Luke is organizing textbooks on his bookshelf. He has an English textbook, a biology textbook, and a history textbook. How many different ways can he line the textbooks up on his bookshelf?

The roots of equation A are  2 and 0.25.

The roots of equation B are 3.14 and -0.64.

To solve for the roots of a quadratic equation using the Quadratic Formula, we can use the formula:

x = (-b ± √(b² - 4ac)) / (2a)

Where a, b, and c are the coefficients of the equation.

For equation A, a = 4, b = -9, and c = 2. Plugging these values into the Quadratic Formula, we get:

x = (-(-9) ± √((-9)² - 4(4)(2))) / (2(4))
x = (9 ± √(81 - 32)) / 8
x = (9 ± √49) / 8
x = (9 ± 7) / 8

This gives us two possible values for x:

x = (9 + 7) / 8 = 2
x = (9 - 7) / 8 = 0.25

Therefore, the roots of equation A are 2 and 0.25.

For equation B, a = 2, b = -7, and c = -1. Plugging these values into the Quadratic Formula, we get:

x = (-(-7) ± √((-7)² - 4(2)(-1))) / (2(2))
x = (7 ± √(49 + 8)) / 4
x = (7 ± √57) / 4

This gives us two possible values for x:

x = (7 + √57) / 4 ≈ 3.14
x = (7 - √57) / 4 ≈ -0.64

To know more about quadratic equation click on below link:

https://brainly.com/question/30098550#

#SPJ11

The expression to represent the total cost of hiring a plumber is y = 50 + 40x

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

Charges = $50 for visiting

Rate = $40 every hours

Represent the number of hour with x and the total charge with y

Using the above as a guide, we have the following:

y = Charges + Rate * x

Substitute the known values in the above equation, so, we have the following representation

y = 50 + 40x

Hence, the equation is y = 50 + 40x

Read more about linear relation at

https://brainly.com/question/30318449

#SPJ1

The simplest form of the given expression x will be 42.

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial.

When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

Here we assume that no of suitcases be x

So, 7/24 = x/144

24x = 1008

x = 42.

Hence the simplest form of the given expression x will be 42.

Learn more about polynomials, by the following link.

https://brainly.com/question/2833285

#SPJ1

The given sequence is not a geometric sequence, the quotients between consecutive numbers are different.

Remember that the recursive formula for a geometric sequence is:

f(n) = r*f(n - 1)

Where r is the common ratio.

Here we have the terms:

5, 11, 29, 83

To get the value of r, take the quotient between consecutive terms:

r = 11/5 = 2.2

r = 29/11 = 2.63

r = 83/29 = 2.86

We should get the same value of r for every ofthese quotients, then we can conclude that the given sequence of numbers is not a geometric sequence, is other type of sequence.

Learn more about geometric sequences at:

https://brainly.com/question/24643676

#SPJ1

The medial triangle of a given triangle ABC has sides parallel to and half the length of the sides of triangle ABC.

To prove that the medial triangle of a given triangle ABC has sides parallel to and half the length of the sides of triangle ABC, we can use the following steps:
Draw triangle ABC and label its vertices as A, B, and C.

Find the midpoints of the sides of triangle ABC. Let's call these midpoints D, E, and F.

Draw the medial triangle DEF, connecting the midpoints of the sides of triangle ABC.

We need to prove that the sides of triangle DEF are parallel to the sides of triangle ABC. To do this, we can use the fact that the midpoints of the sides of a triangle divide the sides into two segments of equal length.

Since the midpoints of the sides of triangle ABC are D, E, and F, we know that AD = DB, BE = EC, and CF = FA.

We can also use the fact that if two lines are parallel and the corresponding angles are equal, then the corresponding sides are also parallel.

Since AD = DB and BE = EC, we know that angle ADB = angle BEC and angle BDE = angle CEF.

Therefore, we can conclude that the sides of triangle DEF are parallel to the sides of triangle ABC.

To prove that the sides of triangle DEF are half the length of the sides of triangle ABC, we can use the fact that the   midpoints of the sides of a triangle divide the sides into two segments of equal length.

Since the midpoints of the sides of triangle ABC are D, E, and F, we know that AD = DB, BE = EC, and CF = FA.

Therefore, we can conclude that the sides of triangle DEF are half the length of the sides of triangle ABC.

So, the medial triangle of a given triangle ABC has sides parallel to and half the length of the sides of triangle ABC.

Learn more about Triangle

brainly.com/question/2773823

#SPJ11

The angle οf elevatiοn is 63.4 degrees.

