Zack and Jack share a sum of money in the ratio 12:11 Zack got £14 more than Jack. How much did Zack receive?

Answer:

Step-by-step explanation:

In the equation ax + b = 0, the value of x is not fixed and can vary based on the values of a and b. The purpose of this equation is to find the value of x that satisfies the equation, given the values of a and b.

For example, if a = 3 and b = -6, then the equation becomes 3x - 6 = 0. Solving for x, we get x = 2. Thus, 2 is the value of x that satisfies the equation.

The reason 0 is often used as an answer to this equation is because it represents a special case where b = 0. In this case, the equation becomes ax = 0, and the only solution is x = 0. However, in general, the value of x can be any real number that satisfies the equation.

To design a cylindrical can (with a lid) to contain 1 liter (= 1000 cm3) of water, using the minimum amount of metal, we need to consider the following parameters:Height and Diameter of the canThickness of the metalMaterial used for making the canLet's assume we use Aluminium as a material. Now, let's start designing the can:Height of the can:

Volume of water = 1000 cm3Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³h = (4000 cm³) / (π d²) h = (4000 cm³) / (3.14 * d²) h = (1273.24) / d²Diameter of the can:

Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³d² = (4000 cm³) / h d² = (4000 cm³) / (1273.24/d²) d² = 3.1425d = 17.8 cmThickness of the metal:We can assume the thickness to be 0.5 mm.Material used for making the can:AluminiumTotal Surface Area of the can:Total Surface Area of cylinder = 2πrhTotal Surface Area of cylinder = 2π(d/2)(1273.24/d²)Total Surface Area of cylinder = 1273.24/d Total Surface Area of lid = πr²Total Surface Area of lid = π (d/2)²Total Surface Area of lid = π (17.8/2)²Total Surface Area of lid = 248.5Total Surface Area of the Can = 1273.24/d + 248.5Now, we can calculate the minimum amount of Aluminium required to make the can by minimizing the Total Surface Area of the can.Total Surface Area of the can = 1273.24/d + 248.5d (in cm)Total Surface Area of the can = 1273.24/7.09 + 248.5(7.09)Total Surface Area of the can = 584.24Therefore, the minimum amount of Aluminium required to make the can is 584.24 cm².

for such more questions on Total Surface Area

https://brainly.com/question/31186196

#SPJ11

There will be 30 yards of the string that will be leftover.

What are Arithmetic operations?

It is a field of mathematics that deals with the study of numbers and the operations on those numbers that are relevant to all other areas of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division. The term "arithmetic operator" refers to the operator that does the calculation.

Given that,

Total Length of string = 50 yards.

The total number of students = 24.

Total used string = 24 × 30 = 720.

We know that 1 foot = 12 inches,

So, 150 feet = 1800 inches.

Therefore, yards of string leftover = (1800 - 720)/36

                                                         = 1080/36

                                                         = 30 yards.

Hence, there will be 30 yards of string that will be leftover.

To learn more about arithemetic operations, refer to:

https://brainly.com/question/25834626

#SPJ4

The number of students traveling are 2 students out of the 30 who are traveling out of the country this summer.  If 1/3 of the students are traveling somewhere this summer, then we can calculate the number of students who are traveling by multiplying the total number of students by 1/3:

Number of students traveling = 30 x 1/3 = 10  

Now, we need to find out how many of these 10 students are traveling out of the country. We know that 1/5 of the students who are traveling are going out of the country, so we can find the number of students who are traveling out of the country by multiplying the total number of traveling students by 1/5:

Number of students traveling out of the country = 10 x 1/5 = 2

Therefore, there are 2 students out of the 30 who are traveling out of the country this summer.

It's important to note that fractions can be converted to decimals or percentages to make them easier to work with. For example, 1/3 can be written as 0.33 or 33%, and 1/5 can be written as 0.20 or 20%. This can be particularly useful when dealing with more complex problems or when working with larger numbers.

