Find the radius of convergence of the power series. (if you need to use or –, enter infinity or –infinity, respectively. ) [infinity] (−1)n xn 2n n = 0

The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).

Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic equation by solving this system of linear equations:

(x₁, y₁) = (- 3.5, 0)

12.25 · a - 3.5 · b + c = 0       (1)

(x₂, y₂) = (11.5, 0)

132.25 · a + 11.5 · b + c = 0       (2)

(x₃, y₃) = (8.5, - 54)

72.25 · a + 8.5 · b + c = - 54     (3)

The solution of the system is a = 3.6, b = - 54, c = 144.9. Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:

y ≥ 3.6 · (x² - 15 · x + 40.25)

y ≥ 3.6 · (x - 11.5) · (x + 3.5)

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The correct representation of the inequality is -6x + 15 < 10 - 5x and an open circle is at 5 and a bold line starts at 5 and is pointing to the right.

In mathematical concept, an inequality is a representation of an order linking two numbers or algebraic expressions together. These orders are called inequality signs such as greater than (>), less than (<), greater than or equal to(≥), or less than or equal to(≤). Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations.

From the given information, we are given the inequality:

= -3(2x - 5) < 5(2 -x)

Open brackets, we get:

= -6x + 15 < 10 - 5x

Subtract 15 from both sides, we have:

= -6x + 15 - 15 < 10 - 5x - 15

= -6x < -5x - 5

Add 5 to both sides

= -6x + 5 < -5x - 5 + 5

= -6x + 5 < -5x

= -x < - 5

= x < 5

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Answer:

-7.1931540532314155

Step-by-step explanation:

-7.1931540532314155

For this exercise, you could get the following lengths by using a scale (ruler):

A line segment can be defined as the part of a line in a geometric figure such as a triangle, that is bounded by two (2) distinct points and it typically has a fixed length.

In Geometry, a line segment can be measured by using the following measuring instruments:

In this scenario, you're required to determine the lengths of the given line segments. However, the geometric figure wasn't included and as such an accurate answer can't provided.

For instance, you could get the following lengths by using a scale (ruler):

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The greatest force acting on the ball to slow it down is Gravitational force.

When ball is thrown upwards then there will be two forces on the ball opposite to the motion of ball

1. Gravitational force (mg)

2. Air friction or air drag

Both forces are opposite to the motion of the ball and it will cause the decrease in the speed of the ball.

Now here due to less value of drag coefficient on the ball we will say that ball will decrease its speed more due to gravitational force compare to friction force of air.

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Answer:

4x +6

Step-by-step explanation:

No explanation

Straight answer

Answer:

First and second angles going upward

Answer: 2, 4, 6

Step-by-step explanation:

The equation be x/100 [tex]*[/tex] 28,600 = 33,500, then we get 17%.

Trevor's total employee benefits exists 17.1% of his gross pay.

Therefore, the correct answer is option d. 17.1.

If you would like to know Trevor's total employee advantages, you can estimate this utilizing the subsequent steps:

To find the percentage of the total employee benefits x% of $28,600 exists $33,500.

To estimate the value of x, bring the variable to the left side and bring all the remaining variables to the right side. Simplify the values to estimate the result.

x/100 [tex]*[/tex] 28,600 = 33,500

x = 33,500 [tex]*[/tex] 100 / 28,600

x = 117.13% = 117%

117% - 100% = 17%

x = 17%

The correct result would be 17%.

Trevor's total employee benefits exists 17.1% of his gross pay.

Therefore, the correct answer is option d. 17.1.

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Answer:

It is D

Step-by-step explanation:

Answer:

B. 10/13

Step-by-step explanation:

There are 52 cards in a deck. Divide that by 4 and get 13, thats how many diamonds there are. There are 36 number cards. Since 9 of the cards in diamonds are numbers, we dont count those ones. 13-9 is 4, so we add that to our total to get 40. 40/52 is the same as 10/13.