Angle οf elevatiοn is the angle between the hοrizοntal line οf sight and an οbject abοve the οbserver. It is measured with an angle starting frοm the hοrizοntal line and increasing in the upward directiοn. It is alsο knοwn as the angle οf elevatiοn οr inclinatiοn. The angle οf elevatiοn is used in navigatiοn, astrοnοmy and trigοnοmetry.

Tο find the angle οf elevatiοn, we can use the fοrmula fοr finding angles in a triangle. This fοrmula states that the sum οf all angles in a triangle is 180 degrees. Tο sοlve fοr the angle οf elevatiοn, we need tο begin by first finding the length οf the οppοsite side οf the triangle. This is dοne by subtracting the distance οf the snake frοm the fοοt οf the pοle frοm the height οf the pοle.

Therefοre, the length οf the οppοsite side οf the triangle is 7 feet. Nοw, we can use the tangent fοrmula tο sοlve fοr the angle οf elevatiοn. This fοrmula states that the tangent οf an angle is equal tο the length οf the οppοsite side divided by the length οf the adjacent side.

Let's find the angle of elevation.

tan ∅ = opposite / adjacent

where

∅ = angle of elevation

Therefore,

tan ∅ = 27 / 20

∅ = tan⁻¹ 1.35

∅ = 53.471144633

∅ = 53.5 degrees

For more questions related to tangent,

brainly.com/question/4470346

#SPJ1

By forming and solving the equations we know that the speed of the plane was 220 mph.

In mathematical formulas, the equals sign is used to indicate that two expressions are equal.

A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation.

like 3x + 5 = 15, for instance.

Equations come in a wide variety of forms, including linear, quadratic, cubic, and others.

So, d = rt.

t = d/r

The distances are equal.

140/r = 440/(r + 150)

Cross multiply:

140(r + 150) = 440r

140r + 21,000 = 440r

300r = 21,000

r = 70

70 + 150 = 220 mph

Therefore, by forming and solving the equations we know that the speed of the plane was 220 mph.

Know more about equations here:

brainly.com/question/22688504

#SPJ1

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

Answer:

Step-by-step explanation: I don’t know

Answer:

51.2

Step-by-step explanation:

By dividing :0

The graph that shows the number of bottles that need to be sold to earn back the money spent on water is Graph C.

The number of bottles that need to be sold to earn back the amount spent on water is :

= Total spent / profit per bottle

= 50 / 2

= 25 bottles

Graph C starts from - $ 50 to show that the amount you have is - $ 50 to show the amount spent on the bottles.

Graph C then ends at 25 bottles to show that this is where you would need to stop to have made back what you spent.

Find out more on graphs at https://brainly.com/question/3889458

#SPJ1

a) 0.33143; b) 17586.76

a) 33.143 / 100

   33.143 ÷ 100

       = 0.33143

b) 175.876 / 0.01

   175.876 ÷ 0.01

       = 17586.76

Learn more about long division

brainly.com/question/28824872

#SPJ11

Answer:

[tex] - \frac{5x}{34} + 14y + 9[/tex]

Step-by-step explanation:

Just making sure. If the way the equation is written is

[tex]1 + 1 - \frac{5}{34} x + 14y + 7[/tex]

then yeah, that's the answer. If it's formatted differently, send a comment so that I could give you the proper answer.

Answer:

29+3374=32483 that is the solution for the question

hope this helps <3

Answer:

X=5

Step-by-step explanation:

instructions refer to the image

The coefficients of the terms in the polynomial are 8, 6, and 8, and the degrees are 2, 1, and 0

The coefficient of a term in a polynomial is the number that is multiplied by the variable. The degree of a term is the exponent of the variable. In the polynomial 8x^(2)+6x+8, there are three terms:

- The first term is 8x^(2). The coefficient of this term is 8, and the degree is 2.
- The second term is 6x. The coefficient of this term is 6, and the degree is 1.
- The third term is 8. The coefficient of this term is 8, and the degree is 0 (since there is no variable).

Therefore, the coefficients of the terms in the polynomial are 8, 6, and 8, and the degrees are 2, 1, and 0.

Learn more about Coefficient

brainly.com/question/28975079

#SPJ11

The Big Ideas or Focal Points in the mathematics curriculum for grade 6 are: 1. Ratios and Proportional Relationships
2. The Number System.  3. Expressions and Equations.  4. Geometry.  5. Statistics and Probability.

1. Ratios and Proportional Relationships: Students should be able to understand and use ratios to describe relationships between quantities, and use proportional reasoning to solve problems.

2. The Number System: Students should be able to understand and use negative numbers, and perform operations with multi-digit numbers and decimals.

3. Expressions and Equations: Students should be able to write and evaluate expressions, and use equations to solve problems.