In summary, by using the information given, we can determine that out of the 30 students in Mr. Hall's class, 10 are traveling somewhere this summer, and out of those 10 students, 2 are going out of the country. This type of problem-solving helps build math skills that are applicable in real-world scenarios, such as budgeting and planning for travel.

To know more about  traveling click here:

brainly.com/question/17235551

#SPJ4

Cοnsequently, 960 tiles οf a 50 by 25 cm size will be needed tο cοver the 15m x 8m flοοr.

Cοmparing a quantitative measurement with a recοgnized standard amοunt οf sοme kind is the act οf measurement. Fοr instance, in the measurement 10 kg, kg is indeed the basic measure used tο describe mass οf a physical quantity, and 10 is the size οf the physical quantity.

Calculate the flοοr's tοtal square fοοtage in meters, then divide it intο the area οf each tile tο determine the necessary number οf tiles. The measurements must first be changed tο a cοmparable unit. By dividing by 100, we may cοnvert centimeters tο meters:

15m = 1500cm

8m = 800cm

In square meters, the flοοr space is as fοllοws:

1500cm x 800cm = 1200000cm² = 120m²

The area οf the each tiles in square meters must nοw be determined. The size οf each tile, which is 50 by 25 centimetres, is as fοllοws:

50cm x 25cm = 1250cm² = 0.125m²

Lastly, by dividing the entire flοοr area even by area οf each tile, we can determine the necessary number οf tiles:

120m² / 0.125m² = 960 tiles

The flοοr will therefοre need 960 tiles that are 50 cm by 25 cm in size tο cοver its 15 m × 8 m surface.

To know more about Measure visit:

brainly.com/question/4725561

#SPJ1

Answer:Given : number of hours spent studying for a history final exam and the score on that exam.

To Find : Which value is an outlier

(1.5, 65)

(3.5, 71)

(4.5, 98)

(6.5, 88)

Solution:

Number of hours spent studying =x            

Exam score   = y

x         y

1.5       65

2         68

3.5      71

4.5      98

6         82

1.5 -   2   difference = 0.5

2 - 3.5     difference = 1.5

3.5 - 4.5   difference = 1

4.5 - 6       difference = 1.5

No outlier

65  - 68   Difference  3

68 - 71      Difference  3

71 -  98      Difference  27

71 - 82     Difference  11

Hence 98 is outlier

(4.5    ,  98 )  is outlier

Learn More:

Mrs. Juarez graded ten English papers and recorded the scores. 92 ...

brainly.in/question/16382460

If the first quartile is 142 and the semi-interquartile range is 18, find ...

brainly.in/question/13279139

first quartile is 20 then semi-inter quartile range is

brainly.in/question/13187486

Step-by-step explanation:

We have that, given the system with a component that can fail, we can find the following probabilities

a) To approximate the probability that the system will continue to function after 3625 days, we can use the exponential distribution and its associated properties. The probability that the system is still working after 3625 days is equal to the probability that none of the 120 components have failed, which is equal to:

Probability = e(-120*(3625-25)/25) = 0.091

b) To approximate the probability that the system will continue to function after 4250 days, we must take into account the time required to replace a defective component. Since the time required to replace a defective component is a random variable that is uniformly distributed over (0,0,5), the expected time to replacement is 0.25. Therefore, the probability that the system is still working after 4250 days is equal to:

Probability = e(-120*(4250-25)/25) * e(-120*(0.25)/25) = 0.018

See more information on exponential distribution in: https://brainly.com/question/28256132

#SPJ11

Answer:

4.75 liters of punch

Step-by-step explanation:

2.8 + 0.75 = 3.55

3.55 + 1.2 = 4.75 liters of punch

The total surface area of the remaining portion is approximately 23.14 in.

To find the total surface area of the remaining portion of a wooden sphere after two equal caps have been removed, use the formula SA = 4πr2. A sphere is symmetrical, and thus, the diameter of the wooden sphere is equal to the diameter of the remaining portion. The radius of the remaining portion is equal to half the diameter of the sphere minus the radius of the cap.

