simplify the following algebraic expressions.
-2x + 5 + 10x - 9

3(x + 7) + 2(-x + 4) + 5x

The required first five terms of the sequence are 2, 10, 50, 250, and 1250.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The first five terms of the sequence, a(n), defined by the recurrence relation a(n+1) = 5a(n) and a(1) = 2, are as follows:

a(1) = 2

a(2) = 5a(1) = 5 × 2 = 10

a(3) = 5a(2) = 5 × 10 = 50

a(4) = 5a(3) = 5 × 50 = 250

a(5) = 5a(4) = 5 × 250 = 1250

Therefore, the first five representations of the sequence are 2, 10, 50, 250, and 1250.

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Answer:

The first chart.

Step-by-step explanation:

The first table. The chart gives a ratio of 1:4, which is the same as the amount the teenager made.

Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2

A mathematical depiction of two equal variables, one on either side of a "equals" sign, is called an equation. Equations can be used to solve common problems. To solve challenges in real life, we frequently turn for pre algebra assistance. Lessons in pre-algebra cover the foundational ideas of mathematics.

Here,

Given : synthetic division for

x³ + 3x² + 8x + 14

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

x + 2

Write the problem in synthetic division format

-2  | 1 3 8 14

         -2 -2  

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

     1   1  6

Carry down the leading coefficient, unchanged, to below the division symbol

-2  |    1 3 8 14

           -2 -2

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

         1  1   6

Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:

1(-2)=-2

-2 |  1 3 8 14

        -2 - 2

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

     1    1   6

=> We get:

As

x² +x+6+ [tex]\frac{2}{x+2}[/tex]

and remainder is 2

Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2.

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Answer:

Step-by-step explanation:

axf

Answer:

X > -20

Step-by-step explanation:

-10 - 9/2 x < 80

Move 10 to the other side

- 9/2 x < 80 + 10

Simplify

-9/2 x < 90

-9 x < 180

x > -20

(We switch the inequality sign if we are dividing with negatives)

Answer:316.8

Step-by-step explanation:

Answer:316.8

Step-by-step explanation:

The difference between the expansions of (A + B)^2 and (A - B)^2 is the sign of the middle term. In the second case it is negative, due to the negative sign on B.

Here we have two perfect square trinomials, these are:

(A + B)^2

(A - B)^2

Notice that the only difference between these is the sign of the second element.

Now we can expand these two expressions as:

(A + B)^2 = (A + B)*(A + B) = A^2 + 2AB + B^2

The second expression gives:

(A - B)^2 = (A - B)*(A - B) = A^2 + 2*A*(-B) + (-B)^2

                                       = A^2 - 2AB + B^2

There we can see that the only difference between these two expansions is the sign of the middle term. Where in the second case it is negative, due to the negative sign on B.

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The value of s that makes the inequality true is 6

An inequality can simply be defined as a mathematical relation that makes a non-equal comparison between two variables, numbers, ratios or other mathematical expressions.

It is used in comparing two numbers on the number line on the basis of their size.

The inequality signs are;

From the expression given, we have;

7s < 42

Make 's' the subject by dividing both sides by 7, we have;

s > 42/7

s> 6

Hence, the value is greater than 6

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In order to win his master's tournament, William needs to make the most of his strengths and use the strategies that best suit his playing style.

Mathematics is the study of numbers, shapes, and patterns. It is a universal language that helps us to understand and describe the world around us. Math is used to solve problems and to make predictions. It is used to analyze data and to make decisions. Math is a powerful tool that allows us to communicate ideas and to make sense of the world. Math helps us to understand the physical laws that govern the universe and to make sense of our ever-changing world.

First and foremost, he needs to focus on improving his technical skills. He should practice using a variety of shots and playing on different surfaces. This will give him the confidence and control he needs to succeed.

William should also develop a strategy for each match. This should include analyzing his opponent’s playing style and strengths, understanding the court conditions, and setting a specific set of goals for each game. He should also practice mental conditioning to help him stay focused and be able to handle the pressure.

Finally, William should take care of his physical health. This includes getting enough sleep, eating healthy, and exercising regularly. He should also make sure he is properly hydrated and fueled during the tournament.

By taking the necessary steps and making the most of his strengths, William can put himself in a good position to win the tournament. With hard work and dedication, he can make his dream a reality.

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In order to win his master's tournament, William needs to make the most of his strengths and use the strategies that best suit his playing style.

