find the point on the line 6x 3y 5=0 which is closest to the point (5,3).

Answer: x+42x-2

Step-by-step explanation:

Answer: Part A: 4x    Part B: 4x

Step-by-step explanation: you have to add them

\((\stackrel{x_1}{-19}~,~\stackrel{y_1}{17})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{17}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-19)}) \implies y -17 = - 1 ( x +19) \\\\\\ y-17=-x-19\implies {\Large \begin{array}{llll} y=-x-2 \end{array}}\)

Answer:

y = -x - 2

Step-by-step explanation:

We are given that a line has a slope (m) of -1 and passes through (-19,17).

We want to write the equation of this line in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name

As we are already given the slope of the line, we can plug it into the equation.

Replace m with -1.

y = -1x + b

This can be rewritten to:

y = -x + b

Now, we need to find b.

As the equation passes through (-19,17), we can use its values to help solve for b.

Substitute -19 as x and 17 as y.

17 = -(-19) + b

17 = 19 + b

Subtract 19 from both sides.

-2 = b

Substitute -2 as b into the equation.

y = -x - 2

To use differentials to estimate the value of 1.2√4, we need to first find a suitable function and a point close to the one we want to estimate. Since we are dealing with square roots, we can use the function f(x) = √x. The point closest to 4.2 (1.2 added to 4) that we know the exact value for is 4, as √4 = 2.

1. Find the derivative of f(x) = √x:
f'(x) = (1/2)x^(-1/2)

2. Evaluate the derivative at the known point, x = 4:
f'(4) = (1/2)(4)^(-1/2) = (1/2)(2)^(-1) = 1/4

3. Compute the differential, using Δx = 0.2 (the difference between 4.2 and 4):
Δy = f'(4)Δx = (1/4)(0.2) = 0.05

4. Estimate the value of 1.2√4 by adding Δy to the exact value at x = 4:
1.2√4 ≈ 2 + 0.05 = 2.05

Now, let's compare this to the exact value of 1.2√4:
Exact value: 1.2√4 = 1.2(√4.2) ≈ 1.2(2.0494) ≈ 2.0593

The estimated value using differentials is 2.05, while the exact value is approximately 2.0593. The two values are relatively close, demonstrating the effectiveness of using differentials for estimation.

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(a) The promoter's expected profit is$2,514.

(b) This is obtained by multiplying the potential losses in each scenario (no rain and rain) by their respective probabilities and summing them up. The insurance company should charge an amount equal to the expected value of the losses to cover the promoter's full losses. It is  $9,643

To calculate the promoter's expected profit, we need to consider the profit in both the rainy and non-rainy scenarios, taking into account the probability of rain.

(a) Expected Profit:

Let's calculate the profit in each scenario first:

Profit if it does not rain = $30,393

Profit if it rains = -$16,072

Now we need to calculate the expected profit:

Expected Profit = (Probability of no rain * Profit if no rain) + (Probability of rain * Profit if rain)

Probability of no rain = 1 - Probability of rain = 1 - 0.6 = 0.4

Expected Profit = (0.4 * $30,393) + (0.6 * -$16,072)

Expected Profit = $12,157.2 - $9,643.2

Expected Profit = $2,514

The promoter's expected profit is $2,514.

(b) Insurance Premium:

To calculate the insurance premium, the insurance company needs to cover the promoter's potential loss of $16,072 in case it rains.

Insurance Premium = Expected Loss * Probability of Loss

Expected Loss = Potential Loss if it rains = $16,072

Probability of Loss = Probability of rain = 0.6

Insurance Premium = $16,072 * 0.6

Insurance Premium = $9,643.2

The insurance company should charge approximately $9,643 to insure the promoter's full losses.

