Simplify.
(-10 + 3i)²
Write your answer in the form a + bi.
Submit

Answer:

y=-5x+b

Steps:

1. Put slope into y=mx+b formula

2. Plug in point: -8=-5(2)+b

3. Solve for b: 2=b

The solution to the differential equation is given by R = ±1/√(C-a*x), where C is a constant of integration.

To solve this differential equation, we first separate the variables and integrate the equation:

dR/dx = a(R^2+16)

∫ dR/dx  = ∫a(R^2+16)dx

R = ±1/√(C-a*x) + K

where K is an arbitrary constant.

To find the constant of integration, we use the initial condition. We plug in the initial values for x and R to find the constant of integration. For example, if x = 0 and R = 2, then we get

2 = ±1/√(C-0) + K

2 = ±1/√C + K

K = 2±1/√C

Therefore, the solution to the differential equation is given by R = ±1/√(C-a*x) where C is the constant of integration.

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When opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram. (PA = RT and PT = AR)

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

A quadrilateral is a specific type of polygon known as a parallelogram if it contains two parallel opposed sides. A parallelogram has the following qualities:

Each coordinate of the Parallelogram :

P (-3, 0) , A(3, -1) , R ( 2, -5) and T(-4, -4)

Length of PA = √((3 + 3)² + (-1 - 0)²) = √(36 + 1) = √37

Lenght of TR = √((-4 - 2)² + (-4 + 5)²) = √(36 + 1) = √37

Length of PT = √((-3 + 4)² + (0 + 4)²) = √(16 + 1) = √17

Length of AR = √((3-2)² + (-1 + 5)²) = √(16 + 1) = √17

Here, PA = RT and PT = AR ,

so when opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram.

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When opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram. (PA = RT and PT = AR)

What is meant by quadrilateral?

Each coordinate of the Parallelogram :

P (-3, 0) , A(3, -1) , R ( 2, -5) and T(-4, -4)

Length of PA = √((3 + 3)² + (-1 - 0)²) = √(36 + 1) = √37

Lenght of TR = √((-4 - 2)² + (-4 + 5)²) = √(36 + 1) = √37

Length of PT = √((-3 + 4)² + (0 + 4)²) = √(16 + 1) = √17

Length of AR = √((3-2)² + (-1 + 5)²) = √(16 + 1) = √17

Here, PA = RT and PT = AR ,

So when opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram.

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Answer:

Prabin types 765/9 i.e, 85 words in one minute. Therefore in 30 minutes prabin will type 30 x 85 i.e., 2550 words. Again, he types 1 word in 9/765 minutes. Therefore , he will type 12750 words in 12750 x (9/765) minutes, i.e, 150 minutes.

Prabin would type 2,550 words in half an hour at the same speed. It would take him 150 minutes to type 12,750 words at the same speed.

To find out how many words Prabin would type in half an hour, we need to determine how many minutes are in half an hour. Since there are 60 minutes in an hour, half an hour would be 30 minutes. Now, we can set up a proportion to find the number of words Prabin would type in half an hour:

765 words / 9 minutes = x words / 30 minutes

Cross-multiplying, we get:

9 * x = 765 * 30

Simplifying, we find:

x = (765 * 30) / 9

x = 2,550 words

To find out how long it would take Prabin to type 12,750 words at the same speed, we can set up another proportion using the given information:

765 words / 9 minutes = 12,750 words / t minutes

Cross-multiplying, we get:

9 * (12,750) = 765 * t

Simplifying, we find:

t = (9 * 12,750) / 765

t = 150 minutes

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Answer:

If 55% of people brought their own skates, 45% did not.

Since 100 - 55 = 45.

45% of 200 = 90

The answer is: 90 people didn't bring their skates.

A stationary point of a function f(x) is a point where the derivative of f(x) is equal to 0. These points are called “stationary” because at these points the function is neither increasing nor decreasing.

Once we have identified the dy dx = 0 solutions, we may utilise the first derivative to ascertain the characteristics of the stationary points. Think about the equation y = x2 + 1.

By differentiating and setting the derivative to zero, we may determine that there is a stationary point at x = 0 since dy dx = 2x = 0. Recall that placing f by x and f by y equal to zero will reveal the location of a function f's stationary point.

