For fractions A=\(\frac{n^{2}+2n+1 }{n^{2}+1 } where n is an integer.Find the value of n so that fraction A has the largest value

Answer: x and x+5

Step-by-step explanation:

\(x^{2} +5x\)

common factor of that expression is x, so you can factor it out into

x(x+5)

Answer:

Step-by-step explanation: I think it's D

Answer:

khanya pays higher

Step-by-step explanation:

You have to find the $/hr ratios:

khanya's is 480/8->$60/hr

rex's is 660/12->%55/hr

Khanya pays the higher rate

The boy can have 9 dimes, 0 nickels, and 8 pennies.

We have,

a boy finds $1.05 in dimes, nickels, and pennies.

Let's assume that the boy has x number of dimes, y number of nickels, and z number of pennies.

We know that the total value of these coins is $1.05, and there are 17 coins in total.

Now, let's convert the values into cents.

We have 10 cents for each dime, 5 cents for each nickel, and 1 cent for each penny.

Therefore, the equation we can set up is:

10x + 5y + z = 105

(since $1.05 is equal to 105 cents)

We also know that the total number of coins is 17, so:

x + y + z = 17

Now, we have a system of equations.

Let's solve it using a method called substitution.

From the second equation, we can express z in terms of x and y:

z = 17 - x - y

Substituting this value of z into the first equation, we get:

10x + 5y + (17 - x - y) = 105

Simplifying this equation, we get:

9x + 4y = 88

Now we have a new equation to work with.

We can rearrange it to solve for x:

x = (88 - 4y) / 9

To find the possible values for x and y, we can try different values of y and calculate the corresponding values for x.

Since the number of coins cannot be negative, we can start by setting y to 0 and calculate x:

x = (88 - 4(0)) / 9

x = 88 / 9

x ≈ 9.78

Since the number of coins must be a whole number, we can round x down to the nearest whole number, which gives us x = 9.

Now, let's substitute this value of x back into our second equation:

9 + y + z = 17

Simplifying this equation, we get:

y + z = 8

We can now try different values of y and calculate the corresponding values of z that satisfy this equation.

Let's start with y = 0:

0 + z = 8

z = 8

So, one possible solution is x = 9, y = 0, and z = 8.

This means the boy can have 9 dimes, 0 nickels, and 8 pennies.

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After forming a system of equations according to the given information

We find that the boy can have  5 pennies, 13 dimes, and 2 nickles.

Given that,

The boy finds a total of $1.05 in dimes, nickels, and pennies.

There are 17 coins in total.

Number of pennies  = 5

Let "d" represent the number of dimes.

Let "n" represent the number of nickels.

Let "p" represent the number of pennies = 5

We know that,

1 $ = 100 cent

1 cent = 0.01$

According to the given information:

The system of equations be:

0.10d + 0.05n + 0.01 x 5 = 1.05   ......(i)

d + n + 2 = 17 .....(ii)

Proceeding with equation (i):

After simplifying:

0.10d + 0.05n = 1

Multiply 10 both sides

10d + 5n = 10  ....(iii)

Proceeding with equation (i):

After simplifying:

d + n = 15  .

Multiply 5 on both sides,

5d + 5n = 75 ....(iv)

Subtract (iii) from (iv):

5d = 65

d = 13

So, there are 13 dimes.

Now substitute this value of d into (iv),

n = 2

So, there are 2 nickels.

Hence.

We find that the boy can have  5 pennies, 13 dimes, and 2 nickles.

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The complete question is attached below:

A boy finds $1.05 in dimes, nickels, and pennies.

Dimes are 10 cents coins, Nickle is 5 cents coins and pennies are 1 cent coins. If there are 17 coins and the number of pennies is 5 in all.

How many coins of each type can he have?

