If x^{2} + y*sqrt{xy} = 10 and y^{2} + x*sqrt{xy} = 20, what is x?

Answer: sinθ=-12/13

Step-by-step explanation:

[tex]\displaystyle\\Given:\ cot\theta=\frac{5}{12} \ \ \ \ \pi < \theta < \frac{3\pi }{2} \ \ \ \ Find:\ sin\theta\\\\\frac{cos\theta}{sin\theta} =\frac{5}{12}[/tex]

 Multiply both parts of the equation by 12sinθ:

[tex]12cos\theta=5sin\theta[/tex]

Squared both parts of the equation:

[tex](12cos\theta)^2=(5sin\theta)^2\\\\144cos^2\theta=25sin^2\theta\ \ \ \ (1)\\[/tex]

[tex]Find\ sin\theta[/tex]

Add 144sin²θ to both parts of the equation (1):

[tex]144cos^2\theta+144sin^2\theta=25sin^2\theta+144sin^2\theta\\\\144(sin^2\theta+cos^2\theta)=169sin^2\theta\\\\144(1)=169sin^2\theta\\\\144=169sin^2\theta\\\\Thus,\ 169sin^2\theta=144[/tex]

Divide both parts of the equation by 169:

[tex]\displaystyle\\sin^2\theta=\frac{144}{169} \\\\sin\theta=б\sqrt{\frac{144}{169} } \\\\sin\theta=б\sqrt{\frac{12^2}{13^2} } \\\\sin\theta=б\sqrt{(\frac{12}{13})^2 } \\\\sin\theta=б\frac{12}{13}[/tex]

[tex]\displaystyle\\As, \ \pi < \theta < \frac{3\pi }{2} \ \ \ \ \Rightarrow\ \ \ \angle\theta\ is \ in\ the\ 3rd\ quadrant\\\\ So \ sin\theta\ takes \ negative \ values\\\\sin\theta=-\frac{12}{13}[/tex]

The formula for finding the hypotenuse of an isosceles right triangle when given the area is A = (1/2)bh, where A is the area, b is the base, and h is the height.

To calculate the hypotenuse, first solve for h, which is h = 2A/b. Then, use Pythagorean theorem to solve for the hypotenuse c, which is c = sqrt((b^2)+(2A/b)^2). To illustrate the formula, consider a triangle with an area of 20 and a base of 10. First, solve for h, which is h = 2(20)/(10) = 4. Then, solve for c, which is c = sqrt((10^2)+(4^2)) = sqrt(196) = 14. Therefore, the hypotenuse of the isosceles right triangle with an area of 20 and a base of 10 is 14.

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There are infinitely many solutions and thus infinitely many values for x and y in the first system of equations. There are no solution for the second system of equations.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side

The first system of equations are,

y = 1/2 x + 1

-2x + 4y = 4

Multiplying throughout the first equation by 4, we get

4y = 2x + 4

and the second equation is 4y = 2x + 4

Both the equations are same and so the lines coincide.

They have infinitely many solutions.

The second system of equations are,

y = -x - 3

y + x = 2 ⇒ y = -x + 2

Both are in the form of y = mx +c, which is the equation of the line in slope intercept form.

Here m is the slope.

Given lines have the coefficient of x same, and so slopes are same.

So the lines are parallel.

Two parallel lines does not have a solution.

Hence the first system of equations have infinitely many solutions and second system of equations does not have any solution.

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The value of b is 2. Therefore (2, 1) is the midpoint of the line segment with endpoints (-4, 2) and (8, 0)

An equation is an expression that shows the relationship between numbers and variables.

If a point O(x, y) divides line segment AB with endpoints A(x₁, y₁) and B(x₂, y₂) in the ratio of 1:1 (midpoint). The coordinates of O is:

x = (x₁ + x₂)/2

y = (y₁ + y₂)/2

Given that (2, 1) is the midpoint of the line segment (-4, b) and (8, 0). Therefore:

1 = (0 + b)/2

b/2 = 1

b = 2

The value of b is 2.

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Calculating the pixel ratio of a website involves measuring the width and height of each element on the page and then dividing the width by the height.