The diameter of the wooden sphere is 11.8 in. As such, the radius of the sphere is 5.9 in. If two equal caps are removed, the diameter of the remaining portion is equal to 11.8 in - 2x R_cap, where R_cap is the radius of the cap. Since the caps are equal, we can simplify the formula to

D = 11.8 - 2R_cap. R_cap is equal to the radius of a circle with area equal to the surface area of one cap. As such, we can use the formula SA = 2πrh + πr2 to find the surface area of the cap. We know the diameter of the sphere is 11.8 in. Thus, the radius of the sphere is 5.9 in. We also know that the height of the cap is 5.9 in. Since the caps are equal, we can use the formula to find the surface area of one cap and multiply by 2 to get the total surface area of both caps.

SA_cap = 2π(5.9 in)(5.9 in) + π(5.9 in)

2SA_cap = 2π(34.84 in2) + π(34.84 in2)

SA_cap = 2π(34.84 in2) + 109.45 in2SA_cap ≈ 219.74 in

Since the surface area of the cap is equal to 219.74 in, we can use the formula to find the radius of the cap.

219.74 in = 2πrh + πr22(219.74 in2)

= 2π(5.9 in)h + π(5.9 in)22(219.74 in2)

= 37.699 in2 + 109.45 in23r2

= 72.533 in2r ≈ 4.545 in

Using the formula D = 11.8 - 2R_cap, we can find the diameter of the remaining portion of the wooden sphere.

D = 11.8 - 2(4.545 in)D ≈ 2.71 in

The radius of the remaining portion of the wooden sphere is equal to 5.9 in - 4.545 in. Thus, the radius of the remaining portion of the sphere is 1.355 in. Finally, we can find the total surface area of the remaining portion of the sphere.

SA = 4πr2SA = 4π(1.355 in)2SA ≈ 23.14 in

Therefore, the total surface area of the remaining portion is approximately 23.14 in.

To learn more about total surface area of sphere refer :

https://brainly.com/question/14692728?

#SPJ11

Answer: a > -1

Explanation is in the image.

Answer:

[tex]a > -1[/tex]

Step-by-step explanation:

1) Write the equation

[tex]-2a+14 < 5a+21\\[/tex]

2) Collect like terms on their corresponding side

[tex]-7a < 7[/tex]

3) Divide -7 from both sides and flip the sign

[tex]a > -1[/tex]

The rewritten expression  3.00 +2.25(m-1) is 2.25m + 0.75.

The cost for a taxi ride is $3.00 for the first mile and $2.25 for each additional mile.

Therefore, let's rewrite the expression 3.00 +2.25(m-1) for the cost of the taxi ride in dollars as a sum of two terms, where m represents the miles travelled.

Hence,

Therefore, the cost using expression is as follows:

3 + 2.25(m - 1)

3 + 2.25m - 2.25

combine like terms

2.25m + 3 - 2.25

2.25m + 0.75

learn more on expression here: https://brainly.com/question/11121991

#SPJ1

The equivalent resultant force is 1228.3 N and its location along AB, measured from A is 4.7 m.

The system of four forces acts on the roof truss. Determine the equivalent resultant force and specify its location along AB, measured from A.For the given system of forces, the components of each force should be determined first.The angle between the horizontal and the 500 N force is 60 degrees.Cos 60 = adjacent/hypotenuse Adjacent = cos 60 x 500 = 250 N This force is resolved into two components; one horizontal and the other vertical.250 N is the horizontal component.

The vertical component of this force is resolved as follows:Sin 60 = opposite/hypotenuse Opposite = sin 60 x 500 = 433 NThe system is now resolved and we get:Resolve force 700 N into components. The angle between the horizontal and the 700 N force is 30 degrees.Cos 30 = adjacent/hypotenuse Adjacent = cos 30 x 700 = 606 N

The vertical component of this force is resolved as follows:Sin 30 = opposite/hypotenuse Opposite = sin 30 x 700 = 350 N
Resolve force 600 N into components. This force acts horizontally and thus, it has no vertical component.Resolve force 800 N into components. This force acts vertically and thus, it has no horizontal component.

