I will give brainliest!!!!

(i) y = ±√(-x² + 2ax - a² + (b² - r²)) + b

(ii) y = ±√(-25)

The square root of a negative number is not real, there are no real y-coordinates for the given values of a, b, r, and x. There are no points on the circle with those coordinates.

(i) To express y in terms of a, b, x, and r, we can rearrange the equation of the circle as follows:

(x - a)² + (y - b)² = r²

Expanding the square terms, we get:

x² - 2ax + a² + y² - 2by + b² = r²

Rearranging the equation to isolate the y term, we have:

y² - 2by = r² - x² + 2ax - a² - b²

Completing the square by adding (b² - r²) to both sides, we obtain:

y² - 2by + (b² - r²) = -x² + 2ax - a²

Factoring the left side as a perfect square, we have:

(y - b)² = -x² + 2ax - a² + (b² - r²)

Taking the square root of both sides, we get:

y - b = ±√(-x² + 2ax - a² + (b² - r²))

Finally, isolating y, we have:

y = ±√(-x² + 2ax - a² + (b² - r²)) + b

(ii) Given a = 2, b = 3, r = 5, and x = 5, we can substitute these values into the equation we derived in part (i). Plugging in the values, we have:

y = ±√(-(5)² + 2(5)(2) - (2)² + (3)² - (5)²) + 3

Simplifying the equation:

y = ±√(-25 + 20 - 4 + 9 - 25) + 3

y = ±√(-25)

Since the square root of a negative number is not real, there are no real y-coordinates for the given values of a, b, r, and x. Therefore, there are no points on the circle with those coordinates.

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Answer:

f(10) = 3

Step-by-step explanation:

If f(x) = \(-\frac{3}{5} x + 9\) , in order to find the result for f(10) we just need to substitute 10 instead of x and we will get...

\(f(x) = -\frac{3}{5} x + 9\\\\f(10) = -\frac{3}{5} (10) + 9\\f(10) = - 6 + 9\\f(10) = 3\)

Point A (1, 0) and point B (3/5, 4/5) both lie on the unit circle with center at the origin.

A circle is a geometric shape defined as the set of all points in a plane that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius.

Center: The center is a fixed point in the plane from which all points on the circle are equidistant. It is denoted by the coordinates (h, k), where h represents the x-coordinate and k represents the y-coordinate of the center.

Radius: The radius is the distance between the center of the circle and any point on the circle. It is denoted by the letter "r". The radius is constant for all points on the circle.

Diameter: The diameter is a line segment passing through the center of the circle and with endpoints on the circle. It is twice the length of the radius, and it divides the circle into two equal halves.

In the xy-plane, the unit circle with center at the origin (0, 0) is defined by all the points that are at a distance of 1 unit from the origin.

Point A: (1, 0)

Point A lies on the x-axis and is 1 unit away from the origin. It represents a point on the unit circle.

Point B: (3/5, 4/5)

Point B lies on the unit circle but is not one of the standard points (such as (1, 0), (-1, 0), (0, 1), or (0, -1)). Instead, it represents a point on the unit circle with coordinates (3/5, 4/5). The x-coordinate of B is 3/5, and the y-coordinate is 4/5. The distance between point B and the origin (0, 0) is 1 unit, which satisfies the condition of being on the unit circle.

Therefore, point A (1, 0) and point B (3/5, 4/5) both lie on the unit circle with center at the origin.

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Answer:

8.8%

Step-by-step explanation:

Answer:

8.8

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.25 foot

Answer:

2 feet, 4 inches.

Step-by-step explanation:

The guy above only gave feet.

Answer:

1) 18 m^3

2) 2 rows per layer.

3) 3 bales per row.

Step-by-step explanation:

Volume of bale = 1 m^3

Layer has 3 layers tall ams 6 layers.

Total volume = 1 x 3 x 6 = 18 m^3

The most stable arrangement will be to have 2 rows of 3 bales per layer.

There could be 3 bales per row

The number of negative real zeros is either 2 or 0.

How to use Descartes's rule ?

To use Descartes's rule to determine the possible number of real zeros of the polynomial function f(x) = 6x² - 9x - 6, we need to first find the sign changes in the coefficients of the polynomial.

The coefficient of the highest power of x is 6, which is positive. The coefficient of the next highest power of x is -9, which is negative. The coefficient of the constant term is -6, which is negative as well. So, there are two sign changes in the coefficients of the polynomial.

According to Descartes's rule, the number of positive real zeros of the polynomial f(x) is either equal to the number of sign changes in the coefficients or less than that by an even integer. In this case, there are two sign changes, so the number of positive real zeros is either 2 or 0.

Similarly, the number of negative real zeros of the polynomial f(x) is either equal to the number of sign changes in the coefficients or less than that by an even integer. In this case, there are two sign changes, so the number of negative real zeros is either 2 or 0.

