I NEED heLP ON THIS ASAP!!!

The roots in simplest form are x=-8+6i and x=-8-6i.

The question is asking you to find the roots of -5x^(2)-80x-140=0 in simplest form by completing the square.

To complete the square, follow the steps below:

1. Divide the coefficient of the x^2 term by 2 and add the result to both sides of the equation:
-5x^2/2 + 80x/2 + 140 = 0 + 5x^2/2

2. Square the coefficient of the x^2 term: (5x^2/2)^2

3. Add this result to both sides of the equation: 5x^2/2 + (5x^2/2)^2 + 80x/2 + 140 = 5x^2/2 + (5x^2/2)^2

4. Rewrite the equation as a perfect square on the left side of the equation: (5x^2/2 + 40x/2)^2 = (5x^2/2 + 40x/2)^2 + 140

5. Take the square root of both sides to solve for x:
5x^2/2 + 40x/2 = ± √140

6. Rewrite the equation as two equations in x:
x = -80 ± √140 / 10

7. Simplify:
x = -8 ± √14  / 1

Therefore, the roots of -5x^(2)-80x-140=0 in simplest form by completing the square are x = -8 ± √14 / 1.
To find the roots in simplest form by completing the square for the equation -5x^(2)-80x-140=0, we need to follow these steps:

1. First, we need to isolate the x terms on one side of the equation. We can do this by adding 140 to both sides of the equation:

-5x^(2)-80x=140

2. Next, we need to factor out the coefficient of the x^(2) term, which is -5:

-5(x^(2)+16x)=-140

3. Now we need to complete the square by adding the square of half of the coefficient of the x term to both sides of the equation:

-5(x^(2)+16x+64)=-140+320

4. Simplify the right side of the equation:

-5(x+8)^(2)=180

5. Divide both sides of the equation by -5:

(x+8)^(2)=-36

6. Take the square root of both sides of the equation:

x+8=±6i

7. Solve for x:

x=-8±6i

To know more about perfect square click on below link:

https://brainly.com/question/13521012#

#SPJ11

$630,463.17

The revenue function in dollars from the sale of x campers is given by:

R(x) = 66,000x + 46,000(10+x)^(-1) - 8000

We can simplify this function as follows:

R(x) = 66,000x + 46,000/(10+x) - 8000

= 66,000x + 4600/(1+x/10) - 8000

To find the x-value that maximizes revenue, we need to find the critical points of the function R(x) and then determine whether each critical point corresponds to a local maximum, local minimum, or neither.

Taking the derivative of R(x) with respect to x, we get:

R'(x) = 66,000 - 4600/(1+x/10)^2

Setting R'(x) equal to zero, we get:

66,000 - 4600/(1+x/10)^2 = 0

Multiplying both sides by (1+x/10)^2, we get:

66,000(1+x/10)^2 - 4600 = 0

Expanding and simplifying, we get:

(x+10)^2 = 44/3

Taking the square root of both sides, we get:

x+10 = ±(2*sqrt(11))/3

Subtracting 10 from both sides, we get:

x = -10 ± (2*sqrt(11))/3

So the critical points of R(x) are:

x = -10 + (2sqrt(11))/3 and x = -10 - (2sqrt(11))/3

To determine whether each critical point corresponds to a local maximum, local minimum, or neither, we can use the second derivative test. Taking the second derivative of R(x), we get:

R''(x) = 9200/(1+x/10)^3

At the critical point x = -10 + (2*sqrt(11))/3, we have:

R''(-10 + (2sqrt(11))/3) = 9200/(1+(-10+(2sqrt(11))/3)/10)^3

= 9200/(1+2*sqrt(11)/30)^3

≈ -318.68

Since R''(-10 + (2sqrt(11))/3) is negative, the critical point x = -10 + (2sqrt(11))/3 corresponds to a local maximum of R(x).

Similarly, at the critical point x = -10 - (2*sqrt(11))/3, we have:

R''(-10 - (2sqrt(11))/3) = 9200/(1+(-10-(2sqrt(11))/3)/10)^3

= 9200/(1-2*sqrt(11)/30)^3

≈ 318.68

Since R''(-10 - (2sqrt(11))/3) is positive, the critical point x = -10 - (2sqrt(11))/3 corresponds to a local minimum of R(x).

Therefore, the x-value that maximizes revenue is x = -10 + (2*sqrt(11))/3, and the maximum revenue is:

R(-10 + (2sqrt(11))/3) = 66,000(-10 + (2sqrt(11))/3) + 46,000/(10-10+(2*sqrt(11))/3) - 8000

≈ $630,463.17

Learn more about revenue

brainly.com/question/8645356

#SPJ11

Answer:

Step-by-step explanation:

The quadrilateral with the specified value for x has a 45° angle.

