How many solutions x2 = 12

Answer:

7 + 2 = 9, so AC = 7/9 and CD = 2/9

1 + 2 = 3, so AB = 1/3 = 3/9 and

BD = 2/3 = 6/9

AB + BC = AC

3/9 + BC = 7/9, so BC = 4/9

AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2

Answer:

-8/3

Step-by-step explanation:

Slope = (-1-7)/(6-3) = -8/3

Answer:

-8/3

Step-by-step explanation:

You can use the slope formula which is (y2 - y1) / (x2 - x1). So using these values we get

(-1 - 7) / (6 - 3) = -8/3

Answer:

First Bed: 15 white 20 pink

Second Bed: 30 white and 60 pink= 90 hydrangeas

Total Flowers: 45 white and 80 pink

Step-by-step explanation:

Questions like these are normally jsut trial and error. If the numbers that are given to you end with a 5 or 0, you should experiment with numbers that end in  a 5 or 0.

Answer:

x = 45

Step-by-step explanation:

2x+x+45 = 180

3x+45 = 180

3x = 135

x= 45

Angle D = 45

Angle C =  90

This is an isosceles triangle btw

Hope this helps!

PLS mark Brianliest!!

The joint relative frequency for school children who plan to attend camp and have swimming lesson is 44%.

The correct option to the given question is option d.

We are required to find the joint relative frequency for school children who plan to attend camp and have swimming lessons, rounded to the nearest percent.

To find the joint relative frequency, we use the formula as follows:

Joint relative frequency = frequency of interest / total frequency

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 42 / 96

(As we are looking for the students who plan to attend camp and have swimming lessons, we are interested in the first column of the table and the entry at the intersection of the first row and second column.)

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 0.4375

Joint relative frequency for school children who plan to attend camp and have swimming lessons (rounded to the nearest percent) = 44%(option d).

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The snow that will be gotten daily of the line plot is redistributed equally will be 1/2.

A line plot, also known as a line graph, is a type of graph that displays information as a series of data points connected by straight lines. Line plots are often used to show how a particular variable changes over time or to compare two or more variables.

To create a line plot, you typically need to have a set of data points that represent the variable you want to graph. You then plot each data point on a graph, with the x-axis representing time or some other variable, and the y-axis representing the value of the variable you're graphing.

The snow that will be gotten daily of the line plot is redistributed equally will be:

= (1/8 + 2/8 + 3/8 + 4/8 + 5/8 + 6/8 + 7/8 + 8/8) / 9

= 36/8 / 9

= 1/2

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As a result, when the entire circumference is 20 feet, the Norman window's maximum area measurements are as follows: x = 8 feet, or around 2.546 feet, is the width, Height: 9.087 feet, or about y = 16 - 16/feet.

Perimeter is the total distance around the boundary of a two-dimensional shape, such as a polygon, a circle, or a rectangle. It is the sum of the lengths of all sides or edges of the shape.

Area is a measure of the size or extent of a two-dimensional surface or region. It is the amount of space enclosed within a closed shape or boundary.

Let's assume that the width of the rectangular part of the window is x and the height is y.

The perimeter of the window is given by:

Perimeter = width + height + semicircle circumference

Perimeter = x + y + πx/2

We are given that the total perimeter is 20 feet, so we can write:

x + y + πx/2 = 20

We can solve for y in terms of x:

y = 20 - x - πx/2

The area of the window is given by:

Area = rectangular part area + semicircle area

Area = xy + πx^2/8

We can substitute the expression we obtained for y into the equation for the area:

Area = x(20 - x - πx/2) + πx^2/8

Simplifying this expression, we get:

Area = 20x - (π/2)x^2 + πx^2/8

Area = 20x - (π/2)x^2/4

To find the maximum area, we can take the derivative of the area function with respect to x and set it equal to zero:

d/dx (Area) = 20 - (π/2)x/2 = 0

Solving for x, we get:

x = 8/π

Substituting this value back into the expression for y that we obtained earlier, we get:

y = 20 - 8/π - π(8/π)/2 = 20 - 4π/π - 16/π = 20 - 4 - 16/π = 16 - 16/π

Therefore, the dimensions of the Norman window of maximum area when the total perimeter is 20 feet are:

Width: x = 8/π feet (approximately 2.546 feet)

Height: y = 16 - 16/π feet (approximately 9.087 feet)

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The dimensions of the Norman window of maximum area when the total perimeter is 20 feet are:

Width: x = 8/π feet (approximately 2.546 feet)

Height: y = 16 - 16/π feet (approximately 9.087 feet)

Perimeter is the total distance around the boundary of a two-dimensional shape, such as a polygon, a circle, or a rectangle. It is the sum of the lengths of all sides or edges of the shape.