Mathematics is the study of numbers, shapes, and patterns. It is a universal language that helps us to understand and describe the world around us. Math is used to solve problems and to make predictions. It is used to analyze data and to make decisions. Math is a powerful tool that allows us to communicate ideas and to make sense of the world. Math helps us to understand the physical laws that govern the universe and to make sense of our ever-changing world.

First and foremost, he needs to focus on improving his technical skills. He should practice using a variety of shots and playing on different surfaces. This will give him the confidence and control he needs to succeed.

William should also develop a strategy for each match. This should include analyzing his opponent’s playing style and strengths, understanding the court conditions, and setting a specific set of goals for each game. He should also practice mental conditioning to help him stay focused and be able to handle the pressure.

Finally, William should take care of his physical health. This includes getting enough sleep, eating healthy, and exercising regularly. He should also make sure he is properly hydrated and fueled during the tournament.

By taking the necessary steps and making the most of his strengths, William can put himself in a good position to win the tournament. With hard work and dedication, he can make his dream a reality.

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Five vectors in Span (V₁ V₂) where V₁ = (8 2 7 ) and V₂ = (-6 4 0 ) is.

n(V₁ + V₂), n ∈ I, I = 1, 2, 3, 4, 5.

In mathematics, the set of all linear combinations of the vectors in S is referred to as the linear span, Denoted span(S), Either the intersection of all linear subspaces containing S, or the smallest subspace containing S, can be used to describe it. A vector space is therefore nothing more than the linear range of a set of vectors.

The vectors that are in the same span should be a multiple of the vectors

V₁ = (8 2 7 ), V₂ = (-6 4 0 )

Now, V₁ + V₂ = (2 6 7).

So, The five vectors in the span of V₁ and V₂ is,

2×(2 6 7).

= (4 12 14).

- 2×(2 6 7).

= (- 4 - 12 - 14).

3×(2 6 7).

= (6 18 21)

- 3×(2 6 7)

= (- 6 - 18 - 21).

5×(2 6 7).

= (10 30 35).

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The graphs as per the transformations are given below.

What are transformation of graphs?

There are four transformations that happens in a graph -

When a figure is translated, it is moved in any direction.

Flipping a figure over a line is called reflection.

Rotation is the process of turning a figure a specific amount around a point.

When we dilate a figure, we increase or decrease its size.

The triangle CHV have points C(-4,5), H(-3,3) and V(-3,5). When it is reflected across x=-3. The image gets mirrored in the negative y-axis with the points C(-4,-2), H(-3,0) and V(-3,-2).

The parallelogram CJWY have points C(-3,-1), J(-2,-1), W(-2,-4), Y(-1,-4). It needs to be translated by (x,y)->(x+2,y+0)

C=(-3+2,-1+0)=(-1,-1)

J=(-2+2,-1+0)=(0,-1)

W=(-2+2,-4+0)=(0,-4)

Y=(-1+2,-4+0)=(1,-4)

The parallelogram TSCH have points T(-1,3), S(1,4), C(1,-1), H(3,0). It needs to be translated by (x,y)->(x+0,y-1)

T=(-1+0,3-1)=(-1,2)

S=(1+0,4-1)=(1,3)

C=(1+0,-1-1)=(1,0)

H=(3+0,0-1)=(3,-1)

The triangle RDP have points R(0,0), D(-2,-2) and P(3,-3). On rotation of 180 degrees graph (x,y) becomes (-x,-y).

R=(0,0)

D=[-(-2),-(-2)]=(2,2)

P=[-(3).-(-3)]=(-3,3)

Therefore, the transformations are made.

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Greatest common factor (GCF) of 50 and 65 is 5.

We will first find the prime factorization of 50 and 65. After we will calculate the factors of 50 and 65 and find the biggest common factor number .

Step-1: Prime Factorization of 50

Prime factors of 50 are 2, 5. Prime factorization of 50 in exponential form is:

50 = 21 × 52

Step-2: Prime Factorization of 65

Prime factors of 65 are 5, 13. Prime factorization of 65 in exponential form is:

65 = 51 × 131

Step-3: Factors of 50

1, 2, 5, 10, 25

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 50 and 65. The biggest common factor number is the GCF number.

So the greatest common factor 50 and 65 is 5.

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The action which would be better is the latter since it provides a higher average return in the span of 5 years.