Ratio is a comparison of two numbers or values expressed as a fraction or proportion. Ratios are used to compare different measures, such as costs, efficiency, productivity, or profitability, and to evaluate the relative importance of different elements. Ratios are also used to compare different items to each other, such as the ratio of sales to expenses. Ratios can be used to compare different time periods, and to assess the performance of a company over time.

The result is the pixel ratio, which can be used to determine how much of an element is visible on the page and how much is hidden. To calculate the pixel ratio, you can use a variety of tools, such as online tools, browser extensions, or specialized software. It is also important to note that the pixel ratio will vary depending on the device used to view the website, so it is important to test the website on multiple devices. Once the pixel ratio is calculated, it can be used to optimize the website for different devices.

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Answer:

When adding the fractions 2/7 and 3/7 you'll get 5/

Step-by-step explanation:

pls mark as brainliest

The table is completed using the function f(x) = 3ˣ and g(x) = 3x as shown below

x    f(x)    g(x)

0     1       0

1      3      3

2     9      6

f(x) has a greater rate of change between 1 and 2

f(x) has a greater rate of change between 0 and 2

The table is completed by substituting the values of x into the functions of f(x) and g(x)

The rate of change between 1 and 2

f(x)

= change in y / change in x

= (9 - 3) / (2 - 1)

= 6

g(x)

= change in y / change in x

= (6 - 3) / (2 - 1)

= 3

The rate of change between 0 and 2

f(x)

= change in y / change in x

= (9 - 1) / (2 - 0)

= 4

g(x)

= change in y / change in x

= (6 - 0) / (2 - 0)

= 3

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The angle of refraction is 32 degrees. The result is obtained by using the formula from the Snell's Law.

The Snell's Law is a formula to describe the relationship between the angles of incidence and refraction when a light passes through two medias. It can be expressed as

n₁ / n₂ = sin θ₂ / sin θ₁

Where

We have:

Find the angle of refraction!

Using the formula of Snell's Law, we'll get the refracted angle.

n₁ / n₂ = sin θ₂ / sin θ₁

1.5 / 2.0 = sin θ₂ / sin 45°

3 / 4 = sin θ₂ / (½√2)

sin θ₂ = 3(½√2)/4

sin θ₂ = 3/8 √2

sin θ₂ = 0.53

θ₂ = arc sin 0.53

θ₂ = 32°

Hence, the refracted angle is 32 degrees.

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Answer:

A.

Step-by-step explanation:

looking at the scatter plot, we can sort of determine a line of best fit, so if we imagine a linear line passing through the middle of the plots, the slope of the line would be positive :)

Answer:

87-5x Gespil=13+8x

Step-by-step explanation:

dubble started with 87, so we but 87 as the y-intercept. Every month he LOSES elentires, therefore minus. The months are represented by x, because we don’t know how many have passed. Same thing for Gespil except it increases for her.
if possible could i maybe get brainilest???? if i cant then its okay.

The equation which gives solutions, x=0 and y=-6.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y=-x-6............................(1)

x+3y=-18.........................(2)

now, solving both equation we get

x+3y=-18

x + 3(-x-6) = -18

x - 3x - 18 = -18

-2x = 0

x= 0

and, y= -0 -6 = -6

Hence, the solution is x=0 and y=-6.

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The coordinates of B is (-2, -6)

The formula to determine the midpoint of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

From the formula the coordinates of B is solved knowing that midpoint is

M (3,-1) and A is (8,4) and say B (x₁, y₁)

3 = (8 + x₁)/2

6 = 8 + x₁

x₁ = -2

-1 = (4 + y₁)/2

-2 = 4 + y₁

y₁ = -6

hence B is (-2, -6)

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The solution for the equation 5t - 3 = 3t - 5 is when value of t is equal to -1.

Therefore the answer is A. -1.

To find the solution, you can start by isolating the variable t on one side of the equation by adding 3 to both sides and subtracting 3t from both sides:

5t - 3 + 3 = 3t - 5 + 3

5t = 3t - 2

Then subtract 3t from both sides:

5t - 3t = 3t -2 - 3t

2t = -2

Finally, divide both sides by 2 to solve for t:

t = -2/2

t = -1

So, the value of t that satisfies the equation 5t - 3 = 3t - 5 is -1.