Area is a measure of the size or extent of a two-dimensional surface or region. It is the amount of space enclosed within a closed shape or boundary.

Let's assume that the width of the rectangular part of the window is x and the height is y.

The perimeter of the window is given by:

Perimeter = width + height + semicircle circumference

Perimeter = x + y + πx/2

We are given that the total perimeter is 20 feet, so we can write:

x + y + πx/2 = 20

We can solve for y in terms of x:

y = 20 - x - πx/2

The area of the window is given by:

Area = rectangular part area + semicircle area

\(Area = xy + \pi x^{2/8\)

We can substitute the expression we obtained for y into the equation for the area:

\(Area = x(20 - x - \pi x/2) + \pi x^{2/8\)

Simplifying this expression, we get:

\(Area = 20x - (\pi /2)x^2 + \pi x^{2/8\)

\(Area = 20x - (\pi /2)x^{2/4\)

To find the maximum area, we can take the derivative of the area function with respect to x and set it equal to zero:

d/dx (Area) = 20 - (π/2)x/2 = 0

Solving for x, we get:

x = 8/π

Substituting this value back into the expression for y that we obtained earlier, we get:

y = 20 - 8/π - π(8/π)/2 = 20 - 4π/π - 16/π = 20 - 4 - 16/π = 16 - 16/π

Therefore, the dimensions of the Norman window of maximum area when the total perimeter is 20 feet are:

Width: x = 8/π feet (approximately 2.546 feet)

Height: y = 16 - 16/π feet (approximately 9.087 feet)

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The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

The Mean is defined as the ratio of sum of numbers present in the data to the total numbers present in the data. Median is defined as the ratio of sum of middle numbers present in the data. Mode is defined as the most recurring number present in the data. Midrange is the ratio of the largest and smallest number in the data to 2.

Let's see how to calculate Mean, Median, Mode and Midrange.

Mean = 13 + 15 + 18 + 18 + 21 / 5

Mean = 85 / 5

Mean = 17

Median = 18 (as it is the middle term of the data)

Mode = 18 (as it is most recurring number)

Midrange = 21 + 13 / 2

Midrange = 34 / 2

Midrange = 17

Therefore, The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

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The triangles are similar by the sas similarity theorem.

The similarity theorem for tri angles states that if two triangles have the same shape, then their corresponding angles are equal and their corresponding sides are proportional.

More specifically, if we have two triangles, Triangle ABC and Triangle DEF, such that:

Angle A = Angle D

Angle B = Angle E

Angle C = Angle F

And also, their corresponding sides are proportional:

AB/DE = BC/EF = AC/DF

Then, we can say that Triangle ABC is similar to Triangle DEF. This means that these two triangles have the same shape and they are only different in size.

The similarity theorem is important in geometry, as it allows us to determine unknown side lengths or angle measures of similar triangles by using proportions. It is also useful in real-life situations where we need to determine the size of objects that are not directly measurable

To prove that two triangles are similar using the SAS (Side-Angle-Side) similarity theorem, you need to show that:

Two pairs of corresponding sides are proportional (have the same ratio).

The included angles (the angle between these two pairs of corresponding sides) are congruent.

So, for the SAS similarity theorem to apply, you need to have two triangles where two pairs of corresponding sides are proportional and the included angle between these sides is congruent. If these conditions are met, then the triangles are similar.

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The required it would take 6 years for the amount to be 2000000.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.

here,

Celestine invested 1500000 simple interest at a rate of 5% per annum which amounted to 2000000.

Amount = 20,000,00
Principal = 15,000,00
Rate = 5% = 0.05

Time =  n years

Amount  = Principal [1 + rate×time]
20,000,00 = 15,000,00 [1 + 0.05×n]
n = 6.6 years

Thus, the required, it would take 6 years for the amount to be 2000000.

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Answer:

I'm sorry i cant help you rn, download symbolab or math solver, I'm sure you will find your answer g

Answer:

D.

Step-by-step explanation:

To tell whether the domains can include 0, all you need to do is find where x = 0, and whether the y-value is real.

h(x) = sqrt(2x^2 + 5x - 3)

= sqrt(0^2 + 5 * 0 - 3)

= sqrt(-3)

Since this includes the square root of a negative number, h(0) is an imaginary number. That means that we can eliminate choices A and B.

