AM i correct?
rational expression question

Answer:  60 years

Step-by-step explanation:

Let x denotes the age of Demochares .

Time he spent as a boy = [tex]\dfrac{x}{4}[/tex]

Time he spent as a youth = [tex]\dfrac{x}{5}[/tex]

Time he spent as a man= [tex]\dfrac{x}{3}[/tex]

Time he spent in dotage= 13 years

As per given , we have the following equation:

[tex]x=\dfrac{x}{4}+\dfrac{x}{5}+\dfrac{x}{3}+13[/tex]

[tex]x=\dfrac{15x+12x+20x}{60}+13[/tex]  [Take LCM]

[tex]x=\dfrac{47x}{60}+13[/tex]

[tex]x-\dfrac{47x}{60}=13[/tex]

[tex]\dfrac{60x-47x}{60}=13[/tex]

[tex]\dfrac{13x}{60}=13[/tex]

[tex]x=13\times\dfrac{60}{13}=60[/tex]

Hence, he is 60 years old.

Step-by-step explanation:

A rectangular lot whose perimeter is 260 ft is fenced along three sides. An expensive fencing along the​ lot's length cost $ 18per foot. An inexpensive fencing along the two side widths costs only $ 3per foot.

So we have

         l + 2 w = 260 -------------------eqn 1

And total cost is 1800 $

That is

                18 l + 2 x 3 w = 1800

                 3l + w = 300 -------------------eqn 2

eqn 2 x 2

                 6l + 2w = 600 -------------------eqn 3

eqn 3 - eqn 1

              6l + 2w - l - 2w = 600 - 260

                   5l = 340

                     l = 68 ft

Substituting in eqn 1        

                   68 + 2 w = 260    

                     2w = 192

                       w = 96 ft

Lot's dimension is 68 ft x 96 ft    

Answer:

option a is correct , watch explanation

Answer:

There are two factors of the function. You already said the first one, x-5. The second factor is Option A

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Answer:

It appears to fly faster than its actual speed.

Step-by-step explanation:

In general, if talking about velocities, the direction of the movement should also be taken into account. For example, if two objects move in opposite directions, a person inside one object observes that the other one moving in the opposite goes faster than its actual speed (because the velocities are summed up). If they are moving in the same direction the opposite phenomenon is true (the velocities are subtracted).

Finally, in this example the planes move in opposite direction, therefore, a plane flying in the opposite direction will appear to fly  faster.

Answer:

Step-by-step explanation:

Answer: interest at the end of 3 months is $4.08

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 3 months = 3/12 = 0.25 years

P = $544

R = 3%

Therefore

I = (544 × 3 × 0.25)/100

I = 408/100

I = 4.08

Answer:

Step-by-step explanation:

I believe the answer is x² + y² = 9²

Answer:

no. of spjeres=10

radius of those cylinders =2cm

radius of the cylinder in which water is poured=10

rise in water water level =10×2÷10 = 2cm

The rise in water level will be 2 centimeters when spheres are fully immersed in a cylinder.

The volume of a cylinder is defined as the space occupied by the cylinder and the volume of any three-dimensional shape is the space occupied by it.

Ten spheres, each with a radius of 2 cm, are fully immersed in a 10 cm cylinder of water.

As per the given question, we have

The number of spheres = 10

The radius of those cylinders = 2cm

The radius of the cylinder in which water is poured = 10

According to the condition, the required solution would be as:

The rise in water level = 10 × 2 ÷ 10

The rise in water level = 20/10

Apply the division operation, and we get

The rise in water level = 2 cm

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To calculate the expected number of applications that went to the right college, we need to consider the probability of each application being placed correctly. Since the applications are placed randomly, each application has an equal chance of going to the right college. The expected number of applications that went to the right college is 1.

To calculate the expected number of applications that went to the right college, we need to consider the probability of each application being placed correctly. Since the applications are placed randomly, each application has an equal chance of going to the right college. Let's say there are n applications and n colleges.

The probability of a specific application going to the right college is 1/n. Therefore, the expected number of applications that went to the right college can be calculated as:

Expected number = Total number of applications * Probability of an application going to the right college

Expected number = n * (1/n)

Expected number = 1

The expected number of applications that went to the right college is 1. This means that, on average, one application will go to the right college.