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If the sidewalk A , B ,C are horizontal to each other and D is connecting them, then we can say that the the sidewalk D is perpendicular to them .

We say that two lines are perpendicular if they form the angle of 90 degree between them. Thus , we can say that the sidewalk D are having a perpendicular relationship whit the other 3 sidewalks.

Horizontal means something which has a parallel relationship with the horizon . The opposite of horizontal is vertical which is also known as the portrait mode. A horizontal line is any line normal to a vertical line. Horizontal lines do not cross each other similarly the vertical lines do not cross each other.

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A chord is the line segment that the two points determine, i.e., the interval on the secant with the two points as its ends.

In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.

given

The Latin verb secare, which means to cut, is where the word secant originates.

A secant crosses a circle at precisely two points in the case of a circle. A chord is the line segment that the two points determine, i.e., the interval on the secant with the two points as its ends.

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Answer: $3

Step-by-step explanation:

Since the company charges $180 for an hour of service, we can say that it charges $180 for 60 minutes of service.

Let the cost of service per minute be C

The equation would be

60C = 180

Simplify, and you'll get

C = 3

And there's your answer.

The correct inequality that describes the problem is 4x ≥ 40. Thus, the correct answer is A.

The answer is A because Ms. Wells is ordering 4 large cheese pizzas, and she expects to spend at least $40 on the pizzas. The inequality 4x ≥ 40 represents the total cost of the pizzas, which is 4 times the cost of each pizza (4x) and should be greater than or equal to $40. This inequality tells us that the total cost of the pizzas is at least $40, which is what Ms. Wells expects.

Option B, 4x > 40x, is incorrect because it doesn't make sense mathematically. The right side of the inequality is 40x, which is not related to the problem, and it also doesn't make sense that each pizza will cost 40 dollars.

Option C, 4x ≤ 40, is incorrect because it represents the total cost of the pizzas as less than or equal to $40, which doesn't match with Ms. Wells' expectation that she expects to spend at least $40 on the pizzas.

This question should be provided with answer choices, which are:

The correct answer is A.

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A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.

A slant asymptote exists of the form y = mx + b where m ≠ 0.

Vertical lines go up and down and are in the form of x = a, where a stands for the common x-coordinate of all locations, whereas horizontal lines go left to right and take the shape of y = b, where b stands for the y-intercept.

A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's domain, the graph can never cross it. There may be multiple vertical asymptotes for a given function. All common factors are cancelled in the denominator, D(x).

A horizontal asymptote exists of the form y = k where x→∞ or x→ -∞ if the value of the one/both of the limits lim ₓ→∞ f(x) and lim ₓ→ -∞ f(x).

A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.

A slant asymptote exists of the form y = mx + b where m ≠ 0.

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The horizontal line test is a method used to determine if a given function is one-to-one, which means that for every unique x-value, there is a unique y-value. A function that is one-to-one can be inverted, meaning that it has an inverse function.

The inverse function of a one-to-one function is a function that undoes the original function.

The horizontal line test is used to determine if a given function is one-to-one by drawing a horizontal line through the graph of the function and seeing if the line intersects the graph at most once.

If the function is one-to-one, it has an inverse function and it can be found by switching the x and y values and solving for y.

For example, if the original function is f(x) = 2x + 1, its inverse function is f^-1(x) = (x-1)/2. This inverse function undoes the original function and it can be used to solve equations, find derivatives, and study geometric transformations.

It's important to note that the horizontal line test is only a sufficient condition, meaning that a function that passes the horizontal line test is one-to-one, but not all one-to-one function pass the horizontal line test.

In conclusion, the horizontal line test is a method used to determine if a given function is one-to-one, which is important because one-to-one functions can be inverted.

The inverse function undoes the original function, and it can be found by switching the x and y values and solving for y. The test is simple and easy to apply, but only a sufficient condition.