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Answer:

A (-4,9) B (-4,11) C (-6,10)

Last option is correct

Step-by-step explanation:

To rotate the vertices about the given point at 90 degrees, we follow the procedures below;

Mathematically, if we have a point (m,n) and we want to rotate it 90 degrees about a given point (x,y). Then the new transformation point will be;

( -(n-y) + x , (m-x) + y)

Let’s now take the points individually;

(3,2 ) about (-4,2)

This becomes

(-(2-2) + (-4), (3+4) + 2) = (-4 , 9)

The point (5,2) about (-4,2) becomes

(-(2-2) + -4, (5 + 4) + 2 )= (-4, 11)

and lastly

The point (4,4) about (-4,2) becomes

(-(4-2) + (-4), (4 + 4) + 2) = (-6, 10)

Answer:

69.08 yd

Step-by-step explanation:

Answer:

Te conozco y sé qué

Como Nuevo de fabrica el otro

The maximum error in D can be expressed as 36Eh²|1 - v²| multiplied by the uncertainty in h, denoted as Δh.

To express the maximum error in D, given the formula D = 12(1 - v²)Eh³ and the uncertainties h = 0.1 ± 0.002 and t = 0.3 ± 0.02, we need to determine how the uncertainties in h and t propagate through the formula. The maximum error in D can be expressed as the sum of the absolute values of the partial derivatives of D with respect to each variable, multiplied by the corresponding uncertainty. In this case, since E is a constant, the maximum error in D can be expressed solely in terms of the uncertainty in h, denoted as Δh.

We start by differentiating D with respect to h, keeping E and v as constants. The derivative of D with respect to h is given by:

dD/dh = 36(1 - v²)Eh²

Next, we calculate the maximum error in D by multiplying the absolute value of the derivative by the uncertainty Δh:

ΔD = |dD/dh| × Δh

Substituting the derivative expression and the uncertainty in h, we have:

ΔD = |36(1 - v²)Eh²| × Δh

Simplifying further, we get:

ΔD = 36Eh²|1 - v²| × Δh

Therefore, the maximum error in D, denoted as ΔD, is equal to 36Eh²|1 - v²| multiplied by the uncertainty Δh.

In summary, the maximum error in D can be expressed as 36Eh²|1 - v²| multiplied by the uncertainty in h, denoted as Δh.

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Answer:

\(4 \frac{1}{5} - \frac{3}{7} \\ =4 + \frac{1}{5} - \frac{3}{7} \\ = \frac{21}{5} - \frac{3}{7} \\ \frac{147 - 15}{35} \\ = \frac{132}{35}

=3 27/35 \\ thank \: you\)

132/35

Step-by-step explanation:

\(4 \frac{1}{5} - \frac{3}{7} \\ \frac{21}{5} - \frac{3}{7} \\ lcm = 35 \\ \frac{21 \times 7}{5 \times 7} - \frac{3 \times 5}{7 \times 5} \\ \frac{147}{35} - \frac{15}{35} \\ = \frac{132}{35} \\ \)

If length of a rectangle is 4 inches shorter than its width and perimeter of  rectangle is 80 inches , then the length of rectangle is 18 in and width of rectangle is 22 in .

The Perimeter of rectangle can be calculated by using formula : \(2(l+w)\) ;

let the width of rectangle be = w ,

it is given that the length is 4 inches shorter than width , that means ;

the width of rectangle is ⇒ \(w-4\) ;

So , the perimeter becomes ⇒ \(80=2(l+w)\)

⇒ \(80=2(w-4+w)\)

⇒ \(40=2w-4\) ;

⇒ \(2w=44\) ;

⇒ \(w=22\) ;

and substituting \(w=22\) , we get \(l=22-4 = 18\) in

Therefore , the length of rectangle is 18 in and width is 22 in .

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The equation for her total cost y would be:

y = 45x

Let's use x to represent the number of months and y to represent the total cost.

For George from Acme TV:

The set-up fee is a one-time payment of \($50\), so it does not depend on the number of months.

For each month, he pays \($35\).

The equation for his total cost y would be:

y = 35x + 50

For Gwen from Metro TV:

There is no set-up fee, so her cost only depends on the number of months.

For each month, she pays \($45\).

