I really need help on this one I am confused and if someone could explain that would be great. also I am sorry the picture is flipped I couldn't turn it.

The Sum is 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)

A finite series is one that has a finite number of terms.

If the series [tex]a_1[/tex]+ [tex]a_2[/tex] + [tex]a_3[/tex] +... + a has n terms and is a finite series with n terms.

As a result, [tex]S_n[/tex] is used to represent the series' sum as follows:

[tex]S_n[/tex]=∑ [tex]a_n[/tex]

Given:

1 + x + x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex]

let P= 1/ 1-x

P - Px= 1

P= 1+ Px

 = 1 + (P)x

 = 1 + (1+ Px) x

 = 1+ x + Px²

 = 1+ x + (1+ Px)x²

 = 1+ x + x² + Px³ and so on

So, 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)

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The average of the number given is $4.84.

The average can be calculated as follows:

Given X

X =$4.25+$6.71+$3.24+$5.06+$4.94

X =$24.2

= X ÷ n

= $24.2 ÷ 5

= $4.84

Hence, the average is $4.84

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The true solution for 2 ln e^ ln (5x) = 2 ln (15) is x = 3.

Given,

2 ln e^ ln (5x) = 2 ln (15)

Apply log rule;

logₐ (aᵇ) = b

ln (e^ln (5x)) = ln (5x)

2 ln (5x) = 2 ln (15)

Divide both sides by 2;

2 ln (5x) / 2 = 2 ln (15)/ 2

ln (5x) = ln (15)

For ln (5x) = ln (15), solve for 5x = 15;

That is,

5x = 15

Then,

x = 15/5

So,

x = 3

Check this by substituting it to 2 ln (5x) = 2 ln (15);

x = 3

2 ln (5 × 3) = 2 ln (15)

x = 3 makes this true.

Therefore,

The true solution for 2 ln e^ ln (5x) = 2 ln (15) is x = 3.

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By evaluating a linear equation, we can see that 677.25 mL will be infused in 5.25 hours.

We know that the solution is being infused at a rate of 2.15 mL per minute.

So, t minutes after the infusion starts, the volume infused is given by the linear equation:

V(t) = 2.15mL*t

Here we want to see how many mL would infuse in 5.25 hours, to do that, we need to write that time in hours:

We know that one hour = 60 min, then:

5.25 h = 5.25*60 min = 315 min

Then the volume infused is:

V(315) = 2.15mL*315 = 677.25 mL

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Answer:

5

Step-by-step explanation:

Answer:

7.4

Step-by-step explanation:

Not completely sure because that equation is really hard to read. You might have put it in wrong.

Answer:

-95x + 91

Step-by-step explanation:

72/9 = 8

83 - 95x + 8

91 - 95x or -95x + 91

Answer: [tex]2\frac{19}{36}[/tex]

Step-by-step explanation:

You subtract the woman's height from her son:

[tex]60\frac{5}{18} -57\frac{3}{4} =\frac{1085}{18} -\frac{231}{4} =\frac{1085*2}{18*2} -\frac{231*9}{4*9} =\frac{2170-2079}{36} =\frac{91}{36} =2\frac{19}{36}[/tex]

Both end points are represented by closed circles, it means both points are included.

The graph is restricted between the end points from left to right and between the end point and the highest point from bottom to top.

Domain, the set of possible x- coordinates:

Range, the set of possible y- coordinates:

Both end points are represented by arrows directed to left and right, it means both ends are indefinite but lines are parallel to the x-axis.

It makes x-values infinite but y-values restricted between the two lines.

Domain, the set of possible x- coordinates:

Range, the set of possible y- coordinates:

Answer:

1.  Domain:  [-2, 6]

   Range:  [-3, 7]

2. Domain:  (-∞, ∞)

    Range:  [1, 5]

Step-by-step explanation:

Definitions

Note:  Assume that each square on the given graphs is 1 unit.

The domain of the function is restricted since the curve has two distince endpoints.  As each endpoint is marked by a closed circle, the x-value of the endpoints is included in the domain.

The function has a maximum point at (-1, 7) and a minimum point at (6, -3).

Therefore, the range of the function is restricted.

As there are arrows at both endpoints of the function, and the function is continuous between the arrowheads, the domain is unrestricted.

The maximum y-value is y = 5.  When x < 1, the line continues indefinitely at y = 5.

The minimum value is y = 1.  When x > 1, the line continues indefinitely at y = 1.

Therefore, the range of the function is restricted.

The function for the length when the width is given is l = 33 - w. The domain of the function is 0 < w < 33 and the graph of the function has been plotted

The total length of the roll = 66 feet

The perimeter of the rectangular paly area = 66

The perimeter of the rectangle = 2(l + w)

Then the equation will be

2(l + w) = 66

l + w = 66/2

l + w = 33

The function for length when the width is given

l = 33 - w

Therefore the domain of the function is 0 < w < 33

When w = 1

l = 33 - 1

l = 32

The first point is (1, 32)

When w = 32

l = 33 - 32

l = 1

The second point is (32, 1)

Draw the graph of the function

Hence, the function for the length when the width is given is l = 33 - w. The domain of the function is 0 < w < 33 and the graph of the function has been plotted

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The vertex of the graph of the parabola is at the point (-1, -6)

We know that for any parabola with a vertex at the point (h, k) and a leading coefficient a, can be written in vertex form as:

y = a*(x - h)^2 + k

In this case the parabola is:

f(x) = (-1)*(x + 1)^2 - 6

Comparing this with the general form, we can see that:

h = -1

k = -6

Then the vertex of the parabola is (-1, -6)

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Answer: B

Step-by-step explanation:

Answer:

16.11 (appx.)