In this situation, partial differentiation with regard to x while treating y as a constant results in three x squared plus six x. Any stationary point's nature can be ascertained by introducing its x coordinate into the second derivative of the function, f. (x). 

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The amount that you when a fair dice is tossed (showing is either 4 or 5, you win $1, if the number of spots showing is 6, you win $4, and if the number of spots showing is 1, 2, or 3, you win nothing) is $1.00

Given,

          when you get either 4 or 5, the reward = $1

           when you get either 6, the reward = $4

              when you get 1, 2, or 3, the reward = $0

We know that,

                     Probability of getting 6 = 1/6

                     Probability of getting 4 = 1/6

                      Probability of getting 5 = 1/6

                      Probability of getting 1 = 1/6

                      Probability of getting 2 = 1/6

                       Probability of getting 3  = 1/6

        Therefore,

                     [tex]X = \frac{1}{6}* 4 + \frac{1}{6}* 1 +\frac{1}{6}* 1+ \frac{1}{6}* 0+ \frac{1}{6}* 0 + \frac{1}{6}*0[/tex]

                          [tex]= \frac{4}{6} + \frac{1}{6}+ \frac{1}{6}[/tex]

                          [tex]= \frac{6}{6}[/tex]

                          [tex]= 1[/tex]

  Hence, the Value of X = $1.

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The units of distance and speed should match, So kilometers per hour (kph) and miles per hour (mph) are the correct units.

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The number of dimes and nickels are equal to 11 and 19 respectively.

In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Since you have a total number of 30 coins, an equation which models this situation is given by;

d + n = 30     ....equation 1.

Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.

Additionally, the coins are worth 2.05 dollars;

0.1d + 0.05n = 2.05     ....equation 2.

Solving both equations simultaneously, we have:

0.1(30 - n) + 0.05n = 2.05

3 - 0.1n + 0.05n = 2.05

3 - 0.05n = 2.05

0.05n = 0.95

n = 0.95/0.05

n = 19 nickels.

For the number of dimes;

d = 30 - n

d = 30 - 19

d = 11 dimes.

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Complete Question:

You have 30 coins worth $2.05 in nickels and dimes. What's in your wallet? Create and solve system of equations to find how many dimes and how many nickels you have.

Hose 1 takes 7 days.

Hose 2 takes 4 days.

That means in a single day, Hose 1 fills 1/7 of the pool and Hose 2 fills 1/4 of the pool.  So in one day, the two hoses will fill 1/7 + 1/4 of the pool.

If t is the number of days it takes to fill the pool with both hoses being used, then

   [tex]t\cdot \left(\dfrac{1}{7} + \dfrac{1}{4}\right) =1[/tex]

will tell us how many days it will take to fill 1 pool

Solving this:

    [tex]\begin{aligned} t\cdot \left(\dfrac{1}{7}\cdot\dfrac{4}{4} + \dfrac{1}{4}\cdot \dfrac{7}{7}\right) &=1 \\[0.5em]t\cdot \left(\dfrac{4}{28} + \dfrac{7}{28}\right) &=1 \\[0.5em]t\cdot \left(\dfrac{11}{28} \right) &=1 \\[0.5em]t &=\dfrac{28}{11} \\[0.5em]\end{aligned}[/tex]

It'll take 28/11 days, or 2 and 6/11 days, or about 2.54 days.

Answer:

136/5

Step-by-step explanation:

18 9/10 + 8 3/10

change to improper fraction

=189/10 + 83/10

Adding, you have:

=272/10

2 can further divide both numbers

= 136/5

The scale factor of the two triangles is 1/4 or 4

You should understand that scale factor is the ratio of any two corresponding lengths.

Looking at the triangles, the larger triangle has sides

The smaller triangle has sides

Scale factor = (Larger length)/ (Smaller length) or (Smaller length/(Larger length)

This is an indication that the triangles have scale factors of:

Scale factor = 12/3 = 4 or

Scale factor = 3/12 = 1/4

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Answer:

all of them are 17

Step-by-step explanation:

7+9=16

16+1+0=17

9+7=16

16+1+0=17

1+0+9=10

10+7=17

7+1=8

8+9+0=17

hope this helped!

