Wayne is hanging a string of lights 89 feet long around the three sides of his rectangular patio, which is adjacent to his house. The length of his patio, the side along the house, is 5 feet longer than twice its width. Find the length and width of the patio.

Answers

Answer 1

SOLUTION:

Case: Rectangles

Method:

The sum is:

w + w + 2w + 5 = 89

4w + 5 = 89

4w = 89 - 5

4w = 84

w = 84/ 4

w= 21 feet

The length, l

l = 2w + 5

l = 2( 21) + 5

l = 42 + 5

l = 47 feet

Final answer:

length of the patio, l = 47 feet

width of the patio, w= 21 feet

Wayne Is Hanging A String Of Lights 89 Feet Long Around The Three Sides Of His Rectangular Patio, Which

Related Questions

3x - 4y = 65x + 8y = -1

Answers

[tex]\begin{gathered} 3x-4y=6 \\ 5x+8y=-1 \\ 3x=6+4y \\ x=2+\frac{4}{3}y \\ \\ 5(2+\frac{4}{3}y)+8y=-1 \\ 10+\frac{20}{3}y+8y=-1 \\ \frac{20y+24y}{3}=-11 \\ \frac{44y}{3}=-11 \\ 44y=-33 \\ y=\frac{-33}{44} \\ y=-\frac{3}{4} \\ \\ 3x-4(-\frac{3}{4})=6 \\ 3x+3=6 \\ 3x=3 \\ x=1 \end{gathered}[/tex]

Ethan's income is 4500 per month a list of some of his expenses appear below what percent of Ethan's expenses is food?

Answers

Ethan's earns 4500$ per month*

the amount spent on the food is 600 $

so percentage will be'

[tex]=\frac{4500}{600}=\frac{1500}{200}=7.5\text{ \%}[/tex]

so the answer is the percentage amount spent on food is, 7.5 %

multiply mentally to find the product

Answers

8 * 404 = 8(----- + 4)

At first, we will split 404 into two numbers one of them is 4

To find the other number subtract 4 from 404

404 - 4 = 400

8 * 404 = 8(400 + 4)

Now we will multiply 8 by 40 and 8 by 4

8(400 + 4) = 8 * 400 + 8 * 4

It is easy to find the product of 8 and 4

8 * 4 = 32

8 * 400 = 3200

Let us add them

3200 + 32 = 3232

The answer is 3232

Please it’s due todayAre there any limitations on the inputs of the equation?Does the graph have any symmetry?If so, where? When will the graph point upward? When will it point downward?

Answers

We have the following:

1.

There is no limitation on the input values, the domain is all real numbers.

2.

Yes, it has an axis of symmetry at the point (0,0)

3.

The graph point upward in the interval:

[tex](0,\infty)[/tex]

The graph point downward in the interval:

[tex](-\infty,0)[/tex]

Determine whether each linear function is a direct a variation. If so, state the constant of variation. If not, explain why notI need help for number 6

Answers

In direct variation function, variables x and y are related by the next formula:

y = kx

where k is the constant of variation.

Isolating k for the above formula, we get:

k = y/x

Computing y divided by x with the values of the table:

[tex]\frac{5}{10}\ne\frac{6}{11}\ne\frac{7}{12}\ne\frac{8}{13}[/tex]

Given that all the quotients are different, then the linear function is not a direct variation

If the point (-6, 4) is dilated by a scale factor of 1/2, the resulting point is (-3,2).TrueFalse

Answers

(-6,4)

Multiply each coordinate by 1/2

( -6 * 1/2 , 4 * 1/2) = (-3,2)

True

Translate and solve: The difference of a and 7 is 11

Answers

Answer:

(B)a=18

Explanation:

The difference of a and 7 translated as an expression is:

[tex]a-7[/tex]

Thus, the equation is:

[tex]a-7=11[/tex]

To solve for a, add 7 to both sides of the equation:

[tex]\begin{gathered} a-7+7=11+7 \\ a=18 \end{gathered}[/tex]

The correct choice is B.

Solve each equation for the given variable.-2x + 5y = 12 for ySolve each equation for y. Then find the value of y for each value if x.y + 2x = 5; x = -1, 0, 3

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

-2x + 5y = 12

y = ?

