Solve problem in the picture!
The equation
(x² + y²)² = 4(x² - y²)
defines a lemniscate (a "figure eight" or "oo-shaped curve"). The point P= (√5/8, √3/8) is on this lemniscate. Determine an
equation for the line , which is tangent to the lemniscate at the point P. The figure below, which is drawn to scale, may help to
understand the problem (and may help you to check your answer for "reasonableness").
Bonus Question: [up to 3 points] Let Q = (2,1), and determine an equation for the line which is tangent to the lemniscate at Q.

Answer:

x = 4

Step-by-step explanation:

In order to find x, we will either have to find the length QT or RT.

In triangle RST, the length RS is given so we can either length RT or ST. However, if we find the length RT, we can find the value of x.

sin Θ = [tex]\frac{opp}{hyp}[/tex]

sin 60° = [tex]\frac{2\sqrt{3} }{RT}[/tex]

RT = [tex]\frac{2\sqrt{3}}{sin 60}[/tex] = 4

tan Θ = [tex]\frac{opp}{adj}[/tex]

tan 45° = [tex]\frac{x}{4}[/tex]

x = tan 45° × 4 = 4

Answer: Let x be the percentage discount given to Scott. Then we can write:

Discounted price for Libby = Original price - 20% of the original price

Discounted price for Scott = Original price - x% of the original price

We know that Libby paid $600 and Scott paid $630 for the same watch, so we can set up the following equation:

Original price - 20% of original price = $600

Original price - x% of original price = $630

Simplifying each equation, we get:

0.8 * Original price = $600

(1 - x/100) * Original price = $630

Dividing the second equation by the first, we get:

(1 - x/100) / 0.8 = 630/600

Simplifying the right-hand side, we get:

(1 - x/100) / 0.8 = 21/20

Multiplying both sides by 0.8, we get:

1 - x/100 = (21/20) * 0.8

Simplifying the right-hand side, we get:

1 - x/100 = 0.84

Subtracting 1 from both sides, we get:

-x/100 = -0.16

Multiplying both sides by -100, we get:

x = 16

Therefore, Scott was given a 16% discount on the original price of the watch.

Step-by-step explanation:

Answer:

Food is brought for us by them.

Answer:

Food is brought for us by them.

Step-by-step explanation:

Answer:

To determine the area of the garden that needs to be covered with plastic, we need to multiply the length by the width of the garden. However, we need to convert the measurements to the same unit of measurement. Let's convert the measurements into yards since we need to find the area in square yards. 12 ft = 4 yards 15 ft = 5 yards 9 ft = 3 yards Now, we can calculate the area: Area = Length x Width Area = 5 yards x 4 yards Area = 20 square yards Therefore, Robert needs 20 square yards of plastic to cover his garden.

Answer: then get help

Step-by-step explanation:

To compute the CPI, we first need to calculate the total cost of the basket in both years:

2017: (10 x $40) + (30 x $10) = $400 + $300 = $700

2018: (12 x $60) + (50 x $12) = $720 + $600 = $1320

Using 2017 as the base year, the CPI in 2017 is 100 (by definition). To calculate the CPI in 2018, we divide the cost of the basket in 2018 by the cost of the basket in 2017, and multiply by 100:

CPI in 2018 = (1320/700) x 100 = 188.57

Therefore, the percentage change in the overall price level is:

% change in price level = (CPI in 2018 - CPI in 2017) / CPI in 2017 x 100

% change in price level = (188.57 - 100) / 100 x 100

% change in price level = 88.57%

So, the overall price level increased by 88.57% from 2017 to 2018.

The value of k in the expression x³ – 6x² – 11x + k is –10.

Polynomial is formed up of the terms Nominal, which means "terms," and Poly, which means "many." A polynomial is a mathematical expression made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division operations.

From the question given above, the following data were obtained:

f(x) = x³ – 6x² – 11x + k

Factor => x + 2

Value of k =?