Answer:

[tex]12,600\ ft[/tex]

Step-by-step explanation:

step 1

Find out the number of revolutions in one hour

we know that

The bicycle wheels are making 30 revolutions per minute

One hour are 60 minutes

so

using proportion

[tex]\frac{30}{1}\ \frac{rev}{min}=\frac{x}{60}\ \frac{rev}{min}\\\\x=60(30)\\\\x=1,800\ rev[/tex]

step 2

Find out how many feet the bicycle will travel in one hour

we know that

A bicycle moves approximately 7 feet with each revolution and the number of revolutions in one hour is 1,800

so

Multiply the number of revolutions in one hour (1,800 rev) by 7 feet

[tex](1,800)7=12,600\ ft[/tex]

Answer: The first number is [tex]-10[/tex] and the second number is [tex]4[/tex]

Step-by-step explanation:

Let be "x" the first number and "y" the second number.

The word "Twice" indicates multiplication.

By definition, the sum is the result of an addition.

"is" indicates an equal sign.

Therefore, "Twice the sum of a number and three times the second number is four" can be expressed as:

[tex]2(x+3y)=4[/tex]   [Equation 1]

A difference is the ressult of a subtraction, then " The difference of 10 times the second number and five times the first is 90" can be expressed as:

[tex]10y-5x=90[/tex]   [Equation 2]

To find the numbers:

1. Solve for "x" from the Equation 1:

[tex]2(x+3y)=4\\\\2x+6y=4\\\\x=\frac{4-6y}{2}\\\\x=2-3y[/tex]

2. Substitute this equation into the Equation 2 and solve for "y":

[tex]10y-5(2-3y)=90\\\\10y-10+15y=90\\\\25y=100\\\\y=\frac{100}{25}\\\\y=4[/tex]

3. Substitute the value of "y" into the equation [tex]x=2-3y[/tex] and evaluate:

[tex]x=2-3(4)\\\\x=-10[/tex]

Answer:

Ron's speed = 3 miles/hour

Stevie's speed = 2.5 miles/hour

On comparing we see Ron is walking faster than Stevie.

Step-by-step explanation:

Given:

Ron takes 10 minutes to walk on a track to cover a distance of 0.5 miles

Stevie takes 6 minutes to walk on a track to cover a distance of 0.25 miles

To find their unit rates in mile per hour and choose the faster one.

Solution:

Unit rate in miles per hour signifies their speeds. Thus, we will find out their speeds.

Ron:

Distance= 0.5 miles

Time = 10 minutes = [tex]10\ min\times \frac{1\ hr}{60\ min}=\frac{1}{6}[/tex] hours

Speed = [tex]\frac{Distance}{Time}=\frac{0.5}{\frac{1}{6}}=0.5\times6=3\ miles/hour[/tex]

Stevie

Distance = 0.25 miles

Time = 6 minutes = [tex]6\ min\times \frac{1\ hr}{60\ min}=\frac{1}{10}[/tex] hours

Speed = [tex]\frac{Distance}{Time}=\frac{0.25}{\frac{1}{10}}=0.25\times10=2.5\ miles/hour[/tex]

Thus, we have

Ron's speed = 3 miles/hour

Stevie's speed = 2.5 miles/hour

On comparing we see Ron is walking faster than Stevie.

Answer:

Step-by-step explanation:

They are not similar.  If they were, ∠LMF and ∠GHF would both have the same angle measure and they do not.

Final answer:

Mathematics question on similar triangles; triangles are similar if they have congruent corresponding angles and proportional sides obtained through AA, SSS, or SAS criterion. A similarity statement describes the correspondence of the vertices.

Explanation:

The question provided falls within the subject of Mathematics, specifically within the study of geometry and the concept of similar triangles. To determine if two triangles are similar, we must check if they have the same shape, which implies that their corresponding angles are equal and their corresponding sides are in proportion. In other words, two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional. This can be verified by angle-angle similarity (AA), side-side-side similarity (SSS), or side-angle-side similarity (SAS). The similarity statement provides the order of correspondence of vertices between similar triangles.

When evaluating if triangles BAO and B1A1O are similar, we must compare their corresponding angles and sides. If the given information indicates that at least two angles of one triangle are congruent to two angles of another triangle (AA criterion), or that the sides are proportional (SSS or SAS criterion), then the triangles are similar. For instance, if ∠BAO ≅ ∠B1A1O and ∠BOA ≅ ∠B1O1A1, then by the AA criterion, the triangles are similar, and we could write the similarity statement as triangle BAO ∼ triangle B1A1O.

