Write the equation of the line that passes through the given points.
(0,6) and (9,10)

To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we can integrate the function from the lower bound of θ to the upper bound of θ and take the absolute value of the integral.

To find the area of the region formed by two petals of r = 8sin(3θ), we can integrate the function over the appropriate range of θ and take the absolute value of the integral. To find dy/dx for the given parametric equations x = t^(1/3) and y = 3 - t, we differentiate y with respect to t and x with respect to t and then divide dy/dt by dx/dt.

To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|. In this case, the lower bound and upper bound of θ will depend on the range of values where the function is below the polar axis. By integrating the expression, we can find the area of the region. To find the area of the region formed by two petals of r = 8sin(3θ), we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|.

The lower bound and upper bound of θ will depend on the range of values where the function forms the desired shape. By integrating the expression, we can calculate the area of the region. To find dy/dx for the parametric equations x = t^(1/3) and y = 3 - t, we differentiate both equations with respect to t. Taking the derivative of y with respect to t gives dy/dt = -1, and differentiating x with respect to t gives dx/dt = (1/3) * t^(-2/3). Finally, we can find dy/dx by dividing dy/dt by dx/dt, resulting in dy/dx = -3 * t^(2/3).

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Answer:

Carbon: 23 Total: 119

Step-by-step explanation:

Carbon:
We know that c : h is 1 : 4. Since we know what h is, 92, we will multiply our inequality to get 96. We will multiply our equality by 23. Giving us c : h is

23 : 92. This means there are 23 carbon molecules.

Total:

For this, we add our carbon and hydrogen atoms together. 96 + 24 = 119 total atoms.

Answer:

Corol´s age: 18 years

Marsha´s age: 46 years

Step-by-step explanation:

c + m = 64      first equation

c - m = 28       second equation

c = Corol´s age

m = Mardha´s age

first equation:

c = 64 - m

second equatión:

(64-m) - m = 28

64 - 28 = m + m

36 = 2m

m = 36/2

m = 18

c = 64 - m

c = 64 - 18

c = 46

Check:

46 + 18 = 64

46 - 18 = 28

Answer:

p

=

2

(

4

x

+

3

)

+

2

(

2

x

−

6

)

or simplified  

p

=

12

x

−

9

Explanation:

By definition the perimeter of an object is the length of all its sides.

Also by definition, for a rectangle the 2 sides of the width are equal and the 2 sides of the length are equal.

Therefore the equation for the perimeter of a rectangle can be written as:

p

=

2

⋅

l

+

2

⋅

w

where  

p

is the perimeter,  

l

is the length and  

w

is the width.

Substituting what was given about the length and width gives the equation:

p

=

2

(

4

x

+

3

)

+

2

(

2

x

−

6

)

Simplifying this equation gives:

p

=

8

x

+

3

+

4

x

−

12

p

=

8

x

+

4

x

+

3

−

12

p

=

12

x

−

9

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Option A is the only Option with the correct domain.

The input and the output of a function are key components in understanding how a function operates. The input refers to the value or values that are given to the function as an argument, while the output refers to the result or results that the function returns after processing the input.

In other words, the input is what you provide to the function, and the output is what you get in return. The input can be a single value or a set of values, depending on the requirements of the function. The output can also be a single value or a collection of values, again depending on the function's purpose.

It's important to note that the input and output of a function are not always the same. The function may perform calculations or transformations on the input, and the output may be different from the input. This transformation is what gives functions their ability to perform specific tasks and solve problems.

In summary, the input is what you give to a function, and the output is what you get in return after the function processes the input.

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Answer:

50, percentage decreased by 60% (percent) of its value = 20

Step-by-step explanation:

Answer:

hope this help you

Step-by-step explanation:

Simplifying

X + -7y = -11

Solving

X + -7y = -11  

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '7y' to each side of the equation.

X + -7y + 7y = -11 + 7y

Combine like terms: -7y + 7y = 0

X = -11 + 7y

Simplifying

X = -11 + 7y

------------------------------------------------------------------------------------------------------------

Solving

5x + 2y = -18

Solving for variable 'x'.

Add '-2y' to each side of the equation.

5x + 2y + -2y = -18 + -2y

Combine like terms: 2y + -2y = 0

5x = -18 + -2y

Divide each side by '5'.

x = -3.6 + -0.4y

Simplifying

x = -3.6 + -0.4y

Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

The visibility requirement is 3 statute miles, and cloud clearance requires maintaining 500 feet below, 1,000 feet above, and 2,000 feet horizontally from clouds during VFR daylight operations over Coopers Town.

