Name the postulate or theorem you can use to prove the triangles congruent.

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

THIS IS FALSE.

Step-by-step explanation:

MARK BRAINLIESSSTTTTT I NEED 2 MORE SO I CAN RANKUPP

Answer:

To determine the possible degree(s) of a function from the graph alone, you need to examine the behavior of the graph at the extremes (far left and far right) and consider the number of turning points or changes in direction. Here's a step-by-step approach:

Look at the far left side of the graph: Determine the behavior of the graph as it approaches negative infinity. Does the graph approach a specific value, such as a horizontal line (asymptote) or the x-axis? If the graph approaches a horizontal line, it suggests a polynomial function of even degree. If the graph approaches the x-axis, it indicates a polynomial function of odd degree or possibly a function with a root of multiplicity greater than one.

Look at the far right side of the graph: Determine the behavior of the graph as it approaches positive infinity. Similar to step 1, observe if the graph approaches a specific value or a horizontal line. The behavior at the far right side should be consistent with the behavior at the far left side. This can help you identify if the function is even or odd degree.

Examine the number of turning points or changes in direction: Count the number of times the graph changes direction. These points are where the slope of the graph changes from positive to negative or vice versa. The number of turning points can provide an indication of the degree of the polynomial. For example, if there are two turning points, it suggests a polynomial function of degree 3.

Remember that this method provides potential degrees, but it may not definitively determine the exact degree of the function. Additional information or analysis might be required for a more accurate determination.

Answer:

Y=X+1=2+1=3

Step-by-step explanation:

{

X

=

2

Y

=

3

Explanation:

Combining the two equations, we find:

2

X

−

1

=

Y

=

X

+

1

Subtract

X

from both ends to get:

X

−

1

=

1

Add

1

to both sides to get:

X

=

2

Then:

Y

=

X

+

1

=

2

+

1

=

3

Answer:

$42.60.

Step-by-step explanation:

You multiply 35.50 by .20 (that's decimal version of 20%) which equals 7.10. Then you add 35.50+7.10=42.60

Answer:

205

Step-by-step explanation:

((2x6)-7+9)^2+45/5

= ((12)-7+9)^2+45/5

= (12-7+9)^2+45/5

= (14)^2+45/5

= 196+45/5

= 196 + 9

= 205

Answer:

False

Hope this helps!

The area of the sidewalk is 388 square feet.

To find the area of the sidewalk you can find the area of each individual shape and add them together.

Area of the first triangle T = (1/2) x 6 ft x 11 ft = 33 sq. ft.

Area of the second triangle = (1/2) x 6 ft x 18 ft = 54 sq. ft.

Area of the rectangle = 6 ft x 30 ft = 180 sq. ft.

Area of the square = 11 ft x 11 ft = 121 sq. ft.

Therefore, the total area of the sidewalk is:

33 sq. ft. + 54 sq. ft. + 180 sq. ft. + 121 sq. ft. = 388 sq. ft.

So, the area of the sidewalk is 388 square feet.

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Answer:

(B=8)(y−8)⋅(y^2 +8y+64)

Step-by-step explanation:  

Changes made to your input should not affect the solution:

(1): "y3"   was replaced by   "y^3".

Factoring:  y3-512

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into

             (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =

           a3+a2b+ab2-ba2-b2a-b3 =

           a3+(a2b-ba2)+(ab2-b2a)-b3 =

           a3+0+0+b3 =

           a3+b3

Check :  512  is the cube of   8

Check :  y3 is the cube of   y1

Factorization is :

            (y - 8)  •  (y2 + 8y + 64)

Factoring  y2 + 8y + 64

The first term is,  y2  its coefficient is  1 .

The middle term is,  +8y  its coefficient is  8 .

The last term, "the constant", is  +64

Step-1 : Multiply the coefficient of the first term by the constant   1 • 64 = 64

Step-2 : Find two factors of  64  whose sum equals the coefficient of the middle term, which is   8 .

