Question Attached in the photo. Please answer with an explanation!! I'm studying for a test tomorrow :,)

The equation of the tangent line to the ellipse 3x^2 + xy + 3y^2 = 7 at the point (1,1) is y = (-7/37)x + 44/37.

To find the equation of the tangent line to the ellipse given by the equation 3x^2 + xy + 3y^2 = 7 at the point (1,1), we can use implicit differentiation.

Taking the derivative of both sides with respect to x, we get:

6x + y + x(dy/dx) + 6y(dy/dx) = 0

Simplifying and solving for dy/dx, we get:

dy/dx = -(6x + y) / (x + 6y)

At the point (1,1), we have x=1 and y=1, so:

dy/dx = -(6(1) + 1) / (1 + 6(1)) = -7/37

Thus, the slope of the tangent line to the ellipse at (1,1) is -7/37.

To find the equation of the tangent line, we can use the point-slope form:

y - y1 = m(x - x1)

where (x1,y1) is the point of tangency, in this case (1,1), and m is the slope we just found. Plugging in the values, we get:

y - 1 = (-7/37)(x - 1)

Simplifying, we can rewrite this equation in slope-intercept form:

y = (-7/37)x + 44/37

Therefore, the equation of the tangent line to the ellipse 3x^2 + xy + 3y^2 = 7 at the point (1,1) is y = (-7/37)x + 44/37.

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The time it takes to read this question is a continuous random variable; the number of marshmallows that can fit into your mouth is a discrete random variable.

The time it takes for an individual to read a question can be considered as a continuous random variable. It is typically measured on a continuous scale and can take on any value within a given range. For example, it may take someone 10 seconds to read a question, while it might take another person 20 seconds. The time it takes to read a question can vary continuously.

On the other hand, the number of marshmallows that a person can fit into their mouth can be considered as a discrete random variable. It is measured on a discrete scale and can only take on whole number values. For instance, a person may be able to fit 2, 3, or 4 marshmallows into their mouth, but they cannot fit a fractional or continuous number of marshmallows. The number of marshmallows is limited to specific integer values, making it a discrete random variable.

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EXPLANATION:

Given;

We are given two triangles labeled MRS and NSR.

Required;

We are required touse the information provided rto rove tside SM is equal to side RN.

Solution;

If two sides and the included angle of one triangle are congruent to the corresponding parts of a second triangle, then we can conclude that both triangles are congruent.

Therefore;

The value of the product expression -3w⁸(-9w) is 27w⁹

From the question, we have the following product expression that can be used in our computation:

-3w^8(-9w)

Rewrite the expression properly

This is represented as

-3w⁸(-9w)

Remove the bracket

So, we have the following representation

-3w⁸(-9w) = -3w⁸ * -9w

Evaluate the product of the constants

-3w⁸(-9w) = 27w⁸ * w

Evaluate the product of the variables

-3w⁸(-9w) = 27w⁹

Hence, the product is 27w⁹

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Answer:

x = 3

y = -7

Step-by-step explanation:

y = -4x + 5

y = 3x - 16

Substitute y in the first equation with 3x - 16

3x - 16 = -4x + 5

+4x         +4x

7x - 16 = 5

+16         +16

7x = 21

÷7    ÷7

x = 3

Then, put x = 3 in y = -4x + 5

y = -4(3) + 5

y = -12 + 5

y = -7

Answer:

x = 3; y = -7

Step-by-step explanation:

Both equations are solved for y.

Let's substitute what y is equal to in the first equation, -4x + 5, for y in the second equation.

The original second equation is:

y = 3x - 16

Now we plug in -4x + 5 for y in the second equation.

-4x + 5 = 3x - 16

Subtract 3x from both sides.

-7x + 5 = -16

Subtract 5 from both sides.

-7x = -21

Divide both sides by -7.

-7x/-7 = -21/-7

x = 3

Now that we know the value of x, we use substitution again.

Take the first original equation, y = -4x + 5, and substitute 3 for x. Then solve for y.

Here is the first original equation:

y = -4x + 5

Substitute 3 for x:

y = -4(3) + 5

y = -12 + 5

y = -7

The solution is: x = 3; y = -7

We can check the solution to make sure it is correct.

Take each original equation and plug in the values we found for x and y. Simplify both sides and see if they are equal. If the two sides are equal, the solution is correct.

Check first equation:

y = -4x + 5

-7 = -4(3) + 5

-7 = -12 + 5

-7 = -7

The solution works on the first equation.

Check second equation:

y = 3x - 16

-7 = 3(3) - 16

-7 = 9 - 16

-7 = -7

The solution works in the second equation.

This shows that our solution is correct.

