The diagonal of a square is 18in. Find the length of a side.


50 points in it for you plus a thanks, 5 star and brainliest

Answers

Answer 1

Answer:

length of a side is 3

Step-by-step explanation:

if it is a square, the sides are equal. The diagonal will divide the square into 2 isosceles right triangles with diagonal is the hypotenuse

Pythagorean theorem: c^2 = a^2 + b^2

since a = b in isosceles right triangle

c^2 = 2a^2

18 = 2a^2

a^2 = 18/2 = 9

a = √9 = 3


Related Questions

(d) (4 points) suppose it takes a half hour for a red truck to pass through the tunnel. if there are no red trucks in the tunnel when it enters the tunnel at 7:35am on a monday, what is the probability it will be the only red truck in the tunnel the whole time it spends in the tunnel? state the appropriate distribution and any parameter values for any random variable(s) you use to model the situation. write the probability statment and show your work to receive full credit. (e) (5 points) let w represent the amount of time in hours it takes for the 9th red truck to arrive at the tunnel on a monday morning. what time do you expect the 9th red truck to arrive at the tunnel on a monday morning (to the nearest 10 minutes)? recall the tunnel opens at 7am. your final answer should be a time.

Answers

(d) The appropriate distribution to use in this situation is the Poisson distribution. We can let X be the number of red trucks that enter the tunnel during the half hour that the first red truck is in the tunnel. The parameter value for the Poisson distribution is λ, which is the average number of red trucks that enter the tunnel in a half hour. We can use the given information to calculate λ:
λ = (average number of red trucks per hour) × (length of time in hours) = (18 red trucks per hour) × (0.5 hours) = 9 red trucks
Therefore, the probability that the first red truck is the only red truck in the tunnel during the half hour it spends in the tunnel is:
P(X = 0) = (λ^0 × e^-λ) / 0! = (9^0 × e^-9) / 0! = (1 × e^-9) / 1 = e^-9 ≈ 0.0001234
So the probability is approximately 0.0001234.

(e) The appropriate distribution to use in this situation is also the Poisson distribution. We can let W be the amount of time in hours it takes for the 9th red truck to arrive at the tunnel on a Monday morning. The parameter value for the Poisson distribution is still λ, which is the average number of red trucks that enter the tunnel per hour. We can use the given information to calculate λ:
λ = (average number of red trucks per hour) = (18 red trucks per hour) = 18 red trucks
The expected value of W is 1/λ = 1/18 hours = 0.0556 hours ≈ 3.33 minutes. Since the tunnel opens at 7am, we can add this expected value to the opening time to find the expected time that the 9th red truck will arrive at the tunnel:
Expected time = 7:00am + 3.33 minutes = 7:03am
So we expect the 9th red truck to arrive at the tunnel at 7:03am on a Monday morning.

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Three friends participate in the loyalty program at a local coffee shop. A participant in the program earns points for each visit that can be used to get drinks and food for free. The graph below shows the point balances of the three friends over several weeks?

help me it's the 23 and the 24 please.

Answers

Answer:

On the graph, the point balances for the three friends on the 23rd week are:

- Friend A: 60 points

- Friend B: 80 points

- Friend C: 40 points

On the 24th week, the point balances are:

- Friend A: 80 points

- Friend B: 100 points

- Friend C: 60 points

It looks like all three friends are earning points and increasing their balances over time. Friend B seems to be earning points at a faster rate than the other two friends, as their balance is consistently higher. Friend C has the lowest balance, but is still earning points and increasing their balance.

PLEASE HELP !!!!!!! i really need help!

Answers

Answer: Ans b.

Vol_total

= 7800 yd^3

Step-by-step explanation:

The bottom part of your shape is a box, basically (rectangular prism) and the volume is:

V=

length×width×height

Those numbers are all given. Because it is a box shape, it doesn't matter which number is which.

V = 22 × 15 × 16

= 5280 yd^3

Now the "roof" part on top is a little bit different. It is a triangular prism. So the side that needs to be the Base of the prism is the front (or back) triangle.