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The fraction that can be equally distribute the equation is 1/9.

The term fraction is defined as the representation of the part of whole thing and it has two parts that is namely numerator and denominator.

Here we have given that is 1/3 gallon of water in a 3 gallon container.

Here we have the amount of water is 1/3 gallon and the container capacity is 3.

Now, we have to equally distribute it across the given contained for that one we have to divide it by the total amount of the container then we get,

=> (1/3)/3

When we rewrite the fraction, the we get the expression as,

=> 1/3 x 1/3

When we multiply this one, then we get,

=> 1/9

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Tom has to put up an additional $2,437.5 in collateral in order to borrow enough money to take his vacation as planned.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

automobile is priced at $3,500.

Tom needs more collateral, so P

=P + 3500 Total Collateral Value

His bank is able to lend up to 80% of the value of the collateral.

=> loan = (80/100)(P + 3500)

=> loan = 0.8P + 2800

Loan amount needed: 4,750.

0.8P + 2800 = 4,750.

=> 0.8P = 1950

=> P = 2,437.5

Tom has to put up an additional $2,437.5 in collateral in order to borrow enough money to take his vacation as planned.

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Answer:

(5,4)

Step-by-step explanation:

first, if you have a calculator you can put the equation into y = and just find the maximum point there

to find the x value of the maximum point you do -B/2A

-80/2(8) = 5 so the x value would be 5

then to find y just plug in 5 for x and you should get 4

Answer:

Maximum value of
[tex]f(x) = - 8x^2 + 80x - 196[/tex]

is

[tex]\boxed{f(x) = 4}[/tex]

Step-by-step explanation:

The maximum or minimum value of a function f(x) occurs when the first derivative equals zero

The first derivative of
[tex]f(x) = - 8x^2 + 80x - 196[/tex]

[tex]f'(x) = \dfrac{d}{dx}\left(-8x^2+80x-196\right)[/tex]

[tex]=-\dfrac{d}{dx}\left(8x^2\right)+\dfrac{d}{dx}\left(80x\right)-\dfrac{d}{dx}\left(196\right)[/tex]

[tex]\dfrac{d}{dx}\left(8x^2\right) = 16x\\\\=- \dfrac{d}{dx}\left(8x^2\right) = -16x\\\\\\\dfrac{d}{dx}\left(80x\right)=80\\\\\dfrac{d}{dx}\left(196\right)=0[/tex]

[tex]\dfrac{d}{dx}\left(-8x^2+80x-196\right) \\\\\\ =-16x + 80 + 0\\\\= -16x + 80\\\\[/tex]

Set this expression equal to 0 and solve for x to find the x value which maximizes or minimizes the function

[tex]-16x + 80 = 0\\\\\implies -16x = -80\\\\x = -80/-16\\\\x = 5\\\\[/tex]

Plug this value of x into the original function to get the maximum or minimum value.

[tex]f(5) = -8(5^2) + 80(5) - 196\\\\= -8 (25) +400 -196\\\\= -200 + 400 - 196\\\\= 4\\\\[/tex]

So the maximum value of [tex]\boxed{f(x) = 4}[/tex] ANS

and occurs at [tex]x = 5[/tex]  

(Strictly speaking to find if this is a maximum or minimum, we have to find the second derivative and see if it is negative or positive. If negative, it is a maximum, if positive it is a minimum

But since the question does not ask for this, I am skipping it. In case you are interested, the second derivative of f(x) is the derivative of f'(x) which will work out to -16 so it is a maximum)

Table B and C

In Table B, the X coordinate of -3 has two different answers which is impossible in a function because it only has one output or one answer which is y.

In Table C, the X coordinate of 0 also has two different outputs or two different answers, and with a function, there is only one y coordinate for each X coordinate.

The quotient rule essentially asserts that we may divide two powers by subtracting the exponents as long as the base is the same. This is a quick way to simplify exponents.