Answer: 10/13

Step-by-step explanation:

There are 52 cards in a deck. Every 13 cards, 9 will be number cards so there are 36 number cards. There are 13 diamond cards. There are 9 diamond cards that are number cards. So the probability of the following is (36+13-9)/52 = 40/52 = 10/13

Answer:

RT = 16[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the sine ratio in right triangle QRT and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{RT}{QR}[/tex] = [tex]\frac{RT}{32}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2 RT = 32[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

RT = 16[tex]\sqrt{3}[/tex]

The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.

According to the given statement

we have to find the explicit rule for the nth term of the given sequence,.

So, For this purpose

The given sequence is :

2, 8, 26, 80, 242.

And according to the ap series formula

[tex]a_{n} = (a_{n-1} -1)*3 +2[/tex]

If we put the terms in it then we get the exact value as the value in the sequence.

So,

[tex]a_{n} = (a_{n-1} -1)*3 +2[/tex]

For [tex]a_{2}[/tex]

[tex]a_{2}[/tex] [tex]= a_{1} *3 +2[/tex]

[tex]a_{2}[/tex] [tex]= 2*3 + 2[/tex]

[tex]a_{2}[/tex] [tex]= 8[/tex]

and by this way we get all the values as same as the sequence.

So, The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.

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The value of the given expression is 7.0 × 10⁸

From the question, we are to determine the value of the given expression

The given expression is

(3.5x10⁶)÷(5x10-³)

The expression can be simplified as follows

(3.5x10⁶)÷(5x10⁻³)

= (3.5 ÷ 5) × (10⁶ ÷ 10⁻³)

= (0.7) × (10⁶⁻⁽⁻³⁾)

= 0.7 × (10⁶⁺³)

= 0.7 × (10⁹)

= 7.0 × 10⁸

Hence, the value of the given expression is 7.0 × 10⁸

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From the attached speed versus time graph, it can be seen that the orange or first or car is speeding up. The third or green car is slowing down, and the blue or second car is maintaining a constant speed.

Speed Analysis from the Graph

The graph in the attachment shows the linear increase in speed of the first car over time. Therefore, we can say that it is accelerating at a certain rate.

The graph shows how the speed of the third car is decreasing with time. This demonstrates that the green vehicle is de-accelerating.

The graph shows a straight line for the second car. It displays that the speed does not alter as seconds or minutes pass. We might infer that the blue car is continuing to travel at its current pace as a result.

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Answer:

A C B

Step-by-step explanation:

Which of the cars is speeding up?  

A

Which of the cars is slowing down?  

C

Which of the cars is maintaining a constant speed?  

B

The coordinates of F is (8.5, 7)

The coordinates of the points are given as:

D = (-2, -5)

F = (5, 3)

DF : FE = 4 : 2

Rewrite the ratio as

m = 4 : 2

The coordinate of the partition is calculated as:

F = 1/(m + n) * (mx2 + nx1, my2 + ny1)

This gives

(5, 3) = 1/(4 + 2) * (4 * x + 2 * -2, 4 * y + 2 * -5)

Evaluate the sum and the product

(5, 3) = 1/6 * (4x - 4, 4y - 10)

Multiply both sides by 6

(30, 18) = (4x - 4, 4y - 10)

By comparison, we have:

4x - 4 = 30

4y - 10 = 18

Solve the equations

x = 8.5

y = 7

So, we have:

F = (8.5, 7)

Hence, the coordinates of F is (8.5, 7)

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From the given information, we get the value of ABC = 120°.

Given: In the figure, O exists the center of the circle and OABC exists as a parallelogram.

Now, the radius of the circle exists

OA = OB = OC

Opposite sides of a parallelogram are equal

AB = OC and OA = BC

In ∆OAB,

OA = OB = AB and,

In ∆OCB,

OC = OB = BC

Therefore, ∆OAB and ∆OCB exist in equilateral triangles.

