y is directly proportional to the square of x. find the percentage increase when x is increased by 5%

Answer:

15 = 9 + j

Step-by-step explanation:

"15 is 9 more than j"

"15 is"  may be written as "15 ="

"9 more than j" may be written as "9+j"

Put these two expression together:

15 = 9 + j

Answer:

See below

Step-by-step explanation:

A) If [tex]DF\cong GH[/tex], then both triangles will be congruent by the ASA postulate

B) If [tex]DE\cong GI[/tex], in addition to one of the corresponding leg pairs being congruent to each other (so EF+IH or DF+GH), then the triangles will be congruent by the HL theorem

The required value of x and y in the given equation are ,

x= 1,

y = -1 .

The algebraic method to solving simultaneous linear equations is known as substitution method. This method, as the name suggests, involves substituting the value of one variable from one equation into the second equation. This makes it much easier to answer a pair of linear equations by combining them into a single linear equation with only one variable.

The given equations are

0.1x - 0.3y = 0.4                             ...(1)

0.3x − 0.2y=0.5                              ....(2)

Multiply both the equations by 10, we get

x - 3y = 4                                           ...(1)

3x − 2y = 5                                        ...(2)

Multiply (1) by 3

3x - 9y = 12

3x − 2y = 5

Subtracting both the equations

-7y = 7

y = -1

From (1):

x - 3(-1) = 4

x + 3 = 4

x = 4 - 3

x = 1

The required value for x and y is,

x= 1,

y = -1

Learn more about Substitution method , visit:

https://brainly.com/question/14619835

#SPJ1

Answer:

a) Algebraic expression for new area =  (x + 5)(x - 5 )

b) New area will be 25 square meters less than old area

Step-by-step explanation:

Lena' s square garden with side x has area x times x or x² square meters

If one side is lengthened by 5 meters that side becomes x + 5 meters

If the other side is shortened by 5 meters that side becomes x - 5 meters

New area = (x + 5)(x - 5 )

Using the identity(a + b)(a - b) = a² - b² we get

(x + 5)(x - 5 ) =x² - 5²

= x² - 25

Area difference square - rectangle =
x² - (x² - 25) = x² - x² + 25

= 25

So the area will decrease  by 25 square meters

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x + 15 < 10 – 5x, which can be simplified to x < 5

and

-6x – 5 < 10 – x, which can be simplified to -5x < 15, and then x > -3

Therefore, the correct options are:

x < 5

A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

The height of the silo is approximately 81 meters to the nearest meter.

One of the most basic areas of mathematics, trigonometry has a wide range of applications. The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry."

Let's draw a diagram to visualize the situation. We have a right triangle with the transit (T), the silo (S), and a point on the ground (G) where the surveyor is standing. The angle of elevation of the silo from the surveyor's position is 52º, and we know the distance TG = 65 m and the height of the transit HT = 1.7 m. We want to find the height of the silo, which is HS.

          S

          |\

          | \

    HS |  \  TG = 65 m

          |   \

          |    \

          |     \

          |      \

          |       \

          |        \

          T--------G

             HT = 1.7 m

Using trigonometry, we have the following equation:

tan(52º) = HS / TG + HT

Solving for HS, we get:

HS = (TG + HT) * tan(52º)

= (65 + 1.7) * tan(52º)

≈ 81.1 m

Therefore, the height of the silo is approximately 81 meters to the nearest meter.

Learn more about Trigonometry, visit:

https://brainly.com/question/11016599

#SPJ1

For someone earning $75,000 per year working 24 hours daily, their equivalent hourly wage would be approximately $8.56 per hour.

If someone worked 24 hours a day, every day of the year, they would work a total of 8,760 hours in a year. To calculate the hourly wage of someone earning $75,000 per year working 24 hours daily, you can divide the yearly salary by the total number of hours worked in a year.

Dividing $75,000 by 8,760 hours gives an hourly wage of approximately $8.56. This means that if someone earned $75,000 per year while working 24 hours a day, they would be earning an equivalent of approximately $8.56 per hour.

Additionally, laws and regulations related to working hours vary by country and industry, and many limit the maximum number of working hours per day or week.

To learn more about time click on,

https://brainly.com/question/13853507

#SPJ4

Answer:

  65 cm

Step-by-step explanation:

You want the perimeter of the shape that results from removing a 60° sector from a circle.

The curved edge of the shape is 5/6 of the circumference of the circle.

