The area of a rectangular tablecloth is 8 3/4 square yards. The width of the tablecloth is 1 7/8 yards. What is the length, in yards, of the tablecloth?

the real solutions to this equation are x = 2√2 and x = -2√2.

Solution:

(a) -n + √(6n + 19) = 2

To find the solution algebraically, we need to isolate the radical on one side of the equation and then square both sides to get rid of the radical.

-n = 2 - √(6n + 19)

(-n - 2)^2 = (2 - √(6n + 19))^2

n^2 + 4n + 4 = 4 - 4√(6n + 19) + 6n + 19

n^2 - 2n - 19 = -4√(6n + 19)

(n^2 - 2n - 19)^2 = (-4√(6n + 19))^2

n^4 - 4n^3 - 18n^2 + 76n + 361 = 96n + 304

n^4 - 4n^3 - 114n^2 + 76n + 57 = 0

This is a quartic equation that can be solved using the Rational Root Theorem or by factoring. However, this equation does not have any real solutions. Therefore, there are no real solutions to this equation.

(b) x^4 - 20x^2 + 64 = 0

This equation can be factored as:

(x^2 - 8)^2 = 0

x^2 - 8 = 0

x^2 = 8

x = ±√8

x = ±2√2

Therefore, the real solutions to this equation are x = 2√2 and x = -2√2.

Remember to check your solutions by plugging them back into the original equation and seeing if they make the equation true.

Learn more about algebraically

brainly.com/question/24875240

#SPJ11

The EMV (Expected Monetary Value) of the gamble is calculated as follows:
EMV = (probability of return) x (value of return)

a. If the forecast is that the return will be $7M, then the EMV of the gamble is:
EMV = (0.4) x ($7M) = $2.8M
If the forecast is that the return will be $2M, then the EMV of the gamble is:
EMV = (0.6) x ($2M) = $1.2M

b. If the forecast is $7M, the range of p for which it will be optimal to choose the gamble is when the EMV of the gamble is greater than the sure thing of $5M. This can be calculated by setting the EMV of the gamble equal to $5M and solving for p:
$5M = (0.4) x ($7M) + (1-p) x ($2M)
$5M = $2.8M + $2M - $2Mp
$2.2M = $2Mp
p = 1.1

Therefore, the range of p for which it will be optimal to choose the gamble is when p > 1.1.

c. The EVII (Expected Value of Imperfect Information) is the difference between the EMV of the gamble with the forecast and the EMV of the gamble without the forecast. This can be expressed as a function of p as follows:
EVII = (p x EMV with forecast) - (1-p) x EMV without forecast
EVII = (p x ($2.8M)) - (1-p) x ($1.2M)
EVII = $2.8Mp - $1.2M + $1.2Mp
EVII = $4Mp - $1.2M

To graph this function, plot p on the x-axis and EVII on the y-axis. The slope of the line will be $4M and the y-intercept will be -$1.2M.

To know more about probability  refer here:

https://brainly.com/question/30034780

#SPJ11

Answer:

380

Step-by-step explanation:

To find out what number is 600% of another number, we need to divide that number by 600% (or 6).

So:

x = 2,280 ÷ 6

x = 380

Therefore, 600% of 380 is equal to 2,280.

Hope this helped !

The equation (bd)/(b-d) = c can be used to determine how many hours a day the remaining women must work in order to produce the same number of articles each day, when some of the women have been released.

An equation is an expression used to relate two or more quantities, usually by using mathematical operators such as addition, subtraction, multiplication and division. An equation typically has an equal sign (=) as its central element, with the left and right sides of the equation representing the two sides of the equation.

The answer to this question can be determined by using the following equation: (bd)/(b-d) = c. This equation is a simple ratio that takes into account the number of hours the women work per day (b), the number of women released (d), and the number of articles produced each day (c).

For example, if a factory had 10 women working 8 hours a day and produced 100 articles each day, and 5 of those women were released, then the equation (8 x 5) / (8-5) = 100 would determine that the remaining women must work 12.5 hours per day in order to produce the same number of articles.

In conclusion, the equation (bd)/(b-d) = c can be used to determine how many hours a day the remaining women must work in order to produce the same number of articles each day, when some of the women have been released.

