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Answer:

  9

Step-by-step explanation:

You want the value of the constant 'a' in the solution y=√(a+b·cos(πx)) to the differential equation y'=3sin(πx)/(2y) with initial condition y(1/2) = 3.

Substitute the initial condition into the equation for y:

  y = 3 . . . . when x = 1/2

  y = √(a +b·cos(πx))

  3 = √(a +b·cos(π/2)) = √a

  3² = a = 9

The value of a is 9.

__

Additional comment

The value of 'b' is -3/π.

It can be found by putting the equation for y in the original differential equation, and solving for b.

By the Definition of congruent property, we have proved that:

VW ≅ VX

Congruent Property:

The three properties of congruence are the reflexive property of congruence, the symmetric property of congruence and the transitive property of congruence. These properties can be applied to line segments, angles, triangles, or any other shape.

Given: VZ ≅ VY and WY ≅ XZ

Prove:  VW ≅ VX

Proof:

(Given): VZ ≅ VY and WY ≅ XZ

By the Definition of Congruent Substitute:

VZ = VY and WY = XZ

⇒ VZ = VX + XZ , and,

    VY = VW + WY

By Substituting  

VX + XZ = VW + WY

Again,

VX + WY = VW + WY

Now,

By Subtraction property of Equality

VX = VW  

VW = VX (Definition of congruent property.)

Complete Question:

IF VZ congruent of VY and WY congruent of XZ. Prove that VW is Congruent of VX.

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The slope-intercept form of the equation of a line is: y = mx + b

Where: y is the dependent variable (usually represented on the vertical axis of a graph). x is the independent variable (usually represented on the horizontal axis of a graph). m is the slope of the line (which represents the rate of change of y with respect to x). b is the y-intercept (which represents the value of y when x is equal to 0). To use this equation, you need to know the slope (m) and the y-intercept (b) of the line. You can find the slope of a line by taking any two points on the line and using the formula:

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

where (x1, y1) and (x2, y2) are any two points on the line. Once you know the slope, you can substitute it and the y-intercept into the slope-intercept form of the equation of the line to get the equation in its final form.

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Answer:

plot the point at 1

Step-by-step explanation:

Answer:

(1,0)

Step-by-step explanation:

S = (-7,0)

T = (3,0)

W = (x,0)

Answer:

y = 5x - 21

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, 4 ) and (x₂, y₂ ) = (8, 19 )

m = [tex]\frac{19-4}{8-5}[/tex] = [tex]\frac{15}{3}[/tex] = 5 , then

y = 5x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, 4 ) , then

4 = 5(5) + c = 25 + c ( subtract 25 from both sides )

- 21 = c

y = 5x - 21 ← equation of line

The difference is not constant, the sequence is not arithmetic.

An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a fixed constant value (known as the common difference). A constant rate of change is modelled by arithmetic sequences in fields like engineering, physics, and financial computations.

For the given series we need to determine if the sequence is arithmetic, by checking difference between consecutive terms is constant.

9 - 7 = 2

12 - 9 = 3

16 - 12 = 4

Since the difference is not constant, the sequence is not arithmetic.

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The farmer now has 1377 sheep. If the farmer loses 32.5% of his 2400 sheep due to the drought, then he will have: 2400 * (1 - 0.325) = 1620 sheep left after the drought.

The farmer had 2400 sheep, but he lost 32.5% of them due to drought. Using the formula for finding percentages, we can calculate that 32.5% of 2400 is 780. So, the farmer had 2400 - 780 = 1620 sheep left after the drought. However, he then lost 15% of those remaining sheep due to sickness. Using the same formula, we can calculate that 15% of 1620 is 243. Therefore, the farmer had 1620 - 243 = 1377 sheep left after the sickness. So, the final number of sheep the farmer has now is 1377.

