ways of birthdays 12^10.

Again, if no member of the club has a birthday in month 'i'; then, all of their birthdays should be on the remaining (12 - 1) = 11 months of the year. So, there are possible choices of birthday months for each of the 10 members of the club. So, the no. of cases for the event (Zi=1) is 11^10.

So, p([tex]Z_{i}[/tex]=1) = Favorable no. of cases for Zi=1) / Total no. of all possible cases

= 11^10 / 12^10

By the classical definition of probability.

= (11/12)^10

p([tex]Z_{i}[/tex] = 1) = (11/12)^10

E(Zi).= (11/12)^10

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Since, a prime number is whole number higher than one that cannot be divided exactly by any other whole number than itself and one. No, there are many prime numbers.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers the range of numbers that includes zero and natural numbers. not a decimal or fraction.

Prime number 2,5,7,13, ......

so there are multiple prime numbers.

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Answer:

5 - [tex]\sqrt{5}[/tex]

Step-by-step explanation:

a polynomial of degree 3 has 3 roots

radical roots occur in conjugate pairs.

given 5 + [tex]\sqrt{5}[/tex] is a root then 5 - [tex]\sqrt{5}[/tex] is also a root.

the 3 roots are therefore

x = 5 and x = 5 ± [tex]\sqrt{5}[/tex]

The value of y obtained after solving the given equation will be equal to 11/3 or 3 2/3.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

3/4y + 1/2 = 3 1/4

Firstly, write the equation in a simplified way,

3/4y + 1/2 = 13/4

3/4y = 13/4 - 1/2

3/4y = (13 - 2)/4

3/4y = 11/4

Now, solve the equation for y,

y = (11 × 4)/(4 × 3)

y = 11/3

In mixed fraction form, it can be written as 3 2/3.

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Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

Answer:

5 1/3 books

Step-by-step explanation:

1 1/3 = 4/3

So, she read

4/3 book = 1/2 day

8/3 book = 1 day

16/3 book = 2 days

16/3 = 5 1/3 books

So, he read 5 1/3 books in two days at this rate

Square root of 1, √1 is a real number as it is a rational number.

√  is a symbol that means square root in mathematics.

Real number is a set of all rational and irrational numbers. It can be plotted on a number line.

A rational number is a number that can be expressed in the form of p/q, where p and q are integers and denominator, q not equal to 0.

Numbers that cannot be plotted on number line, numbers that are not real number are called imaginary numbers.

√1 = 1

1 is a rational number as it can be written as 1/1. All integers are rational numbers in the similar way.

Therefore square root of 1 is a rational number and hence it is a real number.

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Answer:

To express the quadratic expression x^2 - 5x + 8 in the form of (x - a)^2 + b, we need to complete the square. To do this, we can add and subtract the square of half the coefficient of the x term. In this case, that would be (1/2)(-5) = -5/2. Therefore, we add and subtract (1/2)(-5)^2 = (-5/2)^2 = 25/4 to get:

x^2 - 5x + 8 = (x^2 - 5x + (25/4)) + (8 - (25/4))

Next, we need to add and subtract 25/4 in such a way that we can factor the quadratic expression as the square of a binomial. To do this, we add 25/4 to the first term and subtract 25/4 from the second term to get:

x^2 - 5x + (25/4) + (8 - (25/4)) = (x^2 - 5x + 25/4) + (8 - 25/4)

Now we can factor the quadratic expression as the square of a binomial:

(x^2 - 5x + 25/4) + (8 - 25/4) = (x - 5/2)^2 + (8 - 25/4)

Therefore, we can express x^2 - 5x + 8 in the form of (x - a)^2 + b where a is -5/2 and b is 8 - 25/4.

Note that the values of a and b are not whole numbers because we added and subtracted a fraction when completing the square.

