use the given information to complete the proof of the following theorem. the angles opposite the two congruent sides of an isosceles triangle are congruent.

A vector Y is orthogonal to vectors U and V, so Y is orthogonal to the vector (U+V).

In the given question,

Suppose that a vector Y is Orthogonal to vectors U And V.

We have to show that Y is orthogonal to the vector U + V.

As to vectors are orthogonal if and only if their dot product is zero.

So Y∙U = 0 and Y∙V = 0.

To prove that Y is orthogonal to the vector(U+V), we have to show that Y∙(U+V) = 0.

As dot product is distributive. Now

Y∙(U+V) = Y∙U + Y∙V

As Y∙U = 0 and Y∙V = 0. So

Y∙(U+V) = 0 + 0

Y∙(U+V) = 0

Hence, Y is orthogonal to the vector (U+V).

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The probability density function (pdf) for the uniform distribution has the basic formula: f(x) = 1/ (B-A) for A x B.

A continuous probability distribution, the uniform distribution is concerned with equally likely outcomes. It is referred to as having a rectangular distribution on the interval [a,b] or having a uniform distribution for the continuous random variable X. Above is a representation of the probability density function of a continuous uniform distribution. The probability of drawing a heart, club, diamond, or spade is equally likely; hence, the area under the curve is 1, which makes sense given that the total of all probabilities in a probability distribution is 1.

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By using Green's Theorem, it can be calculated that

[tex]\int_c(5y+7e^x)dx+(10x+9cos(y^2))dy[/tex] = [tex]\frac{5}{3}[/tex]

What is Green's Theorem?

Green's Theorem gives a relationship between a line integral along a closed curve C and surface integral around plane region D bounded by C

By Green's Theorem,

[tex]\int_c Pdx+ Qdy = \int\int_D (\frac{\partial P}{\partial y} - \frac{\partial Q}{\partial x})dxdy[/tex]

To evaluate [tex]\int_c(5y+7e^x)dx+(10x+9cos(y^2))dy[/tex] using Green's Theorem,

Region is between the parabola [tex]y = x^2[/tex] and [tex]x = y^2[/tex]

To find point of intersection,

[tex]x = y^2\\x = (x^2)^2\\x = x^4\\x^4 - x = 0\\x(x^3 - 1) = 0\\x = 0 \ or \ x^3 - 1 = 0\\x = 0 \ or \ x^3 = 1\\x = 0 \ or \ x = 1[/tex]

Along y- axis the limit of integration is from y = [tex]x^2[/tex] to y = [tex]\sqrt{x}[/tex]

P = [tex]5y + 7e^x[/tex]

[tex]\frac{\partial P}{\partial y}[/tex] = 5

Q = [tex]10x + 9(cos(y^2))[/tex]

[tex]\frac{\partial Q}{\partial x}[/tex] = 10

By Green's Theorem,

[tex]\int_c(5y+7e^x)dx+(10x+9cos(y^2))dy[/tex]

= [tex]\int_{x = 0}^1\int_{y = x^2}^{\sqrt{x}}(10 -5)dxdy\\\\\int_{x = 0}^1\int_{y = x^2}^{\sqrt{x}}5dxdy\\\\\int_{x = 0}^1 5(\sqrt{x} - x^2)\\\\5[(\frac{2}{3})x^{\frac{3}{2}} - \frac{x^3}{3}]_0^1\\\\5(\frac{2}{3} -\frac{1}{3})\\\\\frac{5}{3}[/tex]

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The slope of the curve at the given point is approximately -28

What is the derivative of a function?

Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.

To find the derivative of y with respect to x using implicit differentiation, we need to take the derivative of both sides of the equation cos(y) = 7x^4 - 7.

On the left side of the equation, we can use the chain rule to find the derivative of cos(y) with respect to x:

d/dx[cos(y)] = -sin(y) * dy/dx

On the right side of the equation, we can use the power rule to find the derivative of 7x^4 - 7 with respect to x:

[tex]d/dx[7x^4 - 7] = 28x^3[/tex]

Substituting these expressions into the original equation, we get:

[tex]-sin(y) * dy/dx = 28x^3[/tex]

To solve for dy/dx, we can divide both sides of the equation by -sin(y):

[tex]dy/dx = -(28x^3)/sin(y)[/tex]

To find the slope of the curve at the given point, we need to substitute the values of x and y into the expression for dy/dx.

The slope at (1, π/2). would be

slope = -(28((1)^3))/sin(π/2) = -28.

Hence, the slope of the curve at the given point is approximately -28.

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About -$10.15 that is, on average you lose about 15 cents.

