Let g(x) = x² – 1. What is the average rate of
change of the function from x = 3 to x = 6?

Answer:

100%?

Step-by-step explanation:

One of the possible solutions to this system of linear inequation is

(10, 5).

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Given, Bilquis has x dimes and y nickels.

We know a nickel is 5 cents and a dime is 10 cents.

She has at least 15 coins,

∴ x + y ≥ 15...(i)

She has no more than $1 combined.

0.05x + 0.1y ≤ 1...(ii)

The possible solution of these two inequalities by the graphing method we get (10, 5)

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Answer:

14.40 rounded, 14.3999 whole number

Step-by-step explanation:

hope this helps :)

Answer:

the third one is the answer.

Step-by-step explanation:

take 0 at the x value, the greatest integer function of 0 is 0 its self. so when you take 0, Y=[x]-2 become -2. so the y-axis Crosses in (0,-2).

Markup adds an increase in the original price of an item, and tips or taxes add money to a bill. Hence, the connection between markups and tips or taxes.

Discounts are given in order to lower the price of an item from its original price, and markdown is the price that is reduced from an item's original price.

What is the difference between Markup and Markdown?
Markup price is the increase in an item (by a certain percentage) over the original price.

Markdown prices are reductions in an item's selling price from its initial selling price expressed as a rate (markdown percentage).

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The rate of interest for an amount which is compounded quarterly is 4.25%

Given,

The principal amount invested by Oliver, P = $820

The time period of the investment, t = 19 years

The interest is compounded quarterly, n = 4

The amount after 19 years, A = $1830

The compound interest formula;

A = [tex]P (1+\frac{r}{n} )^{nt}[/tex]

We have to find the rate of interest;

For that;

A = [tex]P (1+\frac{r}{n} )^{nt}[/tex]

1830 = 820 [tex](1+\frac{r}{4} )^{76}[/tex]

1830/820 = [tex](1+\frac{r}{4} )^{76}[/tex]

₇₆√1830/820 = 1 + r/4

₇₆√1830/820 - 1 = r/4

r = 4 (₇₆√1830/820 - 1)

r = 0.042 x 100

r = 4.25%

That is,

The rate of interest for an amount which is compounded quarterly is 4.25%

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Answer: It is C

Step-by-step explanation:

The slop for Kitten A is 1/4 or 4

Kitten B has a slop of 2/6 or 3 so the answer is,

Answer: w=6

Step-by-step explanation: 1. Simplify. Distribute the -4 to the w and the -3. -4*w is -4w and -4*-3 is +12, so your left with 3w-4w+12=6.

2. simplify again. 3w-4w is -w.

3. -w+12=6. Subtract w to both sides, so its -w=-6. The negatives cancel out, so w just equals 6.

Answer:

  2 2/3 hours

Step-by-step explanation:

You want to know the time it would take Elon, Jeff, and Bruce working together, if Elon and Jeff can complete the work in 3 hours, Jeff and Bruce take 6 hours, and Elon and Bruce take 4 hours.

Job completion time problems like this one are more easily understood in terms of rate of completion. If we let e, j, and b represent the rates of job completion in jobs per hour for each of Elon, Jeff, and Bruce, respectively, then the given relations can be written ...

  e +j = 1/3

  j +b = 1/6

  e +b = 1/4

Adding these equations together gives ...

  (e +j) +(j +b) +(e +b) = (1/3) +(1/6) +(1/4)

  2(e +j +b) = 3/4 . . . . . . . simplify

  e + j + b = 3/8 . . . . . . . . divide by 2

The total rate of job completion when Elon, Jeff, and Bruce work together is 3/8 job per hour. The hours it takes them to do one job is the reciprocal of this:

  1/(3/8 job/hour) = 8/3 hour/job

It would take Elon, Jeff, and Bruce 2 2/3 hours to complete the work if they worked together.

__

Additional comment

For this problem, we don't need to know the individual completion times. If we were to figure them we'd find them to be (working alone) ...

Answer:

Please be more specific

Step-by-step explanation:

The triangle with all sides is are given below

What is a triangle?

Triangles are three-sided closed polygon formed by the intersection of three lines. It is encountered a lot in everyday life. It is one of the basic shapes of geometry. It has three sides, three angles, and three vertices.

