4. Antonio is designing a
swimming pool on a coordinate grid. Is it a rectangle

Answer:

-24v + 8 by the distributive property

Step-by-step explanation:

Start by multiplying 6v by -4

-4 × 6v = -24

Then multiply -2 by -4

-2 × -4 = 8

When we add these together, we get the following:

-24v + 8

If the expression be 23 x² + 3x + 8 then the constant exists 8.

The addition, subtraction, multiplication, and division arithmetic operators are used to write a group of numbers together to form a numerical statement in mathematics. The expression of a number can take on various forms, including verbal form and numerical form.

A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.

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.

During the course of a program's execution, a constant's value cannot change. As a result, the value is constant, as implied by its name. During the course of a program's execution, a variable's value can change. As a result, the value might change, as implied by its name.

Let the expression be 23 x² + 3x + 8

then the constant exists 8.

Therefore, the correct answer is option C. 8.

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a. To choose four numbers that have the smallest possible standard deviation, we want the numbers to be as close together as possible. One possible choice would be to select the number 0 four times. In this case, all the numbers are the same, and there is no variability, resulting in a standard deviation of 0.

b. To choose four numbers that have the largest possible standard deviation, we want the numbers to be as spread out as possible. One possible choice would be to select the numbers 0, 5, 10, and 10. In this case, the numbers are maximally spread out across the range of 0 to 10, resulting in a larger standard deviation.

c. In both cases (a) and (b), there is only one choice that yields the smallest or largest possible standard deviation, respectively. For case (a), choosing four instances of the same number (e.g., 0) is the only way to minimize the standard deviation. Similarly, for case (b), selecting the numbers 0, 5, 10, and 10 provides the maximum spread and thus the largest standard deviation. These choices are unique and cannot be further optimized to reduce or increase the standard deviation.

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\(6\cos^2(\theta )-\cos(\theta )-1=0\hspace{5em}\stackrel{\textit{let's just for a second make}}{\cos(\theta )=Z} \\\\\\ 6Z^2-Z-1\implies (3Z+1)(2Z-1)=0\implies [3\cos(\theta )+1][2\cos(\theta )-1]=0 \\\\[-0.35em] ~\dotfill\)

\(3\cos(\theta )+1=0\implies 3\cos(\theta )=-1\implies \cos(\theta )=-\cfrac{1}{3} \\\\\\ \theta =\cos^{-1}\left(-\cfrac{1}{3} \right)\implies \theta \approx \begin{cases} 109.47^o\\ 250.53^o \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 2\cos(\theta )-1=0\implies 2\cos(\theta )=1\implies \cos(\theta )=\cfrac{1}{2} \\\\\\ \theta =\cos\left( \cfrac{1}{2} \right)\implies \theta = \begin{cases} 60^o\\ 300^o \end{cases}\)

Make sure your calculator is in Degree mode.

Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^

If in  triangle ABC, EG = x inches and BG = (5x - 12) inches, the length of EB is 7x - 12 inches.

In triangle ABC, the centroid G is the point of intersection of the three medians AD, BE, and CF. We are given that EG = x inches and BG = (5x - 12) inches. We need to find the length of EB.

We can use the fact that the centroid G divides each median in the ratio of 2:1. Let M be the midpoint of AC, and let N be the midpoint of BC. Then, we have:

BE/EN = 2/1

Using this proportion, we can solve for EB as follows:

BE/EN = 2/1

BE/(BN + EN) = 2/1

BE/((5x - 12)/2 + x) = 2/1 (substituting BN = (5x - 12)/2 and EN = x)

BE/(7x/2 - 6) = 2/1

BE = 2(7x/2 - 6)

BE = 7x - 12

In conclusion, we can use the fact that the centroid divides each median in the ratio of 2:1 to find the length of EB in triangle ABC. We can solve for the unknown using a proportion and the lengths of the medians that pass through it.

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Complete question is:

Answer:

12

Step-by-step explanation:

i got it right

The area of the surface obtained by rotating the circle \(x^2 + y^2 = r^2\) about the line y = r is π²r² square units.

To find the area of the surface obtained by rotating the circle

\(x^2 + y^2 = r^2\) about the line y = r, we can use the method of cylindrical shells.

The circle \(x^2 + y^2 = r^2\) is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.

When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.

Consider a small strip on the circle at a distance y from the line y = r.

This small strip is at a distance r - y from the y-axis.