The volume is:

V

= BaseArea×height

= Area_triangle× ht

= 1/2 bh × height

= 1/2•21•16 × 15

The key to understanding is knowing the triangle must be the base. And the roof line running front to back will be the height. And also understanding the difference between the height of just a triangle (21) and the height of the prism(15). They are different.

Vol_roof = 2520

Then add them together.

Vol_total

= 5280 + 2520

= 7800 yards cubed

A store imploys 11 woman and 12 men
What percentage of the employees are men?

Answers

12/23 = 0.5217391

0.5217391 x 100 = 52.2 % 1dp
11 women + 12 men = 23 employees

To determine the percentage of employees that are men, we need to divide the number of men by the total number of employees, and then multiply by 100 to get the percentage:

Percentage of employees that are men = (Number of men / Total number of employees) x 100
Percentage of employees that are men = (12 / 23) x 100
Percentage of employees that are men = 52.17%

Therefore, 52.17% of the employees in the store are men.

ou have learned that given a sample of size n from a normal distribution, the CL=95% confidence interval for the mean can be calculated by Sample mean +/- z((1-CL)/2)*Sample std/sqrt(n). Where z((1-cl)/2)=z(.025) is the z score.
a. help(qnorm) function. Use qnorm(1-.025) to find z(.025).
b. Create a vector x by generating n=50 numbers from N(mean=30,sd=2) distribution. Calculate the confidence interval from this data using the CI formula. Check whether the interval covers the true mean=30 or not.
c. Repeat the above experiments for 200 times to obtain 200 such intervals. Calculate the percentage of intervals that cover the true mean=30. This is the empirical coverage probability. In theory, it should be very close to your CL.
d. Write a function using CL as an input argument, and the percentage calculated from question c as an output. Use this function to create a 5 by 2 matrix with one column showing the theoretical CL and the other showing the empirical coverage probability, for CL=.8, .85, .9, .95,.99.

Answers

a. To find the z score for a given confidence level, you can use the `qnorm()` function in R. The `qnorm()` function takes a probability as an argument and returns the corresponding z score. To find the z score for a 95% confidence level, you can use `qnorm(1-.025)`:

```R
z <- qnorm(1-.025)
```

This will give you the z score for a 95% confidence level, which is approximately 1.96.

b. To create a vector `x` with 50 numbers from a normal distribution with mean 30 and standard deviation 2, you can use the `rnorm()` function:

```R
x <- rnorm(50, mean = 30, sd = 2)
```

To calculate the confidence interval for this data, you can use the formula:

```R
CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
```

This will give you the lower and upper bounds of the 95% confidence interval. You can check whether the interval covers the true mean of 30 by seeing if 30 is between the lower and upper bounds:

```R
lower <- CI[1]
upper <- CI[2]
if (lower <= 30 && upper >= 30) {
 print("The interval covers the true mean.")
} else {
 print("The interval does not cover the true mean.")
}
```

c. To repeat the above experiment 200 times and calculate the percentage of intervals that cover the true mean, you can use a for loop:

```R
count <- 0
for (i in 1:200) {
 x <- rnorm(50, mean = 30, sd = 2)
 CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
 lower <- CI[1]
 upper <- CI[2]
 if (lower <= 30 && upper >= 30) {
   count <- count + 1
 }
}
percentage <- count / 200
```

This will give you the percentage of intervals that cover the true mean.

d. To write a function that takes a confidence level as an input and returns the percentage of intervals that cover the true mean, you can use the following code:

```R
calculate_percentage <- function(CL) {
 z <- qnorm(1-(1-CL)/2)
 count <- 0
 for (i in 1:200) {
   x <- rnorm(50, mean = 30, sd = 2)
   CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
   lower <- CI[1]
   upper <- CI[2]
   if (lower <= 30 && upper >= 30) {
     count <- count + 1
   }
 }
 percentage <- count / 200
 return(percentage)
}
```

You can then use this function to create a 5 by 2 matrix with one column showing the theoretical CL and the other showing the empirical coverage probability:

```R
CL <- c(.8, .85, .9, .95, .99)
percentage <- sapply(CL, calculate_percentage)
matrix <- cbind(CL, percentage)
```

This will give you a matrix with the theoretical CL in the first column and the empirical coverage probability in the second column.