Given, angle A =30, b=6

we know cos 30 = √3/2

√3/2 = b/c

√3/2=6/c

c =6/√3/2= 6.9

Similarly for a=13, b =13

using pythagoras theorem,

c^2=a^2+b^2

=18.38

Hence, we can write the rest part

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Answer:

126.72m

Step-by-step explanation: 1.32 x 96 = 126.72, I struggled with that stuff too no shame

Answer:

below

Step-by-step explanation:

point -1,-4

y - -4  = 3 ( x - -1)

y + 4 = 3 ( x+1)     <====== I think this is a far as they want you to take it

y = 3x -1          slope - intercept form

a) The total amount in the account after the last deposit is $26755.96.

b) A total of $16900 was deposited.

c) Amount of each withdrawal is $517.

d) The total amount withdrawn is $31020.

The worth of a present asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.

FV of a single deposit of $ 2800 can be computed as

FV₁ = PV(1+r)ⁿ

PV = $ 2800

r = 6% = 0.06/12

r = 0.005

n= number of periods

= 12 yr × 12 months = 144

FV₁ = 2800 (1 + 0.005)¹⁴⁴

= 2800 (1.005)¹⁴⁴

= 2800(2.0507)

= 5741.96

The FV of monthly deposits can be computed using the formula for the FV of the annuity:

FV₂ = C x [(1+r) n -1/r]

Periodic cash deposit, C = $100

So,

FV = 100 × [((1.055)¹⁴⁴ - 1)/0.005]

= 100 × [(2.0507 - 1)/0.005]

= 100 × [1.0507/0.005]

= 100 × 210.14

= $21014

The total future value of the account is given by

= $5741.96 + $21014

= $26755.96

b) Total deposit = Initial investment amount + amount of monthly deposits

= 2800 + (100 × 144)

= 2800 +14400

= 16900

c) Formula for PV of an annuity can be used to compute monthly withdrawals as:

PV = A x [1-(1+r)⁻ⁿ/r]

So, A = PV/[1-(1+r)⁻ⁿ/r]

PV = $26755.96

n= number of periods = 5 × 12 = 60

r = 0.005 per month

A = 26755.96/ [1- (1+0.005)⁻⁶⁰/0.005]

A = 26755.96/ [1- (1.005)⁻⁶⁰/0.005]

A = 26755.96/ [1- (0.7413)/0.005]

= 26755.96/ [0.2587/0.005]

= 26755.96/(51.74)

= 517.12

So, the amount of each withdrawal for five years is $517.

d) Total amount withdrawn is

= number of withdrawals × amount of each withdrawal

= 60 × 517

=31020

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Answer:

x = 10

Step-by-step explanation:

The angles are supplemental

100 -2x + 10x = 180  Combine like terms

100 + 8x = 180  Subtract 100 from both sides of the equation

8x = 80  Divide both sides by 8

x = 10

Answer:

3

Step-by-step explanation:

2.64 rounded to the nearest whole number would be 3. This is because if a number is 5 or greater than 5, it rounds up, but if a number is under 5, it would round down. Since we are looking at the number to the right of the 2 in 2.64, and because we are looking for the nearest whole number, it would round up to 3. 6 is greater than 5, so we automatically know that we round up.

The third coordinate of the equilateral triangle is [tex](\sqrt3a,0)[/tex]. Ir can be obtained by distance formula.

What is distance formula?

It gives the distance between two coordinates.

Distance formula is given by the following expression:

[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Consider the third cordinate is (x,0) and x is positive because it is on tight side on the x axis.

Now, since the triangle is equilateral hence, the distance of (x,0) from (0, -a) and (0, a) should be equal to distance between (0, -a) and (0, a).

Now, caculate the distance between (0,-a) and (0, a).[tex]\sqrt{(0-0)^2+(-a-a)^2}=2a[/tex]

Now, distance between (x,0) and (0, a) should be 2a.

[tex]\sqrt{(x-0)^2+(0-a)^2}=2a\\\sqrt{x^2+a^2}=2a[/tex]

Now, square on both the sides.

[tex]x^2+a^2=4a^2\\x^2=3a^2\\x=\sqrt3a[/tex]and [tex]-\sqrt3a[/tex]

But the negative value of x is not possible because the coordinate lies on the right side.

Hence, the third coordinate of equilateral triangle is [tex](\sqrt3a,0)[/tex].

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The expression of logarithm will be -In4 x k .

Given,

In the question:

The expression of the logarithms is:

In[tex](\frac{1}{4^k} )[/tex]

To solve the above expression:

Now, According to the question:

In([tex]\frac{1}{4^k}[/tex])

Apply laws of logarithm to simplify the expression

-In[tex]4^k[/tex]

Express the logarithm of a power of an expression as the power times the logarithm of the expression

-k x In4

Multiply the monomials :

-In 4 x k

Hence, The expression of logarithm will be -In4 x k .

