A circle has a diameter of 16 meters. What is the area of the circle?

We can see that the constant of proportionality between x and y is k = 8, using that we can see that when x = 12 the value of y is 96

We know that x and y vary directly, then we can write the equation that relates these variables as.

y = kx

Where k is a constant

We know that y = 48 when x = 6, then we can write.

48 = k*6

48/6 = k

8 = k

The relation is:

y = 8*x

Then if x = 12, we have.

y = 8*12

y = 96

That is the value of y.

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The value of the part of side of triangle given as x is equal to 11/3 in simplified fraction.

What is fraction?

A fraction is referred to as the part of something a whole in maths. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter (¼). Fractions can make calculations faster and easier through making it easier to distribute and judge different numbers. The depiction of fractions appears easier than when decimal values are used.

As given in the question, in the given triangle DE is parallel to AC,

It implies that the ration of the sides are equal.

i.e. AD/DB = CE/EB

Putting the value from the figure given in the question,

we get,

11/x = 9/3

11/x = 3

x = 11/3

Therefore, The value of the x is 11/3 in the form of simplified fraction.

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The total electric force on the 7.00−μC charge is 0.872 N at an angle of 330°.

The force exerted on the 7.00−μC charge by the 2.00−μC charge is

F₁​ ​= \(k_{e}\)q₁q₂​​/r₂ r^

= [(8.99×10⁹N.m²/C²)(7.00×10^−6C)(2.00×10^−6C) ×(cos60°i^+sin60°j^​)]/ (0.500m)²

F₁ ​= (0.252i^+0.436j^​)N

Similarly, the force on the 7.00μC charge by the −4.00−μC charge is

F₂​ ​= \(k_{e}\)q₁​q₃/​r² ​​r^

= [(8.99×10⁹N.m²/C²)(7.00×10^−6C)(−4.00×10^−6C)​×(cos60°i^−sin60°j^​)]/(0.500m)²

F₂​ ​=(0.503i^−0.872j^​)N

Hence, the total force on the charge 7.00−μC  is

F = F₁​​+F₂​

​=(0.755i^−0.436j^​)N

We can also note the total force as:

F = (0.755N)i^−(0.436N)j^​ = 0.872N

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--This question is incomplete; the complete question is

"Three charged particles are located at the corners of an equilateral triangle, as shown in Figure. Calculate the total electric force on the 7.00−μC charge."--

The statement "one can set up a spreadsheet to compute the iterations of Euler's method for approximating solutions to second-order ODEs" is true because this method provides a numerical solution to differential equations by iteratively updating the variables based on the given differential equation.

A spreadsheet can be used to organize and calculate these iterations, making it easier to approximate the solutions to second-order ODEs.

To set up a spreadsheet for Euler's method to approximate solutions to a second-order ODE, one would need to follow these steps:

The spreadsheet would allow you to easily perform the iterative calculations required by Euler's method, and to visualize the behavior of the solution over time.

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Answer:

22 +22 - 8=0

=

-2 +6

=

2

-2 +4+32

2.

=

= = =

I = -4; = 2

x = -13

TI

-2 = 36

2

-2 +(2) – 4(1)(-8)

2 (1)

2

= r = -1 -3: x = -1 +3 = sin   \theta  

Step-by-step explanation:

To find the total number of teams, we multiply the number of ways to select boys and girls: The correct answer is option c) 840.

To find the number of teams that can be selected from eight boys and six girls, where each team contains five boys and four girls, we can use the concept of combinations.

The number of ways to select five boys from eight is given by the combination formula:

C(8, 5) = 8! / (5! * (8 - 5)!) = 56

Similarly, the number of ways to select four girls from six is given by the combination formula:

C(6, 4) = 6! / (4! * (6 - 4)!) = 15

To find the total number of teams, we multiply the number of ways to select boys and girls:

Number of teams = C(8, 5) * C(6, 4) = 56 * 15 = 840

Therefore, the correct answer is option c) 840.

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The measure m∠UTS is approximately 90 degrees.

Rhombus is a parallelogram whose all sides are of equal lengths.

Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).

Its vertex angles are bisected by its diagonals.

The triangles on either side of the diagonals are isosceles and congruent.

We are given that;

Angle VUR=(10x-23)degree

Angle TUV=(3x+19)degree

Now,

Since RSTU is a rhombus, its diagonals are perpendicular bisectors of each other, which means that angle VUT is a right angle. Therefore, we have:

m∠VUR + m∠TUV + m∠VUT = 180°

Substituting the given values, we get:

(10x - 23) + (3x + 19) + 90 = 180

13x + 86 = 180

13x = 94

x = 7.23 (rounded to two decimal places)

Now, we can find m∠UTS as follows:

m∠UTS = m∠VUR + m∠TUV

Substituting the value of x, we get:

m∠UTS = (10x - 23) + (3x + 19)

m∠UTS = (10 × 7.23 - 23) + (3 × 7.23 + 19)

m∠UTS = 72.3 - 23 + 21.69 + 19

m∠UTS = 89.99

Therefore, the answer of the given rhombus will be 90 degrees.