For more questions related to ratio,

https://brainly.com/question/13419413

#SPJ1

Lina hops linearly and Kavier hops exponentially

The equations of the functions are Lina: y = 2x + 3 and Kavier: y = 3(2)^x

Linear pattern

The table of values represent the given parameter

For Lina's distance from the tree, we can see that

As the hop increases by 1, the distance covered increases constantly by 2 feet

This represents a linear function

Exponential pattern

For Kavier's distance from the tree, we can see that

As the hop increases by 1, the distance covered doubles

This represents an exponential function

Lina Linear Function

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

(0, 3) and (1, 5)

A linear function is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 3

Using the points, we have

m + 3 = 5

m = 2

So, we have

y = 2x + 3

Kavier Exponential Function

Here, we have

(0, 3) and (1, 6)

An exponential function is represented as

y = ab^x

Where

a = y when x = 0

So, we have

y = 3b^x

Using the points, we have

3b = 6

b = 2

So, we have

y = 3(2)^x

Hence, Kavier's equation is y = 3(2)^x

Read more about functions at

https://brainly.com/question/1415456

#SPJ1

Answer:

= 42m²

Step-by-step explanation:

The ratio of two similar hexagons is 3:7

where the smaller correspond to 3

And

the bigger correspond to 7

where the area of the smaller haxagon is 18

so if 3 = 18m²

then 7 = ?

therefore

[tex] \frac{7}{3} \times 18 \\ = 42 {m}^{2} [/tex]

therefore the area of the bigger hexagon is 42m²

Area of the parallelogram, using the area formula = 851 in².

The area of a parallelogram, which is expressed in square units, is the total number of unit squares that may fit inside of it (like cm², m², in² etc). It is the region that a two-dimensional parallelogram encloses or encompasses.

Hence, the following formula can be used to determine a parallelogram's area:

Area of a parallelogram is equal to b × h square units, where b is the base's length and h is its height.

Here in the question,

b = 37in.

h = 23in.

Area = b × h

= 37 × 23

= 851 in²

To know more about area of parallelogram, visit:

https://brainly.com/question/19187448

#SPJ1

The resulting polynomial in descending order is 11x7 + 5x6

To combine like terms and write the resulting polynomial in descending order, we need to first identify the like terms and then add or subtract their coefficients. Like terms are terms that have the same variable and the same exponent.

In this case, the like terms are 2x^(7) and 9x^(7).

We can combine these like terms by adding their coefficients:

2x^(7) + 9x^(7) = 11x^(7)

Now we have:

11x^(7) + 5x^(6)

Since the exponents are different, we cannot combine these terms.

Therefore, the resulting polynomial in descending order is 11x7 + 5x6

To know more about polynomial refer here:

https://brainly.com/question/11536910#

#SPJ11

Answer:

132, 115

Step-by-step explanation:

For the first one:

Bsc its parallelogram angle x is 132

Second one:

x + 108 + 68 + 59 = 360

x + 235= 360

x = 360 - 235

x = 115

The quadrilateral formed from the points P(7, -3), Q(0,3), R(-9,5), and S(-2,-1)  is a rhombus.

To find the desired slopes and lengths, we can use the slope formula and the distance formula. The slope formula is (y₂ - y₁)/(x₂ - x₁) and the distance formula is √((x₂ - x₁)² + (y₂ - y₁)²).

Slope of PQ = (3 - (-3))/(0 - 7) = 6/(-7) = -6/7
Slope of QR = (5 - 3)/(-9 - 0) = 2/(-9) = -2/9
Slope of RS = (-1 - 5)/(-2 - (-9)) = (-6)/(7) = -6/7
Slope of SP = ((-3) - (-1))/(7 - (-2)) = (-2)/(9) = -2/9

Length of PQ = √((0 - 7)² + (3 - (-3))²) = √(49 + 36) = √85
Length of QR = √((-9 - 0)² + (5 - 3)²) = √(81 + 4) = √85
Length of RS = √((-2 - (-9))² + ((-1) - 5)²) = √(49 + 36) = √85
Length of SP = √((7 - (-2))² + ((-3) - (-1))²) = √(81 + 4) = √85

Since the opposite slopes are equal and all of the lengths are equal, the quadrilateral is a rhombus.