Next, we shall obtained the value of x from x + 2. This can be obtained as follow:

x + 2 = 0

Collect like terms

x = 0 – 2

x = –2

Finally, we shall determine the the value of k. This can be obtained as  illustrated below:

f(x) = x³ – 6x² – 11x + k

x = –2

Value of k =?  

f(–2) = 0 since x + 2 is a factor

x³ – 6x² – 11x + k = 0

(–2)³ – (–2)² – 11(–2) + k = 0

–8 – (4) + 22 + K = 0

–8 – 4 + 22 + K = 0

10 + k = 0

Collect like terms

k = 0 – 10

k = –10

Therefore, the value of k is –10

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Answer: The height above the ground in feet of a football thrown into the air from the balcony of a house is given by the expression:

h(t) = -12t^2 + 20t + 30

where t is the time in seconds since the ball was thrown.

To find the height of the balcony above the ground, we need to determine the initial height of the football when it was thrown from the balcony. This initial height corresponds to the value of h(0), since the time elapsed since the throw was zero at that moment.

Therefore, we can substitute t = 0 into the expression for h(t):

h(0) = -12(0)^2 + 20(0) + 30 = 30

This means that the balcony is 30 feet above the ground.

Hence, the height of the balcony above the ground is 30 feet.

Step-by-step explanation:

Answer: 9cm

Step-by-step explanation: i hope this this helps!

the approximate annual cost of raising a child born in 2013 at age 17 is about $15,050, assuming that the trend of increasing cost per year continues. we first need to calculate the slope (m) and the y-intercept (b)

what do you mean by approximate ?

Approximate means "close to but not exactly" or "an estimate". In other words, an approximate value is a value that is not exact but is close enough to the actual value to be useful or meaningful in a given context.

In the given question,

To find the equation of the line of fit in slope-intercept form, we first need to calculate the slope (m) and the y-intercept (b) using the two given points (8, 12,800) and (14, 14,420).

m = (y₂ - y₁) / (x₂ - x₁)

m = (14,420 - 12,800) / (14 - 8)

m = 1,620 / 6

m = 270

b = y - mx

b = 12,800 - 270(8)

b = 10,940

Therefore, the equation of the line of fit in slope-intercept form is:

y = mx + b

y = 270x + 10,940

To use this equation to estimate the cost of raising a child born in 2013 at age 17, we can plug in x = 17 and solve for y:

y = 270x + 10,940

y = 270(17) + 10,940

y = 15,050

Therefore, the approximate annual cost of raising a child born in 2013 at age 17 is about $15,050, assuming that the trend of increasing cost per year continues.

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Answer:5

Step-by-step explanation:

The simplified form of the function f(x)=1/2(27) 2x/3 can be expressed as f(x) = (27/2) (2x/3).

Functions are one of the fundamental building blocks of mathematics and are used to describe and analyze relationships between different variables.

The function f(x)=1/2(27) 2x/3 can be simplified by factoring out the common factor of 1/2 and 27.

Thus, the simplified form of the function can be expressed as

f(x) = (27/2) (2x/3).

This function is a polynomial function with degree 1, which means that it is a linear function. The degree of a function is the highest power of the variable in the equation.

The key aspects of this function can be identified by looking at the constant values in the equation.

The constant value 27/2 is the y-intercept, which is the point at which the line crosses the y-axis.

This means that the y-value of the function at x = 0 is 27/2.

The constant value 2/3 is the gradient, which is the slope of the line. This means that for every increase in the x-value, the y-value will increase by 2/3.

This function can be represented graphically as a straight line with a y-intercept of 27/2 and a slope of 2/3.

The graph of this function will pass through the point (0, 27/2) and will have a positive slope of 2/3. This means that the graph will move up and to the right, with each increase in the x-value resulting in an increase of 2/3 in the y-value.

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Answer:

Step-by-step explanation:Let's first substitute the values of A, P, and T in the formula A = P(1 + r)^T.