  5/6C = 5/6(2πr) = 5/6·2·π·(9 cm) = 15π cm ≈ 47 cm

Each straight edge of the shape has a length equal to the radius. Then the straight edges have a total length of ...

  2r = 2(9 cm) = 18 cm

The perimeter of the shape is the sum of the length of its curved edge and the lengths of the straight edges:

  P = 47 cm + 18 cm = 65 cm

The perimeter is about 65 cm.

__

Additional comment

A total circle is 360°, so 1/6 of the circle is 60°. The size of a sector of a circle can be described by the angle measure of its central angle. Here, that means the removed portion is a 60° sector.

The length of DE is 12 unit.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

In Triangle DFC using Trigonometry

sin 45 = B/ H

1/ √2 = DF / 12√2

DF = 12 unit

So, DE= DF + FE

DE = 12 + 9

DE = 12 unit.

Learn more about Trigonometry here:

https://brainly.com/question/29002217

#SPJ1

The average rate of change of the total cost as his shirt production increases from 10 to 20 is 150.

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing.

Given that, the total cost to produce by James shirts is represented by a function, f(x) = 5x²+6.

We are to find the average rate of change of the total cost as his shirt production increases from 10 to 20.

The average rate of change is given by =

f(b) - f(a) / b-a, where a and b are given intervals,

Here, we have, a = 10 and b = 20

f(b) = 5(20)²+6 = 2006

f(a) = 5(10)²+6 = 506

The rate of change =

2006 - 506 / 20-10

= 1500 / 10

= 150

Hence, the average rate of change of the total cost as his shirt production increases from 10 to 20 is 150.

Learn more about average rate of change, click;

https://brainly.com/question/23715190

#SPJ1

Answer:

Part A: The most appropriate design for this investigation would be an experiment. An experiment is the best choice because it allows the teacher to compare the two erasers under the same conditions, which will make it easier to determine if the new eraser reduces paper tears.

Part B: To implement the design, the teacher can set up an experiment by dividing a group of students into two groups. Each group should use the same type and amount of paper, and be given instructions to erase the same number of mistakes. One group should then use the current popular brand of eraser, while the other group should use the new eraser. After the test is completed, the teacher can count the number of paper tears in each group and compare the results.

Part C: One benefit of this design is that the results are more likely to be objective and reliable. By having a controlled experiment, the teacher can be sure that any differences observed are due to the erasers, and not any other factors.

The values of x that satisfy the equation p(−x ≤ t22 ≤ x) = 0.98 are all values between -2.518 and 2.518, inclusive.

The expression p(- x ≤ t22 ≤ x) represents the probability of a t-distribution with 22 degrees of freedom lying between - x and x.

We want to find the values of x such that this probability is 0.98.

We can use a table of t-distribution probabilities or a calculator to find the value of t for which the probability of a t-distribution with 22 degrees of freedom lying between −t and t is 0.98.

This value is , 2.518.

Therefore, we need to solve the inequalities:

-2.518 ≤ -x ≤ 2.518

Solving for x, we get:

-2.518 ≤ -x x ≤ 2.518

Therefore, the values of x that satisfy the equation p(−x ≤ t22 ≤ x) = 0.98 are all values between -2.518 and 2.518, inclusive.

Learn more about the inequality visit:

https://brainly.com/question/25944814

#SPJ12

P(A and B) = P(A) × P(B) is the formula used to assess if two events are independent (B).

P(A) is the chance that event A will occur.

The chance that event B will occur is marked as P(B).

If the chance of both occurrences happening at the same time, P (A and B), equals the product of the individual probabilities of each event, P(A) x P(B), the events are called independent.

If, on the other hand, the chance of both occurrences occurring simultaneously is less than the product of the individual probabilities of each event, the events are deemed dependent.

Learn more about the independent events at

https://brainly.com/question/12619550

#SPJ4

The two lines that are parallel to y = 2x - 1 that pass through the given points are:

a) y = 2x + 1

b) y = 2x

A general linear equation is written in the slope-intercept form as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Two lines are parallel if the slopes are equal but the y-intercepts are different.

So, here we want to find lines parallel to:

y = 2x - 1

These lines have the form:

y = 2x + b

a) If we want our line to pass thrugh A(0,1), we can replace the values of the point to get:

1 = 2*0 + b

1  = b

So the line is y = 2x + 1

b) if we want the line to pass through A(1,2) we can replace the values to get:

2 = 2*1 + b

2 = 2 + b

2 - 2 = b

0  =b

So this line is:

y = 2x

Learn more about linear equations at:

Answer: 11.3 or 11 if you are to round to nearest whole number.