Learn more about rhombus here:

https://brainly.com/question/88523

#SPJ11

The multiplicity of the zero [tex]x=1[/tex] for the function [tex]f(x)=x^2(x-1)^(4)(x+5)[/tex] is 4.


In a polynomial function, the multiplicity of a zero is the number of times that zero appears as a factor in the function. In other words, it is the exponent of the factor corresponding to that zero.

In the given function [tex]f(x)=x^2(x-1)^4(x+5)[/tex], we can see that the zero x=1 corresponds to the factor (x-1)^(4). This means that the multiplicity of the zero x=1 is 4, as it appears as a factor 4 times in the function.

Therefore, the multiplicity of the zero [tex]x=1[/tex] for the function [tex]f(x)=x^2(x-1)^(4)(x+5)[/tex] is 4.

See more about multiplicity at: https://brainly.com/question/11314797

#SPJ11

to get the equation of any straight line, we simply need two points off of it, let's use those two points in the picture below.

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{3}}} \implies \cfrac{ 2 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{ 2 }{ 3 }}(x-\stackrel{x_1}{3}) \\\\\\ y-7=\cfrac{ 2 }{ 3 }x-2\implies {\Large \begin{array}{llll} y=\cfrac{ 2 }{ 3 }x+5 \end{array}}[/tex]

Answer: To rewrite the function to show how quickly the weeds grow each day, we need to use the fact that there are 7 days in a week. Let's divide both sides of the original function by 7 to get:

f(x/7) = 3(1.05)^(x/7)

This function gives the amount of weed growth after x/7 weeks, which is equivalent to x days. To find the daily weed growth rate, we need to take the derivative of this function with respect to x and evaluate it at x=0:

f'(0) = (d/dx) 3(1.05)^(x/7)

Using the chain rule, we get:

f'(0) = 3ln(1.05)/7 ≈ 0.00797

This means that the weeds grow at a daily rate of approximately 0.797%, or 0.00797 as a decimal.

Step-by-step explanation:

This graph shows that Tara’s prints have the potential to be profitable, but will require a significant amount of sales to make a profit.

Profit is the difference between a firm's total revenue and total expenses. It is the amount of money a business has earned after subtracting the cost of goods sold, operating expenses and taxes from its total revenue.

The graph reveals a few key pieces of information that can be used to assess the potential profitability of Tara’s prints. Firstly, the graph shows that there is a fixed cost associated with each print, regardless of how many prints are sold. This cost is represented by the straight line at the bottom of the graph. Additionally, the graph reveals that the cost of the prints increases exponentially as more prints are sold. This means that the more prints Tara sells, the more money she makes. Lastly, the graph shows that the revenue from selling prints is significantly higher than the cost of producing them, indicating that Tara can make a profit if she is able to sell enough prints. Overall, this graph shows that Tara’s prints have the potential to be profitable, but will require a significant amount of sales to make a profit.

For more questions related to revenue,

https://brainly.com/question/8645356

#SPJ1

Answer:     7 .

Step-by-step explanation:

The middle term is, +7x its coefficient is 7 . Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is

Stella's family traveled 2/5 of the total distance to her aunt's house on Sunday.

What is distance ?

Distance is a physical quantity that refers to the length between two points or the amount of space between them. It is typically measured in units such as meters, kilometers, miles, or feet.

Stella's family traveled 3/10 of the distance to her aunt's house on Saturday. Therefore, the remaining distance they had to travel was:

1 - 3/10 = 7/10

On Sunday, they traveled 4/7 of the remaining distance. Therefore, the total distance traveled on Sunday is:

(4/7) x (7/10) = 4/10

Simplifying the fraction 4/10 gives 2/5.

Therefore, Stella's family traveled 2/5 of the total distance to her aunt's house on Sunday.

To know more about distance visit :

https://brainly.com/question/26550516

#SPJ1

Answer:

Step-by-step explanation:

If the graph of the parent function is shifted 7 units up and is steeper than the parent function, which of these could represent the function? answer choices.