Using the principle of discrete probability, the expected value, which is a measure of the mean amount after many plays is - 2/13

Calculating the required probabilities :

P(winning) = P(drawing an Ace) = 4/52 = 1/13

Hence, P(losing) = 1 - 1/13 = 12/13

X :____ 10 _____ - 1

P(X) : _ 1/13_____ 12/13

The expected value :

E(X) = 10 × (1/13) + - 1(12/13)

E(X) = 10/13 - 12/13

E(X) = - 2/13

Hence, the measure of the mean amount is -2/13.

The victory value is $10, and the loss value is $-1.

Out of a total of 52 cards, this deck has 4 aces.

The probability can then be defined as the ratio of the number of desirable outcomes to the number of possible outcomes.

P(win) = number of favorable outcome/number of the possible outcome

= 4/52

= 1/13

P(loss) = number of favorable outcome/number of the possible outcome

= 48/52

= 12/13

Then we have

$10x1/13 + (-1)x12/13

= 10/13-12/13

= -2/13 dollars

= -$0.15

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Your's check would be $198 for two weeks with 9 hours of work from Sunday-Friday.

In a word problem, the mathematical operations are written in text format. To solve such a problem, the text should be understood and simple basic arithmetic operations are applied.

It is given that,

He/She makes $11 for 1 hour and works for 9 hours from Sunday to Friday.

For 9 hours of work, he/she gets, $11 × 9 = $99

Then, for two weeks, the payment = $99 + $99 = $198

So, he gets a biweekly check with $198.

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2. The Equation for  value x is, x= 13 sin 52.

3. The value of m, m = l cos <N

4. The length of Hypotenuse is 7.92 m.

The branch of mathematics concerned with specific functions of angles and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).

Given:

2. P= x

H= 13 cm

Using Trigonometry

sin 52 = P/ H

sin 52 = x/ 13

x= 13 sin 52.

3. P = n, B= m and H= l

Using Trigonometry

cos <N= B/H

cos <N=  m / l

m = l cos <N

and, using Pythagoras theorem

H² = P² + B²

l²= m² + n²

m= √( l² - n²)

4. P = 7m

angle= 62

Using Trigonometry

sin 62 = 7/ H

0.88295 = 7/ H

H = 7/ 0.88295

H = 7.92 m

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The statements that are true regarding the sequence below are

The given sequence include 10/3, 4, 24/5, 244/25

Applying the formula f(x) = 10/3 (6/5)ˣ⁻¹ to it

for x = 1, f(x) = 10/3 (6/5)¹⁻¹ = 10/3

for x = 2, f(x) = 10/3 (6/5)²⁻¹ = 4

for x = 3, f(x) = 10/3 (6/5)³⁻¹ = 24/5

This shows that the formula works for it hence a correct statement

Real numbers include all positive and negative numbers, fractions and decimals alike and the domain are natural numbers which are part of real numbers

The range are also all real numbers and this go beyond natural numbers

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Line integral will be ∫c(x²y + sinx )dy = 1/3π²×π³ + 2π

Given:

C is the arc of parabola y = x² from (0,0) to (π,π²)

Let x be the parameter ; since the parabola is given as function of x

the parametric equations are

x=x,y=x², for 0≤x≤π

By using concept

∫c(x²y + sinx)dy = [tex]\int\limits^0_x {(x^2(x^2) + sinx} \, ).2xdx[/tex]

by applying the limits of integration we get ,

= 2 [ π².π³/6 + [ -πcosπ + sinπ - (0 + sin0)] ]

by calculating,

= 2 ( π².π³/6 + π )

= 1/3 π².π³ + 2π

Thus,

∫c(x²y + sinx )dy = 1/3π²×π³ + 2π

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Answer:(-2,7) is a yes

(2,6) is no pls mark brainiest

Step-by-step explanation: did a question like this and i mastered this subject

It is not possible for a lie detector, or any other type of technology, to accurately determine whether a person is lying more than 50% of the time. Lie detectors, also known as polygraph machines, measure physiological responses such as changes in heart rate, blood pressure, and respiration to determine if a person is telling the truth or not. However, these responses can be affected by many factors, such as anxiety or stress, and are not always reliable indicators of deception. In addition, people can learn how to manipulate their physiological responses in order to deceive the polygraph machine. Therefore, it is not accurate to say that a lie detector can determine whether a person is lying more than 50% of the time

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Answer:

y=5x

Step-by-step explanation:

intercept is 0

Slope is 5

Answer:

$18.15 of taxes

Step-by-step explanation:

based on the givens: 220 (4.6%  + 3.65% )

calculate the sum or difference: 220 x 0.0825

calculate the product: 18.15

cash dividends paid that should be recorded in the financing section of the statement of cash flow is $ 148300

With regards to the above, information, the amount of cash dividends paid that should be recorded is computed as;

= Cash dividends payable at the beginning of the year + Cash dividends declared for the year - Cash dividends payable at the end of the year

= $27,100 + $67,000 - $54,200

= $ 148 300

Therefore, cash dividends paid that should be recorded in the financing section of the statement of cash flow is $ 148300

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Answer:

Step-by-step explanation:

The width of the photograph in millimeters is 240 mm.