The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).

The width of this strip is the change in x, which we can denote as dx.

The area of this small strip is then given by the product of its length and width, which is 2πy dx.

Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):

Total Surface Area = ∫[from -r to r] 2πy dx

Now, we need to express y in terms of x using the equation of the circle \(x^2 + y^2 = r^2:\\y^2 = r^2 - x^2\)

y = ±√(r² - x²)

Since we are considering the upper half of the circle, we take the positive square root:

y = √(r² - x²)

Now, we can rewrite the integral with respect to x:

Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx

To solve this integral, we can make a trigonometric substitution:

Let x = r sin(θ), then dx = r cos(θ) dθ.

When x = -r, θ = -π/2, and when x = r, θ = π/2.

Now the integral becomes:

Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ

Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ

Now, we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

√(1 - sin²(θ)) = cos(θ)

Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ

Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2

Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ

Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]

Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]

Since sin(π) = 0 and sin(-π) = 0:

Total Surface Area = 2πr² [(π/2 - (-π/2))/4]

Total Surface Area = 2πr² (π/2)

Total Surface Area = π²r²

So, the area of the surface obtained by rotating the circle \(x^2 + y^2 = r^2\) about the line y = r is π²r² square units.

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Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

The point on the curve where the tangent line has a slope of 1/2 is (x, y) = (7, -7).

To find the point on the curve x = 3t^2 + 4, y = t^3 - 8 where the tangent line has a slope of 1/2, we need to determine the value of t at which this occurs. First, we find the derivatives of x and y with respect to t:
dx/dt = 6t
dy/dt = 3t^2
Next, we compute the slope of the tangent line by taking the ratio of dy/dx, which is equivalent to (dy/dt) / (dx/dt):
slope = (dy/dt) / (dx/dt) = (3t^2) / (6t) = t/2
Now, we set the slope equal to 1/2 and solve for t:
t/2 = 1/2
t = 1
With t = 1, we find the corresponding x and y values:
x = 3(1)^2 + 4 = 7
y = (1)^3 - 8 = -7
So, the point on the curve where the tangent line has a slope of 1/2 is (x, y) = (7, -7).

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Answer:

4 units

Step-by-step explanation:

The length of the shorter side is equal to the difference in y-coordinates of two vertically opposite vertices. The y-coordinates of the vertices (-1, -5) and (3, -5) are both -5, so the vertical side between them is not the shorter side. The y-coordinates of the vertices (3, -7) and (-1, -7) are both -7, so the vertical side between them is the shorter side. The difference in the x-coordinates of these two vertices is 3 - (-1) = 4, so the length of the shorter side is 4 units.

Answer: Your answer is 2

Step-by-step explanation: I did the k12 quiz here's proof

Answer:

(7^2+11)/5

=(49+11)/5

=60/5

=12

Answer:

Answer is 65

Step-by-step explanation:

Take 7 to the power of two and do 7x7 and whatever answer you get add it to 11 so do 49+11 and then whatever answer you get add it to 5, so 60+5

Hope that helps

A. Up

Parabolas are graphs that make U-shapes and are formed from quadratic equations.

Vertical Parabolas

There are 2 different types of parabolas: vertical and horizontal.

If the x-value is squared, then the parabola is vertical. So, this graph must open up or down.

Positive A-Value

The a-value is the coefficient before the squared term. In a vertical parabola, the graph opens up if the a-value is positive. On the other hand, the graph opens down when the a-value is negative.

In this case, the graph is a vertical parabola that opens up. This means that the range will have a minimum value but no maximum.

Answer:

  B)  108°

Step-by-step explanation:

You want the interior angle measure for a regular pentagon.

The interior angles of a regular n-gon will have measure ...

  180° -360°/n

When n = 5, the interior angles have measure ...

  180° -360*/5 = 180° -72° = 108°

The interior angles of a regular pentagon are 108°.

__

Additional comment

The 360°/n comes from the fact that the sum of exterior angles for any convex polygon is 360°. For a regular n-gon, those exterior angles are congruent, so each is 360°/n. The interior angle is its supplement.

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Answer:

Part A is -5

Part B is 10

Step-by-step explanation:

0=-5(2)+b

Answer:

D (5 , -4)

Step-by-step explanation:

I do not use slope is equal for parallel lines and distance of opposite side of parallelogram is equal to solve, I use a very easy way to identify the 4th vertex.