If you look at the graph of w(x), when x = 0, there is a real value for the y-value on the graph. But, if you think about it, if you have 0 workers, there is no way that you can still be producing wrenches. So, the domain cannot contain 0.

Your answer will be D.

Hope this helps!!

Answer:

Domain: { -4,-3,0,2,3}

Step-by-step explanation:

The domain is the input values

The range is the output values

Domain: { -4,-3,0,2,3}

No, the relationship on the table is not proportional

From the question, we have the following parameters that can be used in our computation:

x   y

____ ____

6 -2

7 -1

8 0

9  1

On the table of values, we can see that:

Using the above as a guide, we have the following:

The relationship is not a proportional relationship

This is so because it does not have a constant rate (addition of 1 to x and y does not represent proportional relationship)

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Answer:

Step-by-step explanation:

Corresponding sides of these triangles are proportional, so you have ...

  x/5 = 20/x

  x² = 5·20 . . . . . . . cross multiply

  x = √100 = 10

and ...

  y/15 = 5/y

  y² = 15·5 . . . . . . cross multiply

  y = √75 ≈ 8.7
_____

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Answer:

$80

Step-by-step explanation:

400 times 20%= 80

400-80= 320

the cost of the computer on the weekend costed 320, so you save $80

Answer:

80$

Step-by-step explanation:

The length of a pendulum that makes one full swing in 1.9 seconds is 3 feet.

As per the given data, the given formula is:

\($T=2 \pi \sqrt{\left(\frac{L}{32}\right)}\) gives the time it takes in seconds.

Where,

T is the time it takes for a pendulum to make one full swing back and forth (in seconds).

L is the length of the pendulum, in feet.

Here we need to find the length of a pendulum that makes one full swing in 1.9 seconds to the nearest foot.

Substitute the given parameters into the formula will give;

\($1.9=2 \pi \sqrt{\left(\frac{L}{32}\right)}\)

Now divide both sides by 2π.

\($ \frac{1.9}{2 \pi}=\sqrt{\left(\frac{L}{32}\right)} \\\)

\($ 0.3024=\sqrt{\left(\frac{L}{32}\right)}\)

Then taking square on both sides.

\($ (0.3024)^2=\frac{L}{32} \\\)

0.09144576 = \($\frac{L}{32}\)

Later multiply both sides by 32.

2.9262 = L

The approximate value of the length of a pendulum:

L ≈ 3

Therefore, the length of a pendulum is about 3 feet.

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Gianna is 90 miles far away in 3 hours of driving.

She drove in total of 180 minutes.

The speed can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s.

Given,

Gianna drives 5 miles in 10 minutes

Speed per minute = 5/10 = 0.5 miles/minute

Gianna drove in total for 3 hours

1 hour = 60 minutes

3 hours = 60 × 3 = 180 minutes

Distance Gianna drove in 180 minutes = speed per minute × time

                                                                = 0.5 × 180

                                                                = 90 miles

Hence, Gianna drove 90 miles in 3 hours, 180 minutes is total time she drove.

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Answer:

mean:4.4

median:8

mode:8 & 6

range;50

Step-by-step explanation:

mean=sum/total

mean= -4 + -10 + 6 + 11 + -16 + 8 + -7 + 8 + 34 + 6/10

mean= 4.4

mode=most occuring number

mode= 8 & 6

median: arrange the data in ascending or descending order

median:-16,-10,-7,-4,8,8,6,6,11,34: in ascending order

median:8+8/2

median :16/2

median: 8

Range: highest value- lowest value

range:34-(-16)

range:50

The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

To determine the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.

Preferred Stock:

Dividends per share of preferred stock = Total dividends for preferred stock / Number of preferred shares

Year 1:

Dividends per share of preferred stock for Year 1 = $50,000 / 40,000 shares = $1.25

Year 2:

Dividends per share of preferred stock for Year 2 = $90,000 / 40,000 shares = $2.25

Year 3:

Dividends per share of preferred stock for Year 3 = $130,000 / 40,000 shares = $3.25

Common Stock:

Dividends per share of common stock = Total dividends for common stock / Number of common shares

Year 1:

Dividends per share of common stock for Year 1 = ($50,000 - Total dividends for preferred stock) / 100,000 shares = ($50,000 - $50,000) / 100,000 shares = $0

Year 2:

Dividends per share of common stock for Year 2 = ($90,000 - Total dividends for preferred stock) / 100,000 shares = ($90,000 - $90,000) / 100,000 shares = $0

Year 3:

