Help picture below problem 18

Nandyan na po

Step-by-step explanation:

Let

[tex]S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n[/tex]

where we assume |r| < 1. Multiplying on both sides by r gives

[tex]r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}[/tex]

and subtracting this from [tex]S_n[/tex] gives

[tex](1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}[/tex]

As n → ∞, the exponential term will converge to 0, and the partial sums [tex]S_n[/tex] will converge to

[tex]\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}[/tex]

Now, we're given

[tex]a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a[/tex]

[tex]a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}[/tex]

We must have |r| < 1 since both sums converge, so

[tex]\dfrac{15}a = \dfrac1{1-r}[/tex]

[tex]\dfrac{150}{a^2} = \dfrac1{1-r^2}[/tex]

Solving for r by substitution, we have

[tex]\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)[/tex]

[tex]\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}[/tex]

Recalling the difference of squares identity, we have

[tex]\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}[/tex]

We've already confirmed r ≠ 1, so we can simplify this to

[tex]\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15[/tex]

It follows that

[tex]\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12[/tex]

and so the sum we want is

[tex]ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}[/tex]

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

Answer: D) 2

Step-by-step explanation:

x² = 9 means what number times itself is equal to 9

We know that 3×3=9 so that is already one solution, but there is another

-3×-3 is also equal to 9

A negative number times a negative number results in a positive number so -3 is another solution.

That gives us two solutions

Answer:

D; only 2

Step-by-step explanation:

Solve for x over the real numbers:

x^2 = 9

Take the square root of both sides:

Answer: x = 3 or x = -3

Using the vertical asymptote of the function, it is found that it is given by:

[tex]f(x) = -1.5\frac{(x - 4)}{x - 2}[/tex]

In this problem, the x-intercept of the graph is x=4, hence the numerator is a(x - 4).

The graph has one vertical asymptote at x=2, hence the denominator is x - 2.

Hence:

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

The y-intercept of the graph is y=−3, hence:

[tex]-3 = \frac{a(0 - 4)}{0 - 2}[/tex]

[tex]-4a = 6[/tex]

[tex]a = -1.5[/tex]

Thus, the function is:

[tex]f(x) = -1.5\frac{(x - 4)}{x - 2}[/tex]

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Answer:

  A/(x+7) +B/(x+4)

Step-by-step explanation:

The denominators of the partial fraction expansion are the factors of the denominator of the rational function.

__

Here, the rational function's denominator can be factored as ...

  x² +11x +28 = (x +7)(x +4)

Then the form of the decomposition is ...

  [tex]\dfrac{x-2}{x^2+11x+28}=\boxed{\dfrac{A}{x+7}+\dfrac{B}{x+4}}[/tex]

_____

Additional comment

Here, A=3. B=-2.

If the factors of the denominator have multiplicity greater than 1, then there is a fraction with each power of that factor up to the multiplicity. For example, if there is a factor (x+4)³, then the decomposition would include fractions A/(x+4) +B/(x+4)² +C/(x+4)³.

Answer: 26 sales

Step-by-step explanation:

If you plug in 26 you will get exactly $1,000

Martin needs to sale 8 pieces to make it $1000.

Martin has to save $1000.

He is using an app to manage all the sales, but if keeps fraction of every sales.

The equation which represents his net pay is P(x)=[tex]x^{2}+20x-196[/tex]

We have to solve the given quadratic equation.

Here, x= (-b±[tex]\sqrt{ b^{2}-4ac }[/tex])/2a

⇒ x= (-20±[tex]\sqrt{400+4*196}[/tex])/2

⇒ x= (-20±[tex]\sqrt{1184}[/tex])/2

⇒ x= -10±[tex]\sqrt{296}[/tex]

⇒ x= -10±17.2

We habe to take the maximum value of x. So we neglect the negative sign.

Hence, x= -10+17.2 = 7.2 = 8 (approx) ,here we can not take 7 because if he sales 7 pieces then the money should less than $1000.

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Answer:

1848 square inches

Step-by-step explanation:

surface area is the combined area of all the outside surfaces.

area of triangle is base x height / 2

There are two, so no need to divide

18 x 12 = 216

Area of rectangle is base x height

15 x 34 + 15 x 34 + 18 x 34 = 1632

Then add

216 + 1632 = 1848

Answer:

1,090

Step-by-step explanation:

Answer:

2 2/10 miles

but on the part where he realized he forgot his books was he at the library already when he realized cuz if not them it's more than 2 2/10

[tex]x^2 -5x +6 =0\\\\\implies x^2 -3x -2x +6 = 0\\\\\implies x(x-3) -2(x-3) =0\\\\\implies (x-3)(x-2)=0\\\\\implies x =3, ~ x = 2[/tex]

Answer:

The value of x = 2 or 3

Step-by-step explanation:

By factorisation ,

=> x² - 5x + 6 =0

=> x² - 3x - 2x + 6 = 0

=> x ( x-3 ) -2 ( x-3 ) = 0

=> (x-2) (x-3) = 0

so, the value of x = 3 or 2

Answer:

B. At most

Gives a maximum that it can be.