4. Geometry: Students should be able to understand and use the properties of shapes and the relationships between them.

5. Statistics and Probability: Students should be able to use data to make predictions and understand the concept of probability.

These Big Ideas or Focal Points are the key concepts that students should master in grade 6 mathematics in order to be prepared for higher-level math courses.

Know more about Focal Points here:

https://brainly.com/question/30761313

#SPJ11

The correct answer to this question is 7/220. To calculate this answer, divide the number of students who preferred the turkey club (7) by the total number of seventh-grade students (220). The fraction form of this answer is 7/220, the decimal form is 0.0318, and the percentage form is 3.18%.

Proportion is a mathematical concept that compares two values, which can be the same or different, using division. It is used to identify the relationship between two or more values. It can also be used to compare the parts of a whole or to compare two different wholes. Proportions can be expressed as a fraction, a decimal, or a percentage.

This answer can be used to estimate the number of students who preferred the turkey club. To do this, multiply the total number of seventh-grade students (220) by the proportion (7/220). This calculation results in 7 students. In other words, approximately 7 of the 220 seventh-grade students preferred the turkey club.

The proportion 7/220 can also be used to estimate the number of students who preferred the turkey club if the total number of seventh-grade students changes. For example, if the total number of seventh-grade students increases to 250, the estimated number of students who preferred the turkey club can be calculated by multiplying the new total (250) by the proportion (7/220). This calculation results in 8 students.

Therefore, the correct answer to the question is 7/220.

For more questions related to numbers

https://brainly.com/question/28223520

#SPJ1

The maximum number of hours that you can park in the garage if you wish to pay no more than $14 is 5 hours.

Here's how to calculate it:

Therefore, the maximum number of hours you can park in the garage if you wish to pay no more than $14 is 5 hours.

For more information about divide, visit:

https://brainly.com/question/25289437

#SPJ11

Answer:

Mother: £200, Sister: £80, Mary: £120

Step-by-step explanation:

Mary has a total of £400 to start off with.

In order to calculate the amount she gives to her mother, we must multiply 400 by .5 (the decimal equivalent of 50%), which leaves us with £200 to her mother.

Do the same with her sister; multiply 400 by .2 (the decimal equivalent of 20%), which leaves us with £80.

To figure out what she is left with,  £400 - 200 - 80 = £120. Mary is left with £120.

Mary will have £120 with her, her mother will have £200 and her sister will have £80.

Percentages are fractions with 100 as the denominator. It is the relation between part and whole where the value of whole is always taken as 100.

Given that, Mary won £400.

She gave 50% to her mother, 20% to her sister and rest she kept with herself,

So,

The amount her mother got =

50% of £400 = 1/2 × 400 = 200

Therefore, her mother got £200.

The amount her sister got =

20% of £400 = 1/5 × 400 = 80

Therefore, her sister got £80.

The amount Mary have = 400 - (200+80) = 400 - 280 = £120

Hence Mary will have £120 with her.

Learn more about percentage, click;

https://brainly.com/question/29306119

#SPJ2

Answer:

You are distributing (multiplying) the three to all the terms in the parentheses.

Start:

3(x-2) = 4x + 2

Next:

3x - 6 = 4x +2

After that simplify:

-8 = x

Hope this helps!

Answer:

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The property we use,

→ Distributive property.

The equation is,

→ 3(x - 2) = 4x + 2

Then the value of x will be,

→ 3(x - 2) = 4x + 2

→ 3(x) - 3(2) = 4x + 2

→ 3x - 6 = 4x + 2

→ 3x - 4x = 2 + 6

→ -x = 8

→ [ x = -8 ]

Hence, the value of x is -8.

Answer:

[tex]\boxed{The \ height \ of \ the \ tabletop \ is \ 63.5 \ centimeters}[/tex]

Step-by-step explanation:

We are given that,

Length of the base = 127 centimeters

Width of the base = 85 centimeters

Area of the trapezoid shaped base = 6,731 square centimeters.

Since, we know,

[tex]\bold{Area \ of \ a\ trapezoid}=\frac{Length +Width}{2}\times Height[/tex]  

So, we get,

[tex]6731=\frac{127+85}{2}\times Height[/tex]

i.e. [tex]6731=\frac{212}{2}\times Height[/tex]

i.e. [tex]6731=106\times Height[/tex]

i.e. [tex]Height=\frac{6731}{106}[/tex]

i.e. Height = 63.5 centimeters

Hence, the height of the tabletop is 63.5 centimeters.

The  product of 3∛6 and 2∛6 is equals to 18.

What is underroot ?