Answer: x = 3; y = -7

Answer:

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

Step-by-step explanation:

\(4(y+1)= \frac{3}{1-y}\)

\(4y+4= \frac{3}{1-y}\)

\((4y+4)(1-y)= 3\)

\(4y(1-y)+4(1-y)=3\)

\(4y-4y^{2} +4-4y=3\)

\(-4y^{2}=3-4\)

\(4y^{2}=1\)

\(y^{2} = \frac{1}{4}\)

\(y=\sqrt{\frac{1}{4} }\)

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

The height of the hill is 520 ft

The height of the hill, h the length of the road, L and the ground form a right angled triangle with length of the road as the hypotenuse side and the height of the hill as the opposite side to the angle the road makes with the horizontal, Ф.

Now, from trigonometric ratios,

sinФ = h/L

Making h subject of the formula, we have

h = LsinФ

Since L = 2500 ft and Ф = 12°, thus

h = LsinФ

h = 2500 ft × sin12°

h = 2500 ft × 0.2079

h = 519.78 ft

h ≅ 520 ft to the nearest foot

So, the height of the hill is 520 ft

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x = r - b • a

you have to isolate the x. variables are annoying xd

Answer: $329.00

Explanation: To reconstruct an original price from a sale price, use:

Original Price – Original Price * Mark-down-percent = Sale Price, or

Original Price * (1 - Mark-down-percent) = Sale Price

To do a double mark-down problem, we must do this twice.  For the 10%:

Original Sale Price * (1 – 10%) = $207.27

Original Sale Price = $207.27/0.9 = $230.30.

For the pre-all-discount price,

Original Price * (1 – 30%) = $230.30

Original Price = $230.30/0.7 = $329.00.

Answer:

x + 6

Step-by-step explanation:

Sum means to add the 2 terms , so

x + 6 ← represents the sum of 6 and x

Answer:

C: 75%

Step-by-step explanation:

27 out of 36 are red.  You find the percentage by diving 27 by 36 and then moving the decimal place over to the right 2 spaces.  27 / 36 = .75

Answer:

67.5

Step-by-step explanation:

More volatility in returns produces a larger difference between the arithmetic and geometric averages.

This is because the arithmetic average calculates the simple average of returns over a period, whereas the geometric average considers the compounding effect of returns.

When returns are volatile, meaning they fluctuate significantly, the arithmetic average tends to overstate the actual compounded growth rate. This is because the arithmetic average assumes that returns are constant over time, which is not the case when there is volatility. On the other hand, the geometric average accounts for compounding by calculating the average rate of return that would produce the same ending value as the actual returns.

The larger the volatility in returns, the more the actual returns deviate from being constant, and the greater the difference between the arithmetic and geometric averages becomes. This is because the geometric average takes into account the compounding effect of different returns over time, resulting in a more accurate representation of the actual growth rate. In contrast, the arithmetic average treats each return equally and does not consider compounding, leading to a higher average.

Therefore, more volatility in returns leads to a larger difference between the arithmetic and geometric averages.

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There are 13,992 integers between 1 and 1,000,000 with a sum of digits equal to 15.

To find the number of integers between 1 and 1,000,000 with a sum of digits equal to 15, we can use a combinatorial approach.

We need to distribute the sum of 15 among the digits of the number. We can think of this as placing 15 indistinguishable balls into 6 distinct boxes (corresponding to the digits).

Using the stars and bars method, the number of ways to distribute the sum of 15 among 6 boxes is given by the combination formula:

C(n + r - 1, r - 1)

where n is the sum (15) and r is the number of boxes (6).

Plugging in the values, we have:

C(15 + 6 - 1, 6 - 1) = C(20, 5)

Calculating this combination, we find:

C(20, 5) = 13,992

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By definition of midpoint, the coordinates of B is (- 5, 4).

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

The midpoint of AB is M (-2, 1).

And, The coordinates of A are (1,−2).

Now, Let the coordinate of B = (x, y)

Then, By definition of midpoint we get;

⇒ (1 + x) / 2 = - 2

⇒ 1 + x = - 4

⇒ x = - 4 - 1

⇒ x = - 5

⇒ (- 2 + y) / 2 = 1

⇒ - 2 + y = 2

⇒ y = 2 + 2

⇒ y = 4

Thus, The coordinate of B = (- 5, 4)

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Answer:

ummmm i uhhh :/

Step-by-step explanation:

Answer:

6.9

7.-5

8.-10

Step-by-step explanation:

The first thing we have to do is calculate the 1/3 dilation for our initial figure. For this each of our points must be multiplied by the scale factor

Graphically you can see the initial points in blue are dilated forming the figure in green

Now to carry out the translation along the vector <-5, -1>, what we must do is transform our Point A into the end point of the vector, that is, into the point (-5, -1) and perform the same calculations for the other points

Finally, the translated and dilated graph can be seen in red

Answer:

49/81

Step-by-step explanation:

(7/9)^2 (Square both the numerator and denominator)

(7^2)/(9^2)

49/81

Answer:

60⁰

Step-by-step explanation:

A triangle has three angles.