Step 02:

We must apply algebraic rules to find the solution.

-2x + 5y = 12

5y = 12 + 2x

y = 12 / 5 + 2x / 5

[tex]y\text{ =}\frac{12}{5}\text{ + }\frac{2x}{5}[/tex]

The answer is:

y = 12 / 5 + 2x / 5

Hello! I think the answer is 398. Would you mind guiding me?

Answers

Given -

Total Personal Videos Players = 400

Video Players with no defects = 398

Number of Video Players sent = 2000

To Find -

The number of Video Players with no defects =?

Step-by-Step Explanation -

Total Personal Videos Players = 400

Video Players with no defects = 398

So,

Two video players in every 400 are defected

So,

2000 = 5 × 400

So,

Total number of Video Players with defects = 5 × 2 = 10

Hence,

The number of Video Players with no defects = 2000 - 10 = 1990

Final Answer -

The number of Video Players with no defects = 1990

Solve the system of two linear inequalities graphically.Sy < -2x + 3y > 6x – 9Step 1 of 3: Graph the solution set of the first linear inequality.

Answers

The red graph represents y < -2x + 3

The blue graph represents y > 6x - 9

The solutions of the system of inequalities lie on the red-blue shaded

The part which has two colors

Since the first inequality is y < -2x + 3, the shaded is under the line

Since the second inequality is y > 6x - 9, the shaded is over the line

The common shaded of the two colors represents the area of the solutions of the 2 inequalities

The type of boundary lines is dashed

The points on the boundary lines are

For the red line (0, 3) and (4, 0)

For the blue line (0, -9) and (1, -3)

There is a common point on the two lines (1.5, 0)

find the perimeter of a garden that measures 6 feet by 3/4 foot?

Answers

The perimeter of a garden that measures 6 feet by 3/4 foot is 13.50 feet.

What is the perimeter?

The perimeter of a rectangle is calculated thus:

Perimeter = 2(Length + Width)

From the information, we want to find the perimeter of a garden that measures 6 feet by 3/4 foot.

This will be illustrated thus:

Perimeter = 2(Length + Width)

Perimeter = 2(6 + 3/4)

Perimeter = 2(6 + 0.75)

Perimeter = 2(6.75)

Perimeter = 13.50

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Adam is working in a lab testing bacteria populations. After starting out with a population of 390 bacteria, he observes the change in population and notices that the population quadruples every 20 minutes.Step 2 of 2 : Find the population after 1 hour. Round to the nearest bacterium.

Answers

The given information is:

The starting population of bacteria is 390.

The population quadruples every 20 minutes.

To find the equation of the population in terms of minutes, we can apply the following formula:

[tex]P(t)=P_0\cdot4^{(\frac{t}{20})}[/tex]

Where P0 is the starting population, the number 4 is because the population quadruples every 20 minutes (the 20 in the power is given by this), it is equal to 4 times the initial number, and t is the time in minutes.

If we replace the known values, we obtain:

[tex]P(t)=390\cdot4^{(\frac{t}{20})}[/tex]

To find the population after 1 hour, we need to convert 1 hour to minutes, and it is equal to 60 minutes, then we need to replace t=60 in the formula and solve:

[tex]\begin{gathered} P(60)=390\cdot4^{(\frac{60}{20})} \\ P(60)=390\cdot4^3 \\ P(60)=390\cdot64 \\ P(60)=24960\text{ bacterias} \end{gathered}[/tex]

Thus, after 1 hour there are 24960 bacterias.

The vertices of a rectangle are located at A(4, -1), B(-4, -1), C(-4, 6), and D(4, 6). What is the distance between the side AB and BC respectively?

Answers

The coordinates of the vertices of a rectangle are:

[tex]\begin{gathered} A\left(4,-1\right) \\ B\left(-4,-1\right) \\ C\left(-4,6\right) \\ D\left(4,6\right) \end{gathered}[/tex]

Plotting these points:

This is a non graded practice that I am doing. I don’t under these questions 5-11

Answers

7. The intersection of two intersecting lines is a point.

In the given image, we see that lines NQ and ML intersect at point P.

Therefore, the intersection of NQ and ML is P.