The components of the forces are summarized in the table below:Force components X component (N)Y component (N)5002504337006063506006000800 This information can now be used to determine the equivalent resultant force and its location.∑Fy = 250 N + 433 N + 350 N - 800 N = 233 N∑Fx = 606 N + 600 N = 1206 N Therefore;∑F = √[(∑Fx)² + (∑Fy)²]= √[(1206)² + (233)²]= 1228.3 N From the force diagram, the distance of the equivalent resultant force from A, measured along AB is given by the ratio of the moment of the force about A and the force itself:Moment of force about A = 250 x 6 + 606 x 2.5 + 600 x 1 = 5750 N.m Therefore, Distance of the force from A = Moment of force about A / ∑F= 5750 N.m / 1228.3 N= 4.7 m (to 1 decimal place)

Therefore, the equivalent resultant force is 1228.3 N and its location along AB, measured from A is 4.7 m.

Learn more about Equivalent resultant force

brainly.com/question/30833433

#SPJ11

The probability that at most of the parts are defective is 0.96.

A machine that manufactures automobile parts produces defective parts of the time. If parts produced by this machine are randomly selected, what is the probability that at most of the parts are defective?

The given probability of producing defective parts is P(defective) = 0.15. Now, we need to find the probability that at most of the parts are defective. This can be done by finding the probability of producing 0, 1, or 2 defective parts.

Let X denotes the number of defective parts. So, we have to calculate the probabilities for P(X = 0), P(X = 1), and P(X = 2). To calculate these probabilities, we will use the binomial probability formula:

P(X = x) ={n}C{x} p^x (1 - p)^{n - x}, Here, n = number of parts produced, p = probability of producing defective parts

x = number of defective parts

First, we need to find P(X = 0),

P(X = 0) = (0.85)^5 = 0.4437

P(X = 1) = {5}C{1} (0.15)^1 (0.85)^4 = 0.3672

P(X = 2) = {5}C{2} (0.15)^2 (0.85)^3 = 0.1459

Now, we can find the probability that at most of the parts are defective as follows:

P{at most 2 defective parts}) = P(X = 0) + P(X = 1) + P(X = 2) = 0.957

Therefore, the probability that at most of the parts are defective is 0.96.

To learn more about probability refer :

https://brainly.com/question/12905909

#SPJ11

Answer:

perimeter=42

Area=90

Step-by-step explanation:

find the length of DEFG:

perimeter=a=b+a+b

28=10+b+10+b

28=20+2b

8=2b

4=b

finding the scale factor:

15/10=3/2

to find the perimeter of WXYZ:

the missing side:

=4x3/2

=6

perimeter=a+b+a+b

perimeter=15+6+15+6

perimeter=42

Area of WXYZ:

Area=bh

Area=15x6

Area=90

Answer:

To rewrite the quadratic equation in the form y = a(x - p)²+q, we need to complete the square.

y = 2x^2 + 16x + 26

y = 2(x^2 + 8x) + 26

y = 2(x^2 + 8x + 16 - 16) + 26 // Adding and subtracting (8/2)^2 = 16 inside the parentheses

y = 2((x + 4)^2 - 16) + 26

y = 2(x + 4)^2 - 32 + 26

y = 2(x + 4)^2 - 6

Therefore, the quadratic equation y = 2x ^ 2 + 16x + 26 rewritten in the form y = a(x - p)²+q is y = 2 * (x + 4) ^ 2 - 6, so the answer is D

Answer:

y= 2(x+4)^2 -6

Step-by-step explanation:

y= 2x^2 + 16x + 26

It is in the form y= ax^2 + bx + c

To rewrite in the form y=a(x-p)^2 + q

We need to fin p and q. We already have a in the original equation.

In y= 2x^2 + 16x + 26,    a=2.