Step-by-step explanation:

Take the problem step by step.

You know she has the monthly fee and a fee for each gigabyte of data she stores in her house.

Take how much she paid and Subtract the monthly fee from it since it has been a month.

$60.95 - $14.95 = $36

Now take that answer and divide it by the cost of each gigabyte to see how many she used that month.

$65 / $5.75 = 11.30434743, which rounds to 11.3 or 11 if you are to round to nearest whole number.

Liam has 19 chairs.

Let x be the number of chairs Liam has.

According to the problem, x = 4a + 3 and x = 2b + 19 for some integers a and b.

Equating these two expressions, we get:

4a + 3 = 2b + 19

4a - 2b = 16

2a - b = 8

Therefore, b = 2a - 8.

Substituting this expression for b into x = 2b + 19, we get:

x = 4a + 35

Now, since x = 4a + 3, we have:

4a + 3 = 4a + 35 - 32

Therefore, x = 4a + 35 = 2(2a + 4) + 3 = 2b + 19, where a = 4 and b = 11.

Thus, Liam has x = 4a + 3 = 4(4) + 3 = 19 chairs.

The solution to this problem involves the use of two key mathematical concepts: algebraic equations and systems of equations.

We are given two equations in terms of the same variable x, each representing a different way of arranging chairs. By setting these two equations equal to each other, we obtain an equation in terms of x that allows us to find a value of x that satisfies both of the original equations simultaneously. This process of setting two equations equal to each other is an example of solving a system of equations.

To solve the resulting equation, we use algebraic manipulation to isolate the variable x on one side of the equation. This involves a combination of simplification, substitution, and rearrangement of terms. Ultimately, we arrive at a specific value of x that satisfies both equations, which is the answer to the problem.

To know more about system of equations visit :

https://brainly.com/question/12526075

#SPJ1

Answer:

B) 5

Step-by-step explanation:

   AB = 4 units

  BC = 3 units

Use Pythagorean theorem to find the length of AC,

                AC² = AB² + BC²

                      = 4² + 3²

                       = 16 + 9

                       = 25

                  [tex]AC = \sqrt{25}\\\\[/tex]

                 AC = 5 units

The area of the shaded region is 64(1 - π) cm².

The area of a semicircle is -

A = πr²/2

Given is a 2 - D figure as shown in the image.

We can write the area of the shaded region as -

A{shaded} = A{square} - 2 x A{semicircles}

A{shaded} = 64 - 2 x 1/2 x π x (8)²

A{shaded} = 64 - 64π

A{shaded} = 64(1 - π)

Therefore, the area of the shaded region is 64(1 - π) cm².

To solve more questions on area & volumes, visit the link

below -

brainly.com/question/29014197

#SPJ1

{Question in english -

Calculate the shaded area of ​​each of the

figures presented below.}

Answer: Let's use algebra to solve this problem.

Let C be Clot's present age and S be Soup's present age. Then, according to the problem:

One year ago, Clot was C-1 years old, and four times Soup's age at that time was 4(S-1).

Clot's age one year ago was one-third of four times Soup's age, so we have:

C - 1 = (1/3) * 4(S - 1)

Simplifying this equation, we get:

C - 1 = (4/3)(S - 1)

C = (4/3)(S - 1) + 1

One year from now, Clot will be C + 1 years old, and Soup will be S + 1 years old. The sum of their ages will be 21, so we have:

(C + 1) + (S + 1) = 21

C + S + 2 = 21

C + S = 19

Now we have two equations with two unknowns. We can substitute the expression for C from the first equation into the second equation to get an equation in terms of S:

(4/3)(S - 1) + 1 + S = 19

Simplifying and solving for S, we get:

S = 6

Substituting S = 6 into the equation C + S = 19, we get:

C + 6 = 19

C = 13

Therefore, Clot's present age is 13 and Soup's present age is 6.

Step-by-step explanation:

The probability that a piece selected at random and is defective given that it is known to be a plate is 0.0588 or 5.88%.

To calculate the probability, we need to use Bayes' theorem: P(defective|plate) = P(plate|defective) * P(defective) / P(plate).

Therefore, P(defective|plate) = 0.2 * 0.0227 / 0.0818 = 0.0588 or 5.88%.

The probability that a cup will be chosen given that it is defective is 0.4 or 40%.