AB // DC   therefore AE = CF  and BE = DF

For D (x,y)

BE = 2 - (-4) = 6        DF = x - (-1) = x + 1 = 6

x = 5

AE = 2-3 = -1             CF = y - (-3) = y + 3 = -1

y = -4

D (5 , -4)

a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

x = (3/2)k + (2/3)

Substituting this value of x into the equation of the curve, we get:

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

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Answer:

8, 3, -2, -7

Step-by-step explanation:

To solve you have to multiply -5 by whatever number is in the x column of the table then add 3. For example, -5*0 = 0, then 0+3 = 3 and that's your answer(s).

Answer:  In order from top to bottom:

9

3

-2

-7

Step-by-step explanation:

To find the y u would replace 'x' in the equation with one of the x's in the colom.

For example:

     y = -5 (-1) + 3

         = 6 + 3

           = 9

REMEBER = A negative times a negative is a positve.

As per the combination method, there are 84 different ways to fill the three offices from a group of nine eligible members.

A combination is a way of selecting objects from a larger set without regard to the order in which they are selected. In other words, combinations are a way of counting how many different groups can be formed from a set of objects, where the order of the objects in the group does not matter.

In our case, n = 9 (the number of eligible members) and r = 3 (the number of offices to be filled). So we can plug these values into the formula and get:

⁹C₃ = 9! / 3!(9-3)! = (9 × 8 × 7) / (3 × 2 × 1) = 84

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Answer:

24.88

Step-by-step explanation:

If the scale of the drawing is 1:30, it means that the vehicle drawing is 30 times smaller than the actual vehicle.

With the above information in mind, we can calculate the length of the vehicle in inches:

Finally we convert inches to feet(dividing inches by 12):

Answer:

y = 108 degrees

Step-by-step explanation:

Set 2x + 16 and 3x - 12 equal to each other.  Subtract 2x on both sides to get this equation 16 = x - 12, add 12 on both sides to get 28 as your x value.  Plug in x for 3x - 12.  You should get 72 degrees on one side and 108 degrees on another side as y since FE makes up as a straight angle.

Answer:

y = 3x - 6

Step-by-step explanation:

The equation is y = mx + b  

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Let's pick 2 points (0, -6) (2,0)

We see the y increase by 6 and the x increase by 2, so the slope is

m = 6/2 = 3

y-intercept located at (0, -6)

So, the equation is

y = 3x - 6

A line segment drawn from the point Kiley's plane takes off to the point Kiley gets of the plane, ends at the coordinates of the point that corresponds with the point she gets off the plane.

A line segment in geometry, represents a part of a line. Line segments are used for the construction of geometric figures. A geometric figure is a figure enclosed by lines, curves and or points.

Parts of the question appear missing including the location of the points on the coordinate plane.

A line segment drawn from the point Kiley's plane takes off to the point Kiley got off the plane is a line that starts from the point Kiley's plane takes off and and ends at the point where Kiley gets off the plane.

Therefore, the point where the line segment will end is the point on the coordinate plane that corresponds with the point Kiley gets off the plane.

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Answer:

The equation is: 20 + 4.5h = 11 + 5.75h

The total cost of the services will be equal at 7.83 or 8 hours.

Step-by-step explanation:

This equation is correct because it shows that these two scenarios equal the same amount of money when there is a certain amount of hours, or "h."

Here is how we solve the equation;

20 + 4.5h = 11 + 5.75h <-----Here is the original equation.

Service A                                                        Service B

1. 20 - 20 + 4.5h                         =               11 - 20 + 5.75h

2.4.5h - 5.75h =  -1.15h                             -9 + 5.75h/5.75 =

3. -1.15h/-1.15 = h                                              9/-1.15 = 7.83

                  h = 7.83 or 8 hours when rounded to the nearest hour

Hope this helps! :)

When four coins are flipped at once, there is probability a 1/4 chance that the penny and nickel will both come up heads.

As per the data given in the above question are as bellow,

The data provided are as ,

As stated in the query,

Four coins are flipped simultaneously.

Flipping a coin might result in either a head or a tail.

Total results equal 2

For each coin, there is a one-in-two chance of obtaining a head.

likelihood of finding heads on both penny and nickel coins

= ( 1 / 2 ) × ( 1 / 2 )

= ( 1 / 4 )

As a result, 1 / 4 represents the likelihood of finding heads on both the penny and nickel.

