for a fixed area, the length of rectangle is inversely proportional to its width. a rectangle has a width of 18 feet and a length of 12 feet. if the length is increased to 20 feet, find the width.

Answer: B

You don't need to rotate it, and the x-axis is the horizontal one, you need to reflect across the vertical axis, then shift it 2 places to the left.

Answer:

Pretty sure it's 3

Answer:

C 3

Step-by-step explanation:

The sample should be taken to provide a 95% confidence interval is 200.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

Confidence is another name for probability in statistics.

Given the planning value for the population proportion,

probability, p = 0.25

q  = 1 - p = 1 - 0.25

q = 0.75

margin of error = E = 0.06

value of z at 95% confidence interval is 1.96,

the formula for a sample is,

n = (z/E)²pq

n = (1.96/0.06)²*0.25*0.75

n = 200.08

n = 200 approx

Hence sample size is 200.

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The solution of the compound inequality is x < 3/4 or x >2.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

A compound inequality:

4x - 5 < -2 or x + 1 > 3.

Solving inequality,

4x < -2 + 5 or x > 2

4x < 3 or x > 2.

x < 3/4 or x >2.

Therefore, the solution is x < 3/4 or x >2.

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Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

To beat the school long jump record, John must jump an additional 5 1/4 inches

From the given question, we are to determine how farther John must jump in order to break the record

From the given information,

"A high school track team's long jump record is 23 ft 1 3/4 in"

and

"John's best long jump is 22 ft 8 1/2 in"

First, we will convert the distances to inches

NOTE: 1 ft = 12 inches

23 ft 1 3/4 in = 276 + 1 3/4 in = 277 3/4 in

22 ft 8 1/2 in = 264 + 8 1/2 in = 272 1/2 in

Now, to determine how farther John must jump, we will subtract the distances

277 3/4 in - 272 1/2 in = 5 1/4 in

Hence, he must jump 5 1/4 in farther

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Answer:

Your answer is 4cm.

Step-by-step explanation:

simple calculation

x (12+x) π = 32 π

x = 4cm

Step-by-step explanation:

1000 devided by 75% gives 250

Answer:

2 weeks

Step-by-step explanation:

Given the function below,

To find the domain of the function above, we factorise the denominators to find x factors,

Factorising the denominator,

The domain of a function is the set of all possible values of x, except for x=0.

Hence, the domain of the function is the set of all possible values of x except -3 and 5/6.

Answer:

Aircraft A: 403 seats

Aircraft B: 298 seats

Step-by-step explanation:

Let's x represent the seats in Aircraft B

We have the equations:

Aircraft A: (x + 105)

Aircraft B: x

We Know

Their total number of seats is 701; find the number of seats for each aircraft.

We Take

x + (x + 105) = 701

2x + 105 = 701

2x = 596

x = 298 seats

So, there are 298 seats in Aircraft B

Aircraft A has how many seats?

We Take

701 - 298 = 403 seats

So, there are 403 seats in Aircraft A

Final Answers:

Aircraft A: 403 seats

Aircraft B: 298 seats

Answer:

15 is the median by using the formula

hope this helps you a lot

The percentage error in the density of metal will be 3.4%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.

The percentage error will be calculated as:-

Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100

Percentage = 0.034x 100

Percentage = 3.4%

Hence, the percentage error will be 3.4% for the densities.

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Using mathematical operators to simplify the linear equation, the value of m is 61

Simplification of a linear equation is the process of reducing the equation to its simplest form by combining like terms, applying the distributive property, and eliminating any unnecessary variables or constants. The goal of simplification is to write the equation in a more readable and manageable form.

In this problem, we can collect like terms and solve for m

324.54 = 9(0.07m + 28.90 + 0.10(28.90))

324.54 = 0.63m + 260.1 + 26.01

324.54 = 0.63m + 286.11

0.63m = 324.54 - 286.11

0.63m = 38.43

m = 61

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The graph of the function y = 5|x - 4| is added as an attachment

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

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Step-by-step explanation:

(a) The lower limit of the 90% confidence interval can be calculated using the formula:

lower limit = sample mean - margin of error

Plugging in the given values, we have:

lower limit = 7.43 - 1.32

lower limit = 6.11 (rounded to 2 decimal places)

Therefore, the lower limit of the 90% confidence interval is approximately 6.11 hours per night.

(b) If 500 random samples like this were selected, and a 90% confidence interval was constructed using each sample, the expected number of intervals that would contain the population mean can be approximated using the margin of error as a guide.

Since the margin of error is 1.32 hours, we can expect roughly 90% of the confidence intervals to contain the true population mean. Therefore, out of 500 samples, we would expect approximately:

500 * 0.9 = 450

So, approximately 450 of these confidence intervals would contain the population mean.

Answer:

minimum value of z is 0

Step-by-step explanation:

if x and y both equal zero, then the value of z is zero, which is your answer.

