Use three strategies to find 3r in terms of x and y, where dx Strategy 1: Use implicit differentiation directly on the given equation Strategy 2: Multiply both sides of the given equation by the denominator of the left side, then use implicit differentiation. Strategy 3: Solve for y, then differentiate. Do your three answers look the same? If not, how can you show that they are all correct answers?

The angle measure of the rhombus with one diagonal of a rhombus is a geometric mean of the length of the other diagonal are measured to be 75.5° .

Let d₁ and d₂ be the lengths of the diagonals of the rhombus and s as the side length. We have,

d₁ = s√2 (since the diagonal is the hypotenuse of a right triangle formed by two sides of length s)

d₁ = √d₂s

Combining these two equations, we get,

s√2 = √d₂s

Squaring both sides, we get,

2s² = d₂

Since the diagonals of a rhombus are perpendicular bisectors of each other, we have,

cosθ = (1/2) (where θ is one of the acute angles of the rhombus)

Using the law of cosines with sides s and d₂/2, we have,

(s² + (d₂/2)² - 2sd₂/2cosθ) = s²

Simplifying, we get,

d₂ = 4s cosθ

Substituting this expression for d₂ in 2s² = d₂, we get,

2s² = 4scosθ

Dividing both sides by 2s and simplifying, we get,

s = 2cosθ

Therefore, the angle measures of the rhombus are,

θ = arccos(s/2)

= arccos(cosθ/2)

= arccos(1/4)

= 75.5°

And the other acute angle has the same measure.

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bro idrk but I think

Answer:  The correct option is

(A) {-1, -5}.

Step-by-step explanation:  We are given to find the zeroes of the quadratic function graphed in the figure shown.

We know that

the zeroes of a quadratic function f(x) are the value of x for which f(x) is equal to zero.

That is, the points on the graph where the curve crosses the X-axis.

From the graph, we note that the curve of the function crosses the X-axis at the points x = 1 and x = -5.

Therefore, the zeroes of the given function are x = -1 an x = -5.

Thus, option (A) is CORRECT.

Answer:

1

1

1

2

2

2

2

Step-by-step explanation:

The estimated quantity of the substance at t = 1.9 is approximately 35.3 units.

To estimate the quantity of the substance at t = 1.9 using linear approximation, we can use the formula:

ΔR ≈ dR/dt * Δt

Given the point R(2) = 35 and the differential equation dR/dt = -1/5(R – 20), we can first find the value of dR/dt at t = 2.

dR/dt(2) = -1/5(R(2) – 20) = -1/5(35 – 20) = -1/5(15) = -3

Now, we can calculate Δt, which is the difference between the given t-value (2) and the desired t-value (1.9):

Δt = 1.9 - 2 = -0.1

Next, we can calculate ΔR using the linear approximation formula:

ΔR ≈ dR/dt * Δt ≈ -3 * (-0.1) = 0.3

Finally, we can estimate the quantity of the substance at t = 1.9 by adding ΔR to the given value of R(2):

R(1.9) ≈ R(2) + ΔR ≈ 35 + 0.3 = 35.3

Therefore, the estimated quantity of the substance at t = 1.9 is approximately 35.3 units.

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Yes, there is a relationship like a straight line between the raises administrators at State University receive and their performance on the job

To obtain this interpretation, we consider the equation of the regression line, which relates the predicted raise amount (y hat) to the job performance rating (x). The y-intercept term in this equation is the value of y hat when x equals zero. Therefore, the estimated y-intercept of $14,000 represents the predicted raise amount for an administrator whose job performance rating is zero, which corresponds to the base raise amount at State University.

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The equation to find the number of hours, t, until Patty and Carol are at the same location is: 70t + 50t = 300.


1. Patty and Carol start driving at the same time, towards each other on the same highway.
2. The distance between their cities is 300 miles.
3. Patty drives at an average speed of 70 mph, so in t hours she covers 70t miles.
4. Carol drives at an average speed of 50 mph, so in t hours she covers 50t miles.
5. As they drive towards each other, the sum of the distances they cover should equal the total distance between their cities.
6. Therefore, combining the distances covered by Patty and Carol, we get: 70t (Patty's distance) + 50t (Carol's distance) = 300 (total distance).

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A rhombus with a diagonal of 26.4 cm and an area of 204.6 square cm has another diagonal of length 15.5 cm

Rhombus is a 2-Dimensional shape. It is a quadrilateral. It is a specialized form of a parallelogram. All sides of a rhombus are equal in length.