Answer: the answers b i think

Good evening ,

Answer:

The right answer is B.

Step-by-step explanation:

If we apply the Pythagorean theorem we get

the length of the other leg is :

√(70^2-35^2)

= √(3 675)

= 60,621778264911.

:)

Answer:

C. $1.80

Step-by-step explanation:

Given:

MSRP of a certain item = $60

Percentage of Selling by store A = 20%

Percentage amount will be = [tex]\frac{20}{100}\times 60 = \$12[/tex]

Sales tax = 5% on purchase price

Amount of sales tax = [tex]\frac{5}{100}\times 60 = \$3[/tex]

Total Cost of item at Store A is MSRP of a certain item plus Percentage amount of selling the item plus Amount of Sales tax.

framing in equation form we get;

Total Cost of item at Store A = [tex]60+12+3 =\$75[/tex]

Also Given:

Percentage of Selling by store B = 30%

Percentage amount will be = [tex]\frac{30}{100}\times 60 = \$18[/tex]

Regular price of item at store B = [tex]60+18 = \$78[/tex]

Percentage of discount of item at store B = 10% on regular price

Amount of discounted item at store B = [tex]\frac{10}{100}\times78 = \$7.8[/tex]

Now regular price of item with discount at store B will be equal to Regular price of item at store B minus Amount of discounted item.

regular price of item with discount at store B = [tex]78-7.8 = \$70.2[/tex]

Sales tax = 5% on purchase price

Amount of sales tax = [tex]\frac{5}{100}\times 60 = \$3[/tex]

Total Cost of item at Store B is regular price of item with discount at store B plus Amount of Sales tax.

framing in equation form we get;

Total Cost of item at Store B = [tex]70.2+3 =\$73.2[/tex]

The result when total cost of the item at Store B is subtracted from the total cost of the item at Store A  = $73.2 - $75 = $1.80.

Hence the result is $1.80.

The equivalent annual cost of the machine, considering a 10% return, is approximately $309,535 per year.

First, accumulate the total cost over the lifespan of the machine which is $750,000 (initial cost) + ($12,000 * 3 years) = $786,000. The equivalent annual cost can be calculated using the formula for the present value of an annuity: PV = PMT [(1 - (1 + r)^-n ) / r], where 'PMT' is the payment per period, 'r' is the rate of return, and 'n' is the number of periods. Rearrange to calculate PMT: PMT = PV * r / (1 - (1 + r)^-n). Substituting in given values gives us, PMT = $786,000 * 0.1 / [1 - (1 + 0.1)^-3] = $309,535/year.

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Answer and explanation :

When we square any number then its gives absolute value for example even when we square the negative numbers it will given positive , that is absolute value

So we can conclude that square of any number is absolute number

And then is we take square root of that absolute number it will always positive and absolute

Answer:

(4 √ 3 + 4 √2 ) m

Step-by-step explanation:

The  insect can travel from one corner directly to opposite corner in four different ways

each can be calculated using Pythagoras theorem

firstly  for one face we need to calculate the diagonal

H² = 1² + 1² = 2

H = √2

then we calculate the diagonal opposite a corner

for example

A to H where A  is at the bottom and H opposite A in another plane at the top in the cubical box

(Interior diagonal for A to H)² = √2² + 1² = 3

Interior diagonal from A to H = √ 3

there are four such corners, the fly will travel 4 √ 3 and it could also go 4 √2 diagonally to the the other corners

maximum possible length in meters = (4 √ 3 + 4 √2 ) m

Answer: 120 pages

Step-by-step explanation:

42 p on Monday

2/5x on Tuesday

1/4x rest of book

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

42+2/5x+1/4x=x

42*20 +8x+5x=20x

840=20x-8x-5x

840=7x

x=840/7

x=120

The required number of pages in the book is given as 120 pages.

Given that,
Mary read 42 pages of a book on Monday she read 2/5 of the book on Tuesday if she still had 1/4 of the book to read how many pages are there in the book is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
let the number of pages in the book be x,
According to the question,
x - 42 - 2/5x = 1/4x
x - 2/5x - 1/4x = 42
x[1 - 2/5 - 1/4] = 42
x[20 - 8 - 5] / 20 = 42
x [7] / 20 = 42
x = 6 × 20
x = 120 pages

Thus, the required number of pages in the book is given as 120 pages.

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I don't know.. can you please explain it?