The formula say that:  p=-b/2a

p= -16/(2*2)

p=-16/4

p=-4

In the formula, we replace a and  y= 2(x-(-4))^2 +q

Obtaining, y= 2 (x+4)^2 + q

Now, to find q we need to obtain a point from the original equation. Commonly the y-intercept. In the form y= ax^2 + bx + c ; C is the y-intercept.

y-intercept: (0,c)

Therefore, in y= 2x^2 + 16x + 26

y-intercept: (0,26)

In the equation we already have:

y= 2(x+4)^2 +q

26= 2(0+4)^2 + q

26=2(4)^2 +q

26= 2(16) + q

26= 32 + q

-6 = q

Joining all the results, we obtain:

y= 2(x+4)^2 -6

Answer:

p = 0, p = -7/3

Step-by-step explanation:

We are given the following equation:
3p² + 7p = 0

We want to solve the equation by factoring.

To factor, we want to look for a common term that we can pull out.

You may notice that both terms have 'p' in common, so we can pull out p from both terms.

This will then make the equation:

p(3p + 7) = 0

Now, we can use zero product property to solve the equation.

p = 0

3p + 7 = 0

Subtract.

3p = -7

Divide.

p = -7/3

Our answers are p = 0 and p = -7/3

Angle L can be calculated as follows:

angle L = angle - 180 LMO stands for angle. MNO \sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

1. We know that sides AB and CD of trapezoid ABCD are parallel. We can use the tangent function to find the length of side AD because angle B is a right angle and angle ABD is 45 degrees:

AD/AB = tan(45)

AD=AB * tan(45) AD=AB

As a result, AD = 10.

2. We know that the sides PQ and RS of the trapezoid PQRS are parallel. We can use the sine function to find the length of side PS because angle Q is a right angle and angle PSQ is 60 degrees:

PS/QS sin(60) =

PS = sin * QS (60)

5 * sqrt = PS (3)

As a result, PS = 5*sqrt (3).

3. We know that the sides UV and WX of a trapezoid UVWX are parallel. We can use the cosine function to find the length of side WU because angle V is a right angle and angle WVU is 30 degrees:

WU/UV cos(30) =

UV * cos WU (30)

5 * sqrt(3) / 2 = WU

As a result, WU = (5/2)*sqrt (3).

4. We know that the sides LM and NO of the trapezoid LMNO are parallel. We can use the sine function to find the length of side MO because angle L is a right angle and angle MNO is 30 degrees:

MO/NO sin(30) =

MO = 4 / 2 MO = NO * sin(30)

As a result, MO = 2.

Because angles MNO and LMO add up to 180 degrees, we can calculate angle LMO as follows:

LMO angle = 180 - angle LMO MNO angle = 150 degrees

Finally, because angle N is a right angle, we can calculate angle L as follows:

angle L = angle - 180 LMO stands for angle. MNO\sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

To know more about Length visit:

https://brainly.com/question/30100801

#SPJ1

It is Arithmetic Sequence. An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence.

For the given sequence

d= 49-56 = -7

d= 42-49 = -7

Thus, there is -7 as a common difference between the terms.

The distance between succeeding terms in an arithmetic series is always the same. It is often referred to as an arithmetic series or arithmetic progression. The following statement can be used to represent an arithmetic sequence: a, (a + d), (a + 2 d), (a + 3 d),..., where a is the first term and d is the constant difference between values.

To determine the sum of an arithmetic sequence, it is generally simple to add or subtract all the terms in a short series together. An individual can quickly determine the sum of an arithmetic series for a particular number of terms by using the generic formula for the nth term of an arithmetic sequence.

Learn more about Arithmetic Sequence here: brainly.com/question/15412619

#SPJ4

Considering the volume of the rectangular prism, the height of the sand inside the box is of 2 feet.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The parameters for this problem are given as follows:

Hence the height of the sand inside the box is given as follows:

2 x 1.5 x h = 6

3h = 6

h = 2 ft.

More can be learned about the volume of a rectangular prism at brainly.com/question/22070273

#SPJ1

The missing side of the rectangle is 21.

