What is the expression represent of the area of this rectangle?

Lines l and m are parallel; line l will map onto line m with a 90° rotation; line l can map onto line m with a vertical line of reflection.

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The value of x is a counter example to the student's conjecture (x = 2).

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that x is a non-negative number, a student conjectured that x + 4 < x².

Since x is a non-negative number, A and B are eliminated.

This leaves C and D at the value of x = 2,

2 + 4 < 2²

6 < 4 is false.

Therefore, the value of x is a counterexample to the student's conjecture (x = 2).

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The common statistical method of expressing the precision of a series of repetitive measurements is the standard deviation.

It should be noted that the standard deviation is the measure of how dispersed the data is in relation to the mean.

It should be noted low standard deviation implies that data are clustered around the mean, and high standard deviation means data are more spread out.

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The orthocenter of the ΔABC is ( -1,5 ).

In a right triangle, the orthocenter is the polygonal vertex of the right angle. When the triangle's vertices and orthocenter are joined, any point becomes the orthocenter of the other three points, according to Carnot (Wells 1991). These four locations thus form an orthocentric system.

Given the  co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

To find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y = mx + b

where m is the slope and b is the y-intercept.

Using the formula of slope given \($m =\frac{y_2 - y_1}{x_2 - x_1}\)  , we will find the slope of AB and BC.

Now, slope of AB is m = (7-3/-1 + 3)  

i.e. m = (4/2) = 2

Putting this 'm' in the general form and using the point B(-1, 1), we get the y-intercept as,

y = mx + b

1 = 2 × (-1) + b

i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is m=(3-7/3+1)  i.e. m=-4/4 i.e. m--1

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is \(m*2=-1\)  i.e. m = -1/2

So, slope of line perpendicular to BC is  i.e.\(m*-1=-1\) i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB m=-1/2 i.e.  and the point opposite to AB

i.e. C(3, 3), we get,

y = mx + b

i.e. \(3=-1/2*3+b\)  

i.e. b = 9/2

So, the equation of line perpendicular to AB is

\(y=-x/2+9/2\)

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC

i.e. A( -3,3 ), we get,

y = mx + b

i.e. 3 = 1 × -3 + b

i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of (x, y).

As, we have y = x + 6 and  y = -x/2 + 9/2

This gives, y = -x/2 + 9/2 → x + 6

y = -x/2 + 9/2

simplifying the above equation, we get

2x + 12 = -x + 9

3x = -3

x = -1.

So, y = x + 6

simplifying the above equation, we get

y = -1 + 6

y = 5.

The value of x = -1 and y = 5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

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Answer:Yea looks like you have it already C

Step-by-step explanation:

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

Given,

The cost of Carpet per square foot = $4

Total cost of the carpet = $616

We know

Area of the rectangle = Length × Width

Length = 14 feet

Consider the width of the rectangular room as x

Then the area of the room = 14x

Total cost of carpet = Area of the rectangular room× Cost of carpet per foot

Substitute the values

14x×4=616

14x=154

x=11 feet

Hence, When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

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A decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.

If the price of cotton falls in the market for a bag of socks, it is likely to have an impact on the overall cost and availability of socks. Cotton is a common material used in the production of socks, and its price plays a significant role in determining the cost of manufacturing.

When the price of cotton falls, it reduces the cost of raw materials for sock manufacturers. As a result, manufacturers may experience lower production costs. This can lead to several outcomes:

1. Decrease in sock prices: With lower production costs, manufacturers have the option to reduce the prices of socks to attract customers. This can result in more affordable socks for consumers, making them more accessible.

2. Increase in sock supply: Lower production costs may incentivize manufacturers to increase their sock production. As a result, the supply of socks in the market could rise, leading to a greater availability of socks for consumers.

3. Potential for improved quality or additional features: Manufacturers may choose to invest the cost savings from lower cotton prices into enhancing the quality of socks or adding extra features. This can result in socks with improved durability, comfort, or design, providing more options for consumers.

It's important to note that the impact of falling cotton prices on sock prices and availability may also depend on other factors, such as production and distribution costs, market competition, and consumer demand. Additionally, the extent to which the price reduction in cotton translates into lower sock prices may vary among different brands and retailers.

Overall, a decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.

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The length of HI is given as follows:

HI = 15.

Two triangles are defined as similar triangles when they share these two features listed as follows:

The proportional relationship for the side lengths in this problem is given as follows:

3/HI = 5/25

Applying cross multiplication, the length of HI is given as follows:

3/HI = 1/5

HI = 3 x 5

HI = 15.

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Step-by-step explanation:

(x² /x² + 7x + 6)÷(9x - 9/x² - 1)

(x²/(x + 1)(x + 6))×((x + 1)(x - 1)/9(x - 1))

(x²/(x + 6))×1/9

x²/9(x + 6)

On solving the provided question, we can say that  - he need 56  answers he need to get correct if he want a grade of 80 percent on a test with 70 questions

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.

Assuming that all of the questions are equally weighted, 56 is equal to 80% of 70. (.80)(70)=56

Therefore, 56 out of 70 is the lowest number you may get correct, or 80%.

\(70-56=14\)

So, the maximum number of questions you may omit is 14.

As an alternative, if you desire 80% accuracy, you can have no more than 20% errors.

