-10 is no less than two times a number +14

The maximum area of a rectangle with a perimeter of 100 cm is 624 cm². The breadth of a rectangle with a perimeter of 100 m and a length of 35 m is 15 m. The length of a rectangle with a breadth of 20 cm and a perimeter of 100 cm is 30 cm. The length of a rectangle whose perimeter and width are given is calculated using the perimeter formula.

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). In the rectangle, the opposite sides are equal and parallel.

Given the perimeter of the rectangle is 100 cm. Then,

\(\begin{aligned}P&=2(l+b)\\100&=2(l+b)\\(l+b)&=50\end{aligned}\)

We cannot consider length and breadth as equal because the length is always greater than the breadth in a rectangle. So assume the value of length as 26 cm and the breadth as 24 cm. Then, the area will be given as A = (a × b) square units.

Then, A = 26×24 = 624 cm². The answer is 624 cm².

b) Given the length of the rectangle is 35 m and the perimeter is 100 m. Then, breadth is

\(\begin{aligned}P&=2(l+b)\\100&=2(35+b)\\50&=35+b\\50-35&=b\\b&=15\end{aligned}\)

The answer is 15 m.

c) Given the breadth of the rectangle is 20 cm and the perimeter is 100 cm. Then, the length is

\(\begin{aligned}P&=2(l+b)\\100&=2(l+20)\\50&=20+l\\50-20&=l\\l&=30\end{aligned}\)

The answer is 30 cm.

d) By substituting the value of width or breadth and perimeter in the perimeter formula P=2(l+w), we can get the value of the length.

The complete question is -

What is the maximum area of a rectangle with a perimeter of 100 cm? What is the breadth of a rectangle if its perimeter is 100 m and its length is 35 m? What is the length of a rectangle whose breadth is 20 cm and whose perimeter is 100 cm? How do you find the length of a rectangle if the perimeter and width are given?

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Here is your answer.

A tank contains 5832 litres of water.

Total amount of water in tank = 5832 litres.

Each day one-third of the water in the tank is removed and not replaced.

Since one third of the water is removed for six days.

1st day = 1/3rd of 5832 litres is removed

\( = \dfrac{5832}{3} = 1944\)

Amount of water left = 5832 - 1944 = 3888 litres

2nd day = 1/3rd of 3888 litres is removed

\( = \dfrac{3888}{3} = 1296 \)

Amount of water left = 3888 - 1296 = 2592 litres

3rd day = 1/3rd of 2592 litres is removed

\( = \dfrac{2592}{3} = 864 \)

Amount of water left = 2592 - 864 = 1728 litres

4th day = 1/3rd of 1728 litres is removed

\( = \dfrac{1728}{3} = 576 \)

Amount of water left = 1728 - 576 = 1152 litres

5th day = 1/3rrd of 1152 litres is removed

\( = \dfrac{1152}{3} =384 \)

Amount of water left = 1152 - 384 = 768 litres

6th day = 1/3rrd of 768 litres is removed

\( = \dfrac{768}{3} = 256 \)

Amount of water left = 1768 - 256 = 512 litres

So, 512 litres water remains in the tank at the end of 6 days

Answer:

4/5, 3/6, 5/12

Step-by-step explanation:

4/5 = 0.8

3/6 = 0.5

5/12 = 0.4166666667

The length of the rectangle is 19.25 cm when it is 2 more than three times the width of 5.75 cm.

A perimeter is a closed path that encompasses, surrounds, or outlines a two-dimensional shape or length in one dimension. A circle's or an ellipse's circumference is its perimeter. There are several applications for calculating the perimeter. The length of fence required to encircle a yard or garden is known as the calculated perimeter.  

The perimeter (circumference) of a wheel/circle describes how far it can roll in one revolution.  Similarly, the amount of string wound around a spool is proportional to the perimeter of the spool; if the length of the string were exact, it would equal the perimeter.

Given that,

Perimeter = 2(l + b) = 50cm

And also given that,

l = 2 + 3b

Substituting the value of l in perimeter we get

2((2 + 3b) + b) = 50cm

2(2 + 4b) = 50cm

4 + 8b) = 50cm

8b = 50 - 4

b = 46/8

b = 5.75

Substituting the value of b in l, we get

l = 2 + 3(5.75)

l = 19.25

Therefore, the length of the rectangle is 19.25 cm when it is 2 more than three times the width of 5.75 cm.

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Answer:

Area

Step-by-step explanation:

got it right on the test :)

A triangular prism is a three-dimensional geometric shape that consists of two triangular bases and three rectangular faces connecting them. It is a polyhedron with six faces, nine edges, and six vertices.