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Answer:

They made a mistake of the value of W.  If half of W is 30, then 1/1 should thus be 60, but it's 15. Leon made a mistake on the value of W. 1/2w-12=18 would actually be 3 based of background information.

Step-by-step explanation:W-

Answer:

Step two

Step-by-step explanation:

step one isn't wrong

and he infact made a mistake

The largest prime factor that always divides the sum of the terms in the sequence is 37.

The sequence is finite and consists of three-digit integers.

The tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term.

From the above property of the sequence, we can see that each digit at the units, tens as well as hundreds place will appear the same number of times in the sequence.

Let "x" be the sum of the digits at unit place in all the terms.

The sum of all the terms is "S".

S = 111*x

S = 3*37*x

We can clearly see that the sum "S" is divisible by 37.

Hence, the largest prime factor that always divides the sum of the terms in the sequence is 37.

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Answer:

x does not equal - 49.

x = 49

Step-by-step explanation:

To find the square you multiply the square root.

- 7 × - 7 = 49

x ≠ - 49

x = 49

Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).

The resulting plot will show the solution curve.

To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.

Let's define new variables:

y = y(x)

z = dz/dx

Now, we have the following system of first-order differential equations:

dy/dx = z (1)

dz/dx = -k/(2y) (2)

To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.

The general formula for the fourth-order Runge-Kutta method is as follows:

k₁ = h f(xn, yn, zn)

k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)

k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)

k₄ = h f(xn + h, yn + k₃, zn + l₃)

yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6

zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6

where f(x, y, z) represents the right-hand side of equations (1) and (2).

We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:

function [x, y, z] = rungeKuttaMethod()

   % Parameters

   k = 1;              % Constant k

   h = 0.01;           % Step size

   x0 = 0;             % Initial x

   xn = 10;            % Final x (adjust as needed)

   n = (xn - x0) / h;  % Number of steps

   % Initialize arrays

   x = zeros(1, n+1);

   y = zeros(1, n+1);

   z = zeros(1, n+1);

   % Initial conditions

   x(1) = x0;

   y(1) = 0;

   z(1) = 0;

   % Runge-Kutta method

   for i = 1:n

       k1 = h * f(x(i), y(i), z(i));

       l1 = h * g(x(i), y(i));

       k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);

       l2 = h * g(x(i) + h/2, y(i) + k1/2);

       k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);

       l3 = h * g(x(i) + h/2, y(i) + k2/2);

       k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);

       l4 = h * g(x(i) + h, y(i) + k3);

       y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;

       z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;

       x(i+1) = x(i) + h;

   end

   % Plotting

   plot(x, y);

   xlabel('x');

   ylabel('y');

   title('Solution y(x)');

end

function dydx = f(x, y, z)

   dydx = z;

end

function dzdx = g(x, y)

   dzdx = -k / (2*y);

end

% Call the function to solve the differential equations

[x, y, z] = rungeKuttaMethod();

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Therefore, the probability of Mrs. Vo winning is 1 - 91/300 - 8/21 = 11/30.

Probability refers to the likelihood or chance that a particular event or outcome will occur. It is a mathematical concept that quantifies the degree of uncertainty associated with an event or situation. Probability is typically expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that it is certain to occur.

by the question.

let's consider the first case: Mrs. Vo spins a number greater than 65 on her first spin. There are a total of 8 numbers greater than 65 on the wheel: 70, 75, 80, 85, 90, 95, 100. Since there are 21 sections on the wheel, the probability of spinning a number greater than 65 on the first spin is 8/21.

The number of possible outcomes for Mrs. Vo's spin is 21, since there are 21 equal portions on the wheel. However, we need to exclude the outcomes that would cause Mrs. Vo's sum to exceed 100, since that would result in an automatic loss. The largest possible outcome on the wheel is 100, so Mrs. Vo cannot spin a number greater than or equal to 35 on her first spin.

The number of outcomes that would give Mrs. Vo a winning sum of at least 66 is the number of outcomes greater than 65, which are 70, 75, 80, 85, 90, 95, and 100. There are 7 such outcomes.

If Mrs. Vo spins a number less than or equal to 65 on her first spin, the probability of this happening is 13/21. The probability of her second spin being between 1 and 35 is 35/100 (since there are 35 numbers between 1 and 35 on the wheel). So, the probability of her total sum being less than or equal to 65 is (13/21) * (35/100) = 91/300.

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