The increase in the price of tacos shifts the demand curve to the left, causing a decrease in the equilibrium price and quantity of hamburgers.

The accompanying supply and demand diagram is depicting the market for hamburgers in your hometown. The event that is given is that the price of tacos increases. This will cause the demand curve to shift to the left, as consumers shift from hamburgers to tacos. As the demand curve shifts to the left, the equilibrium price will decrease and the equilibrium quantity will decrease. This is because the decrease in demand will cause the quantity demanded to fall and the decrease in demand will cause the price to fall. This shift in the supply and demand curves will cause the equilibrium point to move to the left and downward. The new equilibrium price will be lower than the original equilibrium price and the quantity will also be lower.

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Electric potential energy is the energy that is needed to move a charge against an electric field.

Completed question :

A point charge q1 , is held stationary at the origin. A second charge q2 is placed at a point a, and the electric potential energy of the pair of charges is -6.4 x [tex]10^{-8}[/tex] J. When the second charge is moved to point b, the electric force on the charge does 4.2 x [tex]10^{-8}[/tex] J of work. What is the electric potential energy of the pair of charges when the second charge is at point b?

Given data :

PE1 = -6.4 x [tex]10^{-8}[/tex] J

Work done = 4.2 x [tex]10^{-8}[/tex] J

PE1 = PE2 + Work done

PE2  = PE1 - Work done =

= -6.4 x [tex]10^{-8}[/tex] J - 4.2 x [tex]10^{-8}[/tex] J = -10.6 x [tex]10^{-8}[/tex] J

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Answer: the correct value of x in this will be 6.

Step-by-step explanation: According to the equation given ,

f(x) = 64

so , f(x) = 11x - 2 now putting the value of f(x) in this equation

therefore , 64 = 11x - 2

now solving the equation , 11x= 64+2

11x = 66

x = 66/11

x = 6

thus, the value of x obtained from the equation is 6

Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects.

What is integration?

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.

Differentiation is the opposite of integration.

In other words, reversing the differentiation process merely results in integration. The example below demonstrates it:

dy/dx = 2x since y = x2 Consequently,

(dy/dx) dx = 2x dx = x2.

Together, and dx represent the integration of the function with respect to x.

The anti-differentiation is another name for integration. In this procedure, we are given a function's derivative and asked to determine the function (i.e., primitive). We are aware that cos x is the differentiation of sin x.

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The equation of the line is given as y = ( -2/5 )x + 162 , where the slope of the line is m = ( -2/5 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P ( -275 , 52 )

Let the first point be represented as P ( -280 , 54 )

Now , the slope of the line is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 54 - 52 ) / ( -280 - ( -275 ) )

On simplifying the equation , we get

Slope m = 2 / ( -5 )

Slope m = -2/5

Now , the equation of line is  y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 52 = ( -2/5 ) ( x - ( -275 ) )

y - 52 = ( -2/5 )x + 110

Adding 52 on both sides of the equation , we get

y = ( -2/5 )x + 162

Hence , the equation of line is y = ( -2/5 )x + 162

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The area of the triangle is 24 square meters.

The area of the triangle can be calculated using the formula A = 1/2bh, where b is the base and h is the height of the triangle. In this case, the base is 8 meters and the height is 6 meters. Therefore, the area of the triangle is A = 1/2bh = 1/2(8)(6) = 24 square meters. Therefore, the answer is D. 24 square meters.

To calculate the area of the triangle, first the base and the height of the triangle must be known. The base is the length of the bottom line of the triangle, and the height is the length of the line from the peak of the triangle to the base. Once the base and height of the triangle are known, the area formula A = 1/2bh can be used.

The formula can be broken down into several steps. First, the base and the height are multiplied together. In this case, it would be 8 x 6. This gives a result of 48. Then, the result is divided by 2, which gives a result of 24. Therefore, the area of the triangle is 24 square meters. When using the area formula, it is important to remember that the result must be divided by 2 in order to get the correct answer.

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In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.

In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.

dne

Since 9x2 y2 9z2 is a 3-dimensional equation, it cannot be sketched on a 2-dimensional plane. Therefore, the answer is dne.