To calculate the probability, we need to use the information given in the table:

Divide the number of defective cups by the total number of defective products: 10/25 = 0.4 or 40%.

Learn more about Probability:

https://brainly.com/question/24756209

#SPJ4

Complete Question:

The following table shows the relationship of 1100 pieces between good and defective made in a ceramic workshop

cup plate vase total

Good 830 85 1415

Defective 10 5

Overall 510 90

What is the probability that a piece is selected at random and is defective given that it is known to be a plate?

What is the probability that a cup will be chosen given that it is defective?

​

Answer:

Gram.

Step-by-step explanation:

The number of years will take for his money to double is 10.87 years

Let's assume the amount of money Latrell needs to buy the car "P". Since Latrell only has half of that amount, we can say that he has 0.5P. We want to find out how long it will take for Latrell's money to double, so we want to solve for the time "t" in years.

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = final amount of money (in this case, 2P, since we want to find out how long it takes for Latrell's money to double)

P = initial amount of money (0.5P, since that's what Latrell has now)

r = annual interest rate (6.3%)

n = number of times the interest is compounded per year (4, since it's compounded quarterly)

t = time (in years)

Substituting in the values we know, we get:

2P = 0.5P(1 + 0.063/4)^(4t)

Simplifying, we can divide both sides by 0.5P:

4 = (1 + 0.063/4)^(4t)

Taking the natural logarithm of both sides, we get:

ln(4) = 4t ln(1 + 0.063/4)

Dividing both sides by 4 ln(1 + 0.063/4), we get:

t = ln(4) / (4 ln(1 + 0.063/4))

t ≈ 10.87 years

Learn more about compound interest here

brainly.com/question/29189437

#SPJ4

(a) Here's a tree diagram for the sample space of all dinner combinations:

               Fish

          /      |      \

        /        |        \

    Salmon    Trout    Halibut

    / | \      / | \      / | \

 Fries Carrots Coleslaw  Fries Carrots Coleslaw

(b) To determine the total number of dinner combinations, we can multiply the number of fish options by the number of side dish options:

3 fish options * 3 side dish options = 9 dinner combinations

Therefore, Javier has 9 choices for dinner combinations.

Read more about tree diagram here:

https://brainly.com/question/24391505

#SPJ1

For dinner, Javier will choose one of three fish options and one of three side dishes. His choices for fish are salmon, trout, and halibut. His choices for side dishes are fries, cooked carrots, or coleslaw.

(a)Draw a tree diagram for the sample space of all dinner combinations.

(b)How many choices for dinner combinations does Javier have?

Answer:

we can conclude that Ariel takes approximately 0.5233 pages of notes per hour of class.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To find the number of pages of notes Ariel takes during an hour of class, we need to calculate her average rate of note-taking per hour of class for each of the two periods and then find the overall average rate.

For the first period:

Average rate of note-taking = Total pages of notes taken / Total hours of class

Average rate of note-taking = 18 pages / 34.4 hours

Average rate of note-taking = 0.5233 pages per hour (rounded to four decimal places)

For the second period:

Average rate of note-taking = Total pages of notes taken / Total hours of class

Average rate of note-taking = 45 pages / 86 hours

Average rate of note-taking = 0.5233 pages per hour (rounded to four decimal places)

Notice that the two average rates of note-taking are the same. This means that Ariel takes an average of 0.5233 pages of notes per hour of class, regardless of the specific period.

Therefore, we can conclude that Ariel takes approximately 0.5233 pages of notes per hour of class.

To learn more about Algebraic expression from given link.

brainly.com/question/953809

#SPJ1

The  converted value from Celsius to Fahrenheit is given by 39 Celsius is equal to 102.2 Fahrenheit.

Units represents the measure of the temperature in standard form Celsius and Fahrenheit .

Formula relates the Celsius and Fahrenheit are equal to

(°C × 9/5) + 32 =°F

Now, Substitute the value 39 Celsius which required to convert  into Fahrenheit we have,

(39°C × 9/5) + 32

= ( 351 / 5 ) + 32

= ( 70.2 ) + 32

= 102.2°F

Therefore, the converted value from Celsius to Fahrenheit for the given 39 Celsius is given by 102.2 Fahrenheit.

Learn more about Celsius here

brainly.com/question/28880099

#SPJ4

The above question is incomplete, the complete question is:

What is the conversion of 39 degrees Celsius to °F ?