The two triangular bases of a triangular prism are congruent and parallel to each other. The rectangular faces are perpendicular to the triangular bases, and their lateral edges connect the corresponding vertices of the triangular bases.

The triangular bases are identical and parallel to each other. Each base has three vertices, three edges, and one face.There are three rectangular lateral faces connecting the corresponding vertices of the triangular bases. Each lateral face has two edges and one face.

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Answer:  we move (5, 1/3) to (5-3, 1/3*3) = (2, 1)

Step-by-step explanation:

Answers: The correct answer choices are the second figure/graph, and y = x/2.

The length of 2 sides and an angle between them is given A = ½ × b × c × sin(α) If two angles and the length between them is given A = For an isosceles right triangle A = ½ × a.

If the height (i.e. the altitude) and base of an isosceles triangle are known, the area can be easily calculated. The area of the isosceles triangle is calculated by multiplying the height by the base and dividing by two. As a result, an isosceles triangle has two equal sides and two equal angles. The name is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.

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Answer:

The magnitude of the vector is 9.165 and it's direction is 40.6°

Step-by-step explanation:

A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.

Magnitude of vector v is given by

|v| = √6²+7²

= √36+49

= √84

= 9.165

Direction of vector v is obtained by:

\( \tan( \theta) = \frac{x}{y} \)

\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)

\(\theta = {40.6°}\)

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Answer:

Hey there!

Using the foil method: (3x+2)(5x-7)

15x^2+10x-21x-14

15x^2-11x-14

Let me know if this helps :)

Based on the definition of bisection and appropriate theorems, the proof that shows ΔABE ≅ ΔCDE is shown below.

When two lines bisect each other, they divide each other into equal segments, that is congruent segments.

The proof that shows that triangles ABE and CDE are congruent is explained below:

Statement                                         Reasons                                  

1. BD and AC bisect each other      1. Given

2. AE ≅ CE and BE ≅ DE                 2. Definition of bisection

3. ∠AEB ≅ ∠CED                              3. Vertical angles theorem

4. ΔABE ≅ ΔCDE                              4. SAS congruence theorem

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The answer is D: conjecture

The key words in the description are "look for a pattern and then form an educated guess." This suggests making a hypothesis or assumption based on the observed pattern, which is the definition of a conjecture.

The other answer choices are defined as follows:

A. conjugation - the act of changing a verb to agree with its subject

B. conjunction - a connecting word

C. congruence - the state of agreeing, matching, or coinciding

D. conjecture - an opinion or conclusion formed on the basis of incomplete information

So option D, conjecture, is the best match for forming an educated guess based on an observed pattern in induction.

Answer:

Step-by-step explanation:

no thx for 50points

Answer:

(5,6), (-2,8)

Step-by-step explanation:

I have a good math expertise. Don't question my skills as they are correct. woof woof waffling behavior. Thnak you hr welcne

The midpoint of segment YZ is (-a, -2b).

Given the coordinates of the rhombus WXYZ:

W(0, 4b)

X(2a, 0)

Y(0, -4b)

Z(-2a, 0)

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the coordinates of Y and Z:

Midpoint of YZ = ((0 + (-2a)) / 2, (-4b + 0) / 2)

= (-a, -2b)

Therefore, the midpoint of segment YZ is (-a, -2b).

To demonstrate that the segments joining the midpoints of the rhombus are perpendicular, we need to prove that the slopes of these segments are negative reciprocals of each other.

Let's consider the segments joining the midpoints:

Segment joining the midpoints of WX and YZ:

Midpoint of WX: ((0 + 2a) / 2, (4b + 0) / 2) = (a, 2b)

Midpoint of YZ: (-a, -2b)

Slope of WX = (2b - 4b) / (a - 0) = -2b / a

Slope of YZ = (-2b - (-4b)) / (-a - 0) = 2b / a

The slopes of WX and YZ are negative reciprocals of each other, indicating that these segments are perpendicular.

We have shown that the segments joining the midpoints of a rhombus are perpendicular to each other and have equal lengths. Therefore, these segments form a rectangle.

Additionally, the midpoint of segment YZ is (-a, -2b).

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Answer:

i think 1,000,000,000

Step-by-step explanation:

A minimum population size of approximately 7373 to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100.