A polygon with four sides, four angles, and four vertices is called a quadrilateral.

The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.

The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name.

The exterior angles of the given quadrilateral are x°, 3x°, x°, and 3x°.

We are aware that a quadrilateral's total exterior angles are 360°.

Now, x°+3x°+x°+3x°=360°

8x°=360°

x°=45°

Therefore, the quadrilateral with the specified value for x has a 45° angle.

Know more about quadrilaterals here:

https://brainly.com/question/23935806

#SPJ1

Answer:

0.00265251989

Hope this helped.

3525

The next term in the arithmetic sequence that increases by 21, starting at 55, is 76. The next two terms of the Fibonacci sequence are 67 and 109, and the 72nd term is 3525.

  Learn more about arithmetic sequence

  brainly.com/question/25715593

  #SPJ11

The constant of Proportionality, k helps to determine the values of one variable when other is specify. The value of x when y = 3 is equals to the 3/4 or 0.75.

Proportionality defined as ratio that exists between two quantities. Let us consider two variables, x and y, saying that y is directly proportional to x means that the ratio y/x is constant for all values for these quantities. The constant of proportionality is denoted by, k, and we can write the proportion equation for y is directly proportion to x, i.e., y = kx, --(1), where k is constant of proportionality

Also, y =24 when x= 6

To determine the value of k, substitute the known value, y = 24, x = 6

=> 24 = k×6

=> k = 24/6 = 4

so, equation (1) is y = 4x --(2)

To determine the value of x by substituting y = 3,

=> y = 4x

=> 3 = 4x

=> x = 3/4

Hence, required value of x is 3/4.

For more information about Constant of Proportionality, refer: https://brainly.com/question/29372434

#SPJ4

Complete question :

If y is directly proportional with x and y= 24 when x =6. What is the value of x when y= 3?

Answer:

think its this not sure : Alternate interior angles theorem

Step-by-step explanation:

Two families attended a baseball game bought popcorns and souvenir, the cost of each pack of popcorn is $4 and cost of each pack of souvenir is $7.

An expression that depicts the relationship between two or more variables and numbers is called an equation. The provided information can be represented as, using equations:

let x be the price of popcorn and y be the price of souvenir.

First family:

[tex]3x+4y=40[/tex](equation 1)

Second family:

[tex]8x+4y=60[/tex] (equation 2)

We have a system of 2 equations with 2 variables.

3x + 4y = 40

8x + 4y = 60

We are asked for the price of 1 bag of popcorn, x, so we will eliminate y and solve for x.

from equation 2,

[tex]8x+4y=60\\4y=60-8x[/tex]

divide both sides by 4

[tex]\frac{4y}{4} =\frac{60-8x}{4} \\y=15-2x[/tex]

now putting the value of y in equation 1

[tex]3x+4(15-2x)=40\\3x+60-8x=40\\-5x=-20\\x=4\\[/tex]and [tex]y=7[/tex]

Hence, the cost of popcorn is $4 and cost of souvenir is $7.

Learn more about equation at:

brainly.com/question/29174899

#SPJ4

By answering the above question, we may state that Once everyone on unitary method the phone tree has been contacted and advised of the schedule change, the procedure may be repeated.

The unit technique is a strategy for addressing issues that entails first figuring out the value of a single unit, then multiplying that value to figure out the needed value. Simply expressed, the unit technique is used to extract a single unit value from a multiple that is provided.

First, the coordinator phones five persons to let them know that the school's schedule is changing.

Step 2: Those 5 people then each phone 5 more people, resulting in a total of 25 people receiving the news.

Step 3: The 25 call 5 additional individuals each, reaching a total of 125 people.

Step 4: The 125 call 5 additional individuals apiece, reaching a grand total of 625 persons.

Step 5: A total of 3,125 individuals have been told after the 625 phone 5 further persons each.

Once everyone on the phone tree has been contacted and advised of the schedule change, the procedure may be repeated.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1

The height of this prism is equal to 1.5 centimeters.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H

Where:

Substituting the given parameters into the formula for the volume of a rectangular prism, we have;

2.76 = 2.3 × 0.8 × H

Height, H = 2.76/1.84

Height, H = 1.5 centimeters.

Read more on prism here: brainly.com/question/21012007

#SPJ1

We can find g(x) for any value of x by using the function notation g(x) = f(x) + 6.