The figure of Pumpkin according to the transformation is shown below.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

The Transformation rule are as follow:

1. T(-4 , -18) reflect across x = -4.

2. T(-3, 4) (R0, 180)

3. [tex]R_0[/tex] , 180 ( [tex]r_y[/tex] = x+ 11)

4. [tex]r_y[/tex] = 11 ( [tex]R_0[/tex] , 90)  T(6, -10)

5. T(-12, 0),  [tex]r_y[/tex] = -10, ( [tex]R_0[/tex] , 270)

6. T(0, -3),  [tex]r_y[/tex] = x

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Answer:

[tex]V=(3W^{3} + 12W^{2} ) units^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a rectangular prism is equal to

[tex]V=LBH-- >[/tex][tex]EquationA[/tex]

where

L is the length

W is the width

H is the height

we know that

[tex]L=3W--- > EquationB[/tex]

[tex]H = W + 4----- > EquationC[/tex]

substitute equation B and equation C in equation A

[tex]V=(3W)(W)(W+4)[/tex]

Apply distributive property

[tex]V=(3W^{3} + 12W^{2} ) units^{3}[/tex]

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To manufacture a panels that are u = 48 in. wide and 2 in. thick with the profile of the roofing takes the shape of a sine wave with equation y = sin(pi x/12) from flat sheet, the width of the flat sheet would be 49.59in.

Therefore the answer is 49.59

To find the arc length of a continuous function, you need to first define the function and the interval over which you want to find the arc length. Then you can use the following formula:

Arc Length = ∫√(1+(f'(x))^2) dx

Here, f(x) is the function and the interval is [a, b].

The width, w of the flat metal sheet needed to make the panel is the arc length of the sine curve from x = 0 to x = 48in

In this case, f(x) = sin(pi x/12), so the derivative of f(x) is

f'(x) = (pi/12)cos(pi x/12)

Arc Length = ∫√(1+((pi/12)cos(pi x/12))^2) dx from x=0 to x=48

Arc Length ≈ 49.59 in

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As opposed to last year when 113 pies were prepared for the bake sale, 219+ d  expression pies have been prepared throughout the past two years.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

Since we have given that

Number of pies baked for bake sale last year = 219

Number of pies baked for bake sale this year = d

So, total number of pies baked in two years is given by

219 +d

Hence, there are 219+d pies baked in two years.

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The probability of both sprouts blooming under the best conditions is 16 percent.

The probability that two sprouts will both bloom under the best conditions can be calculated using the formula P(A and B) = P(A) * P(B), where P(A) and P(B) are the probabilities of each sprout blooming. Assuming that each sprout has an independent probability of blooming of 0.5, then the probability of both sprouts blooming is 0.5 * 0.5 = 0.25, or 25%. This can also be expressed as a proportion of 1/4, or a percentage of 25%.

In other words, if two sprouts are selected at random, then the probability that both will bloom, under the best conditions, is 25%. This can also be expressed as a probability of 1 in 4, or 16%. This means that out of 4 sprouts, on average, one will bloom, and the other three will not. Therefore, the probability of both sprouts blooming under the best conditions is 16 percent.

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The inverse calculator is a function calculator which finds the inverse of the given function.

Any function can have its inverse value computed using an inverse function calculator. Recall that an inverse function is one that can make another function do the opposite. Another name for it is an anti-function.

It is denoted as:

f(x) = y ⇔ f⁻¹(y) = x

Any function's inverse can be found by first substituting the other variable for the function and then solving for the other variable by substituting each other.

This online calculator for finding the inverse function is very simple to use. To find the inverse of any function, follow the directions below.

Step 1: Type any function into the input field, which is located across the sentence "The inverse function of."

Step 2: Press the "Submit" button located at the calculator's base.

Step 3: A different window will open in which the supplied function's inverse will be calculated.

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Answer:

y = -3x + 6

Step-by-step explanation:

According to the information given, your two points are (2, 0) and (4, -6).

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-6 - 0) / (4 - 2)

Simplify the parentheses.

= (-6) / (2)

Simplify the fraction.

-6/2

= -3

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = -3x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (4, -6). Plug in the x and y values into the x and y of the standard equation.

-6 = -3(4) + b

To find b, multiply the slope and the input of x(4)

-6 = -12 + b

Now, add 12 to both sides to isolate b.

6 = b

Plug this into your standard equation.

y = -3x + 6

This is your equation.

Check this by plugging in the other point you have not checked yet (2, 0).

y = -3x + 6

0 = -3(2) + 6

0 = -6 + 6

0 = 0

Your equation is correct.

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Yes , SAS (Side-Angle-Side) is a second Congruence postulate to prove triangle congruence by showing that two sides and their included angles are congruent.