If rena divides a square into 8 equal part then 1/8 is a unit fraction which she has to write as a label for each parts.

A fraction represents a part of a whole.

Given that rena divides a square into 8 equal part.

A division is a process of splitting a specific amount into equal parts.

Let the whole square is divided into eight equal parts.

Which can be represented by 1/8.

Where the numerator 1 represents the whole and eight represents the parts.

The unit fraction for each part is 1/8 because the square is divided into 8 equal parts.

This means each part is one eighth of the whole.

Hence, if rena divides a square into 8 equal part then 1/8 is a unit fraction which she has to write as a label for each parts.

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Answer:

B

Step-by-step explanation:

3/20x3/20=

15/100x15/100

Answer:

  140 in³

Step-by-step explanation:

The ratio of volumes of similar objects is proportional to the cube of the ratio of the linear dimensions.

__

Here, prism B is half the height of prism A, so will have (1/2)³ = 1/8 of the volume of prism A:

  Vb = (1/8)×Va

  Vb = (1/8)×(1120 in³) = 140 in³

The volume of Prism B is 140 cubic inches.

Answer:

i dont understand i need pic

The correct option regarding the operation of cancellation in a fraction is given by:

A. reducing fractions to make multiplying easier.

It happens when two fractions are multiplying each other, and terms are simplified to make the multiplication easier. For example:

[tex]\frac{2}{3} \times \frac{6}{4} = \frac{6}{3} \times \frac{2}{4} = 2 \times \frac{1}{2} = 1[/tex]

The terms 2 and 4, and 3 and 6, were canceled. Hence option A is correct.

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The dimension of the rectangle is 40meters by 20meters

The perimeter of a figure is the sum of all the external sides of the figure

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

If the length is 20 meters longer than the width, then;

l = 20 + w

Substitute

120 = 2(20+2w)

60 = 20 + 2w

30 = 10 + w

w = 20 meters

Since l = 20  + w

l = 20 + 20

l = 40 meters

Hence the dimension of the rectangle is 40meters by 20meters

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Answer:

Minimum

Step-by-step explanation:

The zeros of a quadratic equation are the points at which the parabola intersects the x-axis.

[tex]\sf x=3 \implies x-3=0[/tex]

[tex]\sf x=7 \implies x-7=0[/tex]

[tex]\sf \implies y=a(x-3)(x-7)[/tex]   (for some constant a)

[tex]\sf \implies y=ax^2-10ax+21a[/tex]

The optimal value is the y-coordinate of the vertex.  

[tex]\sf \implies vertex=(x,-3)[/tex]

The x-coordinate of the vertex is the midpoint of the zeros:

[tex]\sf x=\dfrac{7-3}{2}+3=5[/tex]

[tex]\sf \implies vertex=(5,-3)[/tex]

Therefore, the vertex will be in Quadrant IV and so the parabola opens upwards into Quadrant I.  

So the optimal value is a MINIMUM since the vertex is the minimum point of the curve.

Additional Information to create the equation of the quadratic

Vertex form of quadratic equation:  [tex]\sf y=a(x-h)^2+k[/tex]

where (h, k) is the vertex

[tex]\sf \implies y=a(x-5)^2-3[/tex]

[tex]\sf \implies y=ax^2-10ax+25a-3[/tex]

To find the value of a, compare the constants of both equations:

[tex]\sf 21a=25a-3[/tex]

[tex]\sf \implies -4a=-3[/tex]

[tex]\sf \implies a=\dfrac34[/tex]

So the final equation is:

[tex]\sf factor \ form \implies y=\dfrac34(x-3)(x-7)[/tex]

[tex]\sf standard \ form\implies y=\dfrac34x^2-\dfrac{15}{2}x+\dfrac{63}{4}[/tex]

[tex]\sf vertex \ form \implies y=\dfrac34(x-5)^2-3[/tex]

Answer:

At this distance, Jupiter takes 11.8618 Earth years to complete a single orbit of the Sun. In other words, a single Jovian year lasts the equivalent of 4,332.59 Earth days.

Step-by-step explanation:

that the best i can do !!!!

Trees near the road may have more damage than trees away from it, so the results may overestimate the overall damage to the trees.

The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive

Given, The ranger parks at the side of the road and chooses 100 trees near the road to assess for damage hence, trees near the road may have more damage than trees away from it, so the results may overestimate the overall damage of the trees.

So, Consequently, the results can exaggerate the total amount of tree damage.

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Answer:

zero (0)

Step-by-step explanation:

The degree of the polynomial -57 is zero (0).

Hope it helps you in your learning process.

(receipt one)

burger = 9

18% tip = 2.16

total with tip = 14.16

(receipt two)

salad = 8

total = 11

total with tip = 12.98

(receipt three)

salad = 8

water = 1.5

total = 9.50

18% tip = 1.71

Step-by-step explanation:

calculator

The statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.

A function assigns the value of each element of one set to the other specific element of another set.

Function g is represented by the table.

The line plotted with these data is shown below where y represent the g(x).

In this line,

Thus, the statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.

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