Factor out the greatest negative common factor for the expression.- 8mºn - 40m?n4Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.OA. - 8mºns - 40mºn4-(Factor completely.)OB. There is no common factor other than 1.

Answers

Solution

- The question tells us to factor out the greatest negative common factor of the expression below:

[tex]-8m^3n^5-40m^3n^4[/tex]

- The greatest negative common factor is the negative monomial with the largest magnitude, which divides evenly into each term of the given expression.

- Let us factorize the expression to derive this greatest negative common factor below:

[tex]\begin{gathered} -8m^3n^5-40m^3n^4 \\ -8,m^3,\text{ and }n^4\text{ are all co}mmon\text{ in the expression above.} \\ \text{Thus, we have:} \\ \\ -8m^3n^4(n-5) \end{gathered}[/tex]

Final Answer

The answer is

[tex]-8m^3n^4(n-5)[/tex]

Which of the following represents the translation of R (-3, 4), along the vector <7, -6> <-1, 3>.

Answers

Solution

Step 1:

The translation is a term used in geometry to describe a function that moves an object a certain distance.

Step 2:

Pre-mage R = (-3,4)

Step 3:

When moved along (7, -6) the new coordinates become:

R' = (-3+7 , 4 - 6 ) = (4 , -2)

R' = ( 4 , -2 )

Step 4:

When moved along (-1, 3) the new coordinates become:

R'' = ( 4-1 , -2+3 ) = ( 3 , 1 )

R'' = (3 , 1)

Final answer

[tex]R(-3\text{ , 4\rparen }\rightarrow\text{ R'\lparen4 , -2\rparen }\rightarrow\text{ R''\lparen3 , 1\rparen}[/tex]

The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 30.8 miles per gallon, with a standard deviation of 4.1 miles per gallon. Assume that a Normal model applies. Find the probability that a randomly selected automobile will average: 1. Less than 28 miles per gallon. Chapter 6 Assignment 2. More than 26 miles per gallon.

I need much help with this normal distribution question. ​

Answers

The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean.

What is meant by normal distribution?

The probability density function for a continuous random variable in a system defines the Normal Distribution.

A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction.

The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean. This shows that data close to the mean occur more frequently than data far from the mean. On a graph, the normal distribution is represented by a "bell curve."

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open up or down, vertex:(0,-4), passes through: (-3,5)

Answers

open up or down, vertex:(0,-4), passes through: (-3,5)​

In this problem we have a vertical parabola open upward

the equation in vertex form is equal to

y=a(x-h)^2+k

where (h,k) is the vertex

we have

(h,k)=(0,-4)

substitute

y=a(x)^2-4

Find the value of a

with the point (-3,5)

substitute in the equation

5=a(-3)^2-4

5=9a-4

9a=5+4

9a=9

a=1

therefore

the equation is

y=x^2-4

answer is

f(x)=x^2-4

figure0123456vehicles4122028364452linear ?pattern ?constant?

Answers

Problem

Solution

For this case we need to verify if the pattern is linear so we cna check this doing the following operations:

(12-4)/(1-0) =8

(20-12)/(2-1) =8

(28-20)/(3-2) =8

(36-28)/(4-3) =8

(44-36)/(5-4) =8

(52-44)/(6-5) =8

And as we can see we have the same constant so we can conclude that we have a linear pattern with a constant value of k=8

That means for every increase in the figure the vehicles increase by 8

We can also find the formula for the linear pattern and we have:

4 =8 (0)+b

And solving for b we got

b= 4

And the equation y=mx+b is:

y= 8x +4

32Lucky Lanes Bowling Alley is putting this design on its roof.4 feet4 feet20 feet4 feet4 feet10 feet

Answers

Volume of a composite figure

In order to find the volume of the design, we want to find the volume of the figures that compound it:

Total volume = volume 1 + volume 2

Volume 1

The volume of each box is given by the product of its sides:

side 1 x side 2 x side 3.