Answer:

\(6\frac{11}{15}\)

Step-by-step explanation:

\(2\frac{1}{3}\) equals to \(\frac{7}{3}\)

\(\frac{11}{5}+\frac{11}{5}=\frac{22}{5}\)

but the denominator is not the same in \(\frac{7}{3}\) and \(\frac{22}{5}\). So you would need to find the LCM for 3 and 5. The LCM for 3 and 5 is 15.

\(\frac{7}{3}*\frac{5}{5} =\frac{35}{15}\)

\(\frac{22}{5}*\frac{3}{3} =\frac{66}{15}\)

\(\frac{35}{15} +\frac{66}{15} =\frac{101}{15}\)

\(\frac{101}{15} =6\frac{11}{15}\)

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

Answer: I'm not really sure what the question is but the volume is 224

Step-by-step explanation:

Answer:

3200 of 768 is 416.67%

Step-by-step explanation:

There's your answer hope this helps.

The graph in which point are plotted is given below and Point D and F lie on Y axis and X axis respectively other lie on the different quadrant

What does a math quadrant mean?

The term "quadrant" refers to each of the four divisions of the coordinate plane. Furthermore, when we speak of the sections, we also mean the sections as the coordinate axes split them. This is where the x-axis is, and this is where the y-axis is on the up-down axis. On a coordinate plane, it divides the space into four parts, as you can see.

Point A (-5,4)

Lies in 2 quadrant of the graph

Point B (-3,-2)

Lies in 3 quadrant of the graph

Point C (4,6)

Lies in 1 quadrant of the graph

Point D (0,-4)

Lies on negative y axis of the graph

Point E (2,-1)

Lies in 4 quadrant of the graph

Point F (1,0)

Lies on positive x axis of the graph

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Answer:

The student is incorrect because I I or absolute value would make the -9 to positive 9.  

Step-by-step explanation:

-9<4

on a numberline

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4

but the absolute value of -9 (or) |–9|

is actually positive 9

9>4

on a number line

4 5 6 7 8 9

Answer:

Below

Step-by-step explanation:

edited:  FOR QIII   (I didn't see that part)

Remember for a right triangle  S-O-H-C-A-H-T-O-A

   Tan is OPPOSITE LEG / ADJACENT LEG

   make the right triangle with legs 3 and 4  ( in quadrant III)

      then the hypotenuse is 5

         sin = opp/ hyp =  - 3/5

            cos = -  4/5

                csc = 1/sin = - 5/3

                   sec = 1/cos = - 5/4

                       cot = 1/tan = 3/4

Answer:

Step-by-step explanation:

The missing dimension is:

Explaination:

The missing dimension is: The total height - 2 times (height of the frame)

6w² + 8 - 2(w² - 3w + 2)

6w² + 8 - 2w² + 6w - 4

Answer:  

4w² + 6w + 4

Use "Combine Like Term"  method.

The value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0 is k = -21/5. 

Two lines are parallel only if their slopes are the same. The slope of a line of the form y = mx + b (where m is the slope and b is the y-intercept) is m. The slope of a straight line of the form ax + by + c = 0 can be found using the formula: The calculation formula for the slope cutting shape will change.

So to find the value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0, we need to find the slope of the line 5x - 3y + 44 = 0. To do this, we rearrange the equation into slope-intercept form.

5x - 3y + 44 = 0

-3y = -5x + 44

y = (5/3)x - 14.67

The straight line 5x - 3y + 44 = 0 has a slope of 5/3. In order for the 7x + ky = 35 line to be parallel to this line, the slope of 7x + ky = 35 must also be 5/3. To find the slope of 7x + ky = 35, rearrange the formula into slope-intercept form.

7x+ky=35

y = -(7/k)x + 35/k

Setting the slope of the line 7x + ky = 35 equal to the slope of the line 5x - 3y + 44 = 0 gives:

-(7/k) = 5/3

-7/k = 5/3

-7 * 3 = 5 * k

-21 = 5k

k = -21/5

Therefore, the value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0 is k = -21/5. 

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let's assume the Coordinates be x and y

By using Section formula,

\( \boxed{ x = (\dfrac{x_2 + x_1}{2} )}\)

____________________

\( \boxed {y = (\dfrac{y_2 + y_1}{2} )}\)

____________________

\(\mathrm{Therefore \:\:the\:\: Coordinates\:\: of \:\:the\;\; mid-point\;\: of \;\;the\:\: given\:\: segment\:\; is}\)

\( \huge \boxed{(2,0)}\)

_____________________________

\(\mathrm{ \#TeeNForeveR} \: ☃\)

Answer:

6688

Step-by-step explanation:

I think, I hope!

The correct sequence for the numbers that are given will be:

It can be seen that from the information given, a number has been attached to each diagram. This will be used in answering the questions given.

Therefore, the correct sequence for the numbers are given will be 6408, 4608, 0846, and 8064.

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