Simplify the expression below.

-6x - (-x)

The equation of the tangent line to the hyperbola 4x^2 - 4xy - 3y^2 = 96 at the point (4, 2) is 8x - 3y = 22.

To find the equation of the tangent line to the hyperbola at the point (4, 2), we need to find the slope of the tangent line at that point. This can be done by taking the derivative of the equation of the hyperbola implicitly and evaluating it at the point (4, 2).

Differentiating the equation 4x^2 - 4xy - 3y^2 = 96 with respect to x, we get 8x - 4y - 4xy' - 6yy' = 0. Rearranging the equation, we have y' = (8x - 4y) / (4x + 6y).

Substituting the point (4, 2) into the equation, we have y' = (8(4) - 4(2)) / (4(4) + 6(2)) = 22/40 = 11/20.

Now that we have the slope of the tangent line, we can use the point-slope form of a linear equation to find the equation of the tangent line. Using the point (4, 2) and the slope 11/20, we have y - 2 = (11/20)(x - 4). Simplifying this equation, we get 20y - 40 = 11x - 44, which can be further rearranged as 11x - 20y = 4.

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Answer:

x=3y+15

Step-by-step explanation:

Answer: a

Step-by-step explanation:

Answer:

there is no solution to the problem but after calculating and searching a possible answer is

x = -6

y = 0

Step-by-step explanation:

Elena is correct

Step-by-step explanation:

This is because a straight angle is always equal to 180 therefore in order to find the value of *w* you would have to add up to angles that are given and subtract them from 180, or in this case add up all the angles including *w* to get 180.

Answer:

110 Degrees

Step-by-step explanation:

Every interior triangle equalls 180 degress. So you subtract what you already have from 180.

30+40+x=180

70+x=180

180-70=110

To obtain the rectangle with the maximum value efficiently, you can use the Kadane's algorithm for the maximum subarray sum with slight modifications.

Here's the algorithm:

1. Initialize variables `max_sum` and `result` to negative infinity.

2. Iterate over all possible pairs of columns `(c1, c2)`:

a. Initialize an array `row_sum` of size n with all elements set to 0.

b. Iterate over all rows i from 1 to n:

c. Apply Kadane's algorithm on the `row_sum` array to obtain the maximum sum subarray. Let `cur_sum` be the current sum and `start` and `end` be the indices of the subarray.

d. If `cur_sum` is greater than `max_sum`:

3. Return `result` as the rectangle with the maximum value.

The algorithm runs in O(n^3) time complexity, which is significantly faster than the naive O(n^4) approach.

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Answer:

move 6 places right (1kg=10^6mg=1,000,000mg)

Step-by-step explanation:

ex:

1kg= 1,000,000mg

39kg=39,000,000

4.2kg=4,200,000

Answer:

A

Step-by-step explanation:

You should simplify this, here \(i\) is like a variable.

Now here you just simplify the variables and calculate the numbers.

\(7-8 = -1\)

\(3i+9i=12i\)

equals

\(-1+12i\) which is "A"

I hope it helps you. Please choose my answer as the BRAINLIEST

A) An algebraic expression that could be used to model the situation where a horse's weight decreases by ¹/₂ pounds weekly is w/r, where w is the total weight lost and r is the constant rate of weight loss.

B) Using division operation and decreasing rate, if a horse's weight decreases by ¹/₂ pounds weekly, it will take the horse 11 weeks to lose a total of 5¹/₂ pounds.

An algebraic expression combines constants, variables, and mathematical operations (+, -, ×, ÷) without the equal sign (=) found in equations.

While equations show the equality of expressions, algebraic expressions merely state values.

Division operation is one of the four basic mathematical expressions, including addition, subtraction, and multiplication.

Division operations involve the dividend, the divisor, the equal sign (=), the division operand (÷), and the result called the quotient.

The total weight loss over time = 5¹/₂ pounds

The constant rate of weight loss = ¹/₂ pounds per week

The number of weeks for the horse to lose 5¹/₂ pounds = 11 weeks (5¹/₂ ÷ ¹/₂).