Similar to a parallelogram, it has opposite sides parallel to each other and opposite angles of equal magnitude.

The area of a rhombus is expressed as half of the product of diagonals.

A = 0.5pq

A is the area

p is the length of one diagonal

q is the length of another diagonal

A = 204.6 square cm

p = 26.4 cm

204.6 = 0.5 * 26.4 * q

q = 15.5 cm

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Answer:

x = 30 , y = 54

Step-by-step explanation:

the figure is a trapezium

each lower base angle is supplementary to the upper base angle on the same side, then

4x + y + 6 = 180 ( subtract 6 from both sides )

4x + y = 174 ( subtract 4x from both sides )

y = 174 - 4x → (1)

and

2x + 12 + 2y = 180 → (2)

substitute y = 174 - 4x into (2)

2x + 12 + 2(174 - 4x) = 180

2x + 12 + 348 - 8x = 180

- 6x + 360 = 180 ( subtract 360 from both sides )

- 6x = - 180 ( divide both sides by - 6 )

x = 30

substitute x = 30 into (1)

y = 174 - 4(30) = 174 - 120 = 54

thus x = 30 and y = 54

The number of degrees in the measure of the vertex angle is 50 degrees.

An isosceles triangle has two equal sides and two equal base angles. In your question, the measure of a base angle is 65 degrees. To find the measure of the vertex angle, we'll use the fact that the sum of angles in any triangle is always 180 degrees.

Since both base angles are equal, their combined measure is 2 * 65 = 130 degrees. Now, we subtract the sum of the base angles from the total angle measure of the triangle:

180 degrees (total angle measure) - 130 degrees (sum of base angles) = 50 degrees.

So, the measure of the vertex angle in the isosceles triangle is 50 degrees. In summary, when given the measure of a base angle in an isosceles triangle, we can use the triangle's angle sum property to find the measure of the vertex angle.

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a. There would be  at least 20 students must go on the trip for the average cost per student to fall to $175.

b. As more students go on the trip, the total cost of the trip increases, but the cost per student decreases.

a. To find out how many students must go on the trip for the average cost per student to fall to $175, we can use the formula:

Total Cost = $500 + $150 x Number of Students

Average Cost per Student = Total Cost / Number of Students

Setting the average cost per student to $175 and solving for the number of students, we get:

$175 = ($500 + $150 x Number of Students) / Number of Students

Multiplying both sides by Number of Students, we get:

$175 x Number of Students = $500 + $150 x Number of Students

Simplifying, we get:

$25 x Number of Students = $500

Number of Students = $500 / $25 = 20

Therefore, at least 20 students must go on the trip for the average cost per student to fall to $175.

b. As more students go on the trip, the total cost of the trip increases, but the cost per student decreases. This is because the fixed cost of $500 is spread over more students, making the cost per student lower. So, as more students go on the trip, the average cost per student will continue to decrease.

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x = 3/8.

Starting from the left side of the equation:

2(x+1) - 3(x-2) = 7x + 5

Simplify the expressions in parentheses:

2x + 2 - 3x + 6 = 7x + 5

Combine like terms:

x + 8 = 7x + 5

Subtract 7x from both sides:

-8x + 8 = 5

Subtract 8 from both sides:

-8x = -3

Divide both sides by -8:

x = 3/8

Therefore, the solution to the equation is x = 3/8.

Answer:  M=3

Step-by-step explanation:

Given:

tangent =4cm

secant outside of circle = 2 cm

Find:

M   is secant inside of circle

Theorem:

Tangent-Secant Theorem => tangent² =(secant outside)(full secant)

Solution and Set up:

4²=(2)(2+M)              >Set up from theorem, square 4 and distribute

16=4+4M                  >subtract 4 from both sides

12 = 4M                    >divide both sides by 4

M=3

The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units. So, all the options satisfy the value of a and b except (7, -9).

The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units.

f(x) is a linear function, the area under the curve on the interval [0,4] is a trapezoid with a height of 4 and bases of lengths f(0) and f(4).