The equation 9x2 y2 9z2 is a 3-dimensional equation and cannot be represented on a 2-dimensional plane. Therefore, it is not possible to sketch the surface using this equation. As a result, the answer is dne. The equation contains three variables, x, y and z, and cannot be represented on a graph without the use of three axes. In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.

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The standard deviation of Y is $432.00 and this can be determined by using the formula of standard deviation and the given data.

Given :

A company sells concrete in batches of 5 cubic yards.

The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below.

The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76.

There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by  (Y = 75X - 100).

The formula to obtain the standard deviation is given below:

SD(Y) = SD(75X - 100)

Simplify the above expression by substituting the value of SD(X) and SD(100) in the above expression.

SD(Y) = 75SD(X) - SD(100)

SD(Y) = 75 SD(X) - 0

SD(Y) = 75×5.76

SD(Y) = $432

Therefore, the correct option is B.

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Let's call the two numbers x and y. We know from the problem statement that:

x + y = 1476890

y - x = 1500

To find the greater number, we can use the second equation to solve for one of the variables, and then substitute it into the first equation.

y = x + 1500

Now we can substitute this expression for y into the first equation:

x + (x + 1500) = 1476890

2x + 1500 = 1476890

2x = 1476890 - 1500

2x = 1475390

x = 1475390/2

x = 737695

So the greater number is y = x + 1500 = 737695 + 1500 = 739195

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By using the slope​ formula, the slope of the line through the points (0, 0) and (4, 12) is equal to 3.

You can use mental math to find the slope of the line by simply dividing 12 by 3 because the line passes through the origin (0, 0).

In Mathematics and Geometry, the slope of any straight line can be calculated by using this this mathematical equation (expression);

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following data points located on the line:

Substituting the given points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (12 - 0)/(4 - 0)

Slope (m) = 12/4

Slope (m) = 3.

In conclusion, an equation which represents this line is y = 3x.

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We can start by using the concept of percentage concentration, which states that the percentage of alcohol in a solution is equal to the number of milliliters of alcohol in the solution divided by the number of milliliters of the solution, multiplied by 100.

Let's call the number of milliliters of Solution B that Linda uses x.

We know that:

Solution A is 50% alcohol, so it contains 50/100 = 0.5 = 1/2 of alcohol.

Solution B is 10% alcohol, so it contains 10/100 = 0.1 = 1/10 of alcohol.

The resulting mixture is a 20% alcohol solution.

Linda uses 400 milliliters of Solution A.

We can set up an equation using the percentage concentration concept and the information provided:

(400 * 1/2) + (x * 1/10) = (x + 400) * (20/100)

Solving for x:

200 + x/10 = (x + 400) * 0.2

x/10 = (x + 400) * 0.2 - 200

x/10 = x * 0.2 + 80

9x/10 = x * 0.2 + 80

9x = x*2 + 800

x = 800/8 = 100

So, Linda uses 100 milliliters of Solution B to make the resulting mixture a 20% alcohol solution.

(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -90 m/s.

(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -62 m/s.

(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -34 m/s.

(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7h^2 + 70h m/s.

(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -7(25-1) + 70(4) = -7*24 + 280 = -168 + 280 = -88 m/s.

(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -7(16-1) + 70(3) = -7*15 + 210 = -105 + 210 = -95 m/s.

(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -7(9-1) + 70(2) = -7*8 + 140 = -56 + 140 = -16 m/s.

(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7(1+h)^2 + 70h = -7(1+h)^2 + 70h m/s. The average velocity of an object over a given period of time is calculated by taking the difference between the final and initial positions, and dividing it by the amount of time elapsed. In this exercise, we are given the position of an object along a line as a function of time, s(t) = -7t^2 + 70t. To solve each part, we can plug in the given time intervals into the function, and calculate the difference between the initial and final positions. We then divide this difference by the amount of time elapsed to find the average velocity. For example, in part (a), the average velocity is calculated as -7(5^2-1^2) + 70(5-1) = -90 m/s. In part (b), the average velocity is calculated as -7(4^2-1^2) + 70(4-1) = -62 m/s. In part (c), the average velocity is calculated as -7(3^2-1^2) + 70(3-1) = -34 m/s. Finally, in part (d), the average velocity is calculated as -7(1+h)^2 + 70h m/s

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The approximation of the area under the curve f(x) = [tex]2x^2 + 6[/tex] from x = 2 to x = 4 using left rectangles and a step size of Δx = 0.5 is 60.5 square units to one decimal place.