In this case, we have that

side 1 = 4 ft

side 2 = 4 ft

side 3 = 20 ft - 4 ft = 16 ft

Then,

side 1 x side 2 x side 3.

volume 1 = 4 ft x 4 ft x 16 ft = 256 ft³

volume 1 = 256 ft³

Volume 2

For the second part we have that:

side 1 = 4 ft

side 2 = 4 ft

side 3 = 10 ft

Then,

side 1 x side 2 x side 3.

volume 2 = 4 ft x 4 ft x 10 ft = 160 ft³

volume 2 = 160 ft³

Total volume

The total volume is given by

Total volume = volume 1 + volume 2

Total volume = 256 ft³ + 160 ft³

Total volume = 416 ft³

Answer: 416 ft³

(a) How high is the javelin when it was thrown? How do you know?(b) How far from the thrower does the javelin strike the ground?

Answers

The height of the javelin is given by

[tex]h(x)=-\frac{1}{20}x^2+8x+6[/tex]

Here, x is the horizontal distance from the point at which the javelin is thrown.

a)

When the javelin is thrown, the horizontal distance from the point at which the javelin is thrown is zero. So, put x = 0 to find the height of the javelin when thrown. So, the distance:

[tex]\begin{gathered} h(0)=-\frac{1}{20}(0)^2+8(0)+6 \\ =0+0+6 \\ =6 \end{gathered}[/tex]

Thus, the height of the javelin when it was thrown is 6 ft.

b)

When the javelin strikes the ground the value of h(x) is zero.

Find the value of x when h(x) is zero.

[tex]\begin{gathered} h(x)=0 \\ -\frac{1}{20}x^2+8x+6=0 \\ -x^2+160x+120=0 \\ x^2-160x-120=0 \end{gathered}[/tex]

Now, the roots of the equation are x = 160.74 and x = -0.74.

The distance cannot be negative. So, the javelin is 160.74 ft far from the thrower when it strikes the ground.

In the right trapezoid ABCD, BC is parallel to AD, and AD is contained in the line whose equation is y=−12x+10 y = − 1 2 x + 10 . What is the slope of the line containing BC? Explain how you got your answer

Answers

The slope of BC should be -12 because it is parallel to AD so the slope should be the same

Based on the degree of the polynomial f(x) given below, what is the maximum number of turning points the graph of f(x)
can have?
f(x) = -3+x²-3x - 3x³ + 2x² + 4x4

Answers

The maximum number of turning points based on the degree of the polynomial is 2.

What is the turning point?A polynomial function is a function that can be expressed in the form of a polynomial. The definition can be derived from the definition of a polynomial equation. A polynomial is generally represented as P(x). The highest power of the variable of P(x) is known as its degree.A turning point is a point in the graph where the graph changes from increasing to decreasing or decreasing to increasing.

Turning point = n-1, where n is the degree of the polynomial.

The highest order of the polynomial is 3.n = 3Turning point = 3 - 1 = 2

Therefore, the maximum number of turning points based on the degree of the polynomial is 2.

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An initial amount of $3500 is invested in an account at an interest rate of 6% per year, compounded continuously. Assuming that no withdrawals aremade, find the amount in the account after two years.Do not round any intermediate computations, and round your answer to the nearest cent.

Answers

For this problem we use the continuously compounded interest formula:

[tex]M=M_0e^{rt}[/tex]

where M_0 is the initial amount, r is the interest rate per year and t is the number of years.

Substituting M_0=$3500, r=0.06, and t=2 we get:

[tex]\begin{gathered} M=3500e^{0.06\cdot2}=3500e^{0.12} \\ M=3946.24 \end{gathered}[/tex]

Find the perimeter of the isosceles triangle in simplest form. x2 + 20 units 2x units

Answers

The perimeter of an isosceles triangle is given by:

[tex]P\text{ = 2a + b}[/tex]

From the question, b = 2x; a = x^2 + 20

[tex]P\text{ = 2a }+b=2(x^2+20)+2x=2x^2+40\text{ + 2x}[/tex][tex]P=2x^2\text{ + 2x + 40}[/tex]

how to find the width to a pyramid with the volume height and length

Answers

The volume of a pyramid is given by the formula

[tex]V_{\text{pyramid}}=\frac{1}{3}\times base\text{ area}\times height[/tex]

Write out the given dimensions

[tex]\begin{gathered} \text{Volume}=80\operatorname{cm}^3 \\ \text{Height}=10\operatorname{cm} \\ \text{length}=6\operatorname{cm} \\ \text{width}=\text{unknown} \end{gathered}[/tex]