Step-by-step explanation:

since l and m are parallel and a line intersects them, so we can say that the line is the transversal. from the figure we see that

7x + 12 = 12x - 28 [they are internal alternate angles and alternate angles are always equal to one another]

now, we can find the value of x from the equation

12x - 7x = 28 + 12

⇒ 5x = 40

⇒ x = 8

so the angle (7x+12)° is ((7*8)+12) = 68°

so (12x-28)° is also equal to 68° [cause of being alternate angles]

now, look at the figure,

angle (9y-77)° & (12x-28)° add upto a straight line as in 180°

and we know (12x-28)° = 68°

so now,

9y-77 = 68

⇒9y = 68+77

⇒9y = 145

⇒y = 16.11 (appx.)

Answer:

$497.8

Step-by-step explanation:

1. get the pool volume

volume = 8 x 20 x 14 = 2240 ft3

2. convert ft3 to gallons

2240 x 7.481 = 16757.44

3. You need 17000 gallons

4. Fee you have to pay fee + first 1000 gallon + the rest of the gallon

50 + 12.60 + 16 x 27.20 = 497.8

Answer:

[tex]\frac{-2}{3}[/tex]

Step-by-step explanation:

to find the slope of linear line, you need two points.  It does not matter which pints you use.  I am going to use (0,5) and (3,3)  The slope is the change in y over the change is x.  Our y values are 3 and 5.  Our x values are 3 and 0

[tex]\frac{3-5}{3-0}[/tex] = [tex]\frac{-2}{3}[/tex]

Interest will he pay in 10 years is $3375.

Given:

Bill is a freshman attending a 4-year college. He has been approved for a $5,000 with an APR of 6.75%.

He is not required to make any payment for 10 years since his payment will be deferred while his enroll in school.

1 year interest = 5000*6.75%

= 5000*6.75/100

= 50*6.75

= 50*675/100

= 1*675/2

= 337.5

10 years interest = 10 * 337.5

= 10 * 3375/10

= $3375.

Therefore Interest will he pay in 10 years is $3375.

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Answer:

Down Here ↓↓↓↓↓↓↓

Step-by-step explanation:

Hello!

This is all the information we need to fill up the blank spots:

Two angles whose sum is 180° are supplementary angles.

Vertical angles are formed by the opposite angles when two lines intersect.

Vertical angles are congruent/equal/equal in measure.

A linear pair of angles form adjacent angles, and the sum of their measures is 180°.

Adjacent angles share a common vertex and side.

The transformations to the graphs of each function are presented as follows:

The parent function is defined as follows:

f(x) = log2(x).

Function p(x) is defined as follows:

p(x) = 7log2(x) - 2.

The transformations are listed as follows:

Function r(x) is defined as follows:

r(x) = -2log2(x) + 3.

The transformations are listed as follows:

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Answer:

its c b a

Step-by-step explanation:

other person was wrong

Answer: Many even numbers are divisible by ten. A simple answer to that is 20. 30 is also, and so is 40. Any number going up by 10 will be divisible by 10 and 5. 10 is also divisible by 10 and 5.

The number of pennies that Anya has is equal to 15.6 pennies.

The number of dimes that Anya has is equal to 2.8 dimes.

In order to solve this word problem, we would assign variables to the number of pennies and dimes, the total number of coins, and then translate the word problem into algebraic equation as follows:

Note: 1 penny is equal to 0.05 dollar and 1 dime is equal to 0.10 dollar.

Therefore, translating the word problem into an algebraic equation, we have the following;

p = 10 + 2d                                ......equation 1.

0.05p + 0.1d = 1.06                   .......equation 2.

Substituting equation 1 into equation 2, we have:

0.05(10 + 2d) + 0.1d = 1.06  

0.5 + 0.1d + 0.1d = 1.06

0.5 + 0.2d = 1.06

0.2d = 1.06 - 0.5

0.2d = 0.56

Dimes, d = 0.56/0.2

Dimes, d = 2.8 dimes.

For the number of pennies, we have:

p = 10 + 2d

p = 10 + 2(2.8)

p = 10 + 5.6

p = 15.6 pennies.

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Five solutions of the given equation x- (3/2)y = -2 is given by as follow:

( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).

Plotted graph of the given function is attached.

As given in the question,

Given equation is equal to :

x- (3/2)y = -2

Simplify the given equation we get,

2x - 3y = -4

⇒ y = ( 1 / 3) ( 2x + 4 )

Now , five solutions of the given function to be plotted on the graph.