The visibility and cloud clearance requirements to operate VFR during daylight hours over the town of Coopers Town between 1,200 feet AGL and 10,000 feet MSL are as follows:

1. Visibility: The minimum visibility required is 3 statute miles.

2. Cloud clearance: Maintain a distance of at least 500 feet below, 1,000 feet above, and 2,000 feet horizontally from clouds.

According to VFR regulations, pilots flying during daylight hours must adhere to certain visibility and cloud clearance requirements for safety. The visibility requirement of 3 statute miles means that the pilot must have a clear horizontal view of at least 3 miles ahead.

This ensures sufficient visual reference to navigate and avoid other aircraft or obstacles.

Regarding cloud clearance, pilots must maintain a safe distance from clouds to ensure visibility and separation from potential hazards. The requirement is to remain at least 500 feet below clouds to avoid inadvertently entering them.

Additionally, pilots must maintain a minimum of 1,000 feet above clouds to prevent the risk of collision or reduced visibility due to cloud turbulence. Lastly, a horizontal separation of 2,000 feet from clouds helps ensure adequate maneuvering space and visual reference in relation to cloud formations.

These visibility and cloud clearance requirements help maintain safety and situational awareness for VFR operations during daylight hours over Coopers Town.

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To find the 4th order Newton's divided-difference interpolating polynomial for f(x)=ln(x) with x=1,4,5,6,8, we first need to calculate the divided differences:

A. (a) The 4th order Newton's divided-difference interpolating polynomial for the function f(x) = ln(x) using the given data points is:

P(x) = ln(1) + (x - 1)[(ln(4) - ln(1))/(4 - 1)] + (x - 1)(x - 4)[(ln(5) - ln(4))/(5 - 4)(5 - 1)] + (x - 1)(x - 4)(x - 5)[(ln(6) - ln(5))/(6 - 5)(6 - 1)] + (x - 1)(x - 4)(x - 5)(x - 6)[(ln(8) - ln(6))/(8 - 6)(8 - 1)]

B. (a) To find f(x) at x = 7 and x = 9 using the interpolating polynomial, substitute the respective values into the polynomial expression P(x) obtained in the previous part.

Explanation:

A. (a) The 4th order Newton's divided-difference interpolating polynomial can be constructed using the divided-difference formula and the given data points. In this case, we have five data points: (1, ln(1)), (4, ln(4)), (5, ln(5)), (6, ln(6)), and (8, ln(8)). We apply the formula to calculate the polynomial.

B. (a) To find the value of f(x) at x = 7 and x = 9, we substitute these values into the polynomial P(x) obtained in the previous part. For x = 7, substitute 7 into P(x) and evaluate the expression. Similarly, for x = 9, substitute 9 into P(x) and evaluate the expression.

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Answer: $18

Step-by-step explanation:

You had a total of $60.

You spent 30% of your money on shorts.

The question would like to know what that 30% translates to in actual dollars so you need to find out what 30% of $60 is:

= 30% * 60

= $18

Answer:

x=3 I am new to this so I have no idea if this is what you are asking for

Answer:

You will get 75 cards

Step-by-step explanation:

The answer is 32

Emily signed 2/5 so 75 divided by 5 is 15

15x2 is 30

75-30=45

45 divided by 1/9 is 5

30+5=35

so then 45-5=40

20% of 40 is 8

30+5+8 = 43

75-43=32

Step-by-step explanation:

-2*x^5+3*x^4-5*x^3

Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

a

x

b

=x

a+b

.

3{x}^{1+4}+3x{x}^{3}-5{x}^{2}{x}^{3}-5{x}^{2}x3x

1+4

+3xx

3

−5x

2

x

3

−5x

2

x

Simplify 1+41+4 to 55.

3{x}^{5}+3x{x}^{3}-5{x}^{2}{x}^{3}-5{x}^{2}x3x

5

+3xx

3

−5x

2

x

3

−5x

2

x

Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

a

x

b

=x

a+b

.

3{x}^{5}+3{x}^{1+3}-5{x}^{2}{x}^{3}-5{x}^{2}x3x

5

+3x

1+3

−5x

2

x

3

−5x

2

x

Simplify 1+31+3 to 44.

3{x}^{5}+3{x}^{4}-5{x}^{2}{x}^{3}-5{x}^{2}x3x

5

+3x

4

−5x

2

x

3

−5x

2

x

Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

a

x

b

=x

a+b

.

