Write an equation of a line that would be perpendicular to y =-x-8

Answer:

x-2,y= 3, it can also be written as (2 ,3)

Step-by-step explanation:

2x-7y=5x-7-2x-7=5x-75x+2x=

7+77x=14x=2y=5x-7=5*2-7=10-..

In the function, the thing that is represented is the area of the walkway along the length of the flower patch.

From the information given, Sam created function A to represent the total area taken up by the flower patch and walkway by multiplying the functions modeling the new total length and width.

Therefore, the thing that is represented is the area of the walkway along the length of the flower patch.

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the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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Answer:

18 cm

Step-by-step explanation:

i may be wrong though because of the way you asked your question,  but I am smart so i think i got this answer correct.

The given system of equations to have a Unique solution, the value of k must be any real number except 1 (k ≠ 1).

The value of k for which the given system of equations has a unique solution, we can use the concept of determinants. The system of equations is as follows:

kx + 2y = 3   -- (1)

3x + 6y = 10  -- (2)

To have a unique solution, the determinant of the coefficients of x and y must not be zero.

The determinant of the coefficient matrix for the system is:

D = | k   2 |

       | 3   6 |

By calculating the determinant, we have:

D = (k * 6) - (2 * 3)

D = 6k - 6

For the system to have a unique solution, the determinant D must not equal zero.

6k - 6 ≠ 0

Simplifying the inequality:

6k ≠ 6

Dividing both sides by 6:

k ≠ 1

Therefore, for the given system of equations to have a unique solution, the value of k must be any real number except 1 (k ≠ 1).

In other words, if k is not equal to 1, the system of equations will have a unique solution. If k is equal to 1, the system will either have infinitely many solutions or no solution.

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Statement:

R is the midpoint of QS.

To find out:

The measure of QS.

Solution:

Answer:

QS is 76.

Hope you could understand.

If you have any query, feel free to ask.

Answer:

AD = 6

Step-by-step explanation:

5+x-----12

5------10

50+10x = 60

10x = 60-50

10x = 10

x = 1

AD = 5+1

AD = 6

Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.

As given in the question,

Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec

First term t₁ = 1 minute 58seconds

Time taken by each successive lap is 5seconds less then the previous lap

Common difference 'd' = -5seconds

let time taken to complete the seventh lap be t₇

t₇ = t₁ + ( 7 - 1 ) d

⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)

       =  1 minute 58 seconds - 30seconds

      = 1 minute 28 seconds

Therefore, the time taken by Adam to complete his seventh lap is equal to

1 minute 28 seconds.

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Answer:

Period is \(\frac{\pi}{2}\)

Step-by-step explanation:

For the function \(y=acos(bx-c)+d\), the period is \(\frac{2\pi}{|b|}\).

Therefore, the period of the function is \(\frac{2\pi}{|b|}=\frac{2\pi}{|4|}=\frac{2\pi}{4}=\frac{\pi}{2}\).

What this means is that the function's wave cycle will repeat every \(\frac{\pi}{2}\) units.

If a line segment connecting two points within a polygon passes outside the object, the polygon is not convex.

Explanation:

A polygon is a closed plane figure with straight sides, formed by connecting multiple line segments. A convex polygon is a polygon in which every interior angle is less than 180 degrees. In a convex polygon, any line segment connecting two points within the polygon is always bounded by the polygon, meaning that it does not pass outside the object.

On the other hand, a polygon that is not convex, also known as a concave polygon, has at least one interior angle greater than 180 degrees. In a concave polygon, a line segment connecting two points within the polygon can pass outside the object, creating a region that is not part of the polygon. Therefore, if a line segment connecting two points within a polygon passes outside the object, the polygon is not convex.

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Answer:

PDF

In a right triangle, if a and b are the measures of the legs and c is the measure of the hypotenuse, then a2 + b2 ... A support wire on a television tower is 90 ... on the ground that is 5 m from the bottom of the pole. How long is the cable? ... 15 centimeters and whose diagonal is 17 ... tether is tied to the pole at a point 40 feet.