To calculate the minimum population size required to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100, we can use the following formula:

n = [(z-value × SD) / ME]²

Where:

n = the minimum sample size required

z-value = the critical value for the desired confidence level (99% in this case)

SD = the known standard deviation (100 in this case)

ME = the desired margin of error (3 in this case)

First, we need to determine the z-value for a 99% confidence level. Using a standard normal distribution table, we find that the z-value for a 99% confidence level is approximately 2.576.

Substituting the values into the formula, we get:

n = [(2.576 × 100) / 3]²

Simplifying this expression, we get:

n = 7373.08

Therefore, we would need a minimum population size of approximately 7373.

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Answer: it should be the first one!! :)

Step-by-step explanation:

Answer:its the first one

Step-by-step explanation:did the test

The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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9. The regression line is given as follows: y = 8.5x + 3.7.

10. The estimate for 2022 is given as follows: 71.7 million dollars.

The regression line is obtained inserting the points of the table into a linear regression calculator.

From the table, the points are given as follows:

(1, 13), (2, 19), (3, 31), (4, 36), (5, 47).

(considering x as the number of years since 2014).

Inserting these points into a calculator, the equation is given as follows:

y = 8.5x + 3.7.

2022 is 8 years after 2014, hence the estimate is given as follows:

y = 8.5(8) + 3.7 = 71.7 million dollars.

(numeric value at x = 8, replace the lone instance of x by 8).

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Answer:

B

Step-by-step explanation:

Predicted increase in fuel efficiency = (300 pounds / 10 pounds per MPG) = 30 MPG

To predict the fuel efficiency of a car based on its weight, we need more information about the specific model and characteristics of the car. Fuel efficiency is influenced by various factors such as engine type, transmission, aerodynamics, and technology advancements.

Weight alone is not sufficient to accurately predict fuel efficiency. However, we can discuss a general observation that lighter vehicles tend to have better fuel efficiency due to reduced weight and improved energy efficiency.

For the purpose of this response, let's assume a hypothetical scenario and provide a general perspective:

If we assume a linear relationship between weight and fuel efficiency, we can use a simple linear regression model to make a prediction. However, please note that this is a hypothetical scenario and does not represent a specific car model or real-world data.

Suppose we have a linear regression model that suggests a 10-pound decrease in weight leads to an increase of 1 mile per gallon (MPG) in fuel efficiency. In this case, if the car has a weight of 4300 pounds, we can calculate the predicted change in fuel efficiency:

Weight difference = 4300 - 4000 = 300 pounds

Predicted increase in fuel efficiency = (300 pounds / 10 pounds per MPG) = 30 MPG

Again, this is a hypothetical scenario, and real-world fuel efficiency is influenced by multiple factors beyond just weight. Actual fuel efficiency values are typically provided by manufacturers based on standardized testing methods like EPA tests.

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Step-by-step explanation:

(a)(i) The average rate of change is:

(895 − 455) / (250 − 150)

4.4

(a)(ii) Since the profit is linear, the slope of the line is equal to the average rate of change.  Using point-slope form:

y − 455 = 4.4 (x − 150)

Simplifying to slope-intercept form:

y − 455 = 4.4x − 660

y = 4.4x − 205

(a)(iii) The break-even point is when the profit is 0.

0 = 4.4x − 205

4.4x = 205

x = 46.6

(b)(i) The "demand function" is the selling pice of the compasses:

p = 40 − 4q²

where p is the price in dollars and q is the quantity in millions of units.

Profit is revenue minus cost.

P = R − C

P = pq − 15q

P = (p − 15) q

P = (25 − 4q²) q

P = 25q − 4q³

where P is the profit in millions of dollars and q is the quantity in millions of units.

(b)(ii) Find values of q when P = 18.

18 = 25q − 4q³

4q³ − 25q + 18 = 0

We know that q=2 is a root of this equation.  Using grouping:

4q³ − 8q² + 8q² − 25q + 18 = 0

4q² (q − 2) + (q − 2) (8q − 9) = 0

(q − 2) (4q² + 8q − 9) = 0

4q² + 8q − 9 = 0

Solve with quadratic formula.

x = [ -b ± √(b² − 4ac) ] / 2a

q = [ -8 ± √(8² − 4(4)(-9)) ] / 2(4)

q = (-8 ± √208) / 8

q = (-8 ± 4√13) / 8

q = (-2 ± √13) / 2

Since q is positive, q = (-2 + √13) / 2, or approximately 0.803.

Answer:

27

Step-by-step explanation:

Answer:

A. Compare the sum 12.50 + 15.67 + 9.32 = 37.49 to the sum 14.333 + 12.100 + 10.780 = 37.213; he spent more time practicing the backstroke than the butterfly.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

i took the qiuz