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Please answer this its for a test

Answers

1) The surface area of the figure is of 72 square units.

2) Removing the top two cubes, the surface area of the figure would be of 60 square units.

How to obtain the surface area of a cube?

The surface area of a cube of side length a is given by the equation presented as follows:

S = 6a².

For this problem, we have that the parameters are given as follows:

12 cubes.Each cube has a side length of one unit.

Hence the surface area of the figure is given as follows:

S = 12 x 6 x 1

S = 72 square units.

Removing the top two cubes, the surface area of the figure would be given as follows:

S = (12 - 2) x 6 x 1

S = 60 square units.

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DUE TODAY PLEASE HELP NOW!!!!!!!!!!!!! 20 POINTS
Here is another triangle similar to DEF found in the lesson section labeled “Shrinking Triangles”.
• Label the triangle D”E”F”.
• What is the scale factor from triangle DEF to triangle D”E”F”?
• What are the coordinates of F”? Explain how you know.
• What are cos(D”), sin(D”), and tan(D”)?

Answers

The scale factor of dilation is 1/40 and the coordinates of F" are (1440, 600)

Labelling the image of the triangle

The image of the label is attached

The scale factor of the dilation

Given that

D'E' = 36 units

Then, we have

D"E" = 0.9 units

The scale factor is calculated as

Scale factor = D"E"/D'E'

So, we have

Scale factor = 0.9/36

Evaluate

Scale factor = 1/40

So, the scale factor of dilation is 1/40

The coordinates of F"

This is calculated as

F = F'/Scale factor

So, we have

F = (36, 15)/(1/40)

F = (1440, 600)

The trigonometry ratios

The trigonometry ratios are calculated as

sin(D") = EF/DF

cos(D") = DE/DF

tan(D") = EF/DE

So, we have the following approximated values

sin(D") = 15/39 = 0.36

cos(D") = 36/39 = 0.92

tan(D") = 0.36/0.92 = 0.39

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Helpppp meee plssss will mark you big brain

Answers

Answer:

Step-by-step explanation:

16. Since the angle between the two values is 90, that is already half of 180, which is the total of all of the angles. So you make the equation, 3n+3+2n+7+90=180, which simplifies down to 5n+100=180, and after solving you get n = 16.

Here is the answer to your question

[tex] = 16[/tex]

what is the lcm of 14 and 18​

Answers

the lcm of 14 and 18 is 126

Please ASAP Help
Will mark brainlest due at 12:00​

Answers

Answer:

plot the point at -5

Step-by-step explanation:

Time length (in months) of uninterrupted functioning of soil moisture measuring
sensors until failure follows a distribution, 1/7e−x/7. The sensors are inspected at
every 2 months.
(a) What is the probability that the sensors need to be replaced at the first inspection?
(b) What is the probability of proper functioning of the sensors till the second scheduled
inspection? (Ans 0.564)

Answers

The probability of proper functioning of the sensors till the second scheduled inspection is `0.564`.

Given that the time length (in months) of uninterrupted functioning of soil moisture measuring sensors until failure follows a distribution, `1/7e−x/7`.The sensors are inspected at every 2 months.(a) Probability that the sensors need to be replaced at the first inspection= Probability that the sensors fail at the first inspection= Probability that the sensors fail before first inspection= Probability that the sensor functioned well up to the first inspection=  `F(2) = 1-e^(-2/7)` (Using the given exponential distribution)Therefore, the probability that the sensors need to be replaced at the first inspection is `0.226`. (Approximately, 0.23)(b) The probability of proper functioning of the sensors till the second scheduled inspection is the probability that the sensors do not fail in the first two months. That is, `P(t≥2)` = `1-P(t<2)`= `1-F(2)` = `1-(1-e^(-2/7))` = `0.564`.Therefore, the probability of proper functioning of the sensors till the second scheduled inspection is `0.564`.

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What should your units on your base area calculations be, and why? How is this different from the units on your volume calculations

Answers

The units for base area calculations are squared units and the units for volume calculations are cubed units. This is because the area and volume calculations require different equations and different units of measurement.

