Subtract --4x2 + 3x - 7 from 8x2 + 2x - 3

The solution will be that the home-decorating company will require 42 yards of fabric for the customer's window treatments.

As per the information we have received from the question,

A single window requires 13 yards and a double window requires 16 yards of fabric. We are asked to find out the length of fabric that will be required by the home-decorating company, in case there were 2 single windows and 1 double window. The total amount of fabric that will be required by the home-decorating company is hence equal to

13×(no of single windows)+ 16×(no of double windows)

Here, no of single windows= 2

And, no of double window= 1

Hence, total fabric length=13×2 + 16×1=26 + 16=42 yards

Hence the solution is 42 yards of fabric.

Read more about simple mathematical equation-solving problems on

https://brainly.com/question/17618820

Answer:

w+h+10=10wh

Step-by-step explanation:

Answer: Rectangle, Rhombus, Square

Step-by-step explanation:

Answer:

The formula for circumference of a circle is C = πd, where C is the circumference and d is the diameter.

We are given that the circumference is 48.984 feet, and we can use the approximation of π as 3.14.

Substituting into the formula, we have:

48.984 = 3.14d

To solve for d, we divide both sides by 3.14:

d = 48.984 / 3.14

d ≈ 15.6 feet

Therefore, the floor's diameter is approximately 15.6 feet.

Answer:

Step-by-step explanation:

slope intercept form: y = mx + b ............where m is slope and b is y-intercept

1st question:

4x + y = 1

y = 1 - 4x

y = -4x + 1

2nd question:

x + 2y = 9

2y = 9 -x

y = (-x + 9)/2

y = \(-\frac{1}{2}x + 4.5\)

Answer:

D. Graph C

Step-by-step explanation:

Step 1:  Identify the parts of the point-slope form to find the correct graph:

Currently, y - 1 = 2(x + 2) is in point-slope form, whose general equation is given by:

y - y1 = m(x - x1), where

1). 15 days

2). 115.2 pounds.

3). 500 meters

1. To find out when the couple will have another day off together, we need to find the least common multiple (LCM) of their work schedules. The LCM of 3 and 5 is 15, so the couple will have another day off together after 15 days.

2. The weight W of an object above the earth varies inversely as the square of the distance D from the center of the earth.

This means that W = k/D^2, where k is a constant.

To find k, we can plug in the values given in the question: 180 = k/4000^2.

Solving for k gives us k = 180*4000^2 = 2880000000. Now we can plug in the new distance, 4000 + 1000 = 5000 miles, to

find the new weight: W = 2880000000/5000^2 = 115.2 pounds.

3. To find the total distance traveled by the fly, we need to find out how long it takes for the turtles to meet.

The combined rate of the turtles is 10 + 20 = 30 m/s, so it will take them 150/30 = 5 seconds to meet.

The fly travels at a constant rate of 100 m/s, so in 5 seconds it will have traveled 100*5 = 500 meters.

Therefore, the total distance traveled by the fly is 500 meters.

Learn more about distance

brainly.com/question/15172156

#SPJ11

The true inferences from the double dot plot for this case from the available options is given by: Option D) The Interquartile range for Ander’s data is 0. 5 greater than the interquartile range for Marcus’s data

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

Lower quartile, also called first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.

Similarly, second quartile (also called median) is approximately in mid of the data.

Third quartile (also called upper quartile)  has approx 75% in its left partition, and on its right lies approx 25% of the data.

Left to right is said in assumption that data was arranged increasingly from left to right

IQR(inter quartile range)  is the difference between third and first quartile.

Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.

Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.

If instead of only observations, the table of unique observation and frequency is given, then we plot dots that many times as the count written in the frequency table. Thus, if its written that the value 2 has 3 has its frequency, then we plot 3 dots one over the other above the value 2 in the horizontal axis.

For this case, getting the quartiles of each dataset one by one.