Side-Angle-Side is the rule used to prove whether a given set of triangles are congruent. The SAS rule states: Triangles are congruent if two sides and an included angle of a triangle are equal to two sides and an included angle of another triangle. An included angle is the angle formed by two given sides.. For example : let's us consider two triangles ∆SQR and ∆TSR ,

In above given figure, sides

RS = RS ( common side)

QS = ST ( S divides QT in two equal parts) and angle between QS and SR equal to angle between SR and ST i.e. ∠QSR = ∠RST = 90° (right angle ) and it is included angle . So, by SAS Congruence rule, both of triangles are congruent. Hence, Δ ABC ≅ Δ PQR.

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The fractions equivalent to 2/5 are 4/10, 6/15, 8/20, etc.

Now, According to the question:-

Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. This is the reason why these fractions get reduced to the same number when they are simplified.

Let us understand the two ways in which we can make equivalent fractions:

Hence, the equivalent fractions for 2/5 are:

(2/5) × (2/2) = (2 × 2) / (5 × 2) = 4/10

(2/5) × (3/3) = (2 × 3) / (5× 3) = 6/15

(2/5) × (4/4) = (2 × 4) / (5 × 4) = 8/20

Thus, 4/10, 6/15, 8/20 are equal to 2/5,

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Answer:

y = - 5/4x -12

Step-by-step explanation:

Original slope= (0- -4)/(5-0)=4/5

slope of perpendicular line of original = -5/4

so the line passes through the point (-8,-2)

(y - -2) = -5/4 (x - -8)

y + 2 = -5/4x - 10

y = - 5/4x -12

The equation of line u passing through the point (-8, -2) and which is perpendicular to the line y that cut the x-axis at x = 5 and y-axis at y = -4 is 5x + 4y + 18 = 0

Given that line, u passes through (-8,-2) and is perpendicular to line y

line y cut x-axis at x=5 and y-axis at y=-4

that is the point of intercept are : (x1, y1) = (5,0) and (x2, y2) = (0, -4)

Now, the equation of line = (y - y1) = m1*(x - x1)

Here m is the slope of line y

m1 = (y1 - y2)/(x1 - x2)

On solving,

m1 = (0 - (-4))/(5 - 0) = 4/5

We know that when two equations are perpendicular then the multiplication of their slopes = -1

m1 * m2 = -1

Now, m2 = -1/m1 = -5/4

Equation of line u passing through the point (-8, -2) and perpendicular to the line = (y - y1) = m2*(x - x1) =>  (y - (-2)) = -5/4*(x - (-8)

5x + 4y + 18 = 0

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Answer:

6.6 in

Step-by-step explanation:

[tex]\angle P=180^{\circ}-37^{\circ}-89^{\circ}=54^{\circ} \\ \\ \frac{p}{\sin P}=\frac{q}{\sin Q} \\ \\ \frac{p}{\sin 54^{\circ}}=\frac{4.9}{\sin 37^{\circ}} \\ \\ p=\frac{4.9\sin 54^{\circ}}{\sin 37^{\circ}} \\ \\ p \approx 6.6[/tex]

Answer:

Step-by-step explanation:

6.6

A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.

A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.

Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.

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a) The equation has a root between x = 0 because there is a change in the sign of the output value.

b) The arrangement is given in the answer.

c) The estimate of the root is given as follows: 0.7469.

The polynomial function is defined as follows:

x³ + 6x - 5 = 0.

The numeric values at x = 0 and x = 1 are given as follows:

Change in the sign, hence necessarily there is a root, as the function is continuous.

The function can be arranged as follows:

x³ + 6x - 5 = 0.

x³ + 6x = 5

x(x² + 6) = 5

x = 5/(x² + 6).

Considering an initial estimate of x = 0, the first estimate of the solution is of:

x = 5/(0² + 6) = 0.8333.

Then the second estimate for the root is of:

x = 5/(0.8333² + 6) = 0.7469.

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The expression for area of a rectangle is A = 12x² + 55x + 50, the equation is second degree and the expression for perimeter is P = 14x + 30.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given information in the question,

Let the length of rectangle, l = (4x + 5) and,

The width of rectangle, w = (3x + 10)

a.

Use the formula of area of rectangle,

A = wl

A = (3x + 10)(4x +5)

So, the expression will be,

A = 12x² + 55x + 50

b.

The degree of the equation for area is second degree.

c.

Use the formula of perimeter of rectangle,

P = 2(l + w)

P = 2(4x +5 + 3x + 10)

P = 2(7x + 15)

Then, the expression of perimeter will be,

P = 14x + 30

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