In mathematics, the symbol "√" is called the radical symbol, and the expression written under it is called a radicand.

To simplify 3∛6, we can use the fact that the cube root of a number can be written as a power of that number with an exponent of 1/3. Therefore, 3∛6 can be rewritten as 6^(1/3) raised to the power of 3.

D) To add 3∛6 and 2∛6, we can first factor out the common term of ∛6:

3∛6 + 2∛6 = (3 + 2)∛6 = 5∛6

So the sum of 3∛6 and 2∛6 is 5∛6.

E) To subtract 2∛6 from 4∛6, we can again factor out the common term of ∛6:

4∛6 - 2∛6 = (4 - 2)∛6 = 2∛6

So the difference between 4∛6 and 2∛6 is 2∛6.

F) To multiply 3∛6 by 2∛6, we can use the fact that the product of two roots with the same index can be found by multiplying the radicands together:

3∛6 x 2∛6 = (3 x 2)∛(6 x 6) = 6∛36

Since the cube root of 36 is 3 (3 x 3 x 3 = 27 and 4 x 4 x 4 = 64), we can simplify this further:

6∛36 = 6 x 3 = 18

Therefore, the product of 3∛6 and 2∛6 is equals to 18.

To learn more about Underroot from given link.

https://brainly.com/question/21492333

#SPJ1

The polyhedron that can be constructed using this net is a triangular pyramid.

A triangular pyramid is a polyhedron that has four faces, with one of the faces being a square and the other three faces being equilateral triangles. The given net shows a square in the center, with three equilateral triangles attached to each of its sides. When the net is folded along the edges, the square becomes the base of the pyramid and the three equilateral triangles become the sides of the pyramid. Therefore, the polyhedron that can be constructed using this net is a triangular pyramid.

Learn about Polyhedron

brainly.com/question/28718923

#SPJ11

Answer:

It's neither of them. The function is neither odd nor even

The sunflower would be 30 inches tall after 30 weeks. The sunflower be after w weeks would be 25 + 0.5 * w inches tall.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

To calculate the height of the sunflower after 10 weeks, we can use the formula:

=>height = starting height + growth rate * time elapsed

where the starting height is 25 inches, the growth rate is 0.5 inches per week, and the time elapsed is 10 weeks.

So the height after 10 weeks would be:

=>height = 25 + 0.5 * 10 = 25 + 5 = 30 inches

Therefore, the sunflower would be 30 inches tall after 10 weeks.

To calculate the height after w weeks, we can use the same formula:

=>height = 25 + 0.5 * w

So the height after w weeks would be:

=>height = 25 + 0.5 * w inches

To learn more about expression refer the below link

https://brainly.com/question/112703

#SPJ1

The function that represents an exponential growth would be = f(X) = 0.3 ( 1.05) ^x. That is option C.

An exponential growth of a function is defined as the growth that shows increase rates with respect to a given time.

There are two types of exponential functions: exponential growth and exponential decay.

The function that shows an exponential growth has the formula = f (x) = b^x, when b > 1.

From the examples given in the options above, the correct option that represents the exponential growth is f(X) = 0.3 ( 1.05) ^x. Thai so because 1.05 is greater than 1.

Learn more about growth here:

https://brainly.com/question/25630111

#SPJ1

Completing the table to show the total cost of uniforms with tax, for groups of students from the four states is as follows:

State              Number     Total Cost

                  of Students    (After-tax)

Idaho                     10        $1,431.00

Mississippi             5          $722.25

Hawaii                  15        $2,106.00

Wisconsin             8          $1,134.00.

The total cost for each group of students from the four states can be determined by multiplication.

The multiplication operation for each group or state first computes the total cost before tax and the total cost after tax.

The total cost after tax uses the sales tax factor or rate to multiply the total cost before tax.

Generally, sales taxes are levied by state and local governments to check the consumption and production of certain items and to increase the revenue of the government.

The price before state sales tax of each uniform = $135

Relevant Taxes and Number of Students:

State           Number of Students     Sales Tax Rate

Idaho                     10                                 6%

Mississippi             5                                  7%

Hawaii                  15                                  4%

Wisconsin             8                                  5%

State              Number      Total Cost     Total Cost

                  of Students    (Before tax)    (After-tax)

Idaho                     10        $1,350            $1,431.00 ($135 x 10 x 1.06)

Mississippi             5           $675             $722.25 ($135 x 5 x 1.07)

Hawaii                  15        $2,025          $2,106.00 ($135 x 15 x 1.04)

Wisconsin             8         $1,080            $1,134.00 ($135 x 8 x 1.05)

Learn more about the sales tax at https://brainly.com/question/30494127

#SPJ1