Given: A = 1,000,000; P = 10,000; T = 2

1,000,000 = 10,000(1 + r)^2

Now let's express it as a quadratic equation. First, divide both sides by 10,000:

100 = (1 + r)^2

Next, expand the square:

100 = 1 + 2r + r^2

Finally, rearrange to form the quadratic equation:

r^2 + 2r - 99 = 0

To represent the formula A = P(1 + r) as a quadratic equation with the given values, we substitute A = 1,000,000, P = 10,000, and T = 2. The resulting equation is 10,000r - 9,000,000 = 0.

To express the formula A = P(1 + r) as a quadratic equation, we substitute the given values for A, P, and T.

Given:

Substituting these values into the formula:

1,000,000 = 10,000(1 + r)

To express this equation as a quadratic form, we can expand the parentheses:

1,000,000 = 10,000 + 10,000r

Now, let's move all the terms to one side to form a quadratic equation:

10,000r - 9,000,000 = 0

Therefore, the quadratic equation that represents A = P(1 + r) with the given values is 10,000r - 9,000,000 = 0.

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Answer:

x = 2;

y = √3

Step-by-step explanation:

Use trigonometry:

[tex] \tan(60°) = \frac{y}{1} [/tex]

Cross-multiply to find y:

[tex]y = 1 \times \tan(60°) = 1 \times \sqrt{3} = \sqrt{3} [/tex]

Use the Pythagorean theorem to find x:

[tex] {x}^{2} = {y}^{2} + {1}^{2} [/tex]

[tex] {x}^{2} = ( { \sqrt{3}) }^{2} + {1}^{2} = 3 + 1 = 4[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{4} = 2[/tex]

The exact values of trigonometric functions are, respectively:

sin (u + v) = - 13 /85

tan (u + v) = - 13 / 84

In this problem we need to determine the exact values of trigonometric functions, this can be done by using trigonometric formulas and relationships between trigonometric functions. We need to use the following expressions:

sin² x + cos² x = 1

sin (u + v) = sin u · cos v + cos u · sin v

tan x = sin x / cos x

tan (u + v) = (tan u + tan v) / (1 - tan u · tan v)

Where x, u, v are measured in radians.

Now we proceed to determine the exact values of each function:

cos u = √[1 - (- 3 / 5)²]

cos u = 4 / 5

sin v = √[1 - (15 / 17)²]

sin v = 8 / 17

sin (u + v) = (- 3 / 5) · (15 / 17) + (4 / 5) · (8 / 17)

sin (u + v) = - 13 /85

tan u = (- 3 / 5) / (4 / 5)

tan u = - 3 / 4

tan v = (8 / 17) / (15 / 17)

tan v = 8 / 15

tan (u + v) = (- 3 / 4 + 8 / 15) / [1 - (- 3 / 4) · (8 / 15)]

tan (u + v) = - 13 / 84

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Answer:

7 days

Step-by-step explanation:

The indicated side lengths are: x ≈ 13.2 units and y ≈ 11.9 units

the ratio between the side opposite the angle and the hypotenuse of the triangle.

given that a triangle with three sides x, y, 18 and angle opposite to side y is 42°.

then by sine formula, trigonometric ratio for the sine of an angle:

sin(42°) = perpendicular /hypotenuse = y/18

y = 18 sin(42°), we find that y ≈ 11.9 units (rounded to the nearest tenth).

To find x,  the cosine of an angle:

cos(42°) =base /hypotenuse=x/18

x = 18 cos(42°)

we find that x ≈ 13.2 units (rounded to the nearest tenth).

Therefore, the indicated side lengths are:

x ≈ 13.2 units

y ≈ 11.9 units

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Answer:

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sandhyamahilane1116

24.02.2021

Math

Secondary School

answered • expert verified

What is a fraction between 6/7 and 1 whole?