Step-by-step explanation:

Answer:

first add 390 to 29 then, divided it to the sequence and there's your answer

Answer:

The numbers are 282,291,300,309,318,327,336,345,354,363,372,381,

Common rhg\(t(29) = 21 + (29 - 1)9\)

\( = 21 + (28)9\)

=21+252

=273

The numbers are 282,291,300,309,318,327,336,345,354,363,372,381

Answer: y = 1/2x + 12

Answer:

(D)

Step-by-step explanation:

Point symmetry refers to an object or shape that forms two similar shapes facing different directions when a point is inserted on the object or shape. This Polygon does not have point symmetry because well it doesn't.

It has line symmetry because you'd be able to draw a line from the point of the arrow downwards and make two halfs of this shape :)

I don't think I need to explain all of them because if you're taking the test you'd probably already learned this stuff. But either ways I understand if you need more clarification, and in case you do just leave a comment and I'll edit this answer :) Have a nice day!

Answer:

2,721,911.31

Step-by-step explanation:

The formula for Population growth rate is given as:

P(t) = Po(1 + r)^t

Where

Po = Initial population = 1,300000

P(t) = Population after t years

r = growth rate = 3%

t = time in years = 25

Hence,

P(25) = 1,300,000(1 + 0.03)^25

P(25) = 2,721,911.3086

P(25) Approximately = 2,721,911.31

The projected population of the county be in 25 years is 2,721,911.31

(a) To calculate the line integral ∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ over the circle C given by (x−8)²+(y−2)² = 16 oriented counterclockwise, we need to parametrize the curve C. The parametric equations for a circle of radius 4 centered at (8, 2) can be written as x = 8 + 4cos(t) and y = 2 + 4sin(t), where t ranges from 0 to 2π.

Substituting these expressions into the integrand and evaluating the dot product, we have:

∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ = ∫(4(8 + 4cos(t))² - (2 + 4sin(t)))dx + 5((2 + 4sin(t))² + (8 + 4cos(t)))dy.

Using the parametric equations and differentiating with respect to t, we can express dx and dy in terms of dt:

dx = -4sin(t)dt,

dy = 4cos(t)dt.

Substituting these expressions into the integral, we get:

∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ = ∫(4(8 + 4cos(t))² - (2 + 4sin(t)))(-4sin(t))dt + 5((2 + 4sin(t))² + (8 + 4cos(t)))(4cos(t))dt.

Integrating with respect to t over the range 0 to 2π, we can evaluate the integral to obtain the final answer.

(b) To calculate the line integral ∫(4(x²−y)⃗ + 5(y²+x)⃗ )⋅⃗ over the circle C given by (x−a)²+(y−b)² = r² in the xy-plane oriented counterclockwise, we need the specific values for a, b, and r. Please provide the values for a, b, and r in order to proceed with the calculation.

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Answer:

The first, third, and fourth.

Step-by-step explanation:

Those answers involve scaling the measurement up, which requires a positive power of 10. For scaling down, you'll need a negative power of 10, e.g., 2x10^-2=0.02.

Answer:

226.08 yd 3

Step-by-step explanation:

Answer:

226.08 yd 3

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We can conclude that C. the neighborhood is significantly less likely to be Democrat.

The null hypothesis was that there is no difference between the proportion of Democrats in the sample and the population. Since the null hypothesis has been rejected, it means that there is a significant difference between the sample and the population proportions. In this case, 60% of the respondents in the random sample are Democrats, which is lower than the 75% Democrat proportion in the community as a whole. Therefore, we can conclude that the neighborhood from which the sample was drawn is significantly less likely to be Democrat compared to the overall community.

The other options are not supported by the given information:

A type I error might or might not have occurred. We cannot determine this based on the information provided. A type I error refers to the incorrect rejection of a true null hypothesis. Without knowing the true proportions of the neighborhood, we cannot determine if a type I error has been committed. Whether a one-tailed test or a two-tailed test was used is not specified in the question.

However, the conclusion that the neighborhood is significantly less likely to be Democrat can be derived from either type of test. Therefore, the correct option is C.

The question was incomplete, Find the full content below:

sixty percent of the respondents in a random sample drawn from a neighborhood are democrats. the community as a whole is 75% democrat. the difference between sample and population has been tested and the null hypothesis has been rejected. what might we conclude? select one:

a. a type i error has been committed

b. a one-tailed test has definitely not been used

c. the neighborhood is significantly less likely to be democrat

d. the difference is not significant

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The function that best approximates f(x) as h approaches 0 is c. tan(x)/x.

For values of h very close to 0, the function that best approximates f(x) = tan(x) is option c. tan(x)/x.