20% of 70 \(= .20)(70) = 14\)

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Answer:

AC = √105 ≈ 10 cm (nearest whole number)

Step-by-step explanation:

Use Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse of a right triangle)

Give one of the legs = 4cm and the hypotenuse = 11 cm:

⇒ 4² + AC² = 11²

⇒ 16 + AC² = 121

⇒ AC² = 121 - 16

⇒ AC² = 105

⇒ AC = ±√105

As distance is positive, length of AC = √105 ≈ 10 cm (nearest whole number)

Step-by-step explanation:

AB²=BC²+CA²

(11)²=(4)²+ CA²

121=16 + CA²

121-16= CA²

105=CA²

√105=CA

10.2=CA

hope this helps you

have a good day

Solution

Answer:

1300

Step-by-step explanation:

130×10 thats the answer yoo

Answer:

10%

Step-by-step explanation:

-The formula for simple interest is I = PRT

-P= Principle (amount of money invested), R= rate%, T= time in years

-I=PRT/100

-So I = 800 * 3% * (5/12)   (convert 5 months to years)

-I = 10%

i hope this helps<3

:)

The amount of interest she receives is $10.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Given that,

Amount invested or principal amount = $800

Rate of interest = 3% = 3/100 = 0.03

Period = 5 months = 5/12 year

Amount of interest obtained in a simple interest is calculated as,

Amount of interest = P R T

Here, P is the principal amount, R is the interest rate and T is the time in years.

Interest received = 800 × 0.03 × (5/12)

                            = 10

Hence the interest received is $10.

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Answer:

12x + 9.5y ≤ 220, x + y ≥ 220

Step-by-step explanation:

A collection of equations with the same variables is known as a system of equations. The only difference is that you're working with inequalities rather than equations in a system of inequalities.

What are inequalities?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

A system of equations has one solution for each variable, whereas a system of inequalities has a range of possible values for each variable.

Set up the equations as follows:

ax + by = c

dx +ey = f

Let the inequitable system exist:

ax + by <c

dx +ey > f

The same technique, such as graphing, substitution, and elimination, can be used to solve both systems.

But there's a difference because:

A system of equations can only have one solution for each variable, whereas a system of inequalities can have any number of solutions for each variable.

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Answer:

y=x-2,

so'n

y-x=2 answer you haven't write value.

Answer:

Note:  The expression "h =300- pi r /pi r" would equate to 299, as written.  I find h = (300 - π\(r^{2}\) )/πr to be the equation for height.

Step-by-step explanation:

The total surface area of a sylinder is 2πr(h+r) where h is the height and r is the radius.  That consists of top and bottom disks, each with an area of π\(r^{2}\), for a total of 2π\(r^{2}\).  The side is a  continous sheet that has an area of 2πrh, where h is the height.  2πr is the circumference of the can, so the surface area of the side is 2πrh.

The total surace area of a closed cylinder is therefore 2π\(r^{2}\) + 2πrh.

2π\(r^{2}\) + 2πrh = 600

π\(r^{2}\) + πrh = 300

πrh = 300 - π\(r^{2}\)

h = (300 - π\(r^{2}\) )/πr

No, the assertion made by your buddy is false. It is impossible to utilize the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate itself. You must employ known facts and theorems rather than the theorem you are attempting to show in order to prove a theorem.

If your buddy is utilizing the SSS congruence theorem (Thm. 5.8) and the parallelogram opposite sides theorem (Thm. 7.3) to demonstrate the theorem, they are not offering a proper proof since they are employing the theorem they are attempting to demonstrate as part of the proof itself. This results in a circular argument and is invalid as evidence

The parallelogram opposing sides theorem has to be proven using other well-known facts and theorems, like the definition of a parallelogram, the definition of congruent figures, and other relevant theorems and postulates from geometry.

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Answer:

Step-by-step explanation:

80 divided into 40 =2

Answer:

D

Step-by-step explanation:

u = 4 since 2u - 1 = 8 - 1 = 7

t = 3 since 5t + 1 = 15 + 1 = 16

and 7t - 5 = 21 - 5 = 16

Hope that helps!

A: \(3x^2y^4\cdot2x^6y=6x^8y^5\)

B: \(xz^3\cdot4x^4z^5=4x^5z^8\)

C: \(4a^3^2\cdot 3a^6b^5=12a^{15}b^5\)

D: \(6s^{5t}\cdot s^{4t}^2=6s^{16t^2+5t}\)

There was some ambiguity you posed with such exponents but I assumed strictly.

Hope this helps.

Answer:

5, 0.55, 2.00, 3 cm.

Step-by-step explanation:

If you're asking about the unit rates, then..

a. For 1 day, there is 5 mm of rain. 15 / 3 = 5

b. One chocolate bar costs $0.55. 2.20 / 4 = $0.55

c. $14.00 / 7 = 2.00 Indu saves $2.00 for one day.

d. 12 / 4 = 3 cm. For one month, philip grew 3 cm.

I hope this helped :)

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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In a simple regression model, the unexplained variation in the response variable is determined by summing the squares of errors. This method, known as residual sum of squares (RSS), quantifies the discrepancy between the observed values and the predicted values by the regression model.

In a simple regression model, the goal is to find a line that best fits the relationship between a single predictor variable (X) and a response variable (Y). However, due to various factors and sources of variability, the observed values of the response variable may not perfectly align with the predicted values based on the regression line.

The errors, or residuals, are the differences between the observed values and the predicted values. To quantify the unexplained variation, the errors are squared to eliminate negative values and emphasize larger deviations. These squared errors are then summed up, resulting in the residual sum of squares (RSS).

By calculating the RSS, one can assess the amount of unexplained variation or "error" in the regression model. A smaller RSS indicates that the model provides a better fit to the data, as it suggests less unexplained variation. On the other hand, a larger RSS implies a less accurate fit, with more unexplained variation in the model.

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The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

(621.49 x  0.1) + 13.99 = x

Step-by-step explanation:

I hope this helps