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Help me please!! Thanks

The given geometric series as shown in the question is seen to; Be converging with its' sum as 81

We are given the geometric series;

27 + 18 + 12 + 8 + ...

Now, we see that;

First term; a₀ = 27

Second Term; a₁ = 2(27/3)

Third term; a₂ = 2²(27/3²)

Fourth term; a₃ = 2³(27/3³)

Thus, the formula is;

2ⁿ(27/3ⁿ)

Applying limits at infinity gives;

2^(∞) * (27/3^(∞)) = 0

Since the  terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

S_n = a/(1 - r)

S_n = 27/(1 - (2/3)

S_n = 81

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Answer:  [tex]\sqrt{13}[/tex] units

Work Shown:

[tex](x_1,y_1) = (-5,-4) \text{ and } (x_2, y_2) = (-2,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-5-(-2))^2 + (-4-(-6))^2}\\\\d = \sqrt{(-5+2)^2 + (-4+6)^2}\\\\d = \sqrt{(-3)^2 + (2)^2}\\\\d = \sqrt{9 + 4}\\\\d = \sqrt{13}\\\\d \approx 3.6056\\\\[/tex]

I used the distance formula.

A slightly alternate method is to form a right triangle and use the pythagorean theorem. The hypotenuse will have the endpoints (-5,-4) and (-2,-6).

Answer:

All of these definitions are correct.

The distance would be 231 miles.

Speed can be calculated as the ratio of distance traveled to the time taken

Given information;

Time taken = 3 hours 30 minutes

Speed = 70 mph

We know that,

Distance = speed x time

Distance = 70 x 3.30

Distance = 231 miles

Thus, the distance would be 231 miles.

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The value of x in the equation (x - 5)² = 25 is 10.

(x - 5)² = 25

Take the square root of both sides

Therefore,

√(x - 5)² = √25

x - 5 = 5

add 5 to both sides

x - 5 + 5 = 5 + 5

x = 10

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So he needs to sell $2,000 in merchandise.

We can assume that we have a proportional relation:

y = k*x

Where y is the commission and x is what Norman sells, then:

$15 = k*$200

k = $200/$15 = 0.075

$37.50 = k*$500

k = $500/$37.50 = 0.075

Then the relation is:

y = 0.075*x

If he wants a commission of $150, then:

$150 = 0.075*x

$150/0.075 = x = $2,000

So he needs to sell $2,000 in merchandise.

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Answer:

2x³+3x²-8x+3

Step-by-step explanation:

So we know x=½,x=1 and x=-3

Then (2x-1)(x-1)(x+3) are the factors

(2x-1)[(x²+3x-x-3)]

(2x-1)[(x²+2x-3)]

2x³+4x²-6x-x²-2x+3

2x³+3x²-8x+3

The actual roots of the function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex] are -9/2, 3/5 and 1.

Given  function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex].

Function is a relationship between two or more variables expressed in equal to form.

The roots of a polynomial function are the zeroes of the polynomial function. A polynomial function is a function that involves only non negative integer powers in an equation.

The polynomial function is given as:

[tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex]

factorize the above function

[tex]f(x)=(2x+9)(5x-3)(x-1)[/tex]

Now put the function f(x) equal to zero.

f(x)=(2x+9)(5x-3)(x-1)

split the function means put all the expressions equal to zero as under:

(2x+9)(5x-3)(x-1)=0

solve each for the value of x

x=-9/2,x=3/5,x=1

Hence the roots of the function [tex]f(x)=10x^{3} +29x^{2} -66x+27[/tex] are which are also the values of x are -9/2,3/5,1.

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Answer:

Step-by-step explanation:

The solution for the inequalities 3y>2x+12, 2x+y<=-5 is the value of x<-27/8 and y<7/4.

Given 3y>2x+12 and 2x+y<=-5.

We are given two inequalities  3y>2x+12 and 2x+y<=-5. Inequality are like equations but in greater than ,less than or in combination with equal to. To solve them we need to first write them properly.

2x-3y<-12

2x+y<=-5

Now assume these are equalities

2x-3y=-12

2x+y=-5

now subtract 2 from 1

2x-3y-2x-y=-12+5

-4y=-7

y=7/4

put the value of y in 2x-3y=-12

2x-3(7/4)=-12

2x-21/4=-12

2x=-12+21/4

2x=(-48+21)/4

2x=-27/4

x=-27/8

Now put the signs between the values

x<-27/8

y<7/4.

Hence the solution of the inequalities 3y > 2x + 12

2x + y ≤ -5 is the value of x<-27/8 and y<7/4.

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[tex]f(x)=x(x-3)(x+3)[/tex]

The price of the light as a function of x is given by the exponential function:

[tex]p(x) = \$375*(0.98)^x[/tex]

We know that the original price of the light is $375.

This value decreases a 2% each year, so each year we need to multiply the above price by (1 - 2%/100%) = (1 - 0.02) = 0.98

Then, if x represents the number of years, the price of the light as a function of x is given by the exponential function:

[tex]p(x) = \$375*(0.98)^x[/tex]

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The mean of the scores if 6 students in a competitive exam is 25 marks.