The units on your base area calculations should be squared units, such as square meters, square centimeters, square inches, or square feet. This is because the area of a two dimensional shape is the amount of space occupied by the shape and is calculated by taking the length of the base and multiplying it by the width of the base. For example, if a rectangle has a length of 5 meters and a width of 3 meters, the area of the rectangle would be 5 x 3 = 15 square meters.

The units on your volume calculations should be cubed units, such as cubic meters, cubic centimeters, cubic inches, or cubic feet. This is because the volume of a three dimensional shape is the amount of space occupied by the shape and is calculated by taking the area of the base and multiplying it by the height of the shape. For example, if a cube has an area of 15 square meters and a height of 4 meters, the volume of the cube would be 15 x 4 = 60 cubic meters.

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write an equation in slope-intercept form of the line that passes through the given points
[tex]\left[\begin{array}{ccc}x&y\\-2&2\\0&1\\2&0\\4&-1\end{array}\right][/tex]

Answers

We can find the slope between the first two points (-2, 2) and (0, 1):

m = (1 - 2) / (0 - (-2))

m = -1 / 2

Now that we have the slope (m), we can use the point-slope form of the equation of a line to find the y-intercept (b). Using the point (0, 1):

y - y1 = m(x - x1)

y - 1 = (-1/2)(x - 0)

y = (-1/2)x + 1

Therefore, the equation of the line in slope-intercept form that passes through the given points is:

y = (-1/2)x + 1

Please mark this answer as brainliest if possible.

What are the x-intercepts for the equation y=0. 2(x+1)(x-14)

Answers

The x-intercepts for the equation y=0 is -1 and 14 respectively

What is intercept?

Intercepts in mathematics are points where a graph crosses the x and/or y axes, or n x-intercept is where the graph crosses (or touches) the x-axis; a y-intercept is where the graph crosses (or touches) the y-axis

The given equation is 2(x+1)(x-14)

Opening the bracket to have

x²-14x+x-14 = 0

Solving the quadratic equation to have

2[x²-13x+14] =0

2x-26x+28 = 0

Dividing by 2 to have

x²-13x-14 =0

(x²-14x)+(x -14) =0

x(x-14) + 1(x-14)

x+1 = 0 and x-14 = 0

there values of x are

x= -1 and x = 14

The intercept of the equation is at x=-1 and x=14

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Is 0.06 bigger than 0.066

Answers

Answer:

Yes, 0.06 is bigger than 0.066, because 0.06 is greater than 0.066 when they are written in decimal form. This is due to the fact that 0.06 has 6 tenths, while 0.066 has 66 hundredths.

Answer:

no

Step-by-step explanation:

that is because 0.6 = 0.6000000

and 0.066 = 0.6600000

What fraction times 4 1/3 is equal to 6 1/2?

Answers

Answer:

3/2

Step-by-step explanation:

4 1/3 = 13/3

6 1/2 = 13/2

fraction x 13/3 = 13/2

=> fraction = 13/2 / 13/3 = 13/2 x 3/13 = 3/2

Nancy has twice as many apples as jay. Jay has 3 more apples than Ava. Nancy has 22 apples. How many apples dose Ava have?

Answers

Answer: 8

Step-by-step explanation: Nancy has 22 apples, it was previously stated that Nancy has TWICE as many apples than Jay meaning Jay has 11 apples. Jay has 3 more apples than Ava meaning Ava has 8.

Help please !!
WHAT does this mean

Answers

The probability that the coin shows heads and the number is two is 0.05.

What is probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, we have

Given: you flip a coin and use a random number generator to generate a number from 1 to 10.

To find the probability, we need to use that we have two independent events. First, flip a coin, and second, generate a number from 1 to 10. They are independent events because their occurrence is not dependent on any other event.

P(A∩B) = P(A).P(B)

Where A represents the event of flipping a coin

B represents the event of generating a number from 1 to 10.

P(A) = 1/2, P(B) = 1/10

P(A) = 0.5 and P(B) = 0.1 we need to replace their values in the initial formula

P(A∩B) = 0.5× 0.1

P(A∩B) = 0.05

Hence, The probability that the coin shows heads and the number is two is 0.05.

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Solve the system of equations graphed on the coordinate axes below.

