find the 31st term 2,10,18

Step-by-step explanation:

f(x) = x² - 3x + 5

f(-2) = (-2)² - 3.(-2) + 5

f(-2) = 4 + 6 + 5

f(-2) = 15

Answer:

Step-by-step explanation:

Comment

In general, f(x) can be thought of as being y. So the equation could read as "Let x = - 2" when y = x^2 - 3x + 5.

Another way of thinking of it is by saying f(-2), wherever you see an x on the right hand side, substitute the value given on the left side (in this case x = - 2

Solution

f(-2) = (-2)^2 - 3x + 5

f(-2) = 4 - 3(-2) + 5                   Combine

f(-2) = 4 + 6 + 5                        Add

f(-2) = 15

Lines AB and CD are both perpendicular to the line EF, then AB |is parallel to CD. The lines CD and GH cannot be defined. The lines AB and GH cannot be defined. Lines IJ and CD are perpendicular

Two lines are said to be parallel if :  m(1) = m(2).

Two lines are perpendicular to each other if : m(1) x m(2) = -1.

We have to classify the set of these lines as; Parallel, Perpendicular or Cannot Be Determined.

1. Lines AB and CD are both perpendicular to the line EF, then AB |is parallel to CD.

2. The lines CD and GH cannot be defined, because the diagram doesn't contain any information about angles at which these lines intersect.

3. The lines AB and GH cannot be defined, because the diagram doesn't contain any information about angles at which these lines intersect.

4. Lines IJ and CD are perpendicular; because they intersect each other at right angle.

Hence, the solutions to the table are shown above as options.

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Answer: 40

Step-by-step explanation:

when x=0, y=0

when x=2.5, y=100

(y2-y1)/(x2-x1)=

(100-0)/(2.5-0)=

100/2.5=40

Answer:

40

Step-by-step explanation:

the point on the graph is (1,40).  The ordered pair is in the form (x,y)  The constant of proportionality is the y/x or 40/1 which equals 40.

Answer:

The answer is 4!

The length of river Nile is 6825 KM and the length of river Congo is 4370 KM

From the question, we are to determine the lengths of the each river

From the given information,

"The longest river in Africa is the Nile it is 2455 KM longer than the Congo river"

Let the length of river Nile be N

and the length of river Conge be C

Thus,

N = C + 2455

Also,

"the sum of the lengths of these rivers is 11,195 KM"

That is ,

N + C = 11195

Substitute the first equation into the second equation

N + C = 11195

C + 2455 + C = 11195

2C + 2455 = 11195

2C = 11195 - 2455

2C = 8740

C = 8740/2

C = 4370

Substitute the value of C into the first equation

N = C + 2455

N = 4370 + 2455

N = 6825

Hence, the length of river Nile is 6825 KM and the length of river Congo is 4370 KM

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Answer:

Step-by-step explanation:

185miles / 75mph =  2.5 hours

The given scenario, "A school administrator gets the alphabetical list of students and chooses every third one to survey", is Systematic Sampling.

In the question, we are asked to identify the type of sampling used in the scenario: "a school administrator gets the alphabetical list of students and chooses every third one to survey", among cluster, convenience, stratified, and systematic.

First, we will understand all these types of sampling:-

In the given scenario, the school administrator is getting the list of students in alphabetical order, similar to taking everyone in a line and counting off "1,2,3,4; 1,2,3,4; etc. And then he is choosing every third student, similar to choosing all those numbered 4.

Thus, the given scenario, "A school administrator gets the alphabetical list of students and chooses every third one to survey", is Systematic Sampling.

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Answer:

Distance is [tex]\sqrt{85}[/tex] or 9.2195...

Hope this helps!

Step-by-step explanation:

d = [tex]\sqrt{(x_{2}-x_{1} )^{2} + (y_{2} - y_{1} )^{2} }[/tex]

d = [tex]\sqrt{(13 - 7 )^{2} + (0-(-7)^{2} }[/tex]

d = [tex]\sqrt{(6)^{2} +(7)^{2} }[/tex]

d = [tex]\sqrt{36 + 49}[/tex]

d = [tex]\sqrt{85}[/tex]

d = 9.2195444...