The area of a trapezoid is the height times the average of the bases.

a. f(x)=-2x+8  f(0)=8, f(4)=0;

  area = 4(8/2) = 16

b. f(x)=x+2; f(0)=2, f(4)=6;

  area = 4(8/2) = 16

c. f(x)=3x-2; f(0)=-2, f(4)=10;

   area = 4(8/2) = 16

d. f(x)=5x-6; f(0)=-6, f(4)=14;

   area = 4(8/2) = 16

e. f(x)=7x-9; f(0)=-9, f(4)=19;

    area = 4(10/2) = 20

Thus, The area is NOT 16 for choice e.

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So, depending on the original coordinates, moving down 9 units and left 2 units will end up in either the third or fourth quadrant of the coordinate plane.

A coordinate is a set of values that specifies the position of a point or an object in a geometric space. In a two-dimensional space, such as the Cartesian plane, a coordinate is typically represented by a pair of numbers (x, y), where x represents the horizontal position (or abscissa) of the point and y represents the vertical position (or ordinate) of the point.

Here,

Starting from an arbitrary point (x, y), if we move down 9 units and left 2 units, we will end up at the point with coordinates (x - 2, y - 9). The new x-coordinate is obtained by subtracting 2 from the original x-coordinate, since we moved 2 units to the left. The new y-coordinate is obtained by subtracting 9 from the original y-coordinate, since we moved 9 units down.

The quadrant we end up in depends on the original coordinates (x, y) and the direction of the movement. If we start in the first quadrant (x > 0, y > 0) and move down and left, we will end up in the third quadrant (x < 0, y < 0).

If we start in the second quadrant (x < 0, y > 0) and move down and left, we will also end up in the third quadrant (x < 0, y < 0).

If we start in the third quadrant (x < 0, y < 0) and move down and left, we will end up in the fourth quadrant (x > 0, y < 0).

If we start in the fourth quadrant (x > 0, y < 0) and move down and left, we will still end up in the fourth quadrant (x > 0, y < 0).

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Optimize crate cost by expressing material cost in terms of x and y, calculating cost of all four sides, and finding minimum cost. Optimal dimensions: x = 16 ft, y = 48 ft. Minimum cost: $8704.

To find the dimensions of the crate that will minimize the total cost of material, we need to use optimization techniques, we need to express the cost of materials in terms of x and y then calculate the cost of all four sides, then find the minimum cost.
Let's start by defining the variables we need to work with:

Let x be the length of one side of the square base (in feet),  Let y be the height of the crate (in feet).
From the given volume, we know that:
V = x^2 * y = 12288 ft^3
We can use this equation to solve for one of the variables in terms of the other:
y = 12288 / (x^2)
Now we need to express the cost of materials in terms of x and y.
The area of the bottom is x^2, so the cost of the bottom is:
[tex]C_b = 10 * x^2[/tex]
The area of each side is x * y, and there are four sides, so the cost of the sides is:
[tex]C_s = 4 * 2 * x * y = 8xy[/tex]
The area of the top is also x^2, so the cost of the top is:
[tex]C_t = 2 * x^2[/tex]
The total cost of materials is the sum of these three costs:
[tex]C = C_b + C_s + C_t = 10x^2 + 8xy + 2x^2[/tex]
Now we can substitute y = 12288 / (x^2) into this equation:
[tex]C = 10x^2 + 8x * (12288 / x^2) + 2x^2[/tex]
Simplifying this expression, we get:
[tex]C = 12x^2 + 98304 / x[/tex]
To find the minimum cost, we need to find the value of x that minimizes this expression. We can do this by taking the derivative of C with respect to x and setting it equal to zero:
C' = 24x - 98304 / x^2 = 0
Solving for x, we get:
x = 16 ft
Now we can use this value of x to find y:
y = 12288 / (16^2) = 48 ft
Therefore, the dimensions of the crate that will minimize the total cost of material are:
- Length of one side of the square base = x = 16 ft
- Height of the crate = y = 48 ft
To check that this is indeed the minimum cost, we can plug these values back into the expression for C and calculate the cost:
C = 10 * 16^2 + 8 * 16 * 48 + 2 * 16^2 = 8704
Therefore, the minimum cost of material for the crate is $8704.

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The height at x = 2 seconds is greater (25 meters), the balloons collided at the highest point at 2 seconds. We can use quadratic functions to solve this.