Answers

The solution to the system of equations is (1,1), which is the point where the two lines intersect on the coordinate axes.

Describe Equation?

An equation is a mathematical statement that shows the equality between two expressions. It contains one or more variables, which are usually represented by letters, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to model and solve various real-world problems in fields such as physics, engineering, and finance. The goal in solving an equation is to find the value of the variable that satisfies the equation. This can be done by applying mathematical operations to both sides of the equation in a systematic way until the variable is isolated on one side.

To solve the system of equations graphed on the coordinate axes, we need to find the point at which the two lines intersect. This point represents the solution to the system of equations.

First, we can set the two equations equal to each other, since they both equal y:

2x-1 = -x+2

Adding x to both sides, we get:

3x-1 = 2

Adding 1 to both sides, we get:

3x = 3

Dividing both sides by 3, we get:

x = 1

Now we can substitute x=1 into either equation to find y:

y = 2(1) - 1

y = 1

Therefore, the solution to the system of equations is (1,1), which is the point where the two lines intersect on the coordinate axes.

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PLEASE HELP IMMA DIE IF I GET THIS WRONG (im over exaggerating
)

Answers

In the given triangle, The value of x will be 6.

What exactly is a triangle?

A triangle is a closed two-dimensional geometric shape that is formed by three straight line segments that connect three non-collinear points. The three line segments that form a triangle are called sides, and the three points where the sides intersect are called vertices.

Triangles can be classified into six types. A triangle with all three sides of equal length is called an equilateral triangle, while a triangle with two sides of equal length is called an isosceles triangle. A triangle with all three angles measuring less than 90 degrees is called an acute triangle, while a triangle with one angle measuring exactly 90 degrees is called a right triangle. A triangle with one angle measuring more than 90 degrees is called an obtuse triangle.

Now,

For given triangle,

The angle bisector is perpendicular to the line having x.

As it divided angle into same ratio then the ratio

[tex]x/5[/tex]=[tex]12/10[/tex]

then x=6/5*5

x=6

Hence,

        The measurement of side x will be 6.

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a dvd rental company charges $10 per month plus $0.75 per rental. Andy wants to spend no more than 25.00 per month on DVD rentals. Select the inequality that represents how many DVDs Andy can rent in one month that satisfies this condition. The number of rentals in a month is represented by n. A. 10.75n < 25

Answers

The answer of the question based on the inequality the answer is  Andy can rent up to 20 DVDs in a month and spend no more than $25.

What is Inequality equations?

An inequality equation is mathematical statement that compares the two values or expressions using inequality symbol such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

The total cost, C, for renting n DVDs in a month is given by:

C = 10 + 0.75n

The question tells us that Andy wants to spend no more than $25 per month on DVD rentals. Therefore, we can write an inequality:

C ≤ 25

Substituting the expression for C from above, we get:

10 + 0.75n ≤ 25

Simplifying the inequality, we can subtract 10 from both sides:

0.75n ≤ 15

Finally, we can divide both sides by 0.75:

n ≤ 20

Therefore, the inequality that represents how many DVDs Andy can rent in one month that satisfies the condition of spending no more than $25 per month is:

n ≤ 20

So, Andy can rent up to 20 DVDs in a month and spend no more than $25.

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(NEED HELP ASAP)

What side is opposite from angle B?
What side is adjacent to angle B but is not the hypotenuse?
What side is hypotenuse?

Answers

Answer:

Step-by-step explanation:

What side is opposite from angle B? AC

What side is adjacent to angle B but is not the hypotenuse? BC

What side is hypotenuse? AB

an ant is about to climb a 50-meter tree. in 2 hours, it can climb 5 meters, but it then slips down 1 meter. how long does it take the ant to reach the top

Answers

The ant will reach the top in 16.67 hours, or approximately 16 hours and 40 minutes

An ant is about to climb a 50-meter tree. In 2 hours, it can climb 5 meters, but it then slips down 1 meter. How long does it take the ant to reach the top?An ant can climb 4 meters in 1 hour since it climbs 5 meters but then slides down 1 meter in 2 hours. Let us assume that it takes the ant n hours to get to the tree's top. We don't understand the precise number of hours, thus we'll use 'n' to represent the number of hours it takes the ant to reach the top of the tree.