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a. The triangle can be sketched as shown in the attached image.

b.  The side length OE is 4√11 inches

c. The measure of ∠G is 27.82°

a. The triangle can be sketched as shown in the attached image.

b. We can use Pythagoras theorem  to calculate the side length OE. That is:

OE = √(15² - 7²)

OE = 4√11 inches

c. Using trig. ratio:

sin G = (4√11)/15    (opposite/hypotenuse)

sin G = 0.8844

G =  sin⁻¹ (0.8844)

G = 27.82°

Thus, the measure of ∠G is 27.82°

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A. Please see attached photo for diagram

B. The length of side OE is 13 inches

C. The measure of  of angle G, ∠G is 62°

We can obtain the the length of OE by using Pythagoras theorem as shown below:

OE² = OG² - GE²

OE² = 15² - 7²

OE² = 225 - 49

OE² = 176

Take the square root of both sides

OE = √176

OE = 13 inches

Thus, the length of OE is 13 inches

The value of angle G, ∠G can be obtained as follow:

Cos G = Adjacent / Hypothenuse

Cos G = 7 / 15

Cos G = 0.4667

Take the inverse of Cos

G = Cos⁻¹ 0.4667

G = 62°

Thus, angle G is 62°

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The functions are arranged/combined as follows

21. 595

22. 6a² + 25ab - 3b² + 6

23. 2b - 2

24. 7x² - 5xy + y²

25. 3x - 24y - 4

Descending powers involves making the highest power to be the first term

The equations are solved one after the other as follows

21.

720 + 40 - 60 - 120 + 15 = 595

22.

25ab + 6a² - 3b² + 6 =

6a² + 25ab - 3b² + 6

23.

= 3a + 2b - 3a + 1 - 3

= 3a - 3a + 2b + 1 - 3

= 2b - 2

24.

= 3x² - 2xy + 4x² - 3xy + y²

= 7x² - 5xy + y²

25.

= 2x + x + 25y - y - 4

= 3x - 24y - 4

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In the given triangle, The value of x will be 6.

What exactly is a triangle?

A triangle is a closed two-dimensional geometric shape that is formed by three straight line segments that connect three non-collinear points. The three line segments that form a triangle are called sides, and the three points where the sides intersect are called vertices.

Triangles can be classified into six types. A triangle with all three sides of equal length is called an equilateral triangle, while a triangle with two sides of equal length is called an isosceles triangle. A triangle with all three angles measuring less than 90 degrees is called an acute triangle, while a triangle with one angle measuring exactly 90 degrees is called a right triangle. A triangle with one angle measuring more than 90 degrees is called an obtuse triangle.

Now,

For given triangle,

The angle bisector is perpendicular to the line having x.

As it divided angle into same ratio then the ratio

[tex]x/5[/tex]=[tex]12/10[/tex]

then x=6/5*5

x=6

Hence,

        The measurement of side x will be 6.

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follow the steps in the picture above

Step-by-step explanation:

look the ans it will make you clear about substitution method clear

The ant will reach the top in 16.67 hours, or approximately 16 hours and 40 minutes

An ant is about to climb a 50-meter tree. In 2 hours, it can climb 5 meters, but it then slips down 1 meter. How long does it take the ant to reach the top?An ant can climb 4 meters in 1 hour since it climbs 5 meters but then slides down 1 meter in 2 hours. Let us assume that it takes the ant n hours to get to the tree's top. We don't understand the precise number of hours, thus we'll use 'n' to represent the number of hours it takes the ant to reach the top of the tree.

The ant climbs 4 meters per hour, thus it climbs 4n meters after n hours.The ant slips down 1 meter each hour, therefore,  it slides down 1n meters after n hours.If the ant climbs 4n meters but slips down 1n meters, it is actually at 3n meters after n hours. Therefore, 3n = 50 since the ant should reach the top of a 50-meter tree.Since 3n = 50, n = 50/3 ≈ 16.67 (to two decimal places). As a result, the ant will reach the top in 16.67 hours, or approximately 16 hours and 40 minutes.

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Answer: 8

Step-by-step explanation: Nancy has 22 apples, it was previously stated that Nancy has TWICE as many apples than Jay meaning Jay has 11 apples. Jay has 3 more apples than Ava meaning Ava has 8.

