Find dy/dx by implicit differentiation.
7x^2 – 2y^2 = 16

dy/dx = ?

Answer:

8.2

Step-by-step explanation:

area=b*h

37.72=b*4.7

b=37.72/4.7

=8.2

Answer:

Step-by-step explanation:

Area of parallelogram= base×perpendicular height

37.72m²=base×4.6m

base= 37.72m²/4.6m²

base= 8.2m

Answer:-3

Step-by-step explanation:

Answer:

p = -3

Step-by-step explanation:

5p + 2 = 4p - 1

-4p -2    -4p -2

p          =       -3

To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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Answer:

43

Step-by-step explanation:

Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer:

Chisquare test

t - test

Correlation

ANOVA, F ratio.

Step-by-step explanation:

The Chisquare test is suitable for testing categorical variables with factors levels more than 3.

The t test of independence is suitable for testing continous variable, however re we use the two independent sample t test.

Correlation test is used to examine the relationship between two continous variable, cannot be used for categorical variables.

Analysis of Variance is use to test categorical variables with at lead three factor levels. The F ratio allows measurement and establishing of statistical significance exists between variables.

The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

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Answer:

A.

C.

D.

Step-by-step explanation:

Use the x-coordinate in place of x and compare the solution to the y-coordinate. All of the answers to these options are true.

Hope it helps!

Answer:

42

Step-by-step explanation:

For the step, let's get an answer about how long it would take for Tina to run around the base in 10 minutes.

For this, you would just need to do: 12 ÷ 2 = 6

So, 6 runs = 10 minutes

Since 70 ÷ 10 = 7 ...

All we will have to do is 7 x 6 which would equal 42.

Therefore, Tina can run 42 circles around the base in 70 minutes.

-kiniwih426

Answer:

132÷3=44 the answer is 44 thanks me later

Answer:

Step-by-step explanation:

x + x^2 = 132

x^2 = 132 - x

x = \(\sqrt{132 - x}\)

Jacob's practice times are less reliable than Carl's practice times because Jacob has a higher IQR than Carl does, which is the proper comparison between Jacob and Carl's IQR.

A measure of dispersion is the Inter-quartile Range of a collection of data values; precisely, the higher the Inter-quartile Range, the less consistent the set of data values is, and the converse is true.

The task's requirements indicate that Carl and Jacob's interquartile ranges should be compared.

As stated, Carl's practice time has an Inter-quartile Range of 1 second, which is smaller than that noted for Jacobs.

Jacob's practice times are thus less reliable than Carl's practice times since Jacob has a higher IQR.

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Answer:

x = 106 degrees

Step-by-step explanation:

x + 104 + 40 + 110 = 360

x + 254 (No more 254)

- 254 (Again no more 254)

x = 106

By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

In this system we have a geometrical system formed by two right triangles with a common hypotenuse. Right triangles are triangles where one of its internal angles are right angles and the sum of the measures of the internal angles within a triangle equals 180°. Then, this geometrical system can be modelled by using the following linear equations:

(x + 20) + 90 + 30 = 180         (1)

20 + 90 + (y + 30) = 180         (2)

By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

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Answer:

Two number: (9 , 12) or (-9 , -12)

Step-by-step explanation:

x² + (x+3)² = 225

2x² + 6x + 9 = 225

2x² + 6x + 216 = 0

2 (x² + 3x + 108) = 0

2 ( x-9) (x+12) = 0

x = 9   or   x = -12

Two number: (9 , 12) or (-9 , -12)

Answer:

She will need 60 bags.

Step-by-step explanation:

You would need to divide 5 marbles by 30 marbles and get 60 groups. So 60 bags.

By the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.

The given inequality is 2ⁿ≥2n.

Let n = 1

2^1 ≥ 2^1

2 ≥ 2 which is true

Inductive Step: Assume 2ⁿ≥2n is true for some arbitrary positive integer k.

We need to prove that 2^(k+1) ≥ 2^(k+1)

2^(k+1) ≥ 2*2^k (by the inductive hypothesis)

2^(k+1) ≥ 2*2^(k+1)

2^(k+1) ≥ 2^(k+1) which is true

Therefore, by the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.

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Answer:

3.8 × 104

Step-by-step explanation:

38,000 (thirty-eight thousand) is an even five-digits composite number following 37999 and preceding 38001. In scientific notation, it is written as 3.8 × 104. Hope this helps! Waiting for my brainliest

Answer:

(x,y)=(0,4)

Step-by-step explanation:

write as systems as equations, multiply both sides of the equation by -1, sum the equations vertically to eliminate at least one variable, divide both sides of the equation by -19, substitute the given value of x into the equation 5x+y=4, The possible solution of the system is the ordered pairs (x,y) =(0,4), then you're done. whew. ;)

Answer: A

Step-by-step explanation:

\(-\frac{4}{x}+1=0\\\\1=\frac{4}{x}\\\\x=4\)

Answer:

15 milk chocolates

Step-by-step explanation:

if half of them is milk chocolate and the other half is dark chocolate which is 15 then u just do 15 x 2= 30 then ÷ by 2 and that = 15

15×2=30

30÷2=15

If half of them is milk chocolate and the other half is dark chocolate which is 15 then u just do 15 x 2= 30 then ÷ by 2 and that = 15, 15×2=30 amd 30÷2=15.