The function g is related to the parent function f by a vertical shift of 6 units. In function notation, we can write g in terms of f as:

g(x) = f(x) + 6

This means that for any value of x, we can find the corresponding value of g by first finding the value of f at that x value, and then adding 6.
For example, if x = 2, we can find g(2) by first finding f(2) and then adding 6:
f(2) = 2^(2) = 4
g(2) = f(2) + 6 = 4 + 6 = 10
So g(2) = 10.

For more such questions on Functions, visit:

brainly.com/question/12431044

#SPJ11

Answer:

x=5, y=-15

Step-by-step explanation:

7x+2y=5

3x+2y=-15

4x=20

 x=5

7(5)+2y=5

       2y=-30

         y=-15

The Gauss-Jordan elimination method can be used to solve this system of linear equations. First, we need to create an augmented matrix containing all the coefficients of the system:

\begin{bmatrix}
   7 & 7 & 7 & 0 \\
   2 & 2 & -4 & 6 \\
   1 & 1 & -2 & -1 \\
   0 & 0 & 1 & 0 \\
\end{bmatrix}

We then use a series of row operations to reduce the matrix to row echelon form:

\begin{bmatrix}
   7 & 7 & 7 & 0 \\
   0 & -4 & -5 & 6 \\
   0 & 1 & -3 & -1 \\
   0 & 0 & 1 & 0 \\
\end{bmatrix}

Finally, we solve the system of equations by performing back substitution and we get the following solution:

x1 = 0, x2 = 6, x3 = 1, x4 = -2, x5 = 1

To know more on Gauss-Jordan elimination

brainly.com/question/21088742

#SPJ11

The possible number of distinct complex roots for a third-degree polynomial function are 0, 1, 2, or 3, making option (B) the correct answer.

A polynomial function of degree n can have at most n distinct roots. For a third-degree polynomial, n=3, so it can have at most 3 roots.

Complex roots of a polynomial come in conjugate pairs. So if a third-degree polynomial has one real root, then the other two roots must be a conjugate pair of complex roots. If the polynomial has two real roots, then the third root must be a complex root that is not real.

Therefore, the possible number of distinct complex roots for a third-degree polynomial function is 0, 1, 2, or 3, making option (B) the correct answer.

Learn more about Polynomials:

https://brainly.com/question/4142886

#SPJ4

Answer:

So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.

Step-by-step explanation:

Assuming that the tape diagram shows the ratio of adult tickets to child tickets as 3:2, we can represent this as follows:

  AAA

  AAA

  AAA

  CCC

  CCC

In this diagram, each square represents a certain number of tickets. To determine how many tickets each square represents, we need to know the total number of squares in the diagram.

There are a total of 3 + 3 + 3 + 2 + 2 = 13 squares in the diagram. Since the theater sold 126 tickets in total, we can divide 126 by 13 to find out how many tickets each square represents:

126 ÷ 13 ≈ 9.69

So each square in the diagram represents approximately 9.69 tickets. However, since we can't sell fractional tickets, we can round this up to 10 tickets per square. Therefore, each square in the diagram represents 10 tickets.

Answer:

I think the answer is C. 65 m

Step-by-step explanation:

Answer:

L=22

Step-by-step explanation:

For the area of a rectangle you have to multiply the width by the length.

This problem would look like L*W=A. Being that you already have the area and the width, you would just have to fill in for these.

L*6.5=143

Then just follow the rules of PEMDAS to sole for L. In this case this would be dividing 6.5 by both sides.

L=22

Answer:

Step-by-step explanation: g

The correct option is For every 2 white marbles, Hal has 3 black marbles​.

The size, number, or amount of one thing or group as compared to the size, number, or amount of another, is called proportion.

A proportion is a mathematical comparison between two numbers. Often, these numbers can represent a comparison between things or people.

Proportion is an equation that defines that the two given ratios are equivalent to each other.

Proportions are actually equations with equal ratios.

A proportion or proportional situation occurs when two things are related in such a way that the ratios of corresponding parts are equal.

Given that, Hal compared the number of black marbles he had to the number of white marbles he had.

Number of black marble = 9

Number of white marble = 2

The proportion is 9 /2

= 3/2

Hence, the correct option is For every 2 white marbles, Hal has 3 black marbles​.

Learn more about proportion click;

https://brainly.com/question/7096655

#SPJ9

Alex will need 150 tiles to make his mosaic.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the tiles in a two-dimensional plane is called the area of the tiles.