Answer:

x = 15°

Step-by-step explanation:

the inscribed angle APB is half the measure of the central angle AOB , so

x = [tex]\frac{1}{2}[/tex] × 30° = 15°

The algebraic expression represents this word description is 7(x - 10) (option D).

One way to approach this problem is to break down the phrase into its components and then use mathematical symbols to represent them.

The phrase contains the word "product," which tells us we need to multiply two quantities.

The first quantity is the number seven, and the second quantity is the difference between a number and ten.

To represent the difference between a number and ten, we can use the variable x to stand for the unknown number.

Then, the difference between x and ten can be expressed as (x - 10).

Putting it all together, the expression that represents the product of seven and the difference between a number and ten is 7(x - 10).

Hence the correct option is (D).

To know more about expression here

https://brainly.com/question/14083225

#SPJ4

Complete Question:

Which algebraic expression represents this word description?

The product of seven and the difference between a number and ten

A. 10-7x

B. 7(10 - x)

C. 7x-10

D. 7(x - 10)

It's not a. If I expanded "a" I would get = (9x - 64y)(9x - 64y) hence the square root. If I did FOIL I would not get the correct answer. "A" is essentially "b" written differently.

Answer:

(3x + 8y) • (3x - 8y)

Step-by-step explanation:

The coordinates of the fourth vertex of the rectangle are (2, 5).

To find the fourth vertex of the rectangle, we need to first determine which sides of the triangle are opposite and parallel to each other. We can see that the two points (-6,3) and (-6,5) lie on a vertical line, which means they are opposite and parallel to each other.

Similarly, the two points (-6,3) and (2,3) lie on a horizontal line, which means they are also opposite and parallel to each other. The fourth vertex of the rectangle must lie at the intersection of these two lines.

The point (-6,3) is the lower left corner of the rectangle, and the point (2,3) is the lower right corner. The distance between these two points is 2 - (-6) = 8. Since the opposite sides of a rectangle are congruent, the distance between the other two corners (-6,5) and the fourth vertex must also be 8.

Since the two points (-6,3) and (-6,5) are on a vertical line, the y-coordinate of the fourth vertex must also be 5. We can find the x-coordinate by moving 8 units to the right of (-6,3), since the rectangle is parallel to the x-axis. Thus, the fourth vertex must be located at the point:

(x,y) = (-6+8, 5)

= (2, 5)

To know more about coordinates here

https://brainly.com/question/27749090

#SPJ4

Answer:

Now, This number is neither a perfect square nor a perfect cube

So, 34 can be evaluated as, 34 = (30 + 4) (15 + 15 + 4)

Here is the evaluated form of 34.

Step-by-step explanation:

is of goggle btw so just change some of the words

Answer:

Step-by-step explanation:

The caterer was able to make 72 (1)/(3) size pieces from the 24 sandwiches.

To find this answer, we can use the following equation:

24 sandwiches × 3 (1)/(3) size pieces per sandwich = 72 (1)/(3) size pieces

This equation tells us that for every sandwich, the caterer was able to make 3 (1)/(3) size pieces. By multiplying the number of sandwiches by the number of (1)/(3) size pieces per sandwich, we can find the total number of (1)/(3) size pieces the caterer was able to make.

Therefore, the caterer was able to make 72 (1)/(3) size pieces from the 24 sandwiches.

To know more about equation click on below link:

https://brainly.com/question/29514785#

#SPJ11

Answer:

15, 15

Step-by-step explanation:

Since this triangle is a right triangle has it's other two angles at 45 degrees, (180-90-45=45 for the last angle) we know that it's a 45-45-90 triangle and can use the rules in the image below to solve the other two sides:

Because the hypotenuse of this triangle is 15[tex]\sqrt{2}[/tex], then we know that the other two side lengths are 15[tex]\sqrt{2}[/tex]/[tex]\sqrt{2}[/tex], or in this case, just 15.

Answer: 15, 15

Step-by-step explanation:

It is a 45, 45, 90 triangle. This means that both of the legs have the same lengths and the hypotenuse is sqrt2 times the length of one of the legs.

Since sqrt2 is irrational, it is easy to look at the coefficient of it. Since the coefficient is 15, the lengths of the sides are also 15.