Given scores of 6 students are: 10,30,50,40,20 in a competitive exam.

We have to find out the mean of the mark of 6 students in a competitive exam.

Mean is the sum of all the values in a set of data, such as numbers, measurements, divided by the number of values. It is also known as average.

Mean=∑X/n

∑X=10+30+50+40+20

=150

N=6

Now to calculate the mean we have to divide 150 by number of students which is 6.

Mean=150/6

=25 marks.

Hence the mean of the scores of 6  students is 25 marks.

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Question is incomplete as it should include :

Marks of students =10,30,50,40,20.

The number that produced a rational number when added to 1/5 is D. -2/3.

A rational number is a number that can be written as a ratio (or fraction) of two integers.

For example, when 1/5 is added to -2/3, it produces a rational number, -7/15, that remains as a fractional value.

Thus, the number that produced a rational number when added to 1/5 is D. -2/3.

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Answer:

It is NOT a function

Step-by-step explanation:

No it is NOT a function.....each value of x can only have one y value....

  this has two y values for   x = 2 :    y = 2 and 4    therefore not a function

Answer:

the answer is (x )

math  way  helps

Step-by-step explanation:

The requried function of function f(g(x)) is given as x² + 6x +5.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Given functions,
f(x)=x²−4 and g(x)=x+3

In order to form a function of function we have to function g(x) in function f(x)

Now,

f(g(x)) =  f(x)=(g(x))²−4

f(g(x)) =  f(x)=(x+3)²−4
f(g(x)) = x² + 6x + 9 -4
f(g(x)) = x² + 6x +5

Thus, the requried function of function f(g(x)) is given as x² + 6x +5.

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Since it has a variable in the denominator, the function f(x) is a parent function classified as rational.

Rational functions are functions that have the input variable, be it x, t, or any other, in the denominator.

The most simple example is given by:

[tex]f(x) = \frac{1}{x}[/tex].

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Answer: Reciprocal

Step-by-step explanation:

Reciprocal functions are functions that contain a constant numerator and x as its denominator. Its parent function is y = 1/x.

Step-by-step explanation:

"integral" means here that the factors in the polynomial are integers.

we have 3 zeros.

the least degree of a polynomial with 3 zeros is 3.

and yes, that works also for 2 zeros (the degree must be at least 2, it must be at least a quadratic equation).

or 4 zeros (at least 4th degree).

it in general n zeros (at least nth degree).

constructing this out of the given zeros is easy.

what happens, when I multiply something by 0 ? the total result will be 0.

and so, we simply multiply 3 short terms with each other, where each term turns 0 for one of the given zeros.

what expression in x turns 0, when x = -1/3 ?

well : x + 1/3 or with integers 3x + 1 (multiplied by 3)

and for x = 2/3 ?

x - 2/3 or with integers 3x - 2

and for x = -1/4 ?

x + 1/4 or with integers 4x + 1

so, our polynomial function (of at least 3rd degree) is then

(3x + 1)(3x - 2)(4x + 1)

basically this could be already the result, depending on what your teacher wants.

for the fully extended form we need to do the multiplications :

(3x + 1)(3x - 2) = 9x² - 6x + 3x - 2 = 9x²- 3x - 2

(9x²- 3x - 2)(4x + 1) = 36x³ + 9x² - 12x² - 3x - 8x - 2 =

= 36x³ - 3x² - 11x - 2

the requested polynomial function is

f(x) = 36x³ - 3x² - 11x - 2

Answer:

1) Equation's:

2) Number of guest and the charge:

Part 1

Turn sentences into equation's (Let 'y' be total cost and x per meal) :

(i) charges $500 and $15 per meal

(ii) charges $350 and $18 per meal

Part 2

            y  =  y

500 + 15x = 350 + 18x

18x - 15x = 500 - 350

3x = 150

x = 150/3

x = 50

Charge at guest's 50 meal:

y = 500 + 15(50)

y = $1250

Point : (50, 1250)

Answer:

Graph is below

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The value of x° + y° is 216°

Note that the shape is a regular pentagon

Sum of angle in a pentagon = 540

Angle on each side = 108°

x = 108°

y = 108°

x° + y° = 108 + 108

x° + y° = 216°

Thus, the value of x° + y° is 216°

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Answer:

A. 100

Step-by-step explanation:

Angle 1 = 40

Angles 1 and 2 are equal. Add the angles 1 and 2 together.

40+40=80

The last step is to subtract 80 from 180.

180-80=100.

∠3=100

Hope this helps!

If not, I am sorry.

361 lollipop candies or 697 gummy bear candies fills the bag of volume 528 in.³, which gives the following possible equation;

Volume of candy bag = 528 in.³

Number of lollipop candies the bag can hold = 361 candies

Number of gummy bear candies the bag can hold = 697 candies

Therefore;

[tex]1 \: lollipop = \frac{528}{361} = 1.46[/tex]

[tex]1 \: gummy \: bear = \frac{528}{697} = 0.76[/tex]

Which gives the following equation;

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Answer:

l/361 + g/697= 1

Khan Academy Sat Practice

Considering the area of the rectangle, it is found that she will need 17 tiles to cover the floor.