Another name for the regression line is the least squares line because it was chosen to make the sum of the squares of the differences between the observed y values ​​and the values ​​predicted by the line as small as possible.

A regression line (LSRL - Least Squares Regression Line) is a straight line that describes how the response variable y changes when the explanatory variable x changes. The line is the mathematical model used to predict the value of y for a given x.

Least squares is a form of mathematical regression analysis used to determine the line of best fit for a data set, providing a visual demonstration of the relationship between data points. Each data point represents the relationship between a known independent variable and an unknown dependent variable.

If the data shows a weak relationship between two variables, the line that best fits this linear relationship is called a least-squares regression line, and it minimizes the vertical distance of the data points from the regression line. The term "least squares" is used because it is the minimum of the sum of squared errors, also known as "variance". In regression analysis, the dependent variable is shown on the vertical y-axis and the independent variable is shown on the horizontal x-axis. These specifications form the equation for the line of best fit, which is determined by the method of least squares.

Learn more about Least square line:

https://brainly.com/question/30044885

#SPJ4

The FRF method is a common technique for analyzing the dynamics of structures and systems, it is typically not used as a primary method for determining a system damping ratio by field measurements.

for such more question on damping ratio

https://brainly.com/question/20115234

#SPJ4

Answer: 20

Step-by-step explanation: The volume formula for a rectangular pyramid is [tex]\frac{lwh}{3}[/tex] so the initial volume would be 540. Since you are dilating it by 1/3 the length, with, and height are all shrinking by 1/3. 1/3*1/3*1/3 is 1/27 so that means the final thing will be 1/27 of its original size.

Answer:

So, first let's understand what a scale factor is. A scale factor is a number that tells you how much you need to multiply the size of an object to make it bigger or smaller. In this case, the scale factor is 1/3, which means we're going to make the pyramid one third of its original size.

Now, let's talk about how we can find the volume of the pyramid. The formula for the volume of a pyramid is:

Volume = (1/3) x base area x height

The base area is the area of the rectangle at the bottom of the pyramid, which we can find by multiplying the length and width:

Base area = 9 cm x 12 cm = 108 square cm

The height of the pyramid is given as 15 cm, so we can substitute these values into the formula:

Volume = (1/3) x 108 square cm x 15 cm

Volume = 540 cubic cm

So the volume of the original pyramid is 540 cubic cm. But we need to find the volume of the pyramid after it is dilated by a scale factor of 1/3. To do this, we need to multiply the original volume by the scale factor cubed. The reason we cube the scale factor is because we're scaling in three dimensions (length, width, and height).

Scale factor cubed = (1/3) x (1/3) x (1/3) = 1/27

Volume of dilated pyramid = 540 cubic cm x 1/27

Volume of dilated pyramid = 20 cubic cm (rounded to the nearest whole number)

So the volume of the pyramid after it is dilated by a scale factor of 1/3 is 20 cubic cm.

Answer:

The equation of the tangent line can be found using the formula y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line.

Step-by-step explanation:

The link represented by function g multiplies the dependent variable by 9 for every increase of 2 units in the independent variable. The equation that represents g is [tex]g(x)= 2 \times3^x[/tex],and the function has a value of 2 at 0

Let x be the independent variable, and let g(x) be the dependent variable.

According to the problem, for every 2 units the independent variable increases, the dependent variable is multiplied by 9. This suggests an exponential relationship of the form:

 [tex]g(x)= a \times b^x[/tex]

where a is the initial value of the dependent variable (when x=0), and b is the growth factor (how much the dependent variable changes for every unit increase in x).

We are given that g(0) = 2, so we can plug in these values and solve for a:

 [tex]g(0)= a \times b^0[/tex]

a = 2

So now we have:

[tex]g(x)= 2 \times b^x[/tex]

We still need to find the growth factor b. We are told that the dependent variable is multiplied by 9 for every 2 units the independent variable increases. In other words:

[tex]g(x+2) = 9 \times g(x)[/tex]

Using our equation for g(x), we can substitute in and simplify:

  [tex]2 \times b(x+2) = 9 \times 2\times b^x[/tex]

Simplifying, we get:

[tex]b^2[/tex] = 9

Taking the square root of both sides (we take the positive square root since b must be positive in order for g to be an increasing function), we get:

b = 3

So the final equation for g(x) is:

[tex]g(x) = 2 \times 3^x[/tex]

For more such questions on variable

https://brainly.com/question/25223322

#SPJ4