The number of dots show frequencies, therefore, from the image attached below, the data we get for Anders is:

1,2,2,3,3,5,5,5,5,5,5,6,6,6,6,7,7,7,7,7

These are total 20 observations.

Mean is the ratio of sum of all observations to the number of observations.

Sum of these values is 100, and therefore, we get:

Mean = 100/20 = 5

50% of 20 is 10 (its half). And 25% is 5, and 75% is 15.

Now, any number between the 10th and 11th value will be median because before and after that will lie ten-ten observations.

We usually take mean of these two values in such case.

The 10th value is 5, and so as the 11th value.

Thus, median of this data set is 5

Similarly, the first quartile can be taken as the average of 5th and 6th value as in mid of both lie values before which lies 25% of the data and after which lies 75% of the data.

The 5th and 6th values are 3 and 5. Their average is (3+5)/2=4

Thus, the first quartile of this data set is 4

Similarly, third quartile can be taken as average of 15th and 16th value = (6+7)/2 = 6.5

Now, the interquartile range of this dataset = third - first quartile = 6.5 - 4 = 2.5

2,3,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,10,10

These are total 20 observations.

Mean is the ratio of sum of all observations to the number of observations.

Sum of these values is 139, and therefore, we get:

Mean = 139/20 = 6.95 (approx 7)

Also, we get:

Median can be average of 10th and 11th value = (7+7)/2 = 7

First quartile can be average of 5th and 6th value = (6+6)/2 = 6

Third quartile can be average of 15th and 16th value = (8+8)/2 = 8

Thus, IQR = third - first quartile = 8-6 = 2

So we see that option A and B are wrong as IQR and median both are different for both the datasets.

Option C is wrong since for Ander's data, we see that both mean and median (which are central measures) evaluates to 5, so Ander's data centers around 5 instead of 6.

Option D is correct as IQR for Ander's data = 2.5 is 0.5 greater than 2 which is IQR for Marcus' data.

Thus, the true inferences from the double dot plot for this case from the available options is given by: Option D) The Interquartile range for Ander’s data is 0. 5 greater than the interquartile range for Marcus’s data.

Learn more about dot plot here:

https://brainly.com/question/22746300

Learn more about quartiles here:

brainly.com/question/9260741

#SPJ1

Answer:

Decreasing

Step-by-step explanation:

Because of minus as a coefficient

If a function f(x) is stretched vertically by a scale factor of k, then

The new function is k . f(x)

Since the given function is

Since the new function is

Then k = 5

f(x) is stretched vertically by a scale factor of 5

The correct answer is

The base graph vertically stretched by a factor of 5

The first choice

Answer:

Slope=1.000/2.000=0.500

b-i

q-i

b-(2*q+6)=0

Step-by-step explanation:

1.1     Solve   b-2q-6  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  b-2q-6  = 0 and calculate its properties

Notice that when b = 0 the value of q is 3/-1 so this line "cuts" the q axis at q=-3.00000

 q-intercept = 6/-2 = 3/-1  = -3.00000

When q = 0 the value of b is 6/1 Our line therefore "cuts" the b axis at b= 6.00000

 b-intercept = 6/1  =  6.00000

Slope is defined as the change in q divided by the change in b. We note that for b=0, the value of q is -3.000 and for b=2.000, the value of q is -2.000. So, for a change of 2.000 in b (The change in b is sometimes referred to as "RUN") we get a change of -2.000 - (-3.000) = 1.000 in q. (The change in q is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  1.000/2.000 =  0.500

 Slope = 1.000/2.000 = 0.500

 b-intercept = 6/1 = 6.00000

 q-intercept = 6/-2 = 3/-1 = -3.00000

The simplified form of the expression 8 + (-7)² - (7 × (-2) + 1 ) is 70.