Answer:First, determine the total number of hours worked by multiplying the hours per week by the number of weeks in a year (52). Next, divide this number from the annual salary.if an employee has a salary of $50,000 and works 40 hours per week, the hourly rate is $50,000/2,080 (40 x 52) = $24.04.

Step-by-step explanation:

Divide the gross pay by the wage hours worked. For example, if your records show that the employee was paid $4,000 for the total month, divide 4,000 by 172 to reach $23.26. This is an accurate representation of an hourly rate for that employee's monthly work.

Functions b(x) is not one-to-one functions as the domain of there inverse is not the range of function then you can't find an inverse function. Function d(x) doesn't include x, then you can't also find an inverse function.

What is Mathematical function ?

Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.

Steps of Finding the inverse of a function f(x):

1. First, replace f(x) with y. This is done to make the rest of the process easier.

2. Replace every x with a y and replace every y with an x.

3. Solve the equation from Step 2 for y. This is the step where mistakes are most often made so be careful with this step.

4. Replace y with  In other words, you’ve managed to find the inverse.

5. Remember: the domain of f is the range of  and the range of f is the domain of [tex]f^{-1}(x)[/tex].

Using this algorithm, you can find the inverse of non.

for f(x) = x^2 +3

y = x^2 + 3

x = y^2 + 3

y = √x-3

[tex]f^{-1}(x)[/tex] = √x-3

The domain and the range of f'(x) :

domain : [3,∞]

Range : [3,∞]

The domain and the range of f(x) :

Domain: x ∈ R (all real number)

Range: y ≥ 3

Functions b(x) is not one-to-one functions as the domain of there inverse is not the range of function then you can't find an inverse function. Function d(x) doesn't include x, then you can't also find an inverse function.

Therefore, for both the given function we cannot find the inverse.

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Answer:

10 visits

Step-by-step explanation:

Let's model the expressions:

Now set them to equal each other to find x, the number of visits

50 + 2x = 30 + 4x Subtract 2x

50 = 30 + 2x Subtract 30

20 = 2x Divide by 2

10 = x

After 10 visits to the gym, the cost will be the same.

Answer: -3

Step-by-step explanation:

The amount saved by repaying the loan early is $831.25

The amount of discount received by purchasing supplies is $3,500

The net amount saved by purchasing supplies rather than repaying loan is $2,668.75

What is ordinary interest?

Ordinary interest is the interest computation that is based on 360-day a  year count rather than 365-day year count, hence, in determining the amount saved by paying $35,000 out of the amount due to Citizens Bank, we time-apportion the interest for 90 days with respect to 360 days not 365 days.

Amount saved in interest=$35,000*9.5%*90/360

Amount saved in interest=$831.25

Using the $35,000 to purchase serving supplies, 10% discount is given off the normal cost of $35,000

Amount saved with discount=10%*$35,000

Amount saved with discount=$3,500

The difference between discount on supplies and interest saved=$3,500-$831.25

The difference between discount on supplies and interest saved=$ 2,668.75

The other factors to consider before making the final decisions include, the fact the loan is more important than the supplies because the loan relates to the firm's financing rather than operational needs of supplies

Secondly, the amount saved in interest may be more if another loan of $35,000 can be borrowed elsewhere with significant lower interest rates

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The difference quotient of the function f(x) = 4x + 2 is 4.

Functions were originally the idealization of how a varying quantity depends on another quantity.