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If the six teams of a baseball league , and each team plays seven games with each other , then the number of games to be played is 105  .

in the question ,

it is given that

the number of teams in the baseball league = 6

number of matches that each team plays with each other = 7 .

Number of ways two teams can be selected out of 6 teams = C(6,2)

and they need to play 7 games with each other ,

so the number of games required to complete the schedule is

= 7 × C(6,2)

= 7 × 15

= 105

Therefore , the number of matches that is needed to complete the schedule is 105 .

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The last function having the greatest rate of change.

What is rate of change?

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.

Consider the first function,

From this function we get two points (2, 1) and (-2, -1).

To find rate using this points.

Rate = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-1-1}{-2-2} = \frac{-2}{-4}=\frac{2}{4} =\frac{1}{2}[/tex]

Consider the second function,

The second function is a vertical line of x = -3.

Since the rate of vertical line is undefined.

Consider the third function,

The third function is a horizontal line y =  4.

Since two points having the same y - value.

Hence, the rate is zero.

Consider, the last function,

From last function we get two points (1, 5) and (-3, -3).

So,

Rate = [tex]\frac{-3-5}{-3-1} = \frac{-8}{-4} = \frac{8}{4} = 2[/tex]

Hence, the last function having the greatest rate.

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Answer:

Graph theory is used in dealing with problems that have a reasonably natural graph/network structure.

Explanation:

For example,

road networks - nodes = towns

road junctions, arcs = roads

Communication networks - telephone systems

'Computer systems'

Foreign exchange/multinational tax planning (network of fiscal flows).

Hope it helped! :)

Graph theory is applied to problems that have a fairly natural graph/network structure.

Graph theory is the study of graphs in mathematics, which are mathematical structures used to model pairwise relationships between objects. In this context, a graph is made up of vertices (also known as nodes or points) connected by edges (also called links or lines).

Graph Theory is the study of relationships. Graph theory, given a set of nodes and connections that can abstract anything from city layouts to computer data, provides a useful tool for quantifying and simplifying the many moving parts of dynamic systems.

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Answer:

x = - 8

Step-by-step explanation:

7(4 - x) = 84 ( divide both sides by 7 )

4 - x = 12 ( subtract 4 from both sides )

- x = 8 ( multiply both sides by - 1 )

x = - 8

As a check

substitute x = - 8 into the left side of the equation and if equal to the right side then it is the solution.

7(4 - (- 8) )

= 7(4 + 8)

= 7(12)

= 84 = right side

Then x = - 8 is the solution to the equation

Answer: 49476

Step-by-step explanation:

Answer: It should be 33.5%

The answer, the money needs to be deposited each month is $557.47.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The future money plan to have 500000

Retirement in 35 years.

The interest 4%.

number of time periods = 35 years * 12 months per year = 420

interest will be .4166666667% per month

The formula = [tex]p(\frac{(1+r/n)^{r/n} -1 }{\frac{r}{n} } )[/tex]

⇒500000*(.014/12) = d(3.98-1)

⇒d = 1666.7/2.98 = 557.47

Hence the money needs to be deposited each month is $557.47

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The solution of the system equation is (-4,-11).

What is system equation?

One or more equations involving a number of variables make up a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

Here the given system equation is,

=> y = 5/2x-1------->1

=> t=2x-3---------->2

Put 1 into 2 then

=> 5/2x-1=2x-3

=>1/2 x=-2

=> x=-4

Put x=-4 into 2 then,

=> y=-8-3=-11.

Hence the solution of the system equation is (-4,-11).

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The x value is 12, length is 14 feet and breath is 9 feet when the area of rectangle is 126 square feet.

Given that,

The rectangle has a surface area of 126 square feet.

The length is x+2 and the breath is x-3.

We have to find the x value, length and breath.

We know that,

The area of the rectangle is length × breath.

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

126= x²-3x+2x-6

126= x²-x-6

x²-x-6-126=0

x²-x-132=0

x²-12x+11x-132=0

x(x-12)+11(x-12)=0

(x-12)(x+11)=0

x-12=0     or   x+11=0

x=12        or    x=-11

We take the x as positive so its 12.

Length is x+2=12+2=14

Breath is x-3=12-3=9

Therefore, The x value is 12, length is 14 feet and breath is 9 feet when the area of rectangle is 126 square feet.

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