The sum of its angles = 180⁰

[ By angle sum property ]

Let the unknown angle be 'x'

Then,

30⁰ + 90⁰ + x = 180⁰

120⁰ + x = 180⁰

x = 180⁰ - 120⁰

x = 60⁰

Therefore, the unknown angle will be equal to 60⁰

Answer:

17,100

Step-by-step explanation

The hundreds place in the number is 113, if you round 113 you get 100 because it is closer to 100 than it is to 200

Answer:

A. – 2m + 4 = -6

Step-by-step explanation:

I should know. I did the question.

The matrix A must have the following form:
A = [ a11 a12 a13 a14 ]
   [ a21 a22 a23 a24 ]
   [ a31 a32 a33 a34 ]
   [ a41 a42 a43 a44 ]
   [ a51 a52 a53 a54 ]

In order for a matrix A to define a mapping from R4 into R5 by the rule T(x) = Ax, the matrix A must have 5 rows and 4 columns.

This is because the number of rows in the matrix determines the dimension of the output space, while the number of columns determines the dimension of the input space. In this case, the output space is R5 and the input space is R4, so the matrix must have 5 rows and 4 columns.

In general, if a matrix A is used to define a mapping from Rn into Rm by the rule T(x) = Ax, then the matrix A must have m rows and n columns.

So, the matrix A must have the following form:

A = [ a11 a12 a13 a14 ]
   [ a21 a22 a23 a24 ]
   [ a31 a32 a33 a34 ]
   [ a41 a42 a43 a44 ]
   [ a51 a52 a53 a54 ]

where each aij is a scalar.

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The probability that between 31.2% and 50.4% of the students in the sample will be minority students is approximately 0.7154, or 71.54%.

To solve this problem, we can use the normal approximation to the binomial distribution, assuming that the sample size is large enough. The mean (μ) of the binomial distribution is given by n * p, where n is the sample size and p is the probability of success. In this case, the sample size is 100 and the probability of success is 0.36.

μ = n * p = 100 * 0.36 = 36

The standard deviation (σ) of the binomial distribution is given by the square root of n * p * (1 - p).

σ = √(n * p * (1 - p)) = √(100 * 0.36 * (1 - 0.36)) ≈ 4.16

To calculate the probability between 31.2% and 50.4%, we need to convert these percentages into z-scores using the formula:

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

For 31.2%:

z1 = (31.2 - 36) / 4.16 ≈ -1.06

For 50.4%:

z2 = (50.4 - 36) / 4.16 ≈ 3.37

Next, we need to find the cumulative probabilities associated with these z-scores using a standard normal distribution table or calculator. The cumulative probability can be interpreted as the area under the normal curve up to a given z-score.

P(31.2% ≤ x ≤ 50.4%) = P(-1.06 ≤ z ≤ 3.37)

Using a standard normal distribution table or calculator, we can find the corresponding cumulative probabilities:

P(-1.06 ≤ z ≤ 3.37) ≈ 0.8577 - 0.1423 ≈ 0.7154

Therefore, the probability that between 31.2% and 50.4% of the students in the sample will be minority students is approximately 0.7154, or 71.54%.

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The time it will take for the ball to hit the ground can be found by solving the quadratic equation \(-16t^2 + 32t + 128 = 0\). One of the solutions will represent the time when the ball hits the ground.

The height of the ball as a function of time can be represented by an equation that considers the initial height, initial speed, and the effects of gravity. The equation takes the form of h(t) = \(-16t^2 + v0t + h0\), where h(t) represents the height at time t, v0 is the initial speed, h0 is the initial height, and -16t^2 represents the effect of gravity.

In this case, the initial height of the ball is 128 feet, the initial speed is 32 feet per second, and we want to find the time it takes for the ball to hit the ground (when the height is 0). We can set h(t) = 0 and solve the equation \(-16t^2 + 32t + 128 = 0\) for t.

By solving the quadratic equation, we can find the two possible values for t. One of the values will represent the time when the ball was thrown up, and the other value will represent the time when the ball hits the ground. We discard the negative value and consider the positive value as the time it takes for the ball to hit the ground.

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Answer:

 It will take 4 seconds for the ball to hit the ground.

Step-by-step explanation:

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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