The given function is,

f(x) = 4x + 2

For a given function f(x), we define the difference quotient as:

[tex]\frac{f(x+ h)-f(x)}{h}[/tex]

Thus, for the given function, difference quotient is given as,

[tex]\frac{f(x+ h)-f(x)}{h}[/tex] = [tex]\frac{4(x+h)+2-(4x+2)}{h}[/tex]

expanding the brackets we get,

[tex]\frac{f(x+ h)-f(x)}{h}[/tex] = [tex]\frac{4x+4h+2-4x-2}{h}[/tex]

Solving we get,

⇒ [tex]\frac{f(x+ h)-f(x)}{h}[/tex] = [tex]\frac{4h}{h}[/tex]

Thus,we get

⇒ [tex]\frac{f(x+ h)-f(x)}{h}[/tex] = 4

Thus, the difference quotient of the function f(x) = 4x + 2 is 4.

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The multiplication of 0.34 by 0.568 will be 0.19312 and the number of significant figures is five.

In positional notation, significant figures are the digits in a number that are trustworthy and required to denote the amount of something. Significant figures are the number of digits that add to the correctness of a value, frequently a measurement.

It should be noted that significant figures are the numbers that are reliable and are usually non zero digits.

In this case, the multiplication of 0.34 by 0.568 will be 0.19312.

Therefore, the number of significant figures is five.

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[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{10} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ \cfrac{1}{10}}(x-\stackrel{x_1}{(-10)}) \implies y -4= \cfrac{1}{10} (x +10) \\\\\\ y-4=\cfrac{1}{10}x+1\implies {\LARGE \begin{array}{llll} y-\cfrac{1}{10}x+5 \end{array}}[/tex]

The ratio between the money he spent and the total sum he had , the ratio between the money left and the total sum he had, the ratio between the money left and the money he spent.​ are 29:60, 31:60 and 31:29 respectively.

Ahmed has L.E. 15 which when converted in piastres, it is 1500 piastres

He spent 725 piasters and the money left with Ahmed is 1500-725 which is 775 piastres

The ratio between the money spent and the total sum is 725:1500 which is simplified to 29: 60 by dividing both with anything which is common in both that is 25

The ratio between the money left and the total sum he had is 775:1500 which is simplified to 31:60 by dividing both with anything which is common in both that is 25

The ratio between the money left and money spent is 775:725 which is simplified to 31:29 by dividing both with anything which is common in both that is 25

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Answer: x = -10

▬▬▬▬▬▬▬▬▬▬

         [tex]4 + 8 \times x = -76[/tex]

▬▬▬▬▬▬▬▬▬▬

[tex]4+8(x)-4=-76-4\\8(x)=-80\\\frac{8(x)}{8}=\frac{-80}{8}\\= -10\\x = -10[/tex]

▬▬▬▬▬▬▬▬▬▬

Answer Explained:

Given the keywords sum(add), times(multiply), as well as a number(variable), we can make an equation out of this, which was 4 + 8 * x = -76. We subtracted the sides by 4, then divided both of the sides by the next factor, 8, to get -10.

Thus,

4 + 8 × -10 = -76

Hope this helped you. :)

The coordinates of G after it is rotated by 90 degrees will be ( 3, 4 ).

The process of changing the location of the image on the coordinate system will be known as the translation.

Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x and y, and make y-negative.

Given that point, G is translated to 90 degrees. The translated coordinates of point G will be calculated as:-

( -x, y ) = ( y, x )

( -4 , 3 ) = ( 3 , 4)

Therefore, the coordinates of G after it is rotated by 90 degrees will be ( 3, 4 ).

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Answer:

[tex] - \frac{8}{5} [/tex]

Step-by-step explanation:

[tex] - 2 \frac{ \\ 2}{5} + \frac{4}{5} = - \frac{8}{5 \\ } [/tex]

Based on the amount that Ron Sample gets at the beginning of each year, the number of years, and the interest compounded annually, the amount that should be invested to award the price is $35,720.80.

The value of $8,000 is constant which makes it an annuity. However, it comes at the beginning of each year which makes it an annuity due.

The amount to be invested to gain this $8,000 every year is therefore the present value of this annuity due based on the interest rate.

Present value of annuity due = Annuity due x (Present value interest factor of annuity due, 6%, 5 years)

= 8,000 x 4.4651

= $35,720.80

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Answer + Step-by-step explanation:

Part A :

Let M(a , b) be a point where the graphs

of the equations y = 8ˣ and y = 2ˣ⁺² intersect.