In a rectangle, opposite sides are congruent and parallel. Therefore, if we know the length and width of a rectangle, we can find the length of any missing side using the formula for the area or the perimeter of a rectangle.

In the given rectangle 8 8 3 12, the two sides are labeled 8 and 12, which represent the length and the width of the rectangle, respectively. To find the missing side, we can use the formula for the perimeter of a rectangle, which is:

Perimeter = 2 x (length + width)

Substituting the given values, we get:

Perimeter = 2 x (8 + 12)

Perimeter = 2 x 20

Perimeter = 40

Since we have the length and width of the rectangle, we can use the perimeter formula to solve for the missing side. We know that the perimeter is equal to the sum of all four sides of the rectangle, so we can write:

Perimeter = 8 + 8 + 3 + x

where x is the missing side.

Substituting the value of the perimeter (40) and simplifying, we get:

40 = 19 + x

x = 21

Find out more about rectangle

brainly.com/question/29123947

#SPJ4

The interest which josh will pay on the electric scooter with a simple annual interest of 3% is 7.50.

Interest rate can be defined as the amount of interest which is due per period, as a proportion of the amount lent, deposited, or borrowed by someone.

The interest rate formula is:

Interest Rate = {(Simple Interest × 100)}/{ (Principal × Time)}

Here,

Josh borrowed 250 from his mother to buy an electric scooter and will pay her back in one year with three simple annual interest.

The amount of interest that Josh will pay is calculated as:

Interest = Principal Amount × Rate of Interest × Time

Interest = 250 × 3

Therefore, Josh will pay his mother $7.50 in interest for the loan.

Learn more about Interest rate here:

https://brainly.com/question/13324776

#SPJ11

We have that, if they put 40 chips in a hat, each one with the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10, and each number is put on four chips. Four tokens are drawn from the hat at random and without replacement, the value of q/p, q,p as probabilities, will be given by 360, therefore, the correct option is (D) 360

The probability that all four tokens have the same number (p) is equal to the total number of possible outcomes that meet that criterion divided by the total number of possible outcomes.

In this case, there are 10 possible numbers that could come up (1-10). Therefore, there are 10 possible outcomes for the four slips of paper that have the same number. Each outcome has the same probability of 1/10, so p = (1/10)^4 = 1/10000.

The probability that two of the slips have a number a and the other two have a number b (q) is equal to the total number of possible outcomes meeting that criterion divided by the total number of possible outcomes.

In this case, there are 10 possible numbers that could be drawn (1-10) and 2 ways to choose 2 different numbers out of 10, so there are 20 possible outcomes for two of the slips bearing a number and the other two bearing a number b. Each outcome has the same probability of 1/20, so q = (1/20)^4 = 1/3200000.

The ratio of q to p is q/p = 3200000/10000 = 360. Therefore, the value of q/p is 360.

See more information about probability in: https://brainly.com/question/24756209

#SPJ11

If the null hypothesis is actually true, then there is a 5% chance that the researcher will end up accepting the alternative hypothesis in error, the statement is true.

If a hypothesis test is performed with a level of significance of 0.05 and the null hypothesis is actually true, then there is a 5% chance (or 0.05 probability) that the researcher will reject the null hypothesis and accept the alternative hypothesis in error.

This is known as a Type I error. The Type I error rate is determined by the level of significance of the test.

In other words, if the null hypothesis is true, but the researcher concludes that it is false (i.e., accepts the alternative hypothesis), this is an incorrect decision that is made with a probability of 0.05 or 5%, assuming a significance level of 0.05.

To learn more about alternative hypothesis:

https://brainly.com/question/25263462

#SPJ11

The work needed to bring two point charges from infinity to their current positions is equal to the Coulomb potential energy of the system, given by: U = kQ1Q2/r, where k is the Coulomb constant, Q1 and Q2 are the two point charges, and r is the distance between them.