     -64    +    -1    =    -65

     -32    +    -2    =    -34

     -16    +    -4    =    -20

     -8    +    -8    =    -16

     -4    +    -16    =    -20

     -2    +    -32    =    -34

     -1    +    -64    =    -65

     1    +    64    =    65

     2    +    32    =    34

     4    +    16    =    20

     8    +    8    =    16

     16    +    4    =    20

     32    +    2    =    34

     64    +    1    =    65

Hope that helps!!

Answer:

8 am

Step-by-step explanation:

First train has a 50 m/hr x 3 hr = 150 mile head start

Second train is going 60 - 50 = 10 m/hr faster and will close this 150 mile distance

 in 15 hours to catch the first train

2pm + 3 hours + 15 hours = 8 am

The experiments consist of rolling a number cube three times and is recorded whether the number was even "E" or odd "O".

Each outcome of the experiment is represented by the three results obtained, for example EOE indicates that the first number was even, the second was odd, and the third was even.

Each outcome is considered to have the same probability and a total of 8 outcomes are listed on the table, this means that the probability of each outcome is 1/8.

Event A: "Exactly one odd number"

This event occurs when only one odd number was registered, this means that out of the 8 outcomes listed, only those with one "O" will correspond to this event:

There are three events that meet the condition for event A.

To calculate the probability of this event, you have to divide the number of successes by the total number of outcomes:

The probability of event A is 3/8.

Event B: "An even number on the first roll"

To determine the probability of event B, the first step is to identify all outcomes that meet this condition. These outcomes will represent the successes of event B.

There are 4 outcomes that registered an even number on the first roll, you can calculate the probability of this event as follows:

The probability of event B is 1/2.

Event C: "An even number on both, the first and the last roll"

First, identify the outcomes that registered an even number (E) on the first and the last roll:

There are 2 outcomes that meet the condition stated for event C. You can calculate the probability of this event as follows:

The probability of C is 1/4.

The store at which the apple will cost the cheapest is: Store A

The formula for the slope between two coordinates is:

Slope = (y₂ - y₁)/(x₂ - x₁)

Now, all the lines in the attached graph pass the origin and so they will all have the coordinate (0, 0)

The slope for each line will give us the cost for each apple in the store.

Thus:

Slope for store A = (3 - 0)/(4 - 0)

Cost for store A apple = $0.75

Slope for Store B = (5 - 0)/(5 - 0)

Cost for store B apple = $1

Slope for Store C = (5 - 0)/(4 - 0)

Cost for store C apple = $1.25

Slope for Store D = (6 - 0)/(3 - 0)

Cost for store C apple = $2

Thus, store A has the cheapest Apple

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Answer:

There are 13 different ways to make 25 cents with quarters, dimes, nickels, and pennies

Step-by-step explanation:

please mark me as brainlist please I

Answer:

\((-\infty,2)\)

Step-by-step explanation:

Since \(-3x+6\nless 0\), then \(x\ngtr 2\), therefore, the domain of the function is \((-\infty,2)\).

Let's begin by listing out the information given to us:

r (1) = 11.4 cm, θ (1) = 70°, θ (2) = 40°, r(2) = ?

The arc length is the same for the 2 circles

r (1) * θ (1) = r (2) * θ (2)

11.4 * 70° = r (2) * 40°

r (2) = 11.4 * 70 ÷ 40

r (2) = 19.95 cm

Hence, the radius of the larger circle is 19.95 cm

Answer:

I was pretty sure it was C.

Step-by-step explanation:

Sorry if I'm wrong.

Answer:

well depends if you alredy have the highth and bace

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{4x+9}{\frac{7}{3} }=\frac{3x}{0.5}\\ \frac{4x+9}{7} =2x\\ 4x+9=14x\\10x=9\\x = 0.9\)

Answer:

A3

Step-by-step explanatio

Answer:

Linear second-order differential equation F(x, y, y′, y″) = 0

y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0  

Step-by-step explanation:

Step(i):-

Given differential equation

y = c₁x + c₂x⁴  ...(i)

Differentiating equation (i) with respective to 'x', we get

y¹ = c₁(1) +  c₂ ( 4 x³ ) ...(ii)

Differentiating equation (ii) with respective to 'x', we get

y¹¹ =   c₂ ( 12 x² )