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Answer:

False

Step-by:-step explanation

2 million years

The oldest reliably classified fossils belonging to the genus Homo date back to a little over 2 million years ago. They belong to H. habilis, a type of ancient hominin that scientists classify as the first of our genus, and which may have led to H. erectus, one of our direct ancestors

Answer:

false

Step-by-step explanation:

most fossils are muuchhh older

Answer:

I believe it is A: (10,10) and B: (18, 14)

The coordinates for points a and b ​are; A: (10,10) and B: (18, 14)

The cartesian coordinate plane is an infinite 2-dimensional plane. Any 2-dimensional figure can be drawn on an infinite 2d plane. Each of the points of a cartesian plane is tracked by a location.

We have been given two identical rectangles linked at one corner at drawn on the coordinates axes.

Given points of a rectangular box are

(2, 6) ( 10, 6) and (10, 14)

The coordinates for points a and b ​are;

A: (10,10)

B: (18, 14)

The coordinates for points a and b ​will be; A: (10,10) and B: (18, 14)

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the radius of convergence (R) is ∞, and the interval of convergence [-∞, 16].let's first solve the inequality 4x - 8 ≤ 56 for x:

1. Add 8 to both sides:
4x ≤ 64

2. Divide both sides by 4:
x ≤ 16

Now, we have the inequality x ≤ 16, which represents the interval of convergence. To find the center of this interval, we need to find the value of x when 4x - 8 = 56:

3. Add 8 to both sides:
4x = 64

4. Divide both sides by 4:
x = 16

Since the power series converges at x = 16, this will be the center of the interval of convergence. The interval of convergence can be written as:

[-∞, 16]

To find the radius of convergence (R), we need  the distance from the center (16) to either end of the interval. Since the interval goes to negative infinity, there is no specific distance, so the radius of convergence is:

R = ∞

In conclusion, the radius of convergence (R) is ∞, and the interval of convergence is [-∞, 16].

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Answer:

x = 3

Step-by-step explanation:

We divide the sides by 3 to get the triangle in question

Answer:

The answer is -5 + (-3).

Step-by-step explanation:

Answer:

-5 is the original position

The swimmer descends 3 meters, so we subtract 3 or add -3. Thus, the answer is:

-5 + (-3)

It takes the sound of a bat's cry 1/165 seconds to reach its prey and echo back

The given parameters are

Speed = 330 meters per second

Distance = 1 meters

The time taken to get to the prey is calculated as

Speed =Distance/Time

Substitute the known values in the above equation

So, we have

330 = 1/Time

Cross multiply the factors of the equation

So, we have

Time * 330 = 1

Divide both sides of the equation by 330

So, we have

Time 1 = 1/330

Similarly, the time taken to get from the prey is calculated as

Speed =Distance/Time

Substitute the known values in the above equation

So, we have

330 = 1/Time

Cross multiply the factors of the equation

So, we have

Time * 330 = 1

Divide both sides of the equation by 330

So, we have

Time 2 = 1/330

The time it takes a bat's cry to reach its prey and echo back is

Time = Time 1 + Time 2

So, we have

Time = 1/330 + 1/330

Evaluate the sum

So, we have

Time = 2/330

Simplify the quotient

So, we have

Time = 1/165

Hence, it takes the sound of a bat's cry 1/165 seconds to reach its prey and echo back

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The probabilities of different events related to the type B' blood in four randomly selected people from the United States are 0.000207, 0.0600,  0.400. The events in parts (a) and (b) are considered unusual.

The probability that a person in the united states has type b* blood is 12%. four unrelated people in the united states are selected at random of different scenarios are calculated.

The probability that all four have type B' blood is 0.000207, The probability that none of the four have type B' blood is 0.0600, The probability that at least one of the four has type B' blood is 0.400, The events in parts (a) and (b) can be considered unusual because their probabilities are less than or equal to 0.05.

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_____The given question is incomplete, the complete question is given below:

The probability that a person in the United States has type B' blood is 12 % Four unrelated people in the United States are selected at random Complete parts (a) through (d) The probability that all four have type B' blood is 000207 (Round to six decimal places as needed) (b) Find the probability that none of the four have type B' blood The probability that none of the four have type B' blood is 0600 (Round to three decimal places as needed) (c) Find the probability that at least one of the four has type B' blood The probability that at least one of the four has type B' blood is 400 (Round to three decimal places as needed) (d) Which of the events can be considered unusual? Explain Select all that apply OA The event in part (a) is unusual because its probability is less than or equal to 0.05 OB. The event in part (c) is unusual because its probability is less than or equal to 0.05 O C. None of these events are r uual O D. The event in part (b) is unusual because its probability is less than or equal to 0.05 Click to select your answer and then click Check Answer

The price pliantness of force using th midpoint method is1.5. This implies that the volume supplied is fairley elastic, as a 1 increase in price leads to a1.5 increase in the volume supplied.