The equation for her total cost y would be:

y = 45x

It's worth noting that these equations assume that the monthly fees remain constant over time, which may not necessarily be the case in real life.

Additionally, these equations do not take into account any potential taxes or additional fees that may be added to the cost of the memberships.

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The solution to the system of equations is (1.6,-1.6).

What is the system of equations?

Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

Here, we have

Given equations:

y = 1.5x - 4....(1)

y = -x....(2)

Substitute y = -x in the first equation

-x = 1.5x - 4

Collect like terms

-1.5x - x = -4

This gives

-2.5x = -4

Divide both sides by -2.5

x = 1.6

Substitute x = 1.6 in y = -x

y = -1.6

Hence, the solution to the system of equations is (1.6,-1.6)

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To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.

To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.

This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.

Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.

Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.

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In summary, the composition of two functions, f ∘ g, combines the outputs of the function g as inputs to the function f.

The composition of two functions, f ∘ g, is a new function that is formed by applying the output of the function g as the input of the function f.

To find the composition of f ∘ g, follow these steps:

1. Start with the function g(x) and evaluate it for a given input value, let's call it 'a'. This will give you g(a).
2. Take the output g(a) and use it as the input for the function f(x). Evaluate f(x) with this input value to get f(g(a)).
3. The final result f(g(a)) is the value of the composition of the two functions f ∘ g at the input 'a'.

In terms of composition notation, f ∘ g is read as "f composed with g" or "f of g". It represents the order in which the functions are applied: g is applied first, and then f is applied to the result of g.

In summary, the composition of two functions, f ∘ g, combines the outputs of the function g as inputs to the function f.

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Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number of customers be x.

Annual gross income in terms of the number of customers:

Annual gross income in terms of profit and expenses:

The above two numbers should be equal, this will give us the number of customers:

Correct choice is D

Answer:6

Step-by-step explanation:

Let the number be x.

Now, 3x+6=24

3x=24-6

3x=18

x=18/3

x=6

Answer:

6

Step-by-step explanation:

We can work the problem backwards

Since something gives 24 that means it equals 24

= 24

Something increased by 6, so something added by 6

Something + 6 = 24

Making something = x

x + 6 = 24

If we subtract 6 from both sides

x = 18

Trice a number, so divide this number by 3

x = 6

Trice of 6 is 18... 18 increased by 6 gives 24

The time it took the penny to hit the ground is 9.56s.

The time it takes for a penny dropped from a height of 95 meters to hit the ground can be calculated using the equation for kinematic motion:

t =\(\sqrt {\frac {2h} {g}}\)

where:

t is the time it takes to fall

h is the height from which the penny is dropped (95 meters)

g is the acceleration due to gravity (9.8 m/s^2)

Plugging in the values, we get:

t = \(\sqrt {(2 \times \frac {95} { 9.8})}\)

t ≈ 9.56 seconds

So it would take approximately 9.56 seconds for a penny dropped from a height of 95 meters to hit the ground.

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Answer:

it's radius is 9 and diameter is 18

Answer:

diameter=18cm

radius =diameter/2=18/2=9cm

The angles of the triangles that measure 90° will be ABC and DEF.

The pairs of line segments that are formed by the triangle sides are line ED and AB.

It should be noted that parallel lines are the lines that maintains the same distance between them and never meet.

Also, the angle that has the same measurement as angle DEA will be BAC. This is based on alternate exterior angles.

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Data:

Quiz taken: 16

Quiz each week: 1

You can express this as a equation:

Q= Total of quizes taken

W= weeks

As each week the number of quizes Q increase in 1 the change is k=1, and Isabela has already taken 16 quizzes. The number of quizzes can be represented as:

Q0 is the number of quizzes Isabela has already taken.

Then, to have a total of 26 quizzes Isabela have to attend:

Q=26

W=?

You can find the number of weeks by clearing of the equation above the W:

Substract in both sides of the equation 16:

The approximate area of the window that is not cleaned by the wiper is:

240 - 100.5 ≈ 139.5 square inches. Answer: \boxed{139.5}.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

To solve this problem, we need to find the area of the trapezoid and subtract the area of the semicircle.