The food product known as chocolate is a liquid, solid, or paste that can be consumed on its own or as a flavoring for other dishes. It is prepared from roasted and ground cacao seed kernels.

cacao has been ingested in some form, and the bulk of Mesoamerican people, including the Maya and Aztecs, prepared chocolate beverages.

The cacao tree's seeds are extremely bitter and must be fermented in order to produce a flavorful product. The seeds are dried, washed, and roasted after fermentation.

Therefore, If half of them is milk chocolate and the other half is dark chocolate which is 15 then u just do 15 x 2= 30 then ÷ by 2 and that = 15, 15×2=30 amd 30÷2=15.

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Answer:

42.5 inches

Step-by-step explanation:

Ivan is 75 inches tall, and Logan would be half his size, 37.5 that is, if he were 5 inches shorter. That means logan is 42.5 inches.

Answer:

Logan is 42.5 inches

Step-by-step explanation:

half of Ivan is 37.5

Logan is 5 inches taller than 37.5 so 42.5

Hope this helps!

Let me know if it does and if the answer is right

Answer:

20

Step-by-step explanation:

percentage error = predictions - actual ÷actual × 100

error

\( \frac{82 - 52 \\ }{52} \times 100\)

=

20

Answer:

M = 84 , r = 32

Step-by-step explanation:

Given M is directly proportional to r then the equation relating them is

M = kr ← k is the constant of proportion

To find k use the condition when r = 2, M = 14 , then

14 = 2k ( divide both sides by 2 )

7 = k

M = 7r ← equation of proportion

(a)

When r = 12

M = 7 × 12 = 84

(b)

When M = 224 , then

224 = 7r ( divide both sides by 7 )

32 = r

Answer:

An Isosceles trapezoid

Step-by-step explanation:

The shape is triangle.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases.

Given a trapezoid,

number of vertex trapezoid have = 4

one less vertex than trapezoid = 4 - 1 = 3

number of sides trapezoid has = 4

one less side than trapezoid = 4 - 1 = 3

the shape which has 3 sides and 3 vertex is triangle.

Hence the new shape is triangle.

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Answer: I know that DC is 12 and AD=8 the others i dont know.

Step-by-step explanation:

This is because opposite sides of a parallelogram are parallel and congruent. therefore AB and DC are equal/congruent.

Answer:

(a) In attachment

(b) x = y² - 2y - 1,    −2 ≤ y ≤ 4

Step-by-step explanation:

(a)

The graph of the given parametric equation is given in the attachment.

The direction in which the curve is traced as t increases, is indicated by black arrows.

(b)

To eleminate the parameter t, we simultaneously solve both the equations.

So, we have the equations:

x = t² - 2   ----- equation (1)

y = t + 1   ----- equation (2)

So, from equation (2), we have:

t = y - 1

Substituting this in equation (1), we get:

x = (y - 1)² - 2

x = y² - 2y + 1 - 2

x = y² - 2y - 1

Now, for limits of y, we use equation (2)

For initial limit, t = -3

y = - 3 + 1 = - 2

For final limit, t = 3

y = 3 + 1 = 4

Therefore, the final relation after eliminating t is:

x = y² - 2y - 1,    −2 ≤ y ≤ 4

The Cartesian equation of the curve after eliminating the parameter t is expressed below.

\(x=y^2-2y-1\)

For, the y values of, \(-2 \leq y \leq 4\)

The parametric equation is the type of equation  in which the variable which is in depended on on is known as parameter. The dependent function in this equation is defined as the continuous function of that variable.

The first equation given in the problem is,

\(x = t^2 - 2 \\t^2=x+2\)                    

The second equation given in the problem is,

\(y = t + 1\\t=y-1\)

Put the values of t in the modified first equation as,

\((y-1)^2=x+2\\y^2+1-2y-2=x\\x=y^2-2y-1\)

The values of t are between -3 to 3.

\(-3 \leq t \leq 3\)

The value of t is -3 then the value of y will be -2 and when the value of t is 4 then the value of y will be 4 from equation 2.

Hence, the Cartesian equation of the curve after eliminating the parameter t is expressed below.

\(x=y^2-2y-1\)

For, the y values of, \(-2 \leq y \leq 4\)

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Answer:

Step-by-step explanation:

You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.

Newton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...

  T = 36 -26·(22/26)^(t/2)

At times of t=4 and t=9, the temperature readings will be ...

__

Additional comment

The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.

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Answer: D - 5 1/4

Step-by-step explanation:

7/8 x 6 = 5.25

5.25 = 21/4

21/4 = 5 1/4

Answer:

D) 5 1/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

letters can be chosen in 26×25=650 ways

digits can be chosen in 10×9×8=720 ways

total number of ways=650×720=468000 ways.

If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:

637 = π(3²)h

Simplifying:

637 = 9πh

h = 637 / (9π)

h ≈ 7.06

Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.

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