To find the time in seconds that the balloons collided at the highest point, we will first find the points where the balloons have the same height (y) by setting the two quadratic functions equal to each other:
-7x² + 26x + 3 = -6x² + 23x + 5
Next, we will solve for x:
x² - 3x - 2 = 0
Now, factor the quadratic equation:
(x - 2)(x - 1) = 0

The solutions for x are 1 and 2 seconds. To find the highest point of collision, we need to determine which of these times results in a greater height. Plug each value of x into one of the original equations and compare the y values:
For x = 1:
y = -7(1)² + 26(1) + 3 = 22
For x = 2:
y = -7(2)² + 26(2) + 3 = 25
The balloons collided at the highest point at 2 seconds.

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If a large airline wants to estimate its average number of unoccupied seats per flight over the past year Then a 92% confidence interval for the population mean number of unoccupied seats per flight is (10.334, 12.266) seats.

To construct a confidence interval for the population mean number of unoccupied seats per flight, we will use the following formula CI = X ± z*(σ/√n)

Where:

X = sample mean = 11.3 seats

σ = sample standard deviation = 4.3 seats

n = sample size = 300

z = z-score corresponding to the desired confidence level of 92%, which we can look up in a standard normal distribution table or use a calculator. For a 92% confidence level, the z-score is 1.75.

Plugging in the values, we get:

CI = 11.3 ± 1.75*(4.3/√300)

CI = 11.3 ± 0.966

Therefore, the 92% confidence interval for the population mean number of unoccupied seats per flight is (10.334, 12.266) seats. This means we can be 92% confident that the true population means a number of unoccupied seats per flight falls within this interval.

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Triangle A′B′C′ is a dilation of ​triangle ABC​ about point P with a scale factor of 1/2. The dilation is a reduction.

A dilation is a transformation that changes the size of a figure, but not its shape. It can be either an enlargement or a reduction depending on the value of the scale factor.

If the scale factor is greater than 1, then the image will be larger than the original figure. This is called an enlargement.

If the scale factor is between 0 and 1, then the image will be smaller than the original figure. This is called a reduction.

In this case, the scale factor is 1/2, which is less than 1. Therefore, the image of triangle ABC is smaller than the original triangle, and the dilation is a reduction.

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(a) The least squares regression equation that models the data is: y = 0.091x + 1.125, where x is the time in years since 1995 and y is the price per gallon.

(b) To estimate the price per gallon in 2030, we need to find the value of y when x = 35 (2030 - 1995). Substituting x = 35 in the equation, we get: y = 0.091(35) + 1.125 = 4.22 dollars per gallon. Therefore, the estimated price per gallon in 2030 is 4.22 dollars.

(a) The least squares regression equation is used to model the relationship between two variables, in this case, time and gasoline price. It calculates the line that best fits the data points and can be used to estimate the value of the dependent variable (gasoline price) for any given value of the independent variable (time).

(b) To estimate the price per gallon in 2030, we simply need to substitute the value of x = 35 in the equation and solve for y. The equation shows that the price per gallon increases by 9.1 cents every year since 1995.

However, this is just an estimate based on the data available, and other factors such as changes in supply and demand, government policies, and global events can also influence gasoline prices in the future.

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The total length of each roll of edging in Mrs. Thomas's scale drawings will be 19.2 cm.

To find the total length of each roll of edging in her scale drawings, we need to convert the length from inches to centimeters using the given scale.

To convert the length to centimeters:

( Length in cm ) / ( Length in inches ) = ( 1  cm ) / ( 5 inches )

x / 96 inches = 1 cm / 5 inches

x 5 inches = 96 inches x 1 cm

5x = 96 cm

x = 96 cm / 5

x = 19.2 cm

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Answer: depends but just subtract 5 from the original rate

Step-by-step explanation:

example

100 to 95 to 90 to 85 to 80 and etc.

To use logarithmic differentiation to find the derivative of the function y = x²/x, we first take the natural logarithm of both sides:

ln(y) = ln(x²/x)

Using the properties of logarithms, we can simplify this to:

ln(y) = 2 ln(x) - ln(x)

Now we differentiate both sides with respect to x using the chain rule:

1/y * y' = 2/x - 1/x

Simplifying this expression, we get:

y' = y * (2/x - 1/x²)

Substituting back in the original expression for y, we have:

y' = x²/x * (2/x - 1/x²)

Simplifying further, we get: y' = 2x - 1/x

Therefore, the derivative of the function y = x²/x using logarithmic differentiation is y' = 2x - 1/x.