Answer:

4.4 ft/s

Step-by-step explanation:

Height = 15ft

Rate= 5 ft/s

Distance from the man to the kite= 32ft

dh/dt = 5 ft/s

h = √32^2 - 15^2

h = √ 1025 - 225

h = √800

h = 28.28ft

D = √15^2 + h^2

dD/dt = 1/2(15^2 + h^2)^-1/2 (2h) dh/dt

= h(225 + h^2)^-1/2 dh/dt

= (h / √225 + h^2)5

= (28.28 / √225 + 28.28^2)5

= (28.28 / √1024.7584)5

= (28.28/32)5

= 0.88*5

= 4.4 ft/s

Final answer:

To complete the statement describing the expression (a+b)(d+e)(a+b)(d+e), we expand it by multiplying each term. Simplifying the expression, we get a²*d² + 2a²de + 2abde + b²e².

Explanation:

To complete the statement describing the expression (a+b)(d+e)(a+b)(d+e), we need to expand it. This can be done by multiplying each term in the first factor by each term in the second factor and then multiplying the result by the third factor. So the expression becomes:

(a+b)(d+e)(a+b)(d+e) = (a*d + a*e + b*d + b*e)(a*d + a*e + b*d + b*e)

We can simplify this further by combining like terms:

(a*d + a*e + b*d + b*e)(a*d + a*e + b*d + b*e) = a²*d² + 2a²de + 2abde + b²e²

Answer:

Market demand at $5 is 12 pork.

Step-by-step explanation:

In a market, the sum of individual demand for a product from buyers is known as market demand.

It is give that the at the price of $3 a pound of pork, Jason buys 8 pounds of pork and Noelle buys 10 pounds of pork.

So, market demand at $3 is

8 + 10 = 18

When the price rises to $5 a pound, Jason buys 5 pounds of pork and Noelle buys 7 pounds of pork.

So, market demand at $5 is

5 + 7 = 12

Therefore, the market demand at $5 is 12 pork.

Answer: Compound interest is $36.61

Step-by-step explanation:

Initial amount deposited into the account is $500 This means that the principal,

P = 500

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 3.5%. So

r = 3.5/100 = 0.035

It was compounded for 2 years. So

t = 2

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. Therefore

A = 500 (1+0.035/1)^1×2

A = 500(1.035)^2 = $535.61

Compound interest = 535.6 - 500 = $35.61

Final answer:

To find the value of alpha given that alpha and beta are conjugate complex numbers, and alpha/beta^2 is real, we can use the equation |alpha - beta| = 2√3. We can substitute alpha = a + bi and beta = a - bi, and solve for a and b to find the value of alpha.

Explanation:

Let α and β be conjugate complex numbers such that α/β² is a real number and |α - β| = 2√3. We need to find the value of α.

Since α and β are conjugate complex numbers, they have the form α = a + bi and β = a - bi, where a and b are real numbers. Substituting these values into the given equation, we get:

|α - β| = |(a + bi) - (a - bi)| = |2bi| = 2|b| = 2√3

From this, we can conclude that |b| = √3. Since |b| is the absolute value of b, it is always positive. Therefore, we have two options: b = √3 or b = -√3.

If b = √3, then α = a + √3i. We can substitute this into the equation α/β² to check whether it is a real number.

α/β² = (a + √3i)/(a - √3i)² = (a + √3i)/(a² - 2a√3i - 3) = [(a(a² - 3) + √3i(3a - a²)] / (a² - 2a√3i - 3)

This expression is not a real number, so b ≠ √3.

If b = -√3, then α = a - √3i. We can substitute this into the equation α/β² to check whether it is a real number.

α/β² = (a - √3i)/(a + √3i)² = (a - √3i)/(a² + 2a√3i + 3) = [(a(a² + 3) - √3i(3a + a²)] / (a² + 2a√3i + 3)

This expression simplifies to (a(a² + 3) - √3(3a + a²))/ (a² + 3) = a - √3(2a + 1)/ (a² + 3)

For this expression to be a real number, the imaginary term √3(2a + 1) must be equal to 0. So, we have √3(2a + 1) = 0.

Solving this equation, we get 2a + 1 = 0, which implies a = -0.5.

Therefore, the value of α is α = -0.5 - √3i.