The quotient rule essentially asserts that we may divide two powers by subtracting the exponents as long as the base is the same. This is a quick way to simplify exponents. A power series is an infinite series in mathematics in which a represents the coefficient of the nth term and c is a constant. Power series may be found in mathematical analysis as Taylor series of indefinitely differentiable functions. The power of a number indicates how many times the number may be multiplied. Exponents and Indices are other names for powers. For example, 8^2 might be labeled "8 to the power 2" or "8 to the second power", or simply "8 squared".

Here,

The quotient rule essentially asserts that as long as the base is the same, we may divide two powers by subtracting the exponents. This is a shortcut for simplifying exponents.

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The measure of the angle ∠B of the triangle ABC will be 27°.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

In ∆ABC, if m∠A is seven more than four times m∠B and m∠C is eleven more than m∠B. Then the equations are given as,

∠A = 4∠B + 7                                ...1

∠C = ∠B + 11                                ...2

∠A + ∠B + ∠C = 180°                   ...3

From equations 1, 2, and 3, then we have

4∠B + 7° + ∠B + ∠B + 11° = 180°

6∠B = 162°

∠B = 27°

The measure of the angle ∠B of the triangle ABC will be 27°.

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The function that represents the data in the table is 3x²+2. The correct answer is B.

The quadratic function is shown in the data table.

We must ascertain the function's equation.

The quadratic equation's generic form is

Let's replace the general form with the three coordinates (1,5, (2,14), and (3,29).

We therefore have;

a+b+c =5——— (1)

4a+2b+c= 14——— (2)

9a+3b+C =29------(3)

When (2) is subtracted from (1), we have;

9= 3a+b(4)

Subtracting (3) from (2) gives us;

15= 5a +b(5)

Subtracting (5) from (4) gives us;

6= 2a

3= a

As a result, the value of an is 3. When we replace this value in equation (4), we obtain;

3(3)+b= 9

b= 0

When a = 3 and b = 0 are substituted in equation (1), we obtain;

a+b+c =5

3+0+c=5

c=2

As a result, c has a value of 2.

As a result, when we substitute a = 3, b = 0, and c = 2 in the quadratic equation's general form y =ax²+bx+c, we obtain;

3x²+2

Consequently, the function that symbolizes the information in the table is 3x²+2

As a result, Option B is the right response.

Your question is incomplete but maybe your full question attached below

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The problem states that a can of tomato sauce contains 8 oz of sauce and a case contains 12 cans. We are trying to find out how many cases of tomato sauce Chef Hugo orders and we know that he gets a total of 480 oz of sauce.

What in mathematics is a linear equation?

According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We can use the formula 12(8)x = 480 to find out the number of cases of tomato sauce that Chef Hugo orders.

Here's the calculation:

12(8)x = 480

96x = 480

x = 5

Therefore, Chef Hugo orders 5 cases of tomato sauce.

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Answer:

2.1

Step-by-step explanation:

σ total ^ 2 = σ randi ^2 + σ leah ^2 = 1.1^2 + 1.8^2 = 4.45

σ total = √4.45 = 2.1

Randi and Leah can expect the total number of hours spent studying to vary by approximately 2.1 hours from the mean.

The correct option is C.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

Given:

Randi and Leah are studying together for an exam.

Let X represent the number of hours Randi spends studying nightly, and let y represent the number of hours Leah spends studying nightly.

The mean of X is 4.5 hours with a standard deviation of 1.1 hours, and the mean of Y is 3.7 hours with a standard deviation of 1.8 hours.

Assuming these are independent random variables,

S = X + Y

σ²  = σ²(Randi)² + σ²(Leah)

    = (1.1)² + (1.8)²

    =√(4.45)

σ  = 2.1

Therefore, the sum is 2.1.

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On solving the provided question, we can say that - There exist 333 integers smaller than 1000 that are evenly divisibility test by 3 if you divide 1000 by 3, which results in 333 with a residual of 1.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

here,

1000/3

remainder = 1

divisor = 333

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On solving the provided question, we can say that in the rectangle L = 6 units and B = 2 units, Perimeter, P = 2(L+B) => P = 2(6+2) => P = 16 units

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here,

in the rectangle

L = 6 units

B = 2 units

Perimeter, P = 2(L+B)

P = 2(6+2)

P = 16 units

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