The present balance in Isabella's bank.statement is; -$9.45

From the task content;

Hence, from the problem statements regarding her deposits, withdrawals, auto-payments, direct deposit and service charge; it follows that;

By finding the LCM of common terms;

x = -$9.45

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The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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Answer:

Step-by-step explanation:

15:3 = 5  and  75:15 = 5

so this is a geomertic sequence with common ratio of 5

a₁ = 3,  r = 5

aₙ = a₁ rⁿ⁻¹

a₇ = 3(5)⁶ = 3(15 625) = 46 875

The probability of out of any two students chosen at random, one student will be absent while the other is present is 29/450 or approximately 0.064.

Let's denote the event that a student is absent as A and the event that a student is present as P.

The probability of a student being absent is P(A) = 1/30, which means the probability of a student being present is P(P) = 29/30.

We want to find the probability that out of any two students chosen at random, one student will be absent while the other is present.

There are two possible cases for this event:

The first student is absent and the second student is present

The first student is present and the second student is absent

Let's calculate the probability of each case separately:

Case 1: The probability of the first student being absent is P(A) = 1/30. The probability of the second student being present is P(P) = 29/30. Therefore, the probability of the first student being absent and the second student being present is:

P(A and P) = P(A) × P(P) = (1/30) × (29/30) = 29/900

Case 2: The probability of the first student being present is P(P) = 29/30. The probability of the second student being absent is P(A) = 1/30. Therefore, the probability of the first student being present and the second student being absent is:

P(P and A) = P(P) × P(A) = (29/30) × (1/30) = 29/900

The total probability of one student being absent and the other being present is the sum of the probabilities of the two cases:

P = P(A and P) + P(P and A) = (29/900) + (29/900) = 58/900

Simplifying the fraction by dividing both the numerator and denominator by 2, we get:

P = 29/450

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Answer:

=====================

Correct choice is C

The distance that exists from the point Z is given as 150,75 feet

The larger triangle is represented by the letters B, A, and C, and the smaller triangle is located here. These points are denoted as z and y, respectively, therefore we have supplied The value of b y is 201. A c equals 512 r, p equals 384 feet, and the z  must now be located. Triangles c, a, and b are simply comparable to triangles r, p, and q, which means that a c upon r p

To solve the problem we have

Δ RPG = ΔCAB

Δc / ΔB = by / zq

ZQ = BY * RP / Ac

= 201 * 384 / 512

= 150 . 75 FEET

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a police officer is determining where to park his vehicle in order to observe traffic at the red light. if AC=512 feet, RP= 384 feet, and point Y is 201 feet from point B, how far is point Z from point Q

Answer:

10

Step-by-step explanation:

Answer:1+3

Step-by-step explanation:

Answer:

4,400

Step-by-step explanation:

120% is equivalent to the fraction 11/5.

Fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin.  

If 1/5 = 20%, then we can convert 120% to a fraction by first dividing by 100 to get the decimal equivalent, and then adding 1 to get the fractional equivalent:

120% = 120/100 = 1.2

1.2 + 1 = 2.2

Therefore, 120% is equivalent to the fraction 11/5.

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the answer is c which is the number 12

The lines given, based on the picture, can be said to be skew.

Skewed lines are two lines that are not parallel to one another, neither do they intersect. Only dimensions greater than two-dimensional space can have skew lines. They must be non-coplanar, which means that they must exist in various planes. Two lines in a two-dimensional space can either intersect or run parallel to one another. Skew lines can never exist in 2D space as a result.

Skew lines occur frequently in real-world circumstances. Let's say there is a line on the ceiling and a line on the wall. These lines can be skew lines because they lie in distinct planes if they are not parallel to one another and do not meet. These lines go on forever in both directions.

The picture shows lines on steps. These steps therefore exist on different planes but are not parallel. They must therefore be skew.

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Answer:

C

Step-by-step explanation:

Answer: We are given Quadrilateral LMNO is reflected over a line.

Also given Quadrilateral LMNO is congruent Quadrilateral CDAB, that is

LMNO ≅ CDAB.

Note: Reflection over a line represents mirror images of the figures.