It should be noted that a scale factor simply shows the relationship between a shape abd the original value given.

In this situation, the photograph is 8 centimeters wide and after Kari enlarges the photograph, it is 3 times as wide as the original.

The photograph in millimeters will be:

= 8 × 3 × 10

= 240 millimeters.

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Answer:

97224

Step-by-step explanation:

BODMAS

B ×

O ×

Division (5/2)

Multiplication (5/2*8)

Addition (89345+7899)

S ×

Do it in this order

625 is the total amount deposited by Peter in his checking account.

1) According to question

Balance after 4 weeks= 537                                     (equation 1)

Balance after 8 weeks= 449                                     (equation 2)

Each week Peter withdraws same amount.

Let the same amount be x.

From equation 1 and 2

Money spent in 4 weeks = 537-449=88

Therefore money spent in one week = 88/4=22

So the amount deposited by Peter=537 +22x 4 weeks

=537+88=625

2) B=625-22t

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The blanks are completed as follows:

Then the inverse Laplace transform is given as follows:

f(t) = e^(9t) + 9te^(9t).

The function for this problem is given as follows:

F(s) = s/(s² - 18s + 81).

Completing the squares at the denominator, we have that:

F(s) = s/(s - 9)².

Applying partial fraction decomposition, the function can be defined as follows:

s/(s - 9)² = A/(s - 9) + B/(s - 9)²

Expanding the right side, we have that:

s/(s - 9)² = [A(s - 9) + B]/(s - 9)²

Hence:

As - 9A + B = s.

Then the system for the coefficients is given as follows:

Thus the function in the transform domain is of:

F(s) = 1/(s - 9) + 9/(s - 9)².

Applying the inverse Laplace transform, the function in the time domain is given as follows:

f(t) = e^(9t) + 9te^(9t).

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Answer:

p = 6

Step-by-step explanation:

5 + 2/3 (2p - 6) = 9

5 + 4/3p - 4 = 9

1 + 4/3p = 9

4/3p = 8

p = 6

Answer:

p= 6

Step-by-step explanation:

Solve for p:

(2 (2 p - 6))/3 + 5 = 9

Put each term in (2 (2 p - 6))/3 + 5 over the common denominator 3: (2 (2 p - 6))/3 + 5 = 15/3 + (2 (2 p - 6))/3:

(15/3 + (2 (2 p - 6))/3) = 9

15/3 + (2 (2 p - 6))/3 = (2 (2 p - 6) + 15)/3:

((2 (2 p - 6) + 15)/3) = 9

2 (2 p - 6) = 4 p - 12:

((4 p - 12) + 15)/3 = 9

Grouping like terms, 4 p - 12 + 15 = 4 p + (15 - 12):

(4 p + (15 - 12))/3 = 9

15 - 12 = 3:

(4 p + 3)/3 = 9

Multiply both sides of (4 p + 3)/3 = 9 by 3:

(3 (4 p + 3))/3 = 3×9

(3 (4 p + 3))/3 = 3/3×(4 p + 3) = 4 p + 3:

(4 p + 3) = 3×9

3×9 = 27:

4 p + 3 = 27

Subtract 3 from both sides:

4 p + (3 - 3) = 27 - 3

3 - 3 = 0:

4 p = 27 - 3

27 - 3 = 24:

4 p = 24

Divide both sides of 4 p = 24 by 4:

(4 p)/4 = 24/4

4/4 = 1:

p = 24/4

The gcd of 24 and 4 is 4, so 24/4 = (4×6)/(4×1) = 4/4×6 = 6:

Answer: p = 6

The initial mass of the sample is =2.39 kg

Radioactivity=Radioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.Radioactive describes something that exhibits or is caused by radioactivity. If something is radioactive, it emits radiation, which usually takes the form of electromagnetic waves or fast-moving elementary particles, such as protons or neutrons.

M(t)= Mo E =2.546 M(3)=2.54-02(3)

=2.54e -0.06

=2.39 kg (initial mass of the sample)

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The dimensions of the product matrix of two of these matrices is BD = 2 * 1 , CA = 1 * 3 and DC = 2 * 3 .