Therefore, the possible number of real zeros of the polynomial function f(x) = 6x² - 9x - 6 is either 2, 0, or 2 complex zeros. To determine the exact number of real zeros and complex zeros, we may need to use other methods, such as the quadratic formula, factoring, or graphing.

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Answer:C

Step-by-step explanation:sorry if i get it wrong

Answer:

A

Step-by-step explanation:

Each rectangle is 1/3 of the area of the complete design.

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

Looking at the design, you will be notice that the main (bigger) rectangle is divided to three smaller rectangles. Thus, each rectangle is one out of three  rectangles i.e. 1/3.

Therefore, each rectangle is 1/3 of the area of the complete design.

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Complete Question

Check attached image

Answer: 8 1/8 in

Hope this helps, tell me if thats wrong!

Answer:10

Step-by-step explanation:

From the question, we can find the expression for the money Isabella needs to pay, as follows:

Where k is the amount of miles. We know that she paid $14.00, so we can find the amount of miles:

So the taxi drove 39 miles.

Answer:

26 Books

Step-by-step explanation:

26 + 36 = 62

Sorry I couldn't explan more, but I hope this helps!

Answer:

2....6......10........14.......18

Step-by-step explanation:

Add 4 each time

Check the picture below.

so let's find "x" or namely the base of the triangle, keeping in mind that the triangle has a height of 3, and that there are four of those triangles, then we'll get their area and the area of the green square and sum them all up.

\(x=\sqrt{4^2 - 3^2}\implies x=\sqrt{7} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Areas}}{\stackrel{four~triangles}{4\left[\cfrac{1}{2}(\underset{b}{\sqrt{7}})(\underset{h}{3}) \right]}~~ + ~~\stackrel{square}{(\sqrt{7})(\sqrt{7})}}\implies 6\sqrt{7}+7 ~~ \approx ~~ \text{\LARGE 22.87}\)

Given a point (3,8) and a line that is parallel to the line shown. We have to find the equation of this line.So, the slope of this line will be the same as the slope of the given line. We can find the slope of the given line by using the slope-intercept form y = mx + b, where m is the slope of the line.For the given equation y = -2x + 6, the slope is -2.

Now, we have a point (3,8) and a slope -2. We can use the point-slope form of the equation of a line:y - y1 = m(x - x1), where (x1,y1) is the given point and m is the slope of the line.Substituting the values of the point and the slope, we get:y - 8 = -2(x - 3)Expanding the right-hand side, we get:y - 8 = -2x + 6Simplifying the equation, we get the final answer:y = -2x + 14This is the equation of the line that passes through (3,8) and is parallel to the given line. It's expressed in slope-intercept form, where the slope is -2 and the y-intercept is 14.

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Using three equal subintervals and a right riemann sum, left riemann sum, and a midpoint sum is -6.4, 3.8, -1.0.

1) Integral with left end points:

         A-left = -3.4*2 + (-0.6)*2 + 0.8*2 = -6.4

2) Integral with right end points:

        A-right = -0.6*2 + 0.8*2 + 1.7*2 = 3.8

3) Integral with midpoints:

         A-mid = -2.2*2 + 0.2*2 + 1.5*2 = -1.0

A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. It bears the name of the German mathematician Bernhard Riemann from the nineteenth century. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use.

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Answer:

Factor by Grouping

2\(x^{3}\) + 5\(x^{2}\)  - 8x - 20

2\(x^{3}\) + 5\(x^{2}\)

\(x^{2}\) (2x + 5)

-8x - 20

-4 (2x + 5)

(2x + 5) (\(x^{2}\) - 4)

(2x + 5) (x - 2) (x + 2)

Solution:

Putting the terms, which have something in common, in brackets:

Factor them by taking the common terms outside the bracket.

Factor by taking the common expression out of the brackets:

The multiplier (x² - 4) is in squared form.

Square root the multiplier of (2x + 5)(x² - 4), aka (x² - 4):

The factorized form is (2x + 5)(x - 2)(x + 2).

If the spheres are connected by a long thin wire, then the two spheres are at the same potential.

In math, the term sphere refers a three dimensional solid, that has all its surface points at equal distances from the center.

Here we have given that the two conducting spheres, here one having twice the diameter of the other, that are separated by a distance large compared to their diameters. Then the smaller sphere (1) has charge q and the larger sphere (2) is uncharged.

And we need to find If the spheres are connected by a long thin wire.

While we looking into the given question when these two conducting spheres are connected together through a thin wire then charge from the smaller sphere will travel through the wire.

Therefore, here this charge will continue to travel towards the neutral sphere until the charge on both the spheres will become equal to each other.

Therefore, their potential will also become equal.

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The rate of change of weight of the rabbit in pounds per week is 0.5 pounds per week.

To calculate the rate of change of weight of Samuel's rabbit in pounds per week, we need to look at how much the weight of the rabbit changes as the number of weeks since birth increases by one. This is also known as the slope of the linear relationship between the number of weeks and the weight of the rabbit.