The area of a trapezoid is given by the formula:

A = (a + b)h/2

where a and b are the lengths of the parallel sides, and h is the height (the perpendicular distance between the parallel sides).

In this case, we have:

a = 24 inches (the top parallel side)

b = 16 inches (the bottom parallel side)

h = 12 inches (the height)

Using the formula, we get:

A = (24 + 16) x 12/2

A = 240 square inches

The area of a semicircle is given by the formula:

A = πr²/2

where r is the radius of the circle.

In this case, the radius is half of the length of the wiper, so we have:

r = 16/2 = 8 inches

Using the formula, we get:

A = π(8²)/2

A ≈ 100.5 square inches

Therefore, the approximate area of the window that is not cleaned by the wiper is:

240 - 100.5 ≈ 139.5 square inches. Answer: \boxed{139.5}.

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The height of the Rectangular prism is approximately 3.0625 cm when the length is 16 cm, the width is 8 cm, and the volume is 392 cm³.the volume of a rectangular prism, which is given as:volume = length x width x height ; 392 cm³ = 16 cm x 8 cm x h

To find the height of a rectangular prism with a given length, width, and volume, we can use the formula for the volume of a rectangular prism, which is given by:

Volume = Length x Width x Height

In this case, we are given the length of 16 cm, the width of 8 cm, and a volume of 392 cm³. We need to find the height of the rectangular prism.

Let's denote the height of the prism as h. Plugging in the given values into the volume formula, we have:

392 cm³ = 16 cm x 8 cm x h

To find the height, we need to isolate the variable h. We can do this by dividing both sides of the equation by the product of 16 cm and 8 cm:

392 cm³ / (16 cm x 8 cm) = h

Simplifying the right side of the equation:

392 cm³ / 128 cm² = h

Simplifying the division:

3.0625 cm = h

The formula is derived from the formula for the volume of a rectangular prism, which is given as:volume = length x width x height

392 cm³ = 16 cm x 8 cm x h

Therefore, the height of the rectangular prism is approximately 3.0625 cm when the length is 16 cm, the width is 8 cm, and the volume is 392 cm³.

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No, the three directions (0 1), (0 1), and (2 0) do not lie in one plane.

To determine if the three directions lie in one plane, we can consider their coordinates and check if they satisfy the condition for coplanarity.

The three directions given are (0 1), (0 1), and (2 0). If these directions lie in one plane, they can be represented as scalar multiples of a single vector. However, it is evident that the first two directions are identical, which means they represent the same vector (0 1). On the other hand, the third direction (2 0) is different from the first two.

Since the third direction is not a scalar multiple of the vector (0 1), the three directions cannot lie in one plane. In a two-dimensional space, any two non-parallel vectors determine a unique plane, but adding a third non-collinear vector would make the system inconsistent.

Therefore, the given directions (0 1), (0 1), and (2 0) do not lie in one plane.

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Answer: y = -0.5*x - 1

Step-by-step explanation:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Here we know that we have a line that passes through the points (-2, 0) and (0, -1)

Then the slope for this line is:

a = (-1 -0)/(0 - (-2)) = -1/2 = -0.5

Then our line is something like:

y = -0.5*x + b

now we know that this line passes trough the point (0, -1), this means that when x = 0, y must be equal to -1

Then we can replace these values in the equation in order to find the value of b.

-1 = -0.5*0 + b

-1 = b

Then the equation is:

y = -0.5*x - 1

Answer:

Y'(-5, 5)

Step-by-step explanation:

To find the coordinates of Y' after the translation, we apply the given rule to the coordinates of point Y(-3, 4).

Using the translation rule (x, y) → (x - 2, y + 1), we can substitute the coordinates of Y(-3, 4) into the rule:

x' = x - 2 = -3 - 2 = -5

y' = y + 1 = 4 + 1 = 5

Therefore, the coordinates of Y' are (-5, 5).