Given :

The dimension of BD :

B dimensions = ( 2 * 2 )

D dimensions = ( 2 * 1 )

Product of BD dimensions = Numbers of rows of B * number of columns in D

= 2 * 1

The dimension of CA :

C dimensions = ( 1 * 3 )

A dimensions = ( 3 * 3 )

Product of CA dimensions = Numbers of rows of C * number of columns in A

= 1 * 3

The dimension of DC :

D dimensions = ( 2 * 1 )

C dimensions = ( 1 * 3 )

Product of CA dimensions = Numbers of rows of D * number of columns in A

= 2 * 3

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A population numbers 12,000 organisms initially and grows by 17.5% each year. The growth function of the population is P =  12,000 x 1.175^t

An exponential growth function can be written as:

P = A (1 + r)ⁿ

Where:

P  = quantity after n periods

n = number of periods

r = growth rate per period

A = initial quantity

In the given problem, the period is the number of years t

A = 12,000

r = 17.5% = 0.175

Hence, the growth function:

P = 12,000  (1 + 0.175)^t

P = 12,000 x 1.175^t

Your question is incomplete, but most probably your question was:

A population numbers 12,000 organisms initially and grows by 17.5% each year. Suppose P represents population, and t the number of years of growth, write the function in terms of t.

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The rate of change of the cost with respect to the weight of the item is equal to 0.55.

Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the shipping costs (y) with respect to the weight of the item (x), with the following data points (2, 7) and (6.09, 8.84):

Rate of change, m = (8.84 - 6.09)/(7 - 2)

Rate of change, m = 2.75/5

Rate of change, m = 0.55.

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The value of x is 21

The measure of angle B is 28°

The measure of exterior angle ACD is 63°

From the question, we are to determine the measure of the angles.

From the given diagram, we can write that

35° + (x + 7)° = 3x° (Exterior angle theorem)

Solve for x in the equation

35° + (x + 7)° = 3x°

35° + x° + 7° = 3x°

35° + 7° = 3x° - x°

42° = 2x°

Divide both sides by 2

42°/2 = 2x°/2

21° = x°

Therefore,

x = 21

The measure of angle B is

Measure of angle B = (x + 7)°

Measure of angle B = (21 + 7)°

Measure of angle B = 28°

The measure of exterior angle ACD

Measure of exterior angle ACD = 3x°

Measure of exterior angle ACD = 3(21)°

Measure of exterior angle ACD = 63°'

Hence, the measure of the exterior angle is 63°

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Answer: You are correct

Step-by-step explanation:

Part A: Two possible financial goals that may require $12,000 is to save for home ownership and education.

Part B: Three possible initial investments to reach the goal of having a future value of $12,000 in 5 years are:

Part C: The total interest earned on each investment is as follows:

The total interest for investment 1 is a product of simple interest formula, which multiplies the principal, interest rate, and time.

The total interests for investments 2 and 3 are the results of the online finance calculator., which inputs the future value, compound interest rate, and compounding period.

Future value = $12,000

Investment Period = 5 years

Simple interest rate = 3% or 0.03

Initial investment, P = A/(1 + rt)

Where P = principal

A = Future Value

r = interest rate

t = time

P = $12,000/(1 + 0.03 x 5)

= 12,000/(1.15)

= $10,435

Total Interest = $1,565 ($12,000 - $10435) or ($10,435 x 3% x 5)

Future value = $12,000

Investment Period = 5 years

Compound interest rate = 3% or 0.03 monthly

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 3%

PMT (Periodic Payment) = $0

FV (Future Value) = $12,000

Results:

Present Value (PV) = $10,330.43

Total Interest = $1,669.57

Future value = $12,000

Investment Period = 5 years

Compound interest rate = 3% or 0.03 annually

N (# of periods) = 5 years

I/Y (Interest per year) = 3%

PV (Present Value) = $0

FV (Future Value) = $12,000

Results:

Periodic Deposits = $2,194.42

Sum of all periodic payments = $10,972.10

Total Interest = $1,027.90

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The number of two-points and three points shot the cruisers scored are 24 and 19 respectively.

The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots.

Therefore, the number of two-points and three-points the cruiser scored is as follows:

let

x = number of two-points

y = number of three-points

Hence, using equation

x + y = 43

2x + 3y = 105

Multiply equation(i) by 2

2x + 2y = 86

2x + 3y = 105

subtract equation(i) from equation(ii)

y = 19

Let's find x as follows:

x = 43 - 19

x = 24

Therefore,

number of two points = 24

number of three points = 19

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