Dividends per share of common stock for Year 3 = ($130,000 - Total dividends for preferred stock) / 100,000 shares = ($130,000 - $130,000) / 100,000 shares = $0

The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:

Step-by-step explanation:

a. Let x be the number of correct answers and y be the number of incorrect answers. Then we have the equation:

3x - y = 82

b. Let z be the total number of questions on the test. Then we have the equation:

x + y = z

or, equivalently,

y = z - x

c. To solve this system of equations by graphing, we can rewrite each equation in slope-intercept form:

3x - y = 82

y = 3x - 82

x + y = z

y = -x + z

We can graph each equation on the same coordinate plane and find the point where the two lines intersect. This point represents the values of x, y, and z that satisfy both equations.

The graph of y = 3x - 82 is a line with a y-intercept of -82 and a slope of 3.

The graph of y = -x + z is a line with a y-intercept of z and a slope of -1.

To graph the system of equations, we can plot the y-intercepts of each line on the y-axis and use the slope to plot additional points. We then connect these points to form the lines.

For example, if z = 50, then the graph of y = -x + 50 would look like:

|

50|   /

 |  /  

 | /  

 |/    

0|------

 |      

To graph the line y = 3x - 82, we can plot the y-intercept of -82 and use the slope of 3 to plot additional points. For example, if x = 0, then y = -82 + 3(0) = -82. So one point on the line is (0, -82). If x = 10, then y = -82 + 3(10) = -52. So another point on the line is (10, -52). We can connect these points to form the line:

|

50|    

 |    

 |    

 |    

 |   /

 |  /  

 | /  

 |/    

0|------/------

 |   /  

    10

The intersection of the two lines is approximately (27, 23), which means Reggie answered 27 questions correctly and 23 questions incorrectly, for a total of 50 questions. We can check that this solution satisfies both equations:

3x - y = 82 becomes 3(27) - 23 = 81, which is close to 82 (due to rounding).

x + y = 50 becomes 27 + 23 = 50, which is true.

Therefore, the solution (x,y,z) = (27, 23, 50) satisfies the system of equations.

Answer:

11. (a) 3/4+1/2=5/4

   (b) 4/5= 8/10 , 16/20

12. 8 children don't like choc ice cream

Step-by-step explanation:

11. 3/4 +2/4=5/4(change 1/2 by making it the same as the one next to it)

12. 3/5 of 20 = 12

     20-12=8

The difference between the selling price and the cost price is the profit he earned.

Profit = Selling Price - Cost Price

Profit = $216 - $180

Profit = $36

To find the percentage profit, we need to calculate what proportion of the cost price the profit represents, and express that as a percentage :

Percentage Profit = (Profit : Cost Price) * 100%

Percentage Profit = ($36 : $180) * 100%

Percentage Profit = 0.2 * 100%

Percentage Profit = 20%

Therefore, his percentage profit is 20%.

Answer:

A

Step-by-step explanation:

5 - \(\frac{3}{2}\) x ≥ \(\frac{1}{3}\)

multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions

30 - 9x ≥ 2 ( subtract 30 from both sides )

- 9x ≥ - 28

divide both sides by - 9 , reversing the symbol as a result of dividing by a negative quantity.

x ≤ \(\frac{28}{9}\)

Answer:

option A

Step-by-step explanation:

because it is non terminating repeating number, hence its rational

Answer:

1cm:20cm

Step-by-step explanation:

10cm:2m

1m=100cm

10cm:200cm

÷10

1cm:20cm

A system of the equation to be Dependent Consistent System the system must have multiple solutions. The correct option is C.

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

For the system of equations to have infinite number of solutions, the lines of the equations must coincide, therefore, the line must overlap on each other.

For the lines to overlap the equations must be in a ratio. Therefore, the ratio of the left sides of the equations must be equal to the right side,

\(\dfrac{35x+14y}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac{7(5x+2y)}{5x+2y} = \dfrac{119}{k}\\\\\\\dfrac71 = \dfrac{119}{k}\\\\k = 17\)

Hence, the value of k must be 17, therefore, the correct option is C.

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Step-by-step explanation:

speed=distance÷time

A.V.S=440÷11=40m/s

hope it helps.. Please mark brainliest.

Answer:

40 m/s

Step-by-step explanation:

Find:

We are asked to find the unit rate, How many meters per 1 second?

Know:

440 meters in 11 seconds

Solve:

440 meters in 11 seconds

  ? meters in 1 second

   440/11  = 40 meters per second

Answer:

The average speed of the person is 40 m/s