All angles of an equilateral triangle are equivalent to 60°.

Hence, ∠ABC = ∠OBA + ∠OBC

∠ABC = 60° + 60°

∠ABC = 120°

Therefore, the value of ∠ABC = 120°.

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Step-by-step explanation:

solution

here

15×5

=75inches

Answer:

I think the answer is 12 because 8/6 is 1.3333.... Continously so the smaller traingel is 1.33333 times smaller then the bigger one. So you jus do 9 x 1.3333... To get the bigger angels side

The explicit formula is Tn = 18[[tex]\frac{2}{3} ^{n-1}[/tex]]

here, we have to find n.

Now, F(2) = 2/3 * f1 = 2/3 * 18 = 12

F(3) = 2/3 * f(2) = 2/3 * 12 = 8

F(4) = 2/3 * F(3) = 2/3 * 8 = 16/3

F(5) = 2/3 * 16/3 = 32/9

These equations form a pattern.

That is Tn = (2/3)^(n-1)(18)

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Answer:

S(1,2)

Step-by-step explanation:

The value that is being altered is the y value if you go from Q to T and then T to S. The x value = 1 and remains the same for point S.

To go from Q to T, you go from 8 to 5 on the y value. Remember x remains the same. That's three units (8 - 5 = 3)

To go from T to S must be 3 units as well, since the small diagonal is bisected. 5 - 3 = 2 is the answer.

So point S is noted as S(1,2)

The end behavior of the given polynomial is that as x → -∞ or  x → ∞, then, f(x) → 5

We are given the polynomial;

f(x) = 5x/(x - 25)

Now, we want to find the limits as x → ±∞. Let us rearrange the given polynomial to get;

f(x) = 5/(1 - (25/x))

Thus, applying limits we have;'

lim x → ±∞ [5/(1 - (25/x))]

From algebraic limit laws we know that;

If f(x) = k, then;

lim x → +∞ [f(x)] = k

Also, lim x → -∞ [f(x)] = k

Thus, applying limits at infinity to our polynomial gives;

lim x → ±∞ [5/(1 - (25/x))] = 5/(1 - 0) = 5

This is because lim x → ∞ for 1/x is 0.

Thus, f(x) has horizontal asymptotes at y = 5

Thus, we conclude that the end behavior is that as x → -∞ or  x → ∞, then, f(x) → 5

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Tthe inequality that describes this graph is y ≤ 1/3x - 4/3

The graph that completes the question is added as an attachment

From the attached graph, we have the following points

(0, -1.3) and (3, -0.3)

The slope is calculated as:

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

Substitute the known values in the above equation

m = (-0.3 + 1.3)/(3 - 0)

Evaluate

m = 1/3

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 1/3(x - 0) - 1.3

Evaluate

y = 1/3x - 4/3

From the graph, we have the following highlights:

The first highlight above implies, the inequality can be any of ≥ and ≤

While the second highlight above implies, the inequality is ≤

Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3

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The end behavior of the power function is as x tends to infinity, f(x) tends to zero.

In this question,

The power function is [tex]f(x)=3^{-x}2[/tex]

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

The graph below shows the behavior of the function f(x).

The above equation has the degree of 1, which is odd and the leading coefficient has the positive coefficient.

Then the end behavior is

As x -> ∞,

⇒ [tex]\lim_{x \to \infty} f(x)[/tex]

⇒ [tex]\lim_{x \to \infty} 3^{-x}2[/tex]

⇒ [tex]2\lim_{x \to \infty} 3^{-x}[/tex]

⇒ [tex]2\lim_{x \to \infty} 3^{-\infty}[/tex]

⇒ 2(0)

⇒ 0

Thus as x → ∞, f(x) → 0.

Hence we can conclude that the end behavior of the power function is as x tends to infinity, f(x) tends to zero.

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Stephen read about 9 pages more each week.

What is a linear equation in math?