Given the expression in the question;

8 + (-7)² - (7 × (-2) + 1 )

Simplify each term, raise -7 to the power 2

8 + (-7)² - (7 × (-2) + 1 )

8 + 49 - (7 × (-2) + 1 )

Multiply 7 by -2

8 + 49 - ( -14 + 1 )

Add -14 and 1

8 + 49 - ( -13)

Remove parenthesis by multiplying -1 by -13

8 + 49 + 13

Now, simplify by adding the number

8 + 49 + 13

57 + 13

70

Therefore, the simplified form of the expression 8 + (-7)² - (7 × (-2) + 1 ) is 70.

Learn more algebra problems here: brainly.com/question/723406

#SPJ1

The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

---------------------------------------------------------------------------

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

---------------------------------------------------------------------------

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

---------------------------------------------------------------------------

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

---------------------------------------------------------------------------

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

---------------------------------------------------------------------------

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

---------------------------------------------------------------------------

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

---------------------------------------------------------------------------

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

Learn more about Simplex Algorithm here:

https://brainly.in/question/46895640

#SPJ11

Your total vacation budget would be $280, considering the $160 spent on groceries and the estimated cost of eating out 3 times at $40 per meal from linear equation concept.

For your vacation at the beach, you have already spent $160 on groceries for the week. In addition, you anticipate spending $40 each time you eat out.

To determine your overall budget for the vacation, you need to consider how many times you plan to eat out during the week. Let's say you plan to eat out 'x' number of times.

Since each time you eat out costs $40, the total amount spent on eating out can be represented by the equation:

Total spent on eating out = $40 * x

Adding this to the amount spent on groceries, the total vacation budget can be calculated as:

Total budget = Amount spent on groceries + Total spent on eating out

Total budget = $160 + ($40 * x)

For example, if you plan to eat out 3 times during the week, the calculation would be:

Total budget = $160 + ($40 * 3)

Total budget = $160 + $120

Total budget = $280

In this case, your total vacation budget would be $280, considering the $160 spent on groceries and the estimated cost of eating out 3 times at $40 per meal.

The total budget will vary depending on the number of times you plan to eat out. By adjusting the value of 'x', you can calculate the specific total budget for your vacation.

for more such question on linear equation visit

https://brainly.com/question/28732353

#SPJ8

Answer:

Step-by-step explanation:

y - 2 = 1/2(x - 10)

y - 2 = 1/2x - 5

y = 1/2x - 3

Answer:

Step-by-step explanation:

You can read the slope right away.

y = 0.5x + b     1/2 = 0.5

The point will determine the y intercept

2 = 0.5*10 + b

2 = 5 + b

2-5 = b

b = - 3

The line is y = 0.5x - 3

Answer:

I dont exactly know I think its 554 ;-; I used triongometric identities

Answer:

√{554×554}=√554²=±554 is your answer

The general solution of the given differential equation is C. sin(x+y)+ y² = c.

The given differential equation is in the form of a first-order homogeneous linear differential equation. To solve it, we can separate the variables and integrate.

First, we rewrite the equation in a more suitable form by rearranging the terms:

sin(x+y) + y² = c

Next, we can separate the variables by moving all the terms involving y to one side and the terms involving x to the other side:

sin(x+y) = c - y²

To solve for y, we can take the arcsine of both sides:

x+y = arcsin(c - y²)

Now, we can isolate y by subtracting x from both sides:

y = arcsin(c - y²) - x

This equation represents the general solution of the given differential equation. It shows that the value of y depends on the value of x and the constant c. The equation involves the inverse sine function, indicating that the solution may consist of multiple branches.

Learn more about differential equation

brainly.com/question/32645495

#SPJ11

Answer:

3rd one

4th one

5th one

8th one

Step-by-step explanation:

solve for the y intercept by plugging in f(0)

0²-4(0)-21= -21

Therefore (0,-21) is a y intercept

Factor to find the x intercepts

(x+3)(x-7)

Therefore the intercepts are

(-3,0) (7,0)

THis function has a positive coeficcent and an even degree

therefore as x approaches infinity it's infinity

and as x approaches negative infinity it's infinity

He can wear 8 different outfits to school.