When x = 0

⇒ y = 4/3

When x = 1

⇒ y = (1/3)(2 +4)

⇒ y = 2

When x = 4

⇒ y = (1/3)( 8 + 4)

⇒y = 4

When x = -2

⇒y = (1/3)(-4 +4)

⇒y=0

When x = -5

⇒y = (1/3)(-10 +4)

⇒y= -2

Five solutions are ( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).

Plotted graph of the given function is attached.

Therefore, five solutions of the given equation x- (3/2)y = -2 is given by as follow:

( 0, 4/3) , ( 1, 2) , ( 4, 4 ) , ( -2, 0 ) , ( -5 , -2 ).

Plotted graph of the given function is attached

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The expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.

According to the question,

We have the following information,

The given verbal phrase is one-half times a number m plus twenty-five.

Now, we will solve it step by step.

Now, we will first find one-half times a number m. We know that we will replace the word times with multiplication. So, we have the following expression:

m/2

Now, adding 25 to this term, we have the following final expression:

m/2+25

Hence, the expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.

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An explicit formula for the arithmetic sequence is aₙ = 10 - 20(n - 1).

Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:

aₙ = a₁ + (n - 1)d

Where:

From the information provided, we have the following parameters:

First term, a₁ = 10

Second term, a₂ = -10

Next, we would determine the common difference as follows:

Common difference, d = a₂ - a₁

Common difference, d = -10 - 10

Common difference, d = -20

Substituting the parameters into the mathematical expression, we have;

aₙ = 10 + (n - 1)(-20)

aₙ = 10 - 20(n - 1).

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Answer:

8c³

Step-by-step explanation:

What is a coefficient?

A coefficient is a number that does not stand alone. For example, 3w means 3 times w, and "w" is a variable, so 3 is a coefficient.

How do we find the first term?

We can find the first term by putting the numbers from greatest to least. For example, if we had the numbers: 3x+7p+2 we would rearrange the series to this: 7p+3x+2. The number that comes first in the series would be the first term.

Answer:

20%

Step-by-step explanation:

2460-1968=492

492/2460=0.20

Check answer2460 x 0.20 = 492

Answer:

97.59

Step-by-step explanation:

975.90*0.10

97.59

Hope this Helps!!!

The cost of repainting the swimming pool is 15,600 pounds

The swimming pool forms a three-dimensional object. Three-dimensional space is a geometric setting in which three values are required to determine the position of an element or its area.

The area of the object is the space the swimming pool occupies

How to find the area of the swimming pool?

Mathematically represented as:  A =lbh metres square

A=40x20x2

A=1200m²

The cost of im² is 13 pounds

Therefore, multiplying the area by cost of 1m per square

Cost=1200x13

Cost=15,600 pounds

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The value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

First, let us know some laws of exponent:

We are given;

[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] and [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex].

Now, we will solve one by one;

[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex]

[tex]= \sqrt[5]{\frac{2^{10}(x^{-10})}{(2^5x^{-15})}}[/tex]

[tex]=[({2^{10}. 2^{-5}) (x^{-10}.x^{15})}]^\frac{1}{5}[/tex]

[tex]=[({2^{10-5}) (x^{-10+15})]^\frac{1}{5}[/tex]

[tex]=[({2^{5}) (x^{5})]^\frac{1}{5}[/tex]

= 2x

So, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x.

Now,

[tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex]

[tex]=\frac{(2^3x^6y^{-3})^\frac{1}{3} }{(2^3x^3y^3)}[/tex]

[tex]=\frac{(2x^26y^{-1})}{(2^3x^3y^3)}[/tex]

[tex]=\frac{1}{(2^{3-1}x^{3-2}y^{3+1})}[/tex]

[tex]=\frac{1}{(2^{2}x^{1}y^{4})}[/tex]

= 1 / 4xy^4

So, the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

Thus, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

Please find the figure for the questions below.

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Answer:

h=24

Step-by-step explanation:

7=3+h/6

-3 -3

4=h/6

x6. x6

24=h

hopes this helps please mark brainliest

Answer:

                             [tex]\overline{TW} \; \& \; \overline{RV}\\\\ \overline{PV} \; \& \; \overline{TU}[/tex]

Step-by-step explanation:

Coplanar: In the same plane.

The notation for a line is a double-ended arrow placed above two points contained on the line.

The symbol denotating two objects are parallel is a vertical double line.

A plane can be named by a capital letter (often written in script), or by the letters naming three non-collinear points in the plane.

The symbol denotating two objects are parallel is a vertical double line.

                             [tex]\overline{TW} \; \& \; \overline{RV}\\\\ \overline{PV} \; \& \; \overline{TU}[/tex]

The notation for a line segment is a bar placed above the endpoints of the line segment.

Answer:

1440/17 degrees (approximately 84.7059 degrees)

19π/9 radians ---> or π * 19/9 radians

Step-by-step explanation:

The conversion factor for radians to degrees is 180/π

8π/17 * 180/π = 1440/17 degrees (approximately 84.7059 degrees)

The conversion factor for degrees to radians is π/180

380 * π/180 = 380π/180 = 19π/9 radians