To approximate the area under the curve f(x) = [tex]2x^2 + 6[/tex] between x = 2 and x = 4 using left rectangles and a step size of Δx = 0.5, we have to divide the interval [2, 4] into a number of sub-intervals of width 0.5 and evaluate the function at the left endpoint of each sub-interval.

First find the number of steps: (4-2)/0.5 = 4

The x-coordinates for the left endpoints of each sub-interval are: 2, 2.5, 3, 3.5, 4

We evaluate the function f(x) = [tex]2x^2 + 6[/tex] at each of these left endpoints and multiply the result by the width of the sub-interval (0.5) to find the area of each rectangle.

For [tex]x = 2[/tex], [tex]f(x) = 2(2)^2 + 6 = 14[/tex]

Area = 0.5 * 14 = 7

For [tex]x = 2.5, f(x) = 2(2.5)^2 + 6 = 19.5[/tex]

Area = 0.5 * 19.5 = 9.75

For [tex]x = 3, f(x) = 2(3)^2 + 6 = 24[/tex]

Area = 0.5 * 24 = 12

For [tex]x = 3.5, f(x) = 2(3.5)^2 + 6 = 29.5[/tex]

Area = 0.5 * 29.5 = 14.75

For [tex]x = 4, f(x) = 2(4)^2 + 6 = 34[/tex]

Area = 0.5 * 34 = 17

The sum of the areas of these rectangles is 7 + 9.75 + 12 + 14.75 + 17 = 60.5

Therefore, the approximation of the area under the curve f(x) = [tex]2x^2 + 6[/tex] from x = 2 to x = 4 using left rectangles and a step size of Δx = 0.5 is 60.5 square units to one decimal place.

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Answer:

Circumference = 113.097 units

Step-by-step explanation:

C = 2[tex]\pi r[/tex]

C = 2(3.14)(36/2)

C = 113.097 units

There are four types of social norms that can help inform people about behavior that is considered acceptable: folkways, mores, taboos, and law.

Social values are the focus of sociology. Cultural norms known as social values describe the overall well-being thought desirable for a structured social existence. These presumptions concern what is morally correct and significant for society. They provide social structures and behavior its ultimate meaning and legitimacy. They are ideals or abstract feelings. "Equality of opportunity" is a prime illustration of social value. It is frequently regarded as a desirable end in and of itself.

When several people interact, a set of norms emerges that governs their interactions and behaviors. Social norms are these standards of group behavior.

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An equation of the line that is parallel to this line and passes through the point (4, 2) is y = 0.5x.

An equation of the line that is perpendicular to this line and passes through the point (4, 2) is y = -2x + 10.

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ -1 = -1

Note: m represents the slope.

From the linear equation 3x - 6y = -8, we have:

y = 3x/6 + 8

y = 0.5x + 8

At point (4, 2), an equation of the line that is parallel to this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

y - 2 = 0.5(x - 4)

y = 0.5x - 2 + 2

y = 0.5x

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

0.5 × m₂ = -1

m₂ = -2

At point (4, 2), an equation of the line that is perpendicular to this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -2(x - 4)

y = -2x + 8 + 2

y = -2x + 10

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The equation of the line perpendicular to -2y = 5x + 8  and passes through (10, -1) is y = 2 / 5 x - 5.

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation is perpendicular to  -2y = 5x + 8  and passes through (10, -1).

Perpendicular lines have slopes that are negative reciprocals of one another.

Therefore,

-2y = 5x + 8

y = - 5 / 2 x - 4

Therefore,

slope = 2 / 5

Let's find the y-intercept using (10, -1)

-1 = 2 / 5(10) + b

-1 = 20 / 5 + b

b = -1 - 4

b = -5

Therefore, the equation of the line is y = 2 / 5 x - 5

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