This is referred to as the concept of increasing a firm's worth to increase the value of stockholders' shares and it is usually considered a long-term goal.

In this scenario, the action which involves the stock price rising from Rs. 1600 to Rs. 3000 provides a higher average return in the span of 5 years which is a long-term goal since it is assumed that shareholders invest in a company to meet their long-term financial goal and the corporate actions which have these general tendencies is lending to people and organizations at a proposed interest rate.

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Answer:

It is the first answer,

Step-by-step explanation:

The hypotenuse is always the longest side and opposite of the right angel.  Side b is the adjacent side to J and c is the opposite side of J.

The area of the new triangle is  600ft²

To increase the size of a triangle by a scale factor of 10/3, multiply each dimension of the triangle by 10/3.

The new dimensions of the triangle will be:

10/3 × 9ft = 30ft

10/3 × 12ft = 40ft

The area of a triangle is given by the formula A = 1/2  × b  ×h,

where b is the length of the base and h is the height of the triangle.

Thus, the area of the new triangle will be:

A = 1/2  × 30 × 40 = 600ft²

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Answer:

Step-by-step explanation:

One side of a square field is 92m. Find the cost of raising lawn on the field at the rate of 1.50 per sq.m

Square area = l²

Square area = 92²

Square area = 8466 m²

Cost = Area × rate of 1.50 per sq.m

Cost = 8466 × 1.50

Cost = 12696

Answer:

y = [tex]\frac{3}{4}[/tex]x + 3

Step-by-step explanation:

find the slope m

m = [tex]\frac{y2 - y1}{x2 - 21}[/tex]

m = [tex]\frac{3 - 0}{0 - - 4}[/tex]

m = [tex]\frac{3}{4}[/tex]

y = mx + b

find b

insert y1 and x1 into the equation

0 = [tex]\frac{3}{4}[/tex](-4) + b

0 = -3 + b

b = 3

y = [tex]\frac{3}{4}[/tex]x + 3

Answer:

1809/27=67 is your answer........

The elevation at which the race ends is given by the equation A = 195 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the elevation at which the race ends be A

Now , the equation will be

The bike road race starts at an elevation of 500 feet

So , the initial elevation = 500 feet

The number of stages = 5 stages

The elevation at first stage = -139 feet

The elevation at second stage = -63 feet

The elevation at third stage = 197 feet

The elevation at fourth stage = 27 feet

The elevation at fifth stage = -327feet

So , the total elevation of all the stages during the bike race = initial elevation + elevation at first stage + elevation at second stage + elevation at third stage + elevation at fourth stage + elevation at fifth stage

Substituting the values in the equation , we get

The total elevation of all the stages during the bike race = elevation at which the race ends A

So ,

Elevation at which the race ends A = 500 + (-139) + (-63) + (197) + (27) + (-327)

On simplifying the equation , we get

Elevation at which the race ends A = 500 - 305

Elevation at which the race ends A = 195 feet

Therefore , the value of A is 195 feet

Hence , the race ends at an elevation of 195 feet

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Taking into account the definition of a system of linear equations, the number of sodas and hot dogs sold is 92 and 45 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

The values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x + y= 137

x= y + 47

To solve a system of equations by the substitution method, an unknown quantity must be solved in one of the equations. Substitute the expression of this unknown in the other equation, obtaining an equation with only one unknown and thus be able to solve it. The value obtained is substituted in the equation in which the unknown appeared. In this way, the two values obtained constitute the solution of the system.

In this case, substituting the second equation in the first one you get:

y + 47 + y= 137

Solving:

y+ y= 137 -47

2y= 90

y= 90÷2

y= 45

Replacing this value in the second equation, you get:

x= 45 + 47

x= 92

Finally, the number of sodas sold is 92 and the number of hot dogs sold is 45.

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Answer:

3.4 seconds

Step-by-step explanation:

Given function:

[tex]h(t)=-4.9t^2+2.45t+48.314[/tex]

where

The ball will strike the ground when its height is zero.

Therefore, to calculate when the ball strikes the ground, substitute h(t) = 0 and solve for t using the quadratic formula.

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Therefore:

Substitute these values into the quadratic formula:

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{(2.45)^2-4(-4.9)(48.314)}}{2(-4.9)}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{6.0025+946.9544}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{952.9569}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm 30.87}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 + 30.87}{-9.8}=-2.9[/tex]

[tex]\implies t=\dfrac{-2.45 -30.87}{-9.8}=3.4[/tex]

As time cannot be negative, t = 3.4 s only.