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Given : 6/7 and 1 whole

To Find : a fraction between 6/7 and 1 whole

Solution:

There exist Infinitely many rational between two different rational numbers

There can be Different ways to find rational number in between two number

one way is to find mean of number

= (6/7 + 1)/2

= 13/14

13/14 is a fraction between 6/7 and 1 whole

6/7 = 18/21

1 = 21/21

19/21 , 20/21 are fraction between 6/7 andfraction

The correct option is $58,527.87

Using the loan details and bonus payment provided, the remaining balance on the loan at the end of 10 years and a month can be calculated as follows:

Number of payments made = 10 years * 12 months/year + 1 month = 121

Monthly interest rate = 4.75% / 12 = 0.3958%

Yearly bonus payment = $4,500

Using the PMT function in Excel, the monthly payment on the loan can be calculated as:

PMT(0.003958, 15*12, 320000) = -$2,378.03

Since the bonus payment is made once a year, it can be applied as a lump sum to the remaining balance at the end of each year. Therefore, the remaining balance after 10 years and a month can be calculated as:

Remaining balance = PV(0.003958, 5*12, -2378.03, 0, 0) - 4500

where PV is the present value function.

Solving this equation yields:

Remaining balance = $58,527.87

Therefore, the answer is $58,527.87.

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Using dilation, we can find the coordinates of the new trapezoid and the coordinates of T" is (-6, -4).

Dilation is the process of increasing an object's size without altering its shape. Depending on the scale-factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation maths, but the square's shape doesn't change.

In geometry, dilation math is used to enlarge and reduce two- or three-dimensional figures.

Here in the question,

The coordinates of point T = (-3, -2)

Now, the trapezoid is dilated about the origin.

The scale factor here is. k = 2.

The new coordinates of the point T":

x coordinate = -3 × 2 = -6

y coordinate= -2 × 2 = -4

The coordinates of T" = (-6, -4).

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subtract each seperately

first the numbers with x

-2 - -10 becomes -2 + 10 which is 8x

now the constants

then -6 - -2 becomes -6 + 2 which is -4

so its 8x - 4

youre welcome b

Answer:

It took Adele's brother 37.45 + 2.10 = 39.55 seconds to run the race.

Answer: We can determine which graph represents which polynomial function by analyzing the factors of each function.

First, let's consider f(x) = (x + 3)(x + 4). The factors are (x + 3) and (x + 4). When we multiply these factors together, we get a quadratic polynomial with a positive leading coefficient. This means that the graph of f(x) will be a parabola that opens upward.

Next, let's consider g(x) = 1/3(x + 3)(x − 4). The factors are (x + 3) and (x - 4). When we multiply these factors together and simplify, we get a quadratic polynomial with a leading coefficient of 1/3. This means that the graph of g(x) will also be a parabola that opens upward, but it will be narrower than the graph of f(x).

Based on this analysis, we can determine that the graph of f(x) corresponds to the wider parabola, and the graph of g(x) corresponds to the narrower parabola. We can also determine this without using graphing software by noting that f(x) has roots at x = -3 and x = -4, while g(x) has roots at x = -3 and x = 4. The graph of f(x) must therefore intersect the x-axis at -3 and -4, while the graph of g(x) must intersect the x-axis at -3 and 4. By examining the graphs, we can see that the wider parabola intersects the x-axis at -3 and -4, so it corresponds to f(x), while the narrower parabola intersects the x-axis at -3 and 4, so it corresponds to g(x).

Step-by-step explanation:

A boat's distance from the coast is measured from station A, where the angle is [tex]50[/tex] degrees, and the shore lies [tex]868[/tex] feet away.

A scalar number known as distance measures "how so much ground an item has traversed" while moving. A vector quantity called displacement describes how far an item is out of place.

A segment's or a room's dimensions are examples of things that may be measured in terms of length. Distance is the separation between two things, like two major cities or 2 points. There will never be a zero sign for either length or distance.

Let Ø be the third angle in the triangle.  Ø=180°-70°-60°=180°-130°=50°

Since we now have an angle and its opposite side, the Law of Sines can be used to find the lengths of other sides.  Let [tex]X[/tex] be the distance from the boat to station A, then

590/sin(Ø)=X/sin(°70)

X=590[sin(70°)/sin(50°)]=868 ft

Distance boat to shore=868sin(70°)[tex]=868 ft[/tex]

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Answer:

y = 2;

x = 2√2

.