From the given image we can see

LM is congruent to CD.

ON is congruent to BA.

LO is congruent to BC.

MN is congruent to AD.

Therefore,  DC segment corresponds to ML.

Hope i helped you out!

If two angles are complementary, then they cannot be congruent. This statement is true. Complementary angles are two angles whose sum is 90°. They do not have to be equal in measure.

On the other hand, congruent angles are angles with equal measure.What are complementary angles?Two angles are said to be complementary when they add up to 90 degrees. This means that the sum of the measures of these angles is 90 degrees.

The measures of complementary angles need not be equal.What are congruent angles? Congruent angles are two or more angles with the same measure. In other words, they have the same angle measurement.

Hence, if two angles are congruent, it means they are exactly equal in measure. If two angles are complementary, they cannot be congruent.

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Answer:

Step-by-step explanation:

2)infinetly many solutions

beacuse y=8x-2  and y-8x=-2 are the same thing without any limitation

Answer:

its b

Step-by-step explanation:

got it right on edge

The volume of the metal in the cylinderical pipe given the dimensions of the larger and smaller cylinders is 271.30 mm³.

A cylinder is a three-dimensional object. It is a prism with a circular base.

Volume of a cylinder = nr^2h

Where:

The volume of the metal in the cylinderical pipe = 3.14 x 10 x [(8.4/2)² - 6/2)²] = 271.30 mm³

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Answer:

x = 0.58 or x = -8.58 to 2 d.p.

Step-by-step explanation:

Question:

Just to write the question in a better format :

\(2x^{2} +16x-10 = 0\)

Solve for x.

Answer:

First we Simplify this by dividing everything by 2:  

\(2x^{2} +16x-10 = 0\) ÷ 2 :

\(x^{2} +8x-5 = 0\)

Now we use the quadratic formula :

\(x = \frac{-b+/-\sqrt{b^{2} -4ac} }{2a}\)  (side note: +/- is meant to be ±)

Now we substitute a with 1, b with +8 and c with -5:

\(x = \frac{-8+/-\sqrt{8^{2} -4(1)(-5)} }{2(1)}\)  \(x = \frac{-8+/-\sqrt{64+20} }{2}\) \(x = \frac{-8+/-\sqrt{84} }{2}\)  

The surd \(\sqrt{84}\) = 2\(\sqrt{21}\) So :

x = -8± 2√21 /2

x = -4 ±√21

This is our answer . Remember it is two answers in 1.

x = -4 +√21 and x = -4 -√21

x = 0.58257569495  or x = -8.58257569496

x = 0.58 or x = -8.58 to 2 d.p.

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The integral of (x + 11) / (x^2 + 4x + 8) dx can be evaluated using partial fraction decomposition. The answer is  ln(|x^2 + 4x + 8|) + 2arctan[(x + 2) / √6] + C.

The integral of (x + 11) / (x^2 + 4x + 8) dx is equal to ln(|x^2 + 4x + 8|) + 2arctan[(x + 2) / √6] + C, where C is the constant of integration.

To explain the answer in more detail, we start by completing the square in the denominator. The quadratic expression x^2 + 4x + 8 can be rewritten as (x + 2)^2 + 4. We can then decompose the fraction using partial fractions. We express the given rational function as (A(x + 2) + B) / ((x + 2)^2 + 4), where A and B are constants to be determined.

By equating the numerators and simplifying, we find A = 1 and B = 10. Now we can rewrite the integral as the sum of two simpler integrals: ∫(1 / ((x + 2)^2 + 4)) dx + ∫(10 / ((x + 2)^2 + 4)) dx.

The first integral is a standard integral that gives us the arctan term: arctan((x + 2) / 2). The second integral requires a substitution, u = x + 2, which leads to ∫(10 / (u^2 + 4)) du = 10 * ∫(1 / (u^2 + 4)) du = 10 * (1 / 2) * arctan(u / 2).