The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:

A = lw

The dimensions in feet are given as follows:

Hence the area in square feet is given by:

A = 4.5 x 3.75 = 16.875 ft².

Each tile has 1 square foot, hence, rounding, she will need 17 tiles to cover the floor.

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The meter mark at which Ario wil be when Miguel starts the race is; 7.4 meters

A ratio such as the ratio 1:4 shows the proportion of two factors. In this case, it shows the ratio between the completed meters vs the remaining meters.

To find the distance, we will have to determine how much 1:4 represents in the total distance.

Total distance = 25 meters - 3 metes = 22 meters

Thus; 22 * 1/ 5 = 22/5 = 4.4

However, we also know they are three meters behind the start.

Thus, the meter mark at which Ario will be when Miguel starts the race

4.4 + 3 =7.4 meters

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We can write the ordered pairs that meet this condition as:

(x, y) = (x, (9 + x)/4 )

An ordered pair on the X-Y plane is written as (x, y).

Here we also have the relation:

-x + 4y = 9

If we isolate y, we get:

4y = 9 + x

y = (9 + x)/4

Now, we can write the ordered pairs that meet this condition as:

(x, y) = (x, (9 + x)/4 )

To get the particular ones you can replace the value of x, for example, if x = 0, then:

(x, (9 + x)/4 ) = (0, 9/4)

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The ratio of orange juice to apple juice to grape juice is 6: 3 : 2

A ratio says how much of one thing there is compared to another thing.

Therefore, we are comparing the numbers of juice produce by a bottling company.

Hence,

number of orange juice = 24

number of apple juice = 12

number of grape juice = 8

Therefore, the ratio of orange juice to apple juice to grape juice is as follows:

ratio = 24 : 12 : 8

divide through by 4

ratio = 6: 3 : 2

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Answer:

5*8 = 40

Step-by-step explanation:

2(3) -1 = 5

3 +5 = 8

area = 5*8 = 40

Answer:

formula-Area=l×b

Step-by-step explanation:

Length (l)=2x-1

Breadth(b)=x+5

We know that,

Area(A)=l×b

=(2x-1)×(x+1)

=(2×3-1)×(3+1)

=5×4

=20cm*2*

Answer:

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

Use the intersecting chords theorem, according to which, the products of the lengths of the line segments on each chord are equal,

or

Substitute the lengths and solve for x:

The matching answer choice is A.

Answer:

Perpendicular: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]

Parallel: [tex]y=3x-7[/tex]

Step-by-step explanation:

So when two lines are perpendicular, that means the the slope is the reciprocal with the opposite sign so: [tex]\frac{a}{b} \text{ has a slope perpendicular to } -\frac{b}{a}[/tex]. In this case we have the equation in slope-intercept form, so it's easy to determine the slope, it's 3. So that means the perpendicular line will have a slope of: [tex]-\frac{1}{3}[/tex]. Since you have a slope of 3/1 which becomes 1/3 and also an opposite sign. This gives you the equation: [tex]y=-\frac{1}{3}x+b[/tex]. We can solve for b, by plugging in a coordinate it passes through. This is given in the problem, with it being (4, 5) = (x, y). So plugging these values in as (x, y) gives you the equation: [tex]5=-\frac{1}{3}(4)+b\implies\frac{15}{3}=-\frac{4}{3}+b\implies\frac{19}{3}=b[/tex]. This gives you the complete equation: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]

So when two lines are parallel, that means they have the slope, and a different y-intercept. This is because if they had the same y-intercept, then the two lines would be the same exact line. We already know the slope, it's 3. So we have the general equation: [tex]y=3x+b\text{ where b}\ne-3[/tex]. The restriction on b, was explained on the previous sentence, if b=-3, then we have the same equation, which is not parallel, they would be the same line, meaning they would intersect at infinite points, which is completely different than two lines that never intersect. So now we can plug in the given point (4, 5) to solve for b. Plugging these coordinates in gives you: [tex]5=3(4)+b\implies5=12+b\implies-7=b[/tex]. This gives you the complete equation: [tex]y=3x-7[/tex]

The side of the edge of the cube is 7. 07cm

Given that a  diagonal of a cube measures the square root of 150 cm and the diagonal of a face measures 10 cm.

Let's find the edge of the face

Note that the face of the cube is in the shape of square .

The diagonal of the face is 10 cm.

The formula for  diagonal of square = [tex]\sqrt{2a}[/tex]

a is the side of the square face

We have that,

[tex]\sqrt{2a} = 10[/tex]

Make 'a' subject of formula

a = [tex]\frac{10}{\sqrt{2} }[/tex]

Find the surd of the equation, we have

a = [tex]\frac{10}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]

a = [tex]\frac{10\sqrt{2} }{2}[/tex]

a = [tex]5\sqrt{2}[/tex]

a = [tex]7. 07cm[/tex]

Thus, the side of the edge of the cube is 7. 07cm

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