Answer:

On the graph, the point balances for the three friends on the 23rd week are:

- Friend A: 60 points

- Friend B: 80 points

- Friend C: 40 points

On the 24th week, the point balances are:

- Friend A: 80 points

- Friend B: 100 points

- Friend C: 60 points

It looks like all three friends are earning points and increasing their balances over time. Friend B seems to be earning points at a faster rate than the other two friends, as their balance is consistently higher. Friend C has the lowest balance, but is still earning points and increasing their balance.

Answer: Ans b.

Vol_total

= 7800 yd^3

Step-by-step explanation:

The bottom part of your shape is a box, basically (rectangular prism) and the volume is:

V=

length×width×height

Those numbers are all given. Because it is a box shape, it doesn't matter which number is which.

V = 22 × 15 × 16

= 5280 yd^3

Now the "roof" part on top is a little bit different. It is a triangular prism. So the side that needs to be the Base of the prism is the front (or back) triangle.

The volume is:

V

= BaseArea×height

= Area_triangle× ht

= 1/2 bh × height

= 1/2•21•16 × 15

The key to understanding is knowing the triangle must be the base. And the roof line running front to back will be the height. And also understanding the difference between the height of just a triangle (21) and the height of the prism(15). They are different.

Vol_roof = 2520

Then add them together.

Vol_total

= 5280 + 2520

= 7800 yards cubed

Answer:

Approximately 4 cm

Step-by-step explanation:

Old mirror's area = S X S = 7 x 7 = 49cm2

Area of old mirror = Area of new mirror
49 = πr2

49 = 22/7 * r2

[tex]\frac{49 * 7}{22}[/tex] = r2

[tex]\frac{343}{22}[/tex] = r2

15.5909 = r2

r = [tex]\sqrt{15.5909}[/tex]
r = 3.948 cm  = approx. 4cm

Hope it helps.

Answer:

Yes, 0.06 is bigger than 0.066, because 0.06 is greater than 0.066 when they are written in decimal form. This is due to the fact that 0.06 has 6 tenths, while 0.066 has 66 hundredths.

Answer:

no

Step-by-step explanation:

that is because 0.6 = 0.6000000

and 0.066 = 0.6600000

The probability that the coin shows heads and the number is two is 0.05.

What is probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, we have

Given: you flip a coin and use a random number generator to generate a number from 1 to 10.

To find the probability, we need to use that we have two independent events. First, flip a coin, and second, generate a number from 1 to 10. They are independent events because their occurrence is not dependent on any other event.

P(A∩B) = P(A).P(B)

Where A represents the event of flipping a coin

B represents the event of generating a number from 1 to 10.

P(A) = 1/2, P(B) = 1/10

P(A) = 0.5 and P(B) = 0.1 we need to replace their values in the initial formula

P(A∩B) = 0.5× 0.1

P(A∩B) = 0.05

Hence, The probability that the coin shows heads and the number is two is 0.05.

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The expressiοn calculates the tοtal cοst οf membership and game dοwnlοads. Sο, the cοrrect οptiοn is (C) 2n + 4.99.

Algebraic expressiοns can include οne οr mοre variables, which are typically represented by letters, such as x, y, οr z. These variables can be used tο represent unknοwn quantities οr tο express relatiοnships between different quantities in a prοblem.

Algebraic expressiοns can alsο include cοnstants, which are fixed numbers, and cοefficients, which are the numbers that multiply the variables in the expressiοn. Fοr example, in the algebraic expressiοn 3x + 2y, the cοnstants are 3 and 2, and the cοefficients are 3 and 2, respectively.

The given prοblem describes twο different charges: a οne-time charge οf $200 tο dοwnlοad a digital sοng, and a membership fee οf $4.99 that must be paid regardless οf hοw many sοngs οr games are dοwnlοaded. Additiοnally, fοr dοwnlοading games, there is a charge οf $2.00 per game.

Therefοre, the tοtal cοst in dοllars tο jοin the streaming service and dοwnlοad games can be represented by the expressiοn:

2n + 200 + 4.99

Here, "n" represents the number οf games dοwnlοaded, and the expressiοn calculates the tοtal cοst οf membership and game dοwnlοads.

Sο, the cοrrect οptiοn is (C) 2n + 4.99.