To understand why, let's examine the behavior of each function as h approaches 0:

a. sin(x): As h approaches 0, sin(x+h) - sin(x) / h approaches the derivative of sin(x), which is cos(x). Therefore, sin(x) is not the best approximation for f(x) as h approaches 0.

b. sin(x)/x: As h approaches 0, sin(x+h) - sin(x) / h approaches the derivative of sin(x), which is cos(x). Dividing by x helps to account for the change in slope as x approaches 0. Therefore, sin(x)/x provides a better approximation for f(x) as h approaches 0.

c. tan(x)/x: As h approaches 0, tan(x+h) - tan(x) / h approaches the derivative of tan(x), which is sec^2(x). Dividing by x helps to account for the change in slope as x approaches 0. Therefore, tan(x)/x provides the best approximation for f(x) as h approaches 0.

d. sec(x): The secant function is the reciprocal of the cosine function, and it does not provide a good approximation for f(x) as h approaches 0.

e. sec^2(x): As h approaches 0, sec(x+h) - sec(x) / h approaches the derivative of sec(x), which is sec(x) * tan(x). Therefore, sec^2(x) does not provide the best approximation for f(x) as h approaches 0.

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330 ways can the instructor choose the first group of four education students.

What is probability in math?

Given:

12 students

3 groups consisting of 4 students.

Mark can't be in the first group.

The combination formula that I used is =  n! / r!(n-r)!

where: n = number of choices ; r = number of people to be chosen.

This is the formula I used because the order is not important and repetition is not allowed.

Since Mark can't be considered in the first group, the value of n would be 11 instead of 12. value of r is 4.

numerator: n! = 11! = 39,916,800

denominator: r!(n-r)! = 4!(11-4)! = 4!*7! = 120,960

Combination = 39,916,800 / 120,960 = 330

Therefore, There are 330 ways that the instructor can choose 4 students for the first group.

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n should be a whole number, we round up to the nearest integer, giving n = 540. Therefore, if Russel wants 0.99 certainty, n should be at least 540.

To determine how large n should be in order to have a certain level of certainty about the true probability p, we can use the concept of confidence intervals.

For a binomial distribution, the estimate of the probability p is X/n, where X is the number of successes (in this case, the number of times tails is obtained) and n is the number of trials (the number of times the coin is flipped).

To find the confidence interval, we need to consider the standard error of the estimate. For a binomial distribution, the standard error is given by:

SE = sqrt(p(1-p)/n)

Since p is unknown, we can use a conservative estimate by assuming p = 0.5, which gives us the maximum standard error. So, SE = sqrt(0.5(1-0.5)/n) = sqrt(0.25/n) = 0.5/sqrt(n).

To ensure that the true p is within 0.1 of the estimate X/n with at least 0.95 certainty, we can set up the following inequality:

|p - X/n| ≤ 0.1

This inequality represents the desired margin of error. Rearranging the inequality, we have:

-0.1 ≤ p - X/n ≤ 0.1

Since p is unknown, we can replace it with X/n to get:

-0.1 ≤ X/n - X/n ≤ 0.1

Simplifying, we have:

-0.1 ≤ 0 ≤ 0.1

Since 0 is within the range [-0.1, 0.1], we can say that the estimate X/n with a margin of error of 0.1 includes the true probability p with at least 0.95 certainty.

To find the value of n, we can set the margin of error equal to the standard error and solve for n:

0.1 = 0.5/sqrt(n)

Squaring both sides and rearranging, we get:

n = (0.5/0.1)^2 = 25

Therefore, n should be at least 25 to know with at least 0.95 certainty that the true p is within 0.1 of the estimate X/n.

If Russel wants 0.99 certainty, we need to find the value of n such that the margin of error is within 0.1:

0.1 = 2.33/sqrt(n)

Squaring both sides and rearranging, we get:

n = (2.33/0.1)^2 = 539.99

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The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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Answer:

7 hours.

Step-by-step explanation:

6x7=42

42+18=60

For number of hours Jimmy rented the bike Krystal's bikes is 8 hours.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Jimmy rented a bike from Krystal's bikes. It costs $18 plus $6 per hour and Jimmy paid $60.

Let the number of hours be x.

Now, 18+6x=60

6x=42

x=8

Therefore, for number of hours Jimmy rented the bike Krystal's bikes is 8 hours.

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