If stephen reeds 278 pages in 7 week ,

To find number of pages read in 1 week, divide 278 by 7

                    = [tex]\frac{278}{7}[/tex]  ⇒ 39.71

Another person reads 31 pages each week.

So stephen reads allmost 40  per week and alice 31.

Then, we need to find the difference between them

Difference = 40 - 31 = 9

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Two angles and a non-included side of one triangle.

The AAS rule states that:

If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

In the diagrams below, if AC = QP,

∠ A = ∠ Q,

∠ B = ∠ R,

then triangle ABC ≅ QRP.

Congruence of triangles: Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

There are 5 main rules of congruency for triangles:

SSS Criterion: Side-Side-Side.

SAS Criterion: Side-Angle-Side.

ASA Criterion: Angle-Side- Angle.

AAS Criterion: Angle-Angle-Side.

RHS Criterion: Right angle- Hypotenuse-Side.

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The equivalent expression of the expression is 128x^5y^6/2x^7y^5

The expression is given as:

128x^5y^6/2x^7y^5

Divide 128 by 2

64x^5y^6/x^7y^5

Apply the law of indices

64y^(6-5)/x^(7-5)

Evaluate the differences

64y/x^2

Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5

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Answer:

Step-by-step explanation:

Opposite angles in a cyclic quadrilateral are supplementary.

  x° = 180° -105°

  x° = 75°

__

The value of the other angle is similarly found:

  w° = 180° -80°

  w° = 100°

__

Additional comment

This result comes from the inscribed angle theorem. That theorem tells you the measure of the inscribed angle is half the measure of the intercepted arc.

The opposite angles of a cyclic quadrilateral intercept the circle at the same two points, dividing the total 360° circle into two parts. Each angle has a measure equal to half its corresponding arc, so the total of the two angles is half the total of the two arcs: 360°/2 = 180°. The angles are supplementary.

Answer:

there are 54 buffalos in 150 acres

Step-by-step explanation:

1. determine the rate of buffalos per acres

45 buffalos per 125 acres =

45 / 125 =

0.36 buffalos per 1 acre

now we know the rate of buffalos per 1 acre, we can multiply it by the required amount of acres (in this case 150)

buffalos per 1 acre x total acres = total buffalos per total acres

0.36 x 150 = 54 buffalos

therefore, there are 54 buffalos per 150 acres.

hope this helps :)

Answer:

B. - Three T-Shirts and Seven Sweatshirts: $37.5 + $203 =240.50

   - Six T-Shirts and Five Sweatshirts: $75 + $145 = $220

Step-by-step explanation:

A. - Three T-Shirts and Seven Sweatshirts: $27 + $213.50 = $240.50

   - Six T-Shirts and Five Sweatshirts: $54 + $152.5 = $206.5

B. - Three T-Shirts and Seven Sweatshirts: $37.5 + $203 =240.50

   - Six T-Shirts and Five Sweatshirts: $75 + $145 = $220

C. - Three T-Shirts and Seven Sweatshirts: $35.01 + $210 = $245.01

   - Six T-Shirts and Five Sweatshirts: $70.02 + $150 = $220.02

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Answer:

2

Step-by-step explanation:

The trick here is to reduce each of the bases to lowest form first

[tex]12 = 3.4 = 3 .2.2 = 3.2^{2}\\12^{3} = (3.2^{2} )^{3} = 3^{3}2^{6} \\6 = 3.2\\6^{5} = (3.2)^{5} = 3^{5} .2^{5} \\\\Numerator = 3^32^63^52^5 = 3^82^{11}\\Denominator computation\\9 = 3^2\\9^{4} = (3^{2} )^4 = 3^{8} \\Denominator = 3^82^{10} \\\\\frac{Numerator}{Denominator } =\frac{{3^8}{2^{11} }}{3^82^{10}} = \frac{2^{11}} {2^{10}} = 2^1 = 2[/tex]