3{x}^{5}+3{x}^{4}-5{x}^{2+3}-5{x}^{2}x3x

5

+3x

4

−5x

2+3

−5x

2

x

Simplify 2+32+3 to 55.

3{x}^{5}+3{x}^{4}-5{x}^{5}-5{x}^{2}x3x

5

+3x

4

−5x

5

−5x

2

x

Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

a

x

b

=x

a+b

.

3{x}^{5}+3{x}^{4}-5{x}^{5}-5{x}^{2+1}3x

5

+3x

4

−5x

5

−5x

2+1

Simplify 2+12+1 to 33.

3{x}^{5}+3{x}^{4}-5{x}^{5}-5{x}^{3}3x

5

+3x

4

−5x

5

−5x

3

Collect like terms.

(3{x}^{5}-5{x}^{5})+3{x}^{4}-5{x}^{3}(3x

5

−5x

5

)+3x

4

−5x

3

Simplify.

-2{x}^{5}+3{x}^{4}-5{x}^{3}−2x

5

+3x

4

−5x

3

Answer:

3 sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp side / hyp

sin 60 = ZY / 6

6 sin 60 = ZY

6 (sqrt(3) /2) = ZY

3 sqrt(3) = ZY

For a triangle with base of 10 inches and altitude of 16 inches, its area will be 80 in² (third option).

Calculation For the Area of the Triangle:

It is given that,

The base of the triangle, B = 10 inches

The altitude from the base of the triangle or height, H = 16 inches

Now, the formula used for finding the area of a triangle is given as follows,

Area, A = (1/2) × B × H

Substituting the given values of B and H in the above formula for area, we get,

A = (1/2) × (10 inches) × (16 inches)

A = 5 × 16 inches²

A = 80 inches²

Thus, the area of the triangle have base 10 inches and altitude 16 inches is 80 square inches.

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domain is x>1 and range is all real numbers

Answer:

He needs 0.275 cups of orange juice to reach his estimates

Step-by-step explanation:

Patel estimates he needs 2 cups of orange juice for his family . He squeezed fresh juice from 5 different oranges and got the following quantities measured in cups.

4/17 cups, 3/10 cups , 9/20 cups, 3/11 cups and 7/15 cups.

Adding them together we will know the amount he got. Therefore,

4/17 + 3/10 + 9/20 + 3/11 + 7/15

(40 + 51)/170  + 9/20 + 3/11 + 7/15

91/170 + 9/20 + (45 + 77)/165

(1820 + 1530)/3400 + 122/165

3350/3400 + 122/165

0.98529411764 + 0.73939393939

1.72468805703

Patel got approximately 1.725 cups of orange juice . He will  require 2 - 1.725 = 0.275 cups of orange juice to reach his estimates.

1/2 cup of orange juice

Answer:

Option D --->  y=5x

Step-by-step explanation:

When a line is directly proportional it means it crosses the origin so has a y- and x-intercept of 0.

So if we use the format y=mx+c, it will work but our c value will be 0 as I explained above .

To work out the gradient we simply take 2 points (0,0) and (1,5)) on the graph and use the gradient formula :

m = change in y ÷ change in x

m = 5÷1

m = 5

Therefore our direct proportion equation will be y=5x

Hope this helped and have a good day

Answer:

HELLLO

Step-by-step explanation:

HELLO

Test the hypothesis step of the scientific method is he performing.

Making conjectures (hypothetical explanations) is a step in the scientific method. Predictions are then derived from the hypotheses as logical conclusions, and experiments or actual observations are conducted based on those predictions.

Since at least the 17th century, the scientific method—an empirical approach to learning—has guided the advancement of science. Since one's interpretation of the observation may be distorted by cognitive presumptions, it requires careful observation and the application of severe skepticism regarding what is observed.

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For given division,

                                  416 is dividend

                                   8 is divisor

                                   0 is remainder   and

                                   52 is quotient

Long division:

                       long division is a standard division algorithm suitable for dividing multi-digit numbers that is simple enough to perform by hand.

                       In the case of long division of numbers, the remainder is always smaller than the divisor. We can verify the quotient and the remainder of the division using the division formula,

                 Dividend = (Divisor × Quotient) + Remainder.

The above formula is also known as division algorithm.