We have,

The boy can choose one pair of pants, one shirt, and one tie can be written as an expression as:

= 1 × 1 × 1

= 1 way.

He can choose one jacket in 8 ways.

Therefore, he can wear can be written as an expression as:

= 1 × 1 × 1 × 8

= 8 different outfits.

Thus,

He can wear 8 different outfits to school.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

As a result, A is the appropriate response. Yes; there is only one output per set of inputs.

A function in mathematics is a formula that links every element of one set (referred to as the domain) to a single value of another set (called the range). To put it another way, a connection among multiple sets is called a function when every element in the domain is related to precisely one element in the range. There are many methods to depict a function, including calculations, tables, graphs, and projection diagrams. For instance, the function represented by the equation f(x) = x2 accepts any input value x and outputs the equivalent value x2. The scope, which in this instance is all real numbers, is the collection of all feasible input values.

given

Each input value (represented by the X) is paired with precisely one output value in the mapping diagram, which illustrates a function (represented by the o).

As a result, A is the appropriate response. Yes; there is only one output per set of inputs.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ4

Answer:

the equation is - \(y=x\)

Explanation:

Given -

\(y=x+4\)

We have to find a line passing through the point \((2,2)\) nd parallel to the given line.

Find the slope of the given line.

It is the coefficeint of \(x\)

m₁ = 1

The two lines are parallel. Hence

m₂=m₁=1 Where m₂is the slope of the second line.

You have slope and the points \((2,2)\)

Find the Y intercept

\(y=mx+c\\2=(1)(2)+C\\2=2+C\\C=2-2=0\)

Y-Intercept \(C=0\) and slope m₂=1

Fix the equation

\(y=x\)

Answer:

-2x - 5 (lesser than or equal to) 15

Answer:

Construct a transversal line through points A and X. i think im not sure

Step-by-step explanation:

The value of the infinite series as n tends to 0 is: 0

Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.

From the infinite series, we want to find the value of the series as n tends to 0.

We are given the series as:

x/2ˣ

At x = 0, we have:

0/2⁰ = 0/1 = 0

Read more about infinite series at: https://brainly.com/question/30221799

#SPJ1

72. 43 miles is traveled in 1 hour

From the information given, we have that;

First, we convert feet to miles

1 foot = 0. 000189 miles

Then 6400 = x miles

cross multiply

x = 6400 ×  0. 000189

x = 1. 2096 miles

We have that;

1. 2096 miles is traveled in 0. 0167 hour

Then x miles is traveled in 1 hour

cross multiply

x = 1. 2096/  0. 0167

x = 72. 43 miles

Thus, 72. 43 miles is traveled in 1 hour.

Learn more about conversion here:

https://brainly.com/question/16851332

#SPJ1

The damping ratio (ζ) is 1, indicating critical damping, and the natural frequency (ωn) is 7.

To illustrate the location of poles and zeros on the s-plane for the given transfer function G(s) = 49/(s+7)(s+7), we first need to factorize the denominator. The transfer function has two poles at s = -7 and s = -7, indicating a double pole at s = -7. The denominator (s+7)(s+7) represents a second-order system.

The poles represent the points on the s-plane where the transfer function becomes infinite, or the system becomes unstable. In this case, the poles are located at s = -7, indicating that the system is critically damped since there is a double pole at the same point.

To determine the damping ratio (ζ) and natural frequency (ωn), we can compare the given transfer function to the standard second-order transfer function form:

G(s) = ωn^2 / (s^2 + 2ζωn s + ωn^2)

By comparing the coefficients, we can see that ωn^2 = 49 and 2ζωn = 14 (since 2ζωn is the coefficient of s). Solving for ωn and ζ, we get:

ωn = sqrt(49) = 7 2ζωn = 14 => ζ = 1

Therefore, the damping ratio (ζ) is 1, indicating critical damping, and the natural frequency (ωn) is 7.

Learn more about damping ratio

https://brainly.com/question/28941371

#SPJ11