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Answer: x(squared) + (y + 2)(squared) = 36

Step-by-step explanation:

The center of the circle is at (0 , -2), so we will eliminate the x value by just writing x(squared), and then we will write the y value as (y + 2)(squared) because the standard form for a circle is

(x - h)(squared) + (y + 2)(squared) = r(squared)

And if we count from the center to the top point of the circle, the number would be 6, so we would square 6 which would be 36.

The area of the quadrilateral can be found by dividing it into two triangles and finding the sum of their areas. The line connecting points B and D divides the quadrilateral into two triangles ABD and BCD. The area of triangle ABD is 1/2 * base * height = 1/2 * 6 * 6 = 18 square units. The area of triangle BCD is 1/2 * base * height = 1/2 * 3 * 8 = 12 square units. Therefore, the area of the quadrilateral is 18 + 12 = 30 square units.

The values of the variables x and y area 42 and 12 respectively

We can see that the quadrilateral that is inscribed in the circle is a parallelogram.

The properties of a parallelogram includes;

Then, from the information given, we have that;

x + 35 = 77

Now. collect the like terms, we get;

x = 77 - 35

subtract the values, we have;

x = 42

Also,

4y + 46 = 94

collect the like terms

4y = 94 - 46

4y = 48

Divide by the coefficient of y, we have;

y = 12

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The percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

Total No. of squares = 10×8 = 80

Total No. of squares shaded = 36

Percentage of the model is shaded = (36/80)×100

= 0.45×100

= 45%

Thus, the percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

The limit of sec(y sec²y - tan²y - 1) as y approaches 1 is undefined. The function is not continuous at the point being approached.

Explanation: To evaluate the limit, we can first simplify the expression inside the secant function using the trigonometric identity:sec²θ - tan²θ = 1/cos²θ - sin²θ/cos²θ = (1 - sin²θ)/cos²θ = cos²θ / cos²θ = 1Substituting this expression back into the limit, we get:lim sec(y sec²y - tan²y - 1)y→1= lim sec(y - 1)y→1As y approaches 1, the argument of the secant function approaches 0, which means that the secant function approaches infinity. Therefore, the limit is undefined.Since the limit is not defined, the function is not continuous at the point being approached. A function is continuous at a point if and only if the limit of the function as x approaches that point exists and is equal to the value of the function at that point. In this case, since the limit does not exist, the function is not continuous at y = 1.

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In the coding section of Lesson 4, Unit 7 on Code.org, you will be working with parameters and return statements to create a Number Crunch function for 2 and 3. To complete this task, follow these steps:

1. Define a function called 'numberCrunch' that takes two parameters: 'num1' and 'num2'.
2. Inside the function, perform the desired calculations using 'num1' and 'num2' (e.g., addition, multiplication, etc.).
3. Use a return statement to return the result of the calculation.
4. Call the 'numberCrunch' function with the values 2 and 3 as arguments, and store the result in a variable (e.g., 'result').
5. Display the result using a console.log or any other preferred method.

Here's an example using addition as the operation:

```javascript
function numberCrunch(num1, num2) {
 return num1 + num2;
}

var result = numberCrunch(2, 3);
console.log(result);
```

Modify the code according to the specific requirements of the lesson and the desired operation.

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The value of M is 4.

The value of M represents the length of the segment that connects the midpoints of the non-parallel sides of trapezoid ABCD. To find the value of M, we can use the fact that the trapezoids are similar.

Now, let's label the points where MN intersects sides BC and FG as P and Q, respectively. We can use the fact that MN is parallel to sides BC and FG to show that triangles BMP and FQN are similar to trapezoids ABCD and EFGH, respectively.

Therefore, we can write:

BM/AB = MP/CD = k

and

FQ/EF = QN/GH = k

Since we know that AB/EF = k, we can substitute this into the first equation to get:

BM/EF = MP/GH

Similarly, we can substitute FQ/EF = k into the second equation to get:

FQ/EF = QN/GH

Now, let's combine these two equations to get:

(BM + FQ)/EF = (MP + QN)/GH

But we know that BM + FQ = EF, and MP + QN = GH. Therefore, we can simplify the equation to get:

EF/EF = GH/GH

Or simply:

1 = 1

This means that our calculations are correct, and that we can use the ratio k to find the value of M. Specifically, since MN is parallel to AB and CD, we know that the length of MN is equal to half the difference between the lengths of AB and CD. Therefore, we can write:

M = (1/2)(AB - CD)/k

When we apply the values on it, then we get,

M = (1/2) (56 - 48) / 1

M = (1/2) x 8 = 4

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