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Answer: $2203.74

Step-by-step explanation:

Answer:

-5.6

Step-by-step explanation:

Let the given function be g(x) = 2x - 1

To get g(-2.3), you will substitute x = -2.3 into the expression as shown;

g(x) = 2x - 1

g(-2.3) = 2(-2.3) - 1

g(-2.3) = -4.6 - 1

g(-2.3) = -5.6

Hence the value is -5.6

Note that the function was assumed. Same procedure can be applies for any function g(x).

Answer:

B 1/7^2

D 7^-10 / 7^-8

Step-by-step explanation:

7^-2

We know that a^-2 = 1/a^2

1/7^2 = 1/49

We also know that anything with a power of 2 in the denominator is good

7^-8 / 7^-10 = 7^2  

7^-10 / 7^-8 = 7^-2 = 1/7^2 = 1/69  that is the second answer

Answer:

Step-by-step explanation:

Answers C and D are correct.  

Note that in C we have    7^(-8)

                                         ---------- ,  

                                          7^(-10)

which is equivalent to 7^(-8 + 10), or 7^2, or 49.

Answer:

19.3

Step-by-step explanation:

The base of the top triangle is 24.158 (approximately) found from the bottom triangle using the sine rule

from that,

sin(53) = r/24.158

or, r = 24.158×sin(53)

or, r = 19.3 (rounded to the nearest tenth)

The points where the tangent is horizontal or vertical are (1, π/2), (1, π), and (1, 0).

Given the polar equation r = 1 - cos(θ), we want to find dy/dx and use it to determine points where the tangent is horizontal or vertical.

First, we need to convert the polar equation to parametric equations:

x = r × cos(θ) = (1 - cos(θ)) × cos(θ)
y = r × sin(θ) = (1 - cos(θ)) × sin(θ)

Now, we can find the derivatives of x and y with respect to θ:

dx/dθ = -sin(θ) × cos(θ) - (1 - cos(θ)) × (-sin(θ)) = sin(θ) × (1 - 2 × cos(θ))
dy/dθ = -sin(θ)² + (1 - cos(θ)) * cos(θ)

Next, we can find dy/dx:

dy/dx = (dy/dθ) / (dx/dθ) = (-sin(θ)² + (1 - cos(θ)) × cos(θ)) / (sin(θ) × (1 - 2 × cos(θ)))

Now, we can find the points where the tangent is horizontal or vertical:

Horizontal tangent: dy/dx = 0
-sin(θ)² + (1 - cos(θ)) × cos(θ) = 0

Vertical tangent: dx/dθ = 0
sin(θ) × (1 - 2 × cos(θ)) = 0

By solving these equations, we can find the values of θ for which the tangent is horizontal or vertical. Then, plug the values of θ back into the polar equation r = 1 - cos(θ) to find the corresponding r values. Finally, we can express these points in polar form (r, θ).

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For the first question: The Watsons' adjusted gross income is $100,805.00 (option c).For the second question: Sadira's taxable income is $50,333.00 (option a).

For the first question:

The Watsons' adjusted gross income is $100,805.00 (option c).

To calculate the adjusted gross income, we start with the total gross wages of $105,430.00 and subtract the contributions to the health care plan ($2,500.00) and the student loan interest paid ($2,300.00). We also add the interest received ($175.00).

Therefore, adjusted gross income = total gross wages - health care plan contributions + interest received - student loan interest paid = $105,430.00 - $2,500.00 + $175.00 - $2,300.00 = $100,805.00.

For the second question:

Sadira's taxable income is $50,333.00 (option a).

To calculate the taxable income, we start with the gross wages of $71,983.00 and subtract the contributions to retirement plans ($6,000.00) and the standard deduction ($18,650.00). We also add the rental income ($9,000.00).

Therefore, taxable income = gross wages - retirement plan contributions - standard deduction + rental income = $71,983.00 - $6,000.00 - $18,650.00 + $9,000.00 = $50,333.00.

Therefore, Sadira's taxable income is $50,333.00.