Answer:

C(x,y,z)=6*x*y+10*x*z+10*y*z

Step-by-step explanation:

Lets assume that x is width, y is length and z is height. To find the area of the top and bottom surfaces we need to simply multiply length and width.

x*y

There is a 2 surface exist (top and bottom) we need to multiply this value with 2 again.

2*x*y

and the cost is 3$ for per square foot and the cost for top and bottom is:

6*x*y$

Surface areas of side surfaces are multiply of width, height and length, height:

x*z+y*z

There are 4 side surfaces exist. Therefore the are need to be multiply with 2.

2*x*z+2*y*z

and the cost is 5$ for per square foot and the cost for side surfaces is:

10*x*z+10*y*z

Total equality for cost is C(x,y,z)=6*x*y+10*x*z+10*y*z

To calculate the cost of materials for a closed rectangular box, use the formulas C(x,y) = 2 * (3xy) for the top and bottom and C(z,y) = 2 * (5zy) for the sides. Then, find the total cost by adding the costs together.

To calculate the cost of materials for a closed rectangular box, we need to consider the dimensions of the box. Let's assume the dimensions are given as x, y, and z in feet.

The cost for the top and bottom parts of the box can be calculated using the formula C(x,y) = 2 * (3xy), where 3 is the cost per square foot and xy is the area of the top and bottom.

The cost for the side parts of the box can be calculated using the formula C(z,y) = 2 * (5zy), where 5 is the cost per square foot and zy is the area of the sides.

Finally, the total cost of materials for the box can be found by adding the costs for the top and bottom parts to the cost of the side parts: C(x,y,z) = C(x,y) + C(z,y).

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Final answer:

To calculate the percentage of calories from fat, multiply the grams of fat by the calories per gram of fat and divide by the total calories consumed.

Explanation:

To calculate the percentage of calories from fat in Nadia's daily intake, we need to know the total number of calories she consumed. Let's assume it was 2000 calories. First, we calculate the number of calories from fat by multiplying the grams of fat consumed (60g) by the number of calories per gram of fat (9 calories/g). This gives us 540 calories from fat. Then, we calculate the percentage by dividing the calories from fat (540 calories) by the total calories consumed (2000 calories) and multiplying by 100. So, the percentage of calories from fat in Nadia's day's intake is 27%.

Working together, Maggie and Tom can paint the fence in 5.1 hours

Given that,

Maggie can paint a fence in 9 hours

So in 1 hour maggie paints, [tex]\frac{1}{9}[/tex] of the house

Tom needs 12 hours to paint the same fence

So in 1 hour, tom can paint [tex]\frac{1}{12}[/tex] of the house

To find: time taken to paint the fence if they work together

Let "a" be the time taken to paint the fence if they work together

So working together, in 1 hour, they can paint [tex]\frac{1}{a}[/tex] of the house

We can frame a equation as:

To see how much of the fence they can paint together in one hour, we add these together.

[tex]\frac{1}{9} + \frac{1}{12} = \frac{1}{a}[/tex]

[tex]\frac{1}{a}[/tex] is how much of the fence they can paint together in one hour.  Therefore "a" is the number of hours it will take them both to paint the fence

On solving,

[tex]\frac{12 + 9}{12 \times 9} = \frac{1}{a}\\\\\frac{1}{a} = \frac{21}{108}\\\\a = \frac{108}{21} = 5.1428[/tex]

So working together, Maggie and Tom can paint the fence in 5.1 hours

Answer:

Not possible

Step-by-step explanation:

The only information we are given are the pairs of angles that are congruent which is not enough information to prove that they are congruent

The triangles cannot be proved congruent by AAA postulates. Then the correct option is D which is not possible.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The two triangles are congruent if two sides are as well and the angle (angle between any of these two sides) among one triangle is congruent to the comparable two sides as well as the angle of a second triangle.

The triangles cannot be proved congruent by AAA postulates. Then the correct option is D which is not possible.

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its a b and c they all equal 45

Answer:

1 * 45

5 * 9

3 * 15

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The volume of rectangular prism is 6840 cubic centimeters.

Step-by-step explanation:

Given,

Area of base of rectangular prism= l*w = 360 cubic centimeters

Height of rectangular prism = h = 19 centimeters

Volume of rectangular prism = Length * Width * Height

Volume of rectangular prism = l*w*h

Volume of rectangular prism = [tex]360*19=6840\ cubic\ centimeters[/tex]

The volume of rectangular prism is 6840 cubic centimeters.

Keywords: prism, rectangle

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