Given BC over AC congruent to EF over EG
Prove FG=10

Answer:(4, 4), (7, 0), (4,-2)

Step-by-step explanation: The median of a triangle is the line segment connecting a vertex to the midpoint of the opposite side. In this triangle, the vertex at (7, 4) is connected to the midpoint of the side opposite it, which is the midpoint of the line segment between (1, 4) and (7, -2). This midpoint is located at (4, 0). Therefore, the median through (7, 4) will consist of the points (4, 4), (7, 0), and (4, -2).

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 first statement is false and the rest of the options are true.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

1. 25% of 512 is equal to 1/4 x 500, false due to 500.

2. 90% of 133 is equal to 0.9 x 133, true because 90% is equal to 0.90.

3. 30% of 44 is equal to 3% of 440, true because the value of both is the same.

4. The percentage of 21 is 28 is equal to the percentage of 30 is 40, true because the percentage of both cases is identical.

The first statement is false and the rest of the options are true.

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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 difference between the two candidates who voted is less than the margin of error, so the result cannot be predicted.

The difference between the two candidates voted is less than the margin of error

4% of 2052 is 4/100 x 2052 = 82.08

44% of 2052 is 902.88

46% of 2052 is 943.92

It increases as the level of confidence increases because the larger the expected proportion of intervals that will contain the parameter the larger the margin of error.

The race was too close to call means it is within the margin of error for one candidate to receive 44% of the popular vote and for the other candidate to receive 46​%, the poll cannot predict the winner.

Therefore, The result cannot be predicted as the race was too close to call.

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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

The greatest integer that does not exceed 1000x is 1. the value of x is approximately 0.001.

What is the area?

The area of a shadow is the amount of surface area that is covered by the shadow. It is the two-dimensional projection of an object onto a surface.

Let the distance between the point source of light and the horizontal surface be h. Since the shadow is a projection of the cube onto the horizontal surface, the shadow has the same proportions as the cube. Therefore, the height of the shadow is h/x times the length of the shadow, which is 48x. The area of the shadow is then:

48x * h/x = 48h

Since the area of the shadow is 48x^2, we have:

48h = 48x^2

h = x^2

We are asked to find the greatest integer that does not exceed 1000x. Substituting the expression for h into the equation, we get:

1000x = 1000x^2

x = 1/1000

Hence, The greatest integer that does not exceed 1000x is 1. the value of x is approximately 0.001.

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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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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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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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Answer: You are correct

Step-by-step explanation:

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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Answer:

500 grams

Step-by-step explanation:

6 weigh 750 so multiply them:
6 × 750 = 4500

4500 grams is equivalent to 4.5 kilograms

the total of all blocks of ice was 5 kg
therefore the remaining one is 0.5kg which is 500g

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

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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She can purchase 3 blue towels and 5 green towels.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

8 x 5 = 40

10 x 3 = 30

40 + 30 = 70

Hence, She can purchase 3 blue towels and 5 green towels.

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Answer:

Step-by-step explanation:

-3x - 2y = -20

3x + y =    10

-y = -10

y = 10

3x + 10 = 10

3x = 0

x = 0

(0, 10)

The answer to the sum is: ∑ k⁴ (k  ranges from 1 to 6)

Express the sum in sigma notation :

According to the question,

1 = lower limit of summation

k = the index of summation

1 + 16 + 81 + 256 + 625 + 1296 = 1² + 4² + 9² + 16² + 25² + 36²

                                                 = 1⁴ + 2⁴ + 3⁴ + 4⁴ + 5⁴ + 6⁴ ( i.e 16 = 4²=(2²)²)

                                                 = ∑ k⁴ (k ranges from 1 to 6)

 So, The answer to the sum is - ∑ k⁴ (k ranges from 1 to 6).    

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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:

Step-by-step explanation:

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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Answer:

y=5x

Step-by-step explanation:

intercept is 0

Slope is 5

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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Answer:

21x^2 - 25x - 28

Step-by-step explanation:

= -3x (4 - 5x) + (3x + 4)(2x - 7)

= -12x + 15x^2 + 6x^2 - 21x + 8x - 28

= 21x^2 - 25x - 28

I hope my answer helps you.

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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Assume that the basis for a subspace V in Rn is v1,..., vp. Show that a vector in Rn is orthogonal to a vector in V if and only if it is orthogonal to every vector v1,..., vp.

An orthogonal vector , In mathematics, orthogonality is an extension of perpendicularity, particularly in vector calculus and linear algebra. Basic geometry dictates that two lines or line segments are only perpendicular if they form a straight angle.

It makes sense to think of vectors as arrows, such as R 2 and R 3, when discussing orthogonal vectors in an inner product space (a real or complex vector space with a notion of vector multiplication).

There are inner product spaces where it makes no sense to conceive of vectors as arrows, yet one still needs to have some understanding of what it means when discussing orthogonal vs. perpendicular.

Hence, It is orthogonal to every vector in vector space, or o V. Every vector in V is a linear combination of these vectors since v1,..., vp serves as the basis for V.

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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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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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