M lies on both graphs

Then

the coordinates of M verify both equations (equation of graph1 and equation of graph 2)

Then

[tex]b=8^{a}\ \text{on the other hand} \ b=2^{a+2}[/tex]

Then

[tex]8^{a}=2^{a+2}[/tex]

Therefore ‘a’ (the x-coordinates of the points M where the two graphs intersect) is a solution to the equation :

[tex]8^{x}=2^{x+2}[/tex]

Part B : check the attached table.

Part C :

Graphically, we try to spot the points of intersection of the two graphs ,the x-coordinates of those points are the solution to our equation.

In our case , obviously the two graphs intersect at only one point M(1 ,8)

Therefore 1 is the only solution to 8ˣ = 2ˣ⁺².

Also ,Check the attached graph.

The number of many matinee and prime-time movie tickets were sold that day are

A linear equation in two variables is one that is written in the form ax + by + c = 0, where a, b, and c are real numbers and also the coefficients of x and y, i.e. a and b, are not equal to zero.

For the given question.

Let 'x' be the number of matinee showings.

Let 'y' be the number of prime-time showings.

Then. the total ticket sold are 1,411.

Thus, x + y = 1,411.

or, x = 1,411 - y

The cost of one matinee showings is $9.

The cost of one prime-time showings is $13.50.

Now, the total cost earned is $17,149.50.

So,

9x + 13.5y = 17,149.50

Put the value of the 'x' in the above equation.

9(1,411 - y) + 13.5y = 17,149.50

Simplifying;

12699 - 9y + 13.5y = 17,149.50

4.5y = 4450.5

y = 989.

Calculate x;

x = 1,411 - 989

x = 422

Therefore, the number of matinee and prime-time movie tickets were sold that day are 422 and 989.

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Answer:

6. B

7. C

8. C

Step-by-step explanation:

6.

3x

------- = 1.5 (x + 1)

x + 1 (x + 1)

3x = 1.5 (x + 1)

3x = 1.5x + 1.5

-1.5x -1.5x

1.5x = 1.5

x = 1

7.

2x + 3y = 15

(x + y = 3)-2

2x + 3y = 15

-2x - 2y = -6

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

y = 9

x + y = 3

x + 9 = 3

-9 -9

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

x = -6

(x, y) = (-6, 9)

8.

(-4x + y = 4) -2

-8x + 2y = -2

8x - 2y = -8

-8x + 2y = -2

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

-10

No Solution

I hope this helps!

Answer:

10x-11 over 4

Step-by-step explanation:

step1:find common denominator

step 2:apply the distributive property

step3: remove the parentheses for addition or subtraction

step4: reorder and gather like terms

step5: collect co-efficients of the like terms

step6: calculate the sum or difference

Answer: The number 0.1453 belong to rational numbers and real numbers.

Step-by-step explanation:

Therefore,

The number 0.1453 belong to rational numbers and real numbers.

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If you contribute $8,000 every year for 5 years, the interest would you would earn during the 5 years is:6005.91

What is future value of annuity?

The future value of the annuity means the future worth of 5 annual contributions  of $8000 every year, based on the fact that the deposits would earn 7.0% interest rate every year, in short, the worth of the savings in 5 years can be determined using the future value of an ordinary annuity as shown below:

FV=PMT*(1+r)^N-1/r

FV=accumulate balance after 5 years=unknown

PMT=annual savings=$8,000

r=interest rate per year=7.0%

N=number of annual payments over 5 years=5

FV=$8000*(1+7.0%)^5-1/7.0%

FV=$46,005.91

Total deposits in 5 years=$8000*5=$40,000

Interest =FV-total deposits

interest=$46,005.91-$40,000

interest=$6,005.91

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Answer:

do u want me to graph or solve it

Step-by-step explanation:

Answer:

97

Step-by-step explanation:

I believe that is your answer

Answer:

Step-by-step explanation:

Answer:hi

Step-by-step explanation:hello