Answer:

Réponse :Explications étape par étapea) Le vecteur AC(xc-xa;yc-ya)vecteur AC(-6;-3

Step-by-step explanation:

Les coordonnées d'un vecteur dans un r.o.n. décrivent le déplacement qu'il représente. Ainsi, un déplacement de « 3 ...

In statistics, a linear relationship is a connection that runs in a straight line between two variables (or linear association).

Both a mathematical representation of a linear relationship, in which the dependent variable is produced by multiplying the independent variable by the slope coefficient and a constant, and a graphic representation of a linear relationship, in which the variable and constant are connected by a straight line.

A polynomial or non-linear (curved) relationship can be contrasted with a linear relationship.

A linear relationship is one that mathematically answers the question:

y = mx + b

Where,

m = slope

b = y-intercept

"X" and "Y" are two variables in this equation.

To know more about linear relationships, visit:

https://brainly.com/question/15070768

#SPJ1

To solve this problem, we can use a system of equations. Let's represent the amount invested in stocks as x, the amount invested in bonds as y, and the amount invested in CDs as z.

The first equation we can create is the total amount invested:

x + y + z = 85000

The second equation is the difference between the amount invested in bonds and CDs:

y - z = 20000

The third equation is the total interest earned:

0.064x + 0.052y + 0.055z = 4780

We can use substitution to solve this system of equations. Let's rearrange the second equation to solve for y:

y = z + 20000

We can then substitute this value of y into the first equation:

x + (z + 20000) + z = 85000

Simplifying gives us:

x + 2z = 65000

Now, let's substitute the value of y into the third equation:

0.064x + 0.052(z + 20000) + 0.055z = 4780

Simplifying gives us:

0.064x + 0.107z = 3780

We can now use the first and third equations to solve for x and z. Let's rearrange the first equation to solve for x:

x = 65000 - 2z

We can then substitute this value of x into the third equation:

0.064(65000 - 2z) + 0.107z = 3780

Simplifying gives us:

4160 - 0.128z + 0.107z = 3780

Combining like terms gives us:

-0.021z = -380

Solving for z gives us:

z = 18095.24

We can now use this value of z to solve for y:

y = z + 20000 = 18095.24 + 20000 = 38095.24

And finally, we can use the value of z to solve for x:

x = 65000 - 2z = 65000 - 2(18095.24) = 28809.52

So, Maricopa Success invested $28809.52 in stocks, $38095.24 in bonds, and $18095.24 in CDs.

Know more about stocks here:

https://brainly.com/question/29992015

#SPJ11

The value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid is (2a)*(2b)*(2c).

To find the value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid, we need to use the formula for the volume of a parallelopiped. The formula is:

V = l*w*h

Where V is the volume, l is the length, w is the width, and h is the height.

Since we are looking for the largest rectangular parallelopiped, we need to maximize the volume. This can be done by finding the maximum values of the length, width, and height.

The maximum values of the length, width, and height can be found by using the semi-axes of the ellipsoid. The semi-axes of the ellipsoid are given by:

a = √(x^2/a^2 + y^2/b^2 + z^2/c^2)

Where a, b, and c are the semi-axes of the ellipsoid, and x, y, and z are the coordinates of the point on the surface of the ellipsoid.

The maximum values of the length, width, and height can be found by setting the derivatives of the volume with respect to x, y, and z to zero:

∂V/∂x = 0

∂V/∂y = 0

∂V/∂z = 0

Solving these equations will give us the maximum values of the length, width, and height. Once we have these values, we can plug them into the formula for the volume of a parallelopiped to find the largest volume.

The largest volume of the rectangular parallelopiped that can be inscribed in the ellipsoid is given by:

V = (2a)*(2b)*(2c)

Where a, b, and c are the semi-axes of the ellipsoid.

Therefore, the value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid is (2a)*(2b)*(2c).

To know more about rectangular parallelopiped refer here:

https://brainly.com/question/14468924#

#SPJ11

Answer:

-4.4166

Step-by-step explanation:

-23/3+(-11/2)+35/4

-24/3-11/2+35/4

use bodmas

addition first then subtract and u find your LCM.

11/2+35/4=57/4 or 14 1/4

LCM=4

-23/3-57/4=-263/12 or -21 11/12.

LCM=12

final answer= -21 11/12.