The ant climbs 4 meters per hour, thus it climbs 4n meters after n hours.The ant slips down 1 meter each hour, therefore,  it slides down 1n meters after n hours.If the ant climbs 4n meters but slips down 1n meters, it is actually at 3n meters after n hours. Therefore, 3n = 50 since the ant should reach the top of a 50-meter tree.Since 3n = 50, n = 50/3 ≈ 16.67 (to two decimal places). As a result, the ant will reach the top in 16.67 hours, or approximately 16 hours and 40 minutes.

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A farmer has 2400 sheep, he loses 32,5% due to the drought. After that he loses 15% due to sickness. How many sheep does he have now?

Answers

The farmer now has 1377 sheep. If the farmer loses 32.5% of his 2400 sheep due to the drought, then he will have: 2400 * (1 - 0.325) = 1620 sheep left after the drought.

The farmer had 2400 sheep, but he lost 32.5% of them due to drought. Using the formula for finding percentages, we can calculate that 32.5% of 2400 is 780. So, the farmer had 2400 - 780 = 1620 sheep left after the drought. However, he then lost 15% of those remaining sheep due to sickness. Using the same formula, we can calculate that 15% of 1620 is 243. Therefore, the farmer had 1620 - 243 = 1377 sheep left after the sickness. So, the final number of sheep the farmer has now is 1377.

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After Angela drank 390 millilitres of soup from a can of the soup was left in the can. How much soup was in the can at first?​

Answers

The volume of soup in the can at first is 546 millilitres.

How to find the amount of soup in the can?

Angela drank 390 millilitres of soup from a can of the soup. 2 / 7 of the soup was left in the can after drinking the soup.

Therefore, the amount of soup in the can at first can be calculated as follows:

let

x = amount of soup initially in the can

Therefore, using equation let's find the volume of soup initially in the can.

2 / 7 x + 390 = x

390 = x - 2 / 7 x

390 =  7x - 2x / 7

390 = 5x / 7

cross multiply

5x = 390 × 7

5x = 2730

divide both sides by 5

x = 2730 / 5

x = 546

Therefore,

volume of soup in the can = 546 millilitres

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The band students at Brookshaw Junior High School got to choose between ordering a hoodie or a T-shirt to wear on spirit day this year. In the seventh grade band, 7 students ordered the hoodie and 18 students ordered the T-shirt. In the eighth grade band, 12 students ordered the hoodie and 15 students ordered the T-shirt. The hoodies cost h dollars each, and the T-shirts cost t dollars each.
Pick all the expressions that represent how much the band students spent on hoodies and T-shirts.

Answers

Answer:

[tex]19h + 33t[/tex]
[tex]7h + 18t +12h + 15t[/tex]

Step-by-step explanation:

The two expressions above are equal and both represent the total spent on hoodies and t-shirts.

[tex]25(h+t) + 27(h + t)[/tex] is incorrect because this implies that the cost of t-shirts and hoodies are interchangeable. The choice in the bottom right is incorrect also because it is equivalent to the aforementioned expression.

The marked price of the mobile set is Rs 2,800 more than the selling price. If the price of the mobile with 13% VAT is Rs 28,476 then find the discount percent given in the mobile. ​

Answers

If the price of the mobile with 13% VAT is Rs 28,476, the discount percent is 10%.

What is the discount?

The discount is the difference between the marked price and the selling price.

Discounts are depicted in percentages to show the rates at which the discounts are given.

The selling price of the mobile set with 13% VAT = Rs. 28,476

The selling price of the mobile set without VAT = Rs. 25,200 (Rs. 28,476/1.13)

The difference (discount) between the marked price and the selling price = Rs. 2,800

The marked price = Rs. 28,000 (Rs. 25,200 + Rs. 2,800)

The discount percent given = 10% (Rs. 2,800/Rs. 28,000 x 100)

Thus, we can conclude that the discount percent is 10%.