To calculate the price pliantness of force using the midpoint system, we need to use the following formula

Pliantness of force = ( Chance Change in volume Supplied)( Chance Change in Price)

First, let's calculate the chance change in volume supplied

Chance Change in Quantity Supplied = (( New Quantity Supplied-original volume Supplied)( Average volume Supplied)) * 100

original volume Supplied = 100

New Quantity Supplied = 300

Average volume Supplied = ( original volume Supplied New Quantity Supplied)/ 2

Average volume Supplied = ( 100 300)/ 2 = 200

Chance Change in Quantity Supplied = (( 300- 100)/ 200) * 100

= ( 200/ 200) * 100

= 100

Next, let's calculate the chance change in price

Chance Change in Price = (( New Price-original Price)/( Average Price)) * 100

original Price = $ 6

New Price = $ 12

Average Price = ( original Price New Price)/ 2

Average Price = ($ 6$ 12)/ 2 = $ 9

Chance Change in Price = (($ 12-$ 6)/$ 9) * 100

= ($ 6/$ 9) * 100

= 66.67

Eventually, we can calculate the price pliantness of force

Pliantness of force = ( Chance Change in volume Supplied)( Chance Change in Price)

= 100/66.67

= 1.5

thus, the price pliantness of force using the midpoint method is1.5. This implies that the volume supplied is fairly elastic, as a 1 increase in price leads to a1.5 increase in the volume supplied.

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The value of the functions dy and Δy when x=π/4 and dx=−0.4 are −4.2 (approx.) and 1.68 respectively.

Let y=3√x

Find the differential dy= dx:

The given equation is y = 3√x.

Differentiate y with respect to x.∴

dy/dx = 3/2 × x^(-1/2)

= (3/2)√x

Therefore, the differential dy = (3/2)√x.dx.

Find the change in y, Δy when x=3 and Δx=0.1:

Given, x = 3 and

Δx = 0.1

Δy = dy .

Δx = (3/2)√3.0.1

= 0.70 (approx.)

Find the differential dy when x=3 and

dx=0.1:

Given, x = 3 and

dx = 0.1.

dy = (3/2)√3.

dx= (3/2)√3.0.1= 0.65 (approx.)

Therefore, the value of the differential dy when x=3 and dx=0.1 is 0.65 (approx).

Let y=3tanx

(a) Find the differential dy= dx:

Given, y = 3tanx.

Differentiate y with respect to x.∴ dy/dx = 3sec²x

Therefore, the differential dy = 3sec²x.dx.

Evaluate dy and Δy when x=π/4 and

dx=−0.4:

Given, x = π/4 and

dx = −0.4.

dy = 3sec²(π/4) × (−0.4)

= −4.2 (approx.)

We know that Δy = dy .

ΔxΔy = −4.2 × (−0.4)

Δy = 1.68

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Answer:

  x = 8

Step-by-step explanation:

You want to know the value of x in this similar triangle geometry.

When a segment is drawn in a triangle parallel to the base, it divides the sides proportionally. Every segment on the left has the same ratio to the corresponding segment on the right:

  x/6 = 4/3

This equation is solved in the usual way. Multiply by the inverse of the coefficient of x:

  6(x/6) = 6(4/3)

  x = 8

__

Additional comment

Every proportion can be written several ways. Another way to write this one is ...

  x/4 = 6/3

  x = 4(2) = 8 . . . . . multiply by 4

If you need to, you can prove the triangles are similar by considering corresponding angles. ∠A≅∠A, ∠APW≅∠AVZ, so the triangles are similar by the AA postulate. (Corresponding angles where a transversal crosses parallel lines are congruent.)

Perhaps not so obvious is the relationship between segments of the long side and segments of the short side. The similarity relation tells us ...