Therefore, the ball strikes the ground 3.4 seconds after it is launched.

Total cost is the sum of all expenses incurred to produce a particular type of product. The answer is $1.50.

Total cost is the sum of all expenses incurred to produce a specific kind of output. Financial reporting, when overhead costs must be allocated to specific assets, is where the total cost approach is more useful from an accounting standpoint.

$8 was spent in total.

Xavier bought four $1.25 snacks.

4 x 1.25 = $5

The 2 cans cost $3 because 5 + 3 = 8, and we know how much the snacks cost ($5), making the total cost ($8).

Each can cost $1.50 because, if the price of the two cans was $3, we would have to divide it by two to get the price of the second can, which comes out to be $1.50. As a result, each can was $1.50.

Therefore, the answer is $1.50.

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The reference angle of 7pi/4 is pi/4

The acute angle formed by the terminal arm or side and the x-axis is known as the reference angle.

There is always a positive reference angle. The reference angle is, in other words, the angle formed by the terminal side and the x-axis. It must always be positive and less than 90 degrees.

considering angle 7 pi/4, the angle is pi/4 away from 2 pi.

7 pi/4 + pi/4 = 8 pi/4 = 2 pi

We can therefore conclude that 7 pi/4 is an angle on the third quadrant and the reference angle is pi/4.

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Hello there!

Answer:

[tex](9, +\infty)[/tex]

Step-by-step explanation:

It has no real roots only if

[tex] \sqrt{b {}^{2} - 4ac } [/tex]

has no roots. That means that b² - 4ac is smaller than 0:

[tex]b {}^{2} - 4ac < 0 \\ 12 {}^{2} - 4 \times 4 \times k < 0 \\ 144 - 16k < 0 \\ 144 - 144 - 16k < - 144 \\ - 16k < - 144 \\ k > 9 \\ k \: \: \: in \: \: \: (9, +\infty)[/tex]

we can approach this from the standpoint of the discriminant, if the discriminant is negative then we only get complex roots or namely "imaginary" solutions or values, well, let's check before that happens, when the discriminant is 0.

[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+k} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]

[tex]0=(12)^2 - 4(4)(k)\implies 0=144-16k\implies 16k=144 \\\\\\ k=\cfrac{144}{16}\implies k=9\hspace{5em} \stackrel{if~k > 9\textit{, then we land on negative territory}}{{\Large \begin{array}{llll} k > 9 \end{array}}}[/tex]

Answer:

245 miles

Step-by-step explanation:

210 = 6 gallons

210/6 = how far you can travel with one gallon

210/6 = 35

7*35 = how far you can travel with 7 gallons

7*35 = 245

Answer:

Ann drove 245 miles during her drive last weekend.

Step-by-step explanation:

If Ann used 7 gallons of gas during her drive last weekend, we can use the car's MPG to find out how far she drove by multiplying the number of gallons used by the MPG:

7 gallons * 35 miles/gallon = 245 miles

Answer:

[tex]\frac{13}{17}[/tex]

Step-by-step explanation:

just a tip use math-way in the future it's always been great

Hope this helps!

The solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .

Given equations ,

[tex]x^{2}[/tex] + 81 = 0  ,[tex]x^{2}[/tex]-22 = -26 , 3[tex]x^{2}[/tex]-18=21 ,2[tex]x^{2}[/tex] +15 = -13

What is Quadratic equation ?

quadratic equation can be defined as the equation which is in the form of a[tex]x^{2}[/tex]+bx + c = 0 .

where a,b,c are constants .

By solving we get ,

[tex]x^{2}[/tex] +81 = 0

[tex]x^{2}[/tex] = -81

x = 9i , -9i

[tex]x^{2}[/tex] - 22 = -26

[tex]x^{2}[/tex] = -26 + 22

[tex]x^{2}[/tex] = -4

x = 2i,-2i

3[tex]x^{2}[/tex] - 18 = 21

3[tex]x^{2}[/tex] = 18+21

3[tex]x^{2}[/tex] = 39

[tex]x^{2}[/tex] = 13

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex]

2[tex]x^{2}[/tex] +15 = -13

2[tex]x^{2}[/tex]  = -13-15

2[tex]x^{2}[/tex]  = -28

[tex]x^{2}[/tex]  = -14

x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i

Hence the solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .

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