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4. 2. 4Practice:Modeling: Slope-Intercept Equation of a Line

Answers

The slope-intercept form of the equation of a line is: y = mx + b

Where: y is the dependent variable (usually represented on the vertical axis of a graph). x is the independent variable (usually represented on the horizontal axis of a graph). m is the slope of the line (which represents the rate of change of y with respect to x). b is the y-intercept (which represents the value of y when x is equal to 0). To use this equation, you need to know the slope (m) and the y-intercept (b) of the line. You can find the slope of a line by taking any two points on the line and using the formula:

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

where (x1, y1) and (x2, y2) are any two points on the line. Once you know the slope, you can substitute it and the y-intercept into the slope-intercept form of the equation of the line to get the equation in its final form.

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Solve the system of equations. − 4 � + 3 � = − 2 � = � − 1 ​ −4x+3y=−2 y=x−1 ​ � = x=x, equals � = y=y, equals

Answers

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

What is system of equations?

A system of equations is the set of two or more equations with the same variables.

An example is: 2x + 3y = 10 and 4x - 5y = -8

To solve the system of equations:

-4x + 3y = -2

y = x - 1

We can substitute the second equation into the first to eliminate y:

-4x + 3(x - 1) = -2

Simplifying and solving for x:

-4x + 3x - 3 = -2

-x = 1

x = -1

Now that we know x = -1, we can use the second equation to find y:

y = -1 - 1

y = -2

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GET 30 POINTS

1) Coordinate point B is at (4,3). What will the coordinates be for B' after a translation of (x-2,y+3)?
*
B' (5,4)
B' (2,6)
B' (6,2)
B' (-2,3)

What is the coordinate for G(3,-2) after it is reflected across the x-axis?
*
(2,3)
(-2,3)
(3,2)
(-3,-3)

What is the translation rule that describes the result of the composition of
(x, y) --> (x+4, y-1) and (x, y) --> (x-5, y-5)?
*
(x, y) --> (x-1, y-6)
(x, y) --> (x+1, y-3)
(x, y) --> (x+9, y+6)
(x, y) --> (x+1, y+6)

thank you so mcuh

Answers

After translatiοn, the cοrrect answer is B' (x+2, y+6).

The cοοrdinate after reflectiοn is (3,2).

The translatiοn rule that describes the result οf cοmpοsitiοn is (x, y) →(x-1, y-6).

What are transfοrmatiοns?

Transfοrmatiοns in a triangle refer tο changes that can be made tο the shape, size, pοsitiοn, οr οrientatiοn οf the triangle οn a cοοrdinate plane. The three main types οf transfοrmatiοns that can be applied tο a triangle are:

Translatiοn: This transfοrmatiοn invοlves mοving the entire triangle tο a new pοsitiοn οn the cοοrdinate plane withοut changing its size οr shape.

Rοtatiοn: This transfοrmatiοn invοlves rοtating the entire triangle arοund a fixed pοint οn the cοοrdinate plane. The fixed pοint is called the center οf rοtatiοn, and the angle οf rοtatiοn determines the amοunt οf turn.

Scaling: This transfοrmatiοn invοlves changing the size οf the triangle by multiplying the x and y cοοrdinates οf each vertex by a fixed factοr.

1) Applying the translatiοn οf (x-2, y+3) tο pοint B(4,3) wοuld result in: B' = (4 + (x-2), 3 + (y+3)) = (x+2, y+6)

Therefοre, the cοrrect answer is B' (x+2, y+6)

2) Reflecting pοint G(3,-2) acrοss the x-axis results in the y-cοοrdinate being negated, and the x-cοοrdinate remains the same. Therefοre, the cοοrdinates οf the reflected pοint wοuld be G(3, 2).

The cοrrect answer is (3,2).

3) Tο determine the cοmpοsitiοn οf (x, y) → (x+4, y⁻¹) and (x, y) →(x-5, y⁻⁵), we need tο apply them in οrder. Firstly, (x, y) → (x+4, y-1) is applied tο pοint (x,y), which results in:(x, y)→ (x+4, y-1)

Next, (x, y) → (x-5, y-5) is applied tο the result frοm the previοus transfοrmatiοn (x+4, y-1), which results in:(x+4, y-1)→(x-1, y-6)

Therefore, the correct answer is (x, y) →(x-1, y-6).

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