The electric potential due to the two charges at the vertex p is given by the sum of the potentials of each charge individually. V = kQ1/r1 + kQ2/r2, where k is the Coulomb constant, Q1 and Q2 are the two point charges, and r1 and r2 are the distances between the charges and the vertex p.The direction of the electric field due to the two charges at the vertex p is given by the vector sum of the electric field of each charge individually. The direction of the electric field due to each charge can be calculated by taking the vector difference between the position of the charge and the position of the vertex p.

The magnitude of the electric field due to the two charges at the vertex p is given by the sum of the magnitudes of the electric fields of each charge individually. Etotal = √(E12 + E22), where E1 and E2 are the electric fields due to the two charges.

For more questions on potential energy

https://brainly.com/question/16167018

#SPJ11

Answer:

Step-by-step explanation:

You want the measures of AO and DO in a trapezium in which AB║CD, the diagonals intersect at O, and AB = 3 cm, CD = 6 cm, CO = 4 cm, OB = 3 cm.

Diagonal AC is a transversal to parallel lines AB and CD, so alternate interior angles BAO and DCO are congruent. Vertical angles AOB and COD are also congruent, so ∆ABO ~ ∆CDO by the AA similarity postulate.

This means the side lengths are proportional, so ...

  AB/CD = AO/CO = BO/DO

  3/6 = AO/4 = 3/DO   ⇒   AO = 2, DO = 6

The measures of AO and DO are 2 cm and 6 cm, respectively.

__

Additional comment

It can help to draw a diagram.

Answer:

Step-by-step explanation:

(3x+1)^2 = 3x+3

9x^2 +6x +1=3x+3

9x^2+3x-2=0

finally we got a trinomial quadratic equation solve by factorizing

9x^2 -6x+3x-2=0

3x(3x-2)+(3x-2)=0

3x-2 = 0 or 3x+1=0

x= 2/3 or x= -1/3

Answer:

TAN is a mathematical function in trigonometry that stands for tangent. It is used to calculate the tangent of an angle in a right triangle, which is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In equations, you can use TAN to find the value of the tangent of an angle. For example, if you have an angle of 30 degrees in a right triangle and you want to find the value of the tangent of that angle, you can use the TAN function in your calculator or programming language.

The syntax of the TAN function is usually "tan(x)", where x is the angle in radians. If your calculator or programming language uses degrees instead of radians, you may need to convert the angle to radians first using the conversion formula: radians = degrees * (pi/180).

For example, to find the value of the tangent of 30 degrees, you can use the TAN function as follows:

In degrees mode: TAN(30) = 0.57735027

In radians mode: TAN(30*pi/180) = 0.57735027

TAN can be used in various trigonometric equations and identities to solve for unknown sides or angles of a right triangle.

Step-by-step explanation:

The expression (6 + 2a) - (-a - 5) is equivalent to 3a + 11. The other options given are not equivalent to (2a + 6) - (-a-5).

In mathematics, a negative sign is a symbol used to represent a negative value or operation. It is represented by the symbol "-", which is usually placed before a number to indicate that the number is negative.

To simplify (2a + 6) - (-a-5), we can distribute the negative sign:

(2a + 6) - (-a-5) = 2a + 6 + a + 5 = 3a + 11

Therefore, the expression equivalent to (2a + 6) - (-a-5) is:

3a + 11

Out of the options given, the equivalent expression is:

(6 + 2a) - (-a - 5)

We can simplify this expression in the same way as above:

(6 + 2a) - (-a - 5) = 6 + 2a + a + 5 = 3a + 11

Therefore, the expression (6 + 2a) - (-a - 5) is equivalent to 3a + 11.

The other options given are not equivalent to (2a + 6) - (-a-5).

To know more about negative sign visit:

https://brainly.com/question/29461821

#SPJ1

Answer:

Step-by-step explanation:

[tex]f(-3)=-(-)3-1=2\\\\f(-2)=-(-2)-1=1\\\\f(0)=-0-1=-1\\\\f(2)=-2-1=-3\\\\f(4)=-4-1=-5\\\\f(x)=5\rightarrow 5=-x-1\rightarrow6=-x \rightarrow x=-6[/tex]