Since the base of the pyramid is a rectangle, the base area is

[tex]A_{\text{rectangle}}=\text{width }\times length[/tex]

Substituting the given dimensions to get the value of the width\

[tex]\begin{gathered} V_{\text{pyramid}}=\frac{1}{3}\times width\times length\times height \\ 80=\frac{1}{3}\times width\times6\operatorname{cm}\times10\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} 80\operatorname{cm}=20\times width \\ \text{width}=\frac{80}{20} \\ \text{width}=4\operatorname{cm} \end{gathered}[/tex]

Hence, the width of the pyramid is 4cm

is there one solution to the following system of equations by elimination 3x + 2y equals 3 3x + 2y equals 19

Answers

3x+2y= 3 (a)

3x+2y= 19 (b)

Subtract (b) to (a) ; elimination method.

3x+ 2y = 3

-

3x+2y= 19

_________

0 = 19

Since both variables were eliminated, the system has no solutions.

option c.

To beA train started from City A to City B at 13:30. The train travelledat an average speed of 180 miles per hour. If the distancebetween City A and City B is 756 miles, at what time did thetrain arrive at City B? Give your answer in a 24-hour clockformat, such as 19:00. DEnter the answer

Answers

Remember that

the speed is equal to divide the distance by the time

speed=d/t

solve for t

t=d/speed

we have

d=756 miles

speed=180 miles per hour

substitute

t=756/180

t=4.2 hours

4.2 hours=4 hours +0.20 hours

Convert 0.20 hours to minutes

Multiply by 60

0.20 h=0.20*60=12 minutes

so

4.2 hours=4 h 12 min

therefore

A train started from City A to City B at 13:30.

13:30+ 4h 12 min=17:42 hrs

The amount of freight transported by rail in the u.s was about 580 billion ton-miles in 1960 and has been increasing at a rate of 2.32% per year since then.a. write a function representing the amount of freight, in billions of ton-miles, transported annually. ( 1960 = year 0 )b. graph the functionc. in what year would you predict that the number of ton-miles would have exceeded or would exceed 1 trillion (1,000 billion)?

Answers

The amount of freight transported by rail was 580 billion ton-miles in 1960.

The amount increased at a rate of 2.32% per year.

a. The growth in freight transport with respect to the passing years can be expressed as exponential growth. The general form of this equation is

[tex]y=a(1+r)^x[/tex]

Where

y represents the final number after "x" periods of time

a represents the initial number at x=0

r represents the growth rate, expressed as a decimal value

x represents the number of time intervals that have passed

For this example, the initial amount is a=580 billion

The growth rate is r=2.32/100=0.0232

You can determine the equation as follows:

[tex]y=580(1+0.0232)^x[/tex]

b. This function is of exponential increase, its domain is all real numbers and its range is all positive real numbers, you can symbolize it as y > 0, it's increasing, and it has a horizontal asymptote as x approaches -∞

To graph it, you have to determine at least two points of the graph, I will determine 3

For x=-100

[tex]\begin{gathered} y=580(1+0.0232)^{-100} \\ y=58.53 \end{gathered}[/tex]

For x=0

[tex]\begin{gathered} y=580(1+0.0232)^0 \\ y=580 \end{gathered}[/tex]

For x=10

[tex]\begin{gathered} y=580(1+0.0232)^{10} \\ y=729.51 \end{gathered}[/tex]

The points are

(-100,58.53)

(0,580)

(10,729.51)

Plot the points and then draw an increasing line from -∞ to +∞

c. To determine the time when the freight transported will exceed 1000 billion tom-miles, you can use the graph, just determine the value of x, for which y=1000

This value is approximate x=23.57

This means that counting from 1960 will take 23 and a half years to reach over a trillion ton-miles transported.

Add the number of years to the initial year to determine the date:

[tex]1960+23=1983[/tex]

By 1983 the number of ton-miles transported will exceed the trillion.

I need help with solving this: what is the 8th term to 1,5,25,125,..

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

1,5,25,125,..

Step 02:

[tex]an=5^{n-1}[/tex]

if n = 8

[tex]a_8=5^{8-1}=5^7=78125[/tex]

The answer is:

8th term is 78125

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