To determine the number of tiles needed to create the mosaic, we need to find out the area of the wall mosaic and then divide it by the area of each tile.

First, let's find the area of the wall mosaic. We can do this by counting the number of squares within the rectangular shape, which is the plan for the mosaic.

By counting, we can see that there are 30 squares in the horizontal direction and 20 squares in the vertical direction. Therefore, the area of the wall mosaic is:

Area of wall mosaic = 30 x 20 = 600 square cm

Now, let's find the area of each tile. The problem tells us that each tile is a square with a side length of 2 cm. Therefore, the area of each tile is:

Area of each tile = 2 x 2 = 4 square cm

Finally, we can find the number of tiles needed by dividing the area of the wall mosaic by the area of each tile:

Number of tiles needed = Area of wall mosaic ÷ Area of each tile

= 600 ÷ 4

= 150

Therefore, Alex will need 150 tiles to make his mosaic.

To know more about an area follow

https://brainly.com/question/30659992

#SPJ9

These are the x-coordinates of the points where the graph intersects the x-axis. We can use these points to sketch the curve of the function.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

The function ƒ(x) = −x³ + 4x² − 2 is a cubic function, which means that it is a polynomial of degree 3. The general form of a cubic function is:

ƒ(x) = ax³ + bx² + cx + d

where a, b, c, and d are constants. In the given function, we have:

a = -1

b = 4

c = 0

d = -2

Therefore, we can rewrite the function as:

ƒ(x) = -x³ + 4x² - 2

This function can be graphed to show the shape of the curve it creates. The graph of a cubic function is a curve that can either be concave up or concave down, depending on the sign of the leading coefficient. In this case, the leading coefficient is negative, so the graph will be concave down. The function has a y-intercept of -2, which means that it intersects the y-axis at the point (0, -2). To find the x-intercepts, we can set ƒ(x) equal to zero and solve for x:

ƒ(x) = -x³ + 4x² - 2 = 0

We can use factoring or the quadratic formula to solve for x, but in this case, the equation can be simplified by factoring out a common factor of x²:

-x²(x - 4) + 2 = 0

Now we can solve for x:

x² = 2/(4 - x)

x = ±√(2/(4 - x))

To know more about equation,

https://brainly.com/question/2228446

#SPJ9

Complete question:

Solve for x when  ƒ(x) = −x³ + 4x² − 2.

Answer:

2500

Step-by-step explanation:

Total spectator 9500

Men 6375

Women and children = 9500-6375= 3125

Women X

Children 4X

If women and children = 3125

4x + X = 3125

5x = 3125

Divide both sides by 5

X = 625

Women 625

Children 625x4 = 2500

The Aerobics instructor teaches 7 classes each Saturday.

what is Algebraic expression?

An Algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.

To find the number of classes the Aerobics instructor teaches on Saturdays, we need to divide the total hours she teaches by the length of each class:

Total hours taught = 5 1/4 hours

Length of each class = 3/4 hour

Number of classes = (Total hours taught) / (Length of each class)

Number of classes = (5 1/4) / (3/4)

We need to convert the mixed number to an improper fraction first:

5 1/4 = (4 x 5 + 1) / 4 = 21/4

Now we can substitute the values:

Number of classes = (21/4) / (3/4)

fractions mean multiplying the first fraction by the reciprocal of the second fraction:

Number of classes = (21/4) * (4/3)

The 4 in the numerator and denominator cancel out, leaving us with:

Number of classes = 21/3

Dividing 21 by 3, we get:

Number of classes = 7

Therefore, To find the number of classes the Aerobics instructor teaches on Saturdays, we need to divide the total hours she teaches by the length of each class:

Total hours taught = 5 1/4 hours

Length of each class = 3/4 hour

Number of classes = (Total hours taught) / (Length of each class)

Number of classes = (5 1/4) / (3/4)

We need to convert the mixed number to an improper fraction first:

5 1/4 = (4 x 5 + 1) / 4 = 21/4

Now we can substitute the values:

Number of classes = (21/4) / (3/4)

Dividing fractions means multiplying the first fraction by the reciprocal of the second fraction:

Number of classes = (21/4) * (4/3)

The 4 in the numerator and denominator cancel out, leaving us with:

Number of classes = 21/3

Dividing 21 by 3, we get:

Number of classes = 7

Therefore, the Aerobics instructor teaches 7 classes each Saturday.