Example:

                       a ÷ b

a is called dividend and b is called divisor

For given question,

                   416 ÷ 8

      that is,

                                      8 )  416  ( 52

                                            40

                                               16

                                               16

                                                0

416 is dividend

8 is divisor

0 is remainder

and 52 is quotient

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Answer:

It should be A

Step-by-step explanation:

I hope this helps

We can verify that for any real numbers x and y, |x y|≤|x| |y| by using the precious real numbers of z, such that z≤|z| and −z≤|z|.

Let us assume that x and y are real numbers.

Therefore x*y is also a real number.

Using the fact that for any real number z, z≤|z| and −z≤|z|, we can say:

-|xy| ≤ xy ≤ |x*y|

|xy| ≤ |x||y|

Case 1 = If xy is positive.

|xy| = xy ≤ |x|*|y|

Case 2 =If xy is negative. In this case, |xy| = -x*y, |x| ≥ 0, and |y| ≥ 0

|xy| = -xy ≤ |x|*|y|

Multiplying both sides by -1,t:

xy ≥ -|x||y|

And since x*y is negative:

|xy| ≤ |x||y|

Therefore, we have proven that for any real numbers x and y, |x y|≤|x| |y|.

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Answer:

which is question ❓ can't find the questions

Answer:

3 trays of corn muffins and 2 trays of bran muffins

Step-by-step explanation:

c = 4m + 3w

b = 2m + 3w

16m and 15w

1 tray of corn muffins and 4 trays of bran muffins = $11

16 - 4 = 12

15 - 3 = 12

12 - 8 = 4

12 - 12 = 0

b = $2

c = $3

c = 3 x 1 = 3

b = 2 x 4 = 8

3 + 8 = 11

-----------------------------------------------------------------------------------------------------------------

2 trays of corn muffins and 3 trays of bran muffins = $12

c = 4m + 3w

b = 2m + 3w

16 - 8 = 8

15 - 6 = 9

8 - 6 = 2

9 - 9 = 0

b = $2

c = $3

c = 3 x 2 = 6

b = 2 x 3 = 6

6 + 6 = 12

-----------------------------------------------------------------------------------------------------------------

3 trays of corn muffins and 2 trays of bran muffins = $13

c = 4m + 3w

b = 2m + 3w

16 - 12 = 4

15 - 9 = 6

4 - 4 = 0

6 - 6 = 0

c = 3 x 3 = 9

b = 2 x 2 = 4

9 + 4 = 13

-----------------------------------------------------------------------------------------------------------------

4 trays of corn muffins and 0 trays of barn muffins = $12

c = 4m + 3w

b = 2m + 3w

16 - 16 = 0

15 - 12 = 3

c = 3 x 4 = 12

b = 2 x 0 = 0

12 + 0 = 12

According to the information provided, the probability that less than 1/3 of the tosses are heads is closest to 0.0049. (Option E)

Probability refers to the branch of mathematics which is concerned with numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1. In probability theory, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin.

Based on the provided data, where p = 0.5 and n = 60

Mean µ = np = 60*0.5 = 30

Standard deviation σ = √np(1-p) = √60(0.5)(0.5) = 3.87

In order to determine probability that less than 1/3 of the tosses are heads, the value of X = 60*1/3 = 20

Finding the z score and determining the probability from the table

z = (x - µ)/σ = (20 -30)/ 3.87 = -2.584

Hence, probability P(z < -2.584) = 0.00488  ≈ 0.0049

Note: The question is incomplete as it is missing options which are A. 0.9951. B. 0.33. C. 0.109. D. 0.09. E. 0.0049.

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Answer: 6

Step-by-step explanation:

Answer: y = 2/3 -2

Step-by-step explanation: using a graph you can plot the point (-3, 2).

After this, you can use the slope of 2/3 to graph the starting point. You go 3 to the left and 2 up going through the y axis of -2. using y = mx + b, you can plug in the slope of 2/3 and the starting point of -2.

Answer:

10 centimeters.

Step-by-step explanation:

First, we need to remember what's the formula to get the volume of a rectangular solid and a cube.

The volume of the first equals:

Volume = Length x Width x Height

While the volume of the cube is:

\(Volume = a^{3}\) where a is the edge.

We are given the measures of the rectangular solid so we can calculate its volume:

\(Volume= (20)(5)(10)=1000\) cubic cms.

Now, we know that  both the volume of the rectangular solid and the cube are the same so we will use this information to calculate the edge of the cube.

\(1000=a^3 \\\sqrt[3]{1000} =\sqrt[3]{a^3} \\10=a\)

Thus the length of an edge of the cube is 10 centimeters