  AV/AP = AZ/AW

  (4+x)/x = (3+6)/6

  4/x +1 = 3/6 +1 . . . . . do the division

  4/x = 3/6 . . . . . . . . subtract 1

  x/4 = 6/3 . . . . . . invert both sides . . . compare to above

Answer:2 hours 20 minutes

Step-by-step explanation:divide 60 by 3

Sorry, now you know that he spends 20 minutes a day combing his hair. You multiply 20 time 7( for the 7 days in a week) = 140. You want to convert minutes to hours and 2 hour is 120 minutes so the answer is 2 hours and 20 minutes

Answer: A) 20 minutes

              B)2 and 1/3 hours

Step-by-step explanation:

A) 1/3 of an hour is 20 minuets because 60÷3=20

   This means that 20 minutes are spent combing his hair each day

B) He spends 20 minutes combing his hair each day so 20×7=140

   140÷60=2 and 1/3 hours per week

Answer:

Step-by-step explanation:

The two square roots of 12.25 are:

(1) 3.5: 3.5 x 3.5 = 12.25

(2) -3.5: -3.5 x -3.5 = 12.25

Both of these numbers squared give a result of 12.25. However, -3.5 is the negative of 3.5, so it's important to specify which root is meant, depending on the context of the problem.

Answer:

Sorry but couldnt answer

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Answer

Area = 21 Sq units

Step-by-step explanation:

Area= 1/2[(x1y2 + x2y3 + x3y1) - (x2y1 + x3y2 + x1y3)]

Area = 1/2[(-5×5 +-3×-2+1×-2) - (-3×-2+1×5+-5×-2)]

Area = 1/2(-42)

Area = -21 sq units

Area = 21 sq units (The area is negative because it is below the x-axis.)

Answer:

x = 4 and y = 9

Step-by-step explanation:

Let x and y be the two numbers. Also,

Let the first number be x and the second number be y.

Converting the word expressions to an equation we get:

                   y = x + 5

               3x + 2y = 30

Only thing left is to substitute y = x + 5 into the second equation

     3x + 2y = 30

     3x + 2(x + 5) = 30   (substituting y as x + 5)

     3x + 2x + 10 = 30   (multiplying by both x and 5)

     5x = 30 - 10     (collecting like terms to one side)

     5x = 20

     \(\frac{5x}{5} = \frac{20}{5}\)     (divide both sides by 5 to get the value of x)

     x = 4

 Now that we know the value of x, we can find y.

      y = x + 5

      y = 4 + 5

      y = 9

If you want to make sure your answer is correct, substitute x and y into the equation.

  3x + 2y = 30

  3(4) + 2(9) = 30

  12 + 18 = 30

  30 = 30

Answer:

a = 5.07

Step-by-step explanation:

Here, we want to get the value of the side marked a

What we have is a right triangle

so, to find the value of a, we are to use the correct trigonometric ratio

The angle given faces a, which makes a the opposite

the side measure faces the right angle and that makes it the hypotenuse

The trigonometric ratio that connects the two is the sine

The sine is the ratio of the opposite to the hypotenuse

mathematically;

sine 25 = a/12

a = 12 * sine 25

a = 5.07

£40 is shared as £5, £15 and £20. 88p is shared as 16p, 32p and 40p. 180° is shared as 40°, 40° and 100°

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

a) Share £40 in the ratio 1:3:4

For the first ratio = (1/8) * £40 = £5

For the second ratio = (3/8) * £40 = £15

For the third ratio = (4/8) * £40 = £20

b) Share 88p in the ratio 2:4:5

For the first ratio = (2/11) * 88p = 16p

For the second ratio = (4/11) * 88p = £32

For the third ratio = (5/11) * 88p = 40p

c) Share 180° in the ratio 2:2:5

For the first ratio = (2/9) * 180° = 40°

For the second ratio = (2/9) * 180° = 40°

For the third ratio = (5/9) * 180° = 100°

The ratios are shown above

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Answer:

\(x\le \:-1\)

Step-by-step explanation:

\(3\left(x-1\right)\le \frac{1}{2}\left(x+1\right)-6\)

\(3x-3\le \:-\frac{11}{2}+\frac{1}{2}x\)

\(3x\le \:-\frac{5}{2}+\frac{1}{2}x\\\)

\(\frac{5}{2}x\le \:-\frac{5}{2}\)

\(5x\le \:-5\)

\(x\le \:-1\)

x = -1

3(-2) ≤ ½(0) - 6

-6 ≤ 0 - 6

-6 ≤ -6

This is true.

x = -2

3(-3) ≤ ½(-1) - 6

-9 ≤ -½ - 6

-9 ≤ \(-\frac{13}{2}\)

This is also true.

Therefore, x ≤ -1.