To learn more about algebraic expression from given link

https://brainly.com/question/28884894

#SPJ1

Answer:x = 3 and y = 5

Step-by-step explanation:

We have two equations:

-3x + 3y = 6 ........(1)

x + 3y = 18 ........(2)

We can use the second equation to solve for y in terms of x:

-4x = -12

x = 4

Now we substitute this expression for y into the second equation:

3 + 3y = 18

3y = 15

y = 5

Therefore, the solution to the system of equations is x = 3 and y = 5.

equation 1: - 3x + 3y = 6

equation 2: x + 3y = 18

start with equation 2:

x + 3y = 18

subtract 3y from both sides:

x = 18 - 3y

plug the new equation into equation 1:

- 3x + 3y = 6

- 3 (18 - 3y) + 3y = 6

multiply:

-54 + 9y + 3y = 6

collect like terms:

-54 + 12y = 6

add 54 to both sides, then divide the whole equation by 12:

12y = 60

y = 5

plug the y value into either equation to solve for x. for example, here is equation 2:

x + 3y = 18

x + 3(5) = 18

x + 15 = 18

x = 3

check answer:

x + 3y = 18

3 + 3(5) = 18

3 + 15 = 18

18 = 18 is true

Answer:

t = 56 degree

Step-by-step explanation:

A triangle is 180 degrees.

The angle on the right is a vertical angle to the 34-degree angle, meaning their angles are equal.

We know two angles; one is 90 degrees, and the other is 34 degrees. To find the angle t, we take

180 - 90 - 34 = 56 degree

So, t = 56 degree

The method for calculating the area of a figure depends on the type of figure.

Here are some common formulas for finding the area of different shapes:

Square: To find the area of a square, you multiply the length of one side by itself: Area = side x side or A = s²

Rectangle: To find the area of a rectangle, you multiply the length by the width: Area = length x width or A = lw

Triangle: To find the area of a triangle, you multiply the base by the height and divide by 2: Area = 1/2 x base x height or A = 1/2 bh

Circle: To find the area of a circle, you multiply pi (3.14) by the radius squared: Area = pi x radius^2 or A = πr^2

Trapezoid: To find the area of a trapezoid, you multiply the average of the bases by the height: Area = 1/2 x (base1 + base2) x height or A = 1/2 (b1 + b2)h

These are just some of the formulas for calculating the area of different shapes. Depending on the figure you're working with, you may need to use a different formula or combination of formulas to find the area.

Learn more about area on:

https://brainly.com/question/25292087

#SPJ1

Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

The OLS estimate of the return to an additional year of schooling is 0.074. This means that for every additional year of schooling, the individual's earnings will increase by 7.4%. This is statistically significant at the 5% level of significance because the t-value is 0.074/0.025 = 2.96, which is greater than the critical value of 1.96.

However, Sharon is not correct in thinking that this is the true return to schooling. This is because there may be other factors that affect earnings that are not included in the model, such as ability or family background. These omitted variables can bias the estimate of the return to schooling.

Sharon could use the information about the starting age and compulsory schooling age to obtain the true return to schooling. This is because these rules create exogenous variation in the amount of schooling that individuals receive. She could use this exogenous variation to estimate the causal effect of schooling on earnings by using an instrumental variables approach. By using the starting age and compulsory schooling age as instruments for years of schooling, she could obtain an unbiased estimate of the true return to schooling.

Learn more about interested

brainly.com/question/27584159

#SPJ11

When he rests for a few hours after coming back from ice-store he rests for 2 hours the time the plane takes off is 9:10 pm.

Total distance traveled is 151 miles.

Dave spends 25 + 10 + 55 + 25 = 115 minutes (or 1 hour and 55 minutes) on stops.

Dave rests for 2 hours.

To calculate the time the plane takes off, we need to add up all the time Dave spends on driving, stops, and rests, and then add that time to the time he starts (12:45 pm).

Time to drive from A to C and back to A: 2 * 6 / 60 = 0.2 hours

Time to drive from A to C to D to B to A: (6 + 24 + 24 + 3) / 60 = 0.95 hours

Time to drive from A to C to D to home to E to market to E: (6 + 24 + 24 + 40 + 5 + 5) / 60 = 2.33 hours

Time to rest: 2 hours

Total time spent: 0.2 + 0.95 + 2.33 + 1.92 = 5.4 hours

Time of departure: 12:45 pm + 5.4 hours = 6:25 pm

Adding 45 minutes for the luggage check and boarding, the plane takes off at 6:25 pm + 0.45 hours = 7:10 pm

Adding another 2 hours for the time zone difference, the plane takes off at 7:10 pm + 2 hours = 9:10 pm.

To learn more about time follow the link: brainly.com/question/28050940

#SPJ4