Substituting back u = x + 2, we get 10 * (1 / 2) * arctan((x + 2) / 2) = 5arctan((x + 2) / 2). Combining the two integrals and adding the constant of integration, we obtain the final result: ln(|x^2 + 4x + 8|) + 2arctan[(x + 2) / √6] + C.

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Answer:

1:3

Step-by-step explanation:

Please study the diagram briefly to understand the concept.

First, we determine the height of the isosceles trapezoid using Pythagoras theorem.

\(4^2=2^2+h^2\\h^2=16-4\\h^2=12\\h=\sqrt{12}\\ h=2\sqrt{3}$ units\)

The two parallel sides of the trapezoid are 8 Inits and 4 units respectively.

Area of a trapezoid \(=\dfrac12 (a+b)h\)

Area of the trapezoid

\(=\dfrac12 (8+4)*2\sqrt{3}\\=12\sqrt{3}$ Square Units\)

For an equilateral triangle of side length s.

Area  \(=\dfrac{\sqrt{3}}{4}s^2\)

Side Length of the smaller triangle, s= 4 Units

Therefore:

Area of the smaller triangle

\(=\dfrac{\sqrt{3}}{4}*4^2\\=4\sqrt{3}$ Square units\)

Therefore, the ratio of the area of the smaller triangle to the area of the trapezoid

\(=4\sqrt{3}:12\sqrt{3}\\$Divide both sides by 4\sqrt{3}\\=1:3\)

Answer:

The equation is: \(\frac{x-7}{5} = 13\) and the number is 72.

Step-by-step explanation:

We have to use mathematical notation to convert the given statement into an equation. As we don't know the exact value of number, we have to use a variable in place of the number.

Let x be the required number then

"A number decreased by 7"

\(x-7\)

"and then  divided by 5"

\(\frac{x-7}{5}\)

" is 13."

\(\frac{x-7}{5} = 13\)

For solving, multiplying both sides of equation by "5"

\(\frac{x-7}{5} * 5 = 13*5\\x-7 = 65\)

Adding 7 on both sides of equation

\(x-7+7 = 65+7\\x = 72\)

Hence,

The equation is: \(\frac{x-7}{5} = 13\) and the number is 72.

Answer:

y = x + 7

Step-by-step explanation:

Calculate the slope of a line that passes through (-2,5) and (1,8).  The slope is the Rise/Run between the 2 points:

Rise = (8 - 5) or 3.

Run = (1-(-2)) = 3

Rise/Run, the slope m, is 3/3 or 1.

The equation can be written as y = 1x + b.

We need to find a value of b that forces the line though both points.  Do that by entering one of the two points into y = 1x + b and solve for b.  I'll use point (1,8)

y = x + b

8 = 1 + b

b = 7

The equation becomes y = x + 7

See the attached graph.

Answer:

1. $2.33

2. $2.99

Step-by-step explanation:

Answer:

bag of chips is 2.19

boxed candy is 1.60

Step-by-step explanation:

Desmos Calculator

If a shuttle was launched every day, about 1 failures would one expect in 300 years.

Finding an estimate or approximation—a value that can be used for a purpose despite the possibility of incomplete, uncertain, or unstable input data—is the process of estimation. Despite this, the value is still useful because it was created using the most up-to-date data.

Here,

There are about 110,000 days in 300 years, so the expected number of failures is about 10/11 ≈ 1.

This assumes the launch conditions are identical for each of the launches, or that whatever variation there might be has no effect on the probability. These are bad assumptions.

If a shuttle was launched every day, one might anticipate one failure every 300 years.

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The length of the rectangular prism is 13 centimetres.

The volume of a rectangular prism is 208 cm³. The area of one end is 16 cm². The length of the rectangular prism can be found as follows:

Therefore,

volume of a rectangular prism = lwh

where

Hence, let's find the length

volume of a rectangular prism = lwh

208 = 16 × l

16l = 208

divide both sides by 16

l = 208 / 16

l = 13 cm

Therefore,

length of the prism = 13 cm

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