Step-by-step explanation:

Use trigonometry:

[tex] \tan(45°) = \frac{y}{2} [/tex]

Use the property of proportion to find x (cross-multiply):

[tex]y = 2 \times \tan(45°) = 2 \times 1 = 2[/tex]

Use the Pythagorean theorem to find x:

[tex] {x}^{2} = {y}^{2} + {2}^{2} [/tex]

[tex] {x}^{2} = {2}^{2} + {2}^{2} = 4 + 4 = 8[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{8} = \sqrt{4 \times 2} = 2 \sqrt{2} [/tex]

The probability that a record player will break down during the guarantee period is 26.4%.

Cumulative distribution shows the probability of a randomly-selected value falling below or equal to a certain value.

To find the probability that a record player will break down during the guarantee period, we need to calculate the probability of the record player breaking down within two years, which is given by the cumulative distribution function of the normal distribution.

This function uses the mean and standard deviation of the distribution, so for the Radio Shack record player, the probability of breaking down within two years is given by the cumulative distribution function

P(X ≤ 2) = CDF(X; 3.3, 0.8)

To find this probability, we can use a normal distribution calculator to find the cumulative probability of X ≤ 2.

The cumulative probability of X ≤ 2 for a normal distribution with a mean of 3.3 and standard deviation of 0.8 is 2.64.

Therefore, the probability that a Radio Shack record player will break down during the guarantee period is 2.64.

This indicates that there is a 26.4% chance that a Radio Shack record player will break down before the end of the two-year guarantee period.

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The slope of a line perpendicular to [tex]2x + 3y = 24[/tex] is 3/2

An equation is a statement that two expressions are equal. It contains one or more variables and may also contain constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

To find the slope of a line perpendicular to the line whose equation is [tex]2x + 3y = 24[/tex], we need to first find the slope of the given line.

We can rearrange the equation into slope-intercept form (y = mx + b) by solving for y:

[tex]2x + 3y = 24[/tex]

[tex]3y = -2x + 24[/tex]

[tex]y = \huge \text(-\dfrac{2}{3}\huge \text )x + 8[/tex]

So the slope of the given line is -2/3.

A line perpendicular to this line will have a slope that is the negative reciprocal of -2/3.

The negative reciprocal of a number is the number flipped upside down and then negated. So the negative reciprocal of -2/3 is:

[tex]-1 \div \huge \text(-\dfrac{2}{3}\huge \text )=\dfrac{3}{2}[/tex]

Therefore, the slope of a line perpendicular to [tex]2x + 3y = 24[/tex] is 3/2

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Answer:

x = 25

Step-by-step explanation:

By the angle sum property,

2x + 2 + 5x + 3 = 180

7x + 5 = 180

7x = 175

x = 25

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Answer:

x = 25

Step-by-step explanation:

2x + 2 + 5x + 3 = 180

7x + 5 = 180 and 7x=175

7x = 175

x = 25

so x is most  likely the answer

x=25 Give her BRAINLEST for figuring it out first

The length of the parking lot in the drawing is 44 centimeters.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.

Since the scale Colton used is 1 centimeter : 2 meters, this means that for every 2 meters in real life, he drew 1 centimeter in his scale drawing.

To find the length of the parking lot in the drawing, we can set up a proportion:

1 cm / 2 m = x cm / 88 m

where x is the length of the parking lot in the drawing in centimeters.

We can solve for x by cross-multiplying:

1 cm * 88 m = 2 m * x cm

88 cm = 2x

x = 44 cm

Therefore, the length of the parking lot in the drawing is 44 centimeters.

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Answer:

Perimeter: Add up all the sides (7.5, 6, 2.5, 3.5, 3.5) to get the answer for the perimeter as 23 ft.

Area: Split the shape into two rectangles either way and multiply the length and width. Then, add the two answers. This would leave us with the answer of the area as 35 square feet.