\(C_{2} = \frac{y^{11} }{12 x^{2} }\) ...(a)

Step(ii):-

Substitute (a) in equation (ii)

\(y^{l} = C_{1} + (\frac{y^{ll} }{12x^{2} } ) (4 x^{3} )\)

\(C_{1} = y^{l} - (\frac{y^{ll} }{12 x^{2} } ) (4 x^{3} )\) ...(b)

\(C_{2} = \frac{y^{11} }{12 x^{2} }\)

Step(iii):-

\(y = (y^{l} - (\frac{y^{ll} }{12 x^{2} } ) (4 x^{3} ) x + \frac{y^{ll} }{12 x^{2} } x^{4}\)

12 x² y = (y¹12 x³ - 4 x⁴ y¹¹) + x⁴ y¹¹

x⁴ y¹¹ - 4 x⁴ y¹¹ + y¹12 x³ - 12 x² y= 0

y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0

Answer:

im taking a nap

Step-by-step explanation:

Based on the information, we can infer that the salary a worker earns depends on the hourly wage they earn. In this case we will have to multiply the value of each hour by the number of hours worked. Additionally, I would agree to have a higher minimum wage to benefit workers.

Based on the information in the graph, we can infer that workers will have wages of $5.2, $6.0, and $6.6. According to the above, the salary varies depending on the number of hours.

On the other hand, I believe that you would agree to a salary increase because this would benefit workers who would be better paid for each hour of work.

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Answer: \({9}\frac{23}{90}\)

Step-by-step explanation:

The probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes is only 0.02%.

P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X = k) = (100 choose k) * 0.078^k * (1 - 0.078)^(100-k)

P(X <= 4) = (100 choose 0) * 0.078^0 * (1 - 0.078)^(100-0) + (100 choose 1) * 0.078^1 * (1 - 0.078)^(100-1) + (100 choose 2) * 0.078^2 * (1 - 0.078)^(100-2) + (100 choose 3) * 0.078^3 * (1 - 0.078)^(100-3) + (100 choose 4) * 0.078^4 * (1 - 0.078)^(100-4)

Using a calculator or software, we can find that:

P(X <= 4) = 0.000203

This means that the probability is 0.02%.

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Charges for TV advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is the percentage of population of 110 million TV households.The CBS television show 60 minutes recently had a rating of 7.8, indicating that 7.8% of the household were tuned to that show.An advertiser conducts an independent survey of 100 households and finds that only 4 were tuned to 60 minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes.Does the result suggest that the rating of 7.8 is too high?

Answer:

1.727 x 10^4

Step-by-step explanation:

2.26 x 10^4 = 22 600

5.33 x 10³ = 5330

22 600 - 5330 = 17 270

17 270 = 1.727 x 10^4

Answer:

\(\huge\boxed{\sf r = 5}\)

Step-by-step explanation:

Given that,

7q + 35 = 7q + 7r

7q - 7q + 35 = 7q - 7q + 7r

35 = 7r

35/7 = r

5 = r

OR

\(\rule[225]{225}{2}\)

Answer:

r = 5

Step-by-step explanation:

Given statement,

→ 7(q + 5) is equivalent to (q + r)7.

Forming the equation,

→ 7(q + 5) = 7(q + r)

Now we have to,

→ Find the required value of r.

Then the value of r will be,

→ 7(q + 5) = 7(q + r)

Applying Distributive property:

→ 7(q) + 7(5) = 7(q) + 7(r)

→ 7q + 35 = 7q + 7r

Cancelling 7q from both sides:

→ 35 = 7r

→ 7r = 35

Dividing the RHS with number 7:

→ r = 35/7

→ [ r = 5 ]

Therefore, the value of r is 5.

Answer:

80

Step-by-step explanation:

25 percent is equal to 1/4

1/4 of 80 is 20

Answer:

80

Step-by-step explanation:

Answer:

Q.1 49x²- 25y²

= (7x)² - (5y)²

= (7x+5y)(7x - 5y)

Q.2 x²y² - 64

=(xy)² - (8)²

=(xy+8)(xy - 8)