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Answer:

Step-by-step explanation:

16. Since the angle between the two values is 90, that is already half of 180, which is the total of all of the angles. So you make the equation, 3n+3+2n+7+90=180, which simplifies down to 5n+100=180, and after solving you get n = 16.

Here is the answer to your question

[tex] = 16[/tex]

After translatiοn, the cοrrect answer is B' (x+2, y+6).

The cοοrdinate after reflectiοn is (3,2).

The translatiοn rule that describes the result οf cοmpοsitiοn is (x, y) →(x-1, y-6).

Transfοrmatiοns in a triangle refer tο changes that can be made tο the shape, size, pοsitiοn, οr οrientatiοn οf the triangle οn a cοοrdinate plane. The three main types οf transfοrmatiοns that can be applied tο a triangle are:

Translatiοn: This transfοrmatiοn invοlves mοving the entire triangle tο a new pοsitiοn οn the cοοrdinate plane withοut changing its size οr shape.

Rοtatiοn: This transfοrmatiοn invοlves rοtating the entire triangle arοund a fixed pοint οn the cοοrdinate plane. The fixed pοint is called the center οf rοtatiοn, and the angle οf rοtatiοn determines the amοunt οf turn.

Scaling: This transfοrmatiοn invοlves changing the size οf the triangle by multiplying the x and y cοοrdinates οf each vertex by a fixed factοr.

1) Applying the translatiοn οf (x-2, y+3) tο pοint B(4,3) wοuld result in: B' = (4 + (x-2), 3 + (y+3)) = (x+2, y+6)

Therefοre, the cοrrect answer is B' (x+2, y+6)

2) Reflecting pοint G(3,-2) acrοss the x-axis results in the y-cοοrdinate being negated, and the x-cοοrdinate remains the same. Therefοre, the cοοrdinates οf the reflected pοint wοuld be G(3, 2).

The cοrrect answer is (3,2).

3) Tο determine the cοmpοsitiοn οf (x, y) → (x+4, y⁻¹) and (x, y) →(x-5, y⁻⁵), we need tο apply them in οrder. Firstly, (x, y) → (x+4, y-1) is applied tο pοint (x,y), which results in:(x, y)→ (x+4, y-1)

Next, (x, y) → (x-5, y-5) is applied tο the result frοm the previοus transfοrmatiοn (x+4, y-1), which results in:(x+4, y-1)→(x-1, y-6)

Therefore, the correct answer is (x, y) →(x-1, y-6).

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The property listed in the first column of the table by filling in the box in the second column of the table with an equivalent expression are: 1. Commutative Property of Addition 2. Additive Identity Property of Zero 3. Multiplicative Identity Property of One.

An expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value or quantity and can be evaluated or simplified to a single value or another expression. Expressions can contain constants, which are fixed values, such as the number 5 or the symbol π, or variables, which are symbols that represent varying values, such as x or y.

Here,

Commutative Property of Addition: The order in which two numbers are added does not change the result.

For example:

g + h = h + g

Additive Identity Property of Zero: Adding zero to any number does not change the value of the number.

For example:

n + 34 = n

Multiplicative Identity Property of One: Multiplying any number by one does not change the value of the number.

For example:

S * 1 = S

Commutative Property of Multiplication: The order in which two numbers are multiplied does not change the result.

For example:

b * x * 1 = x * b * 1

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Answer: So,

If we add them together, we get

5 + 3 + 4 + 1 = 13

Since there are 4 blue chips, the probability would be 4 out of the total number of chips, or 4/13.

Step-by-step explanation: Hope this helps! <3

Answer: 61 N

Step-by-step explanation:

18+15+28=61

Answer:

plot the point at -5

Step-by-step explanation:

Answer: The answer is 3

Step-by-step explanation:

3x+1 take one minus one.
3x1-1 1-1 for exponents value becomes 0
3x0 for every term 0 is = to one in a exponent value so it become 3x1
3x1 = 3
So the answer is 3..

Step-by-step explanation:

In the 3x+1 problem, no matter what number you start with, you will always eventually reach 1. The problemproblm has been shown to be a computationally unsolvable problem.