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Answer:

56

Step-by-step explanation:

Zoe : hanna

3         7

Zoe got 24

3*8 = 24

so multiply each side by 8

Zoe : hanna

3*8         7*8

24           56

Hanna got 56

Answer:

P = 3x + 7

Step-by-step explanation:

The perimeter (P) is the sum of the 3 sides of the triangle, that is

P = x + 5 + x + 4 + x - 2 ← collect like terms

  = 3x + 7

i hope this helps! let me know if you want me to explain more. sorry the picture is a little blurry

Answer:

Step-by-step explanation:

TRUMP2020

Answer:

7. Positive

8. negative

9. undefined

10. undefined

Step-by-step explanation:

Answer:

1) positive 2) negative 3) zero 4) zero

I think :3

Step-by-step explanation:

Answer:

Decreasing

Step-by-step explanation:

Answer:

Unit rate

Step-by-step explanation:

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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The Laplace transform of the given integral equation is:

\(F(s) = L{f(t)} = ∫(0 to ∞) e^(-st)f(t) dt\\f(t) = L^-1{F(s)} = ∫(0 to ∞) e^(st)F(s) ds\)

Given the equation

\(f(t) = 4t + 16sin(t) + ∫(0 to t) e^(t-u)f(u) du\),

we can take the Laplace transform of both sides:

\(F(s) = L{f(t)} = L{4t + 16sin(t)} + L{∫(0 to t) e^(t-u)f(u) du}\)

Using the properties of the Laplace transform, we have:

\(L{4t} = 4/s^2\\L{16sin(t)} = 16/s^2 + 16s\\L{∫(0 to t) e^(t-u)f(u) du} = F(s)L{e^(t-u)} \\= F(s)e^(-u)(1/s-1)^u|(0,t) \\= F(s)(e^(-t)/s - 1)\)

By substituting these results into the equation, we get:

\(F(s) = (4/s^2 + 16/s^2 + 16s) + (F(s)(e^(-t)/s - 1))\)

Solving for F(s) we get:

\(F(s) = (4/s^2 + 16/s^2 + 16s)/(1 - e^(-t)/s)\)

To find f(t) we need to take the inverse Laplace transform of F(s)

\(f(t) = L^-1{F(s)} = L^-1{(4/s^2 + 16/s^2 + 16s)/(1 - e^(-t)/s)}\)

This is the solution of the integral equation in terms of the Laplace transform.

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Answer: 5

Step-by-step explanation: f(3) = 2x - 1

substitute the x with 3. 2(3)-1

6-1

5

Answer:

The answer is 5, hope you like!

above is the solution to the question

Answer:

10 3/5 (10.6)

Step-by-step explanation:

 7 2/5 + 3 1/5

= (7+3) + ( 2/5 + 1/5)

= 10 + 3/5

= 10 3/5

(Which is also 10.6)

Brainlest pls. :)

Answer:

36

Step-by-step explanation:

We have the summation:

\(\displaystyle{\sum_{i=1}^{9} 2i-6\)

Essentially, we want to find the sum of (2i-6) from i=1 to i=9.

First, using summation properties, we can split this to:

\(=\displaystyle{\sum_{i=1}^{9} 2i+\displaystyle{\sum_{i=1}^{9} -6\)

On the right, it will simply be -6 evaluated 9 times. We can also move the constant out from the left:

\(=\displaystyle{2\sum_{i=1}^{9} i+9(-6)\)

For the summation on the left, this will simply be the sum (1+2+3+...+9). This yields 45. Therefore:

\(=2(45)+9(-6)\)

Evaluate:

\(=90-54=36\)

So, our final answer is 36.

you need to see how high up and how far across it takes to get to the next dot.

if starting at (2,1) I gotta go up 1 and to the right 2

slope is vertical count/horizontal count

1/2

you can also solve algebraically but it gets complicated since you need to use 2 points and subtract

y2-y1/x2-x1 (2-1)/4-2) = 1/2

Solution

Distance between X and Y

Distance between Y and Z

Since

Hence, the Triangle is Isosceles

According to the World Health Organization (WHO), the European and Mediterranean populations over the age of 20 have a high percentage of overweight people. In fact, the WHO estimates that approximately 55% of the population in this region is overweight or obese.

This is a significant percentage, and it is important to note that being overweight or obese can increase the risk of numerous health problems, including cardiovascular disease, diabetes, and certain types of cancer.

There are a number of factors that contribute to the high prevalence of overweight and obesity in this region, including changes in diet, decreased physical activity levels, and cultural factors. For example, many people in these regions consume a diet that is high in calories, fat, and sugar, while also engaging in sedentary behaviors.

Overall, the high percentage of overweight and obese individuals in the European and Mediterranean populations over the age of 20 is a cause for concern. It highlights the need for effective public health interventions to promote healthy lifestyles and prevent chronic disease.

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since a year is 12 months thus six months is 6/12 of a year, now let's assume a year is 365 days.

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1000\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases}\)

\(A = 1000\left(1+\frac{0.045}{365}\right)^{365\cdot \frac{1}{2}} \implies A = 1000\left( \frac{73009}{73000} \right)^{182.5} \\\\\\ A\approx 1022.75\hspace{5em}\underset{ \textit{earned interest} }{\stackrel{ 1022.75~~ - ~~1000 }{\approx \text{\LARGE 22.75}}}\)