Looking at the table below, we can see that when the rabbit is born (week 0), it weighs 0.5 pounds. As the number of weeks since birth increases by one, the weight of the rabbit increases by 0.5 pounds. This pattern continues for each subsequent week, with the weight of the rabbit increasing by 0.5 pounds each time.

| Number of Weeks Since Birth | Weight of Rabbit (in pounds) |
|-----------------------------|------------------------------|
|              0              |             0.5              |
|              1              |             1.0              |
|              2              |             1.5              |
|              3              |             2.0              |
|              4              |             2.5              |
|              5              |             3.0              |

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Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

\(\frac{3}{8}+\frac{1}{8}=\boxed{\frac{4}{8}}\)

If the answer is not  \(\frac{4}{8}\)  then it's probably because that it's not in the simplest form.

\(\frac{4}{8} =\frac{4/4}{8/4}=\frac{1}{2}\)

The answer would be a half cup total.

Brainilest Appreciated.

Answer:

The answer is 1/2

Step-by-step explanation:

Percentage is 50%

Dec. Is 0.50

Remeber to fond the GCF and divide both sides by it:

4/8 = the GCF is 4 so 4/4 is 1 , 8/4 is 2

=1/2.

(x - 3)² + y² = 100/9  is the equation of a circle with a radius of 10/3 and a xy-plane with a center at (3, 0) and an endpoint at (1, 83).

The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric about the center for all angles. A circle is a plane figure that is bounded by a single curved line and in which all straight lines drawn from any point inside the circle to the boundary are equal. Its center is the point, and its perimeter is the bounding line.

given

Circle Formula: (x - h)² + (y - k)² = r²  ; (h, k) is the center & r is the radius

Use the distance formula for (3, 0) and (1, 1/8 )

\(r = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }\\ r = \sqrt{( 3 - 1)^{2} + ( 0 - 8/3 )^{2} }\)

\(\sqrt{\frac{100}{9} }\\ r = \frac{10}{3}\)

Center (h, k) = (3, 0)   Radius (r) =  10 / 3

(x - h)² + (y - k)² = r²

(x - 3)² + (y - 0)² = (10/3)²

(x - 3)² + y² = 100/9

So (x - 3)² + y² = 100/9  is the equation of a circle with a radius of 10/3 and a xy-plane with a center at (3, 0) and an endpoint at (1, 83).

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Answer:

10.9

Step-by-step explanation:

Formula = Number x 100

Percent = 6 x 100

55 = 10.91

Following shows the steps on how to derive this formula

Step 1: If 55% of a number is 6, then what is 100% of that number? Setup the equation.

6

55% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

55Y = 6 x 100

55Y = 600

Y = 600

100 = 10.91

(b) To calculate the Fourier transform of (1/3)ⁿ⁻², we'll follow a similar approach. Let's substitute the signal into the D T F T formula

X (\(e^{jw}\)) = Σ (1/3)ⁿ⁻²\(e^{-jwn}\)

Again, let's rewrite the summation limits to simplify the calculation:

X (\(e^{jw}\)) = Σ (1/3)ⁿ⁺¹ \(e^{-jwn}\)

Splitting the summation into two parts

X (\(e^{jw}\)) = (1/3)⁻¹ + Σ (1/3)ⁿ⁺¹ \(e^{-jwn}\)

X (\(e^{jw}\)) = 3 + Σ (1/3)ⁿ⁺¹\(e^{-jwn}\)

The first term in the equation represents a constant, and the second term represents a geometric series. Using the formula for the sum of a geometric series

X (\(e^{jw}\)) = 3 + (1/3) Σ (\(e^{-jw}\))ⁿ

X (\(e^{jw}\)) = 3 + (1/3) ( 1 / (1 -\(e^{-jw}\)))

Simplifying further

X (\(e^{jw}\)) = 3 + 1 / (3 (1 - \(e^{-jw}\)))

Therefore, the of the given signal is

X (\(e^{jw}\)) = 3 + 1 / (3 (1 - \(e^{-jw}\)))

The equation of the circle with center at (-4,0) passing through the point (-2,1) is given as follows:

(x + 4)² + y² = 37.

The equation of a circle of center \((x_0, y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

The coordinates of the center are given as follows:

(-4,0).

Hence:

(x + 4)² + y² = r².

The circle has the circumference passing through the point (-2,1), hence the radius squared is obtained as follows:

r² = (-2 + 4)² + 1²

r² = 36 + 1

r² = 37.

Hence the equation is:

(x + 4)² + y² = 37.

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Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9

The option(1) that is  g(1) is 3 is True and remaining are false.

Function of a variable is when a change in one is accompanied by a change in the other. The graph's x-axis denotes the function's domain, and the y-axis its range.

Eight distinct types of regularly used functions correspond to eight distinct types of function graphs. They include linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal function graphs.

we have,

g(x) = f(x - 3)

As graph in question,

g(1) = f(1-3) = f(-2) = 3

This option is true.

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Answer: 15 i think, please don't be mad if it is wrong

The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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