Given a term in a geometric sequence and the common ratio, find the explicit formula, a11=5120 ans r=-2

Answer:  

1: -2.33 or -7/3

2: - 2.16 or -13/6

3: 3.49 x 10^4

4: 4.28*10-7

5: 0.81 or 9/11

6. 3

7: 8

8: 9 or up

9: 5 or up

10: 0-36

I hope any of this helps.... :D

Hope it helps I alrady solved it

Answer:

The correct option in the attached image is:

D. (-1, 1), (-1, 5), (-7, 1)

Step-by-step explanation:

Please refer to the attached image.

The length of the horizontal segment of the graphed triangle is 3.  The length of the vertical segment of the triangle graphed is 2. We will use the Pythagorean theorem to find the length of the missing side thus:

x² = 2²+3²

x² = 4+9

x² = 13

x = √13 or 3.6

This makes our side lengths 2, 3, and 3.6

For option A, our vertices are (-1, 1), (-1, 4), (-6, 1). This means the length of the horizontal segment 5 and the length of the vertical segment 3.  This missing side length is calculated thus:

x² = 5²+3²

x² = 25+9

x² = 34

x = √34 or 5.83

This is not proportional to the triangle drawn, so it is not similar.

For option B, our vertices are (-1, 1), (-1, 5), and (-6, 1).  This makes the horizontal segment 5 units long and the vertical segment 4 units long.  This makes the missing side length

x² = 4²+5²

x² = 16+25

x² = 41

x = √41 or 6.4

These are not proportional to the triangle drawn, so the triangles are not similar.

For option C, our vertices are (-1, 1), (-1, 4) and (-7, 1).  This makes the length of the horizontal segment 6 and the length of the vertical segment 3.  This makes the missing side length

x² = 3²+6²

x² = 9+36

x² = 45

x = √45 or 3√5 or 6.7

These sides are not proportional to the sides of the triangle drawn, so the triangles are not similar.

For option D, our vertices are (-1, 1), (-1, 5) and (-7, 1).  This makes the length of the horizontal segment 6 and the length of the vertical segment 4.  This makes the missing side length

x² = 6²+4²

x² = 36+16

x² = 52

x = √52 or 2√13 or 7.21

These sides are all twice as long as the sides of the triangle drawn, this indicates that the triangles are similar. Therefore our answer is D.

Answer:

Option B is the right choice.

Step-by-step explanation:

Given:

An are CE and an inscribed angle CBE.

Measure of inscribed angle CBE = 25 °

We have to find the measure of the arc CE.

Concept:

To find the measure of arc CE.

⇒ [tex]\angle CBE = \frac{1}{2} \times m\ (arc\ CE)[/tex]

⇒ [tex]2\times \angle CBE = m\ (arc\ CE)[/tex]

⇒ [tex]2\times 25 = m\ (arc\ CE)[/tex]

⇒ [tex]50 = m\ (arc\ CE)[/tex]

Measure of intercepted arc CE = 50 degrees.

The measure of arc CE = 50° so, option B is the right choice.

Answer:

4 meters

Step-by-step explanation:

7-3=4 m

Answer: Lulu has 4 meters of tape left.

Hope this helps!!

Answer: 14

Step-by-step explanation:

the question is just asking you to replace the x and y with the corresponding numbers.

x = 4

y = -3

Since x is 4 squared it would be 16.

-4 times -3 equals positive 12.

That would make the equation

(16 + 12) divided by 2

16 + 12 = 28 divide that by 2 and you’ll get 14.

Answer: 14

Step-by-step explanation:

First plug 4 in for x.

4^2 is equal to 16 because 4 x 4 is 16.

Next, plug in -3 for y.

-4 x -3

4 times 3 is 12 and they are both negative, therefore it turns out as a positive 12.

Then add the numbers on the top of your equation.

16+12=28.

Finally divide the sum by 2.

28 divided by 2= 14

Your answer is 14.

Hope this helps!

The limit of the given infinite series is undefined.

The given series is:

∑n=1∞(3n5/6n6+1)

To find the limit, we can simplify the series by dividing the numerator and denominator by the highest power of n:

∑n=1∞(3/n-1/6n-1+n-6)

As n approaches infinity, the terms containing n-1 and n-6 approach 0, so we are left with:

∑n=1∞(3/n)

This is a harmonic series with the form 1+1/2+1/3+1/4+... which is known to diverge. Therefore, the limit of the given infinite series is undefined.

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Answer:   = 11.88

This is a 3 step / 4 show workings.

10.7 + Percentage increase = 11%

10.7 + (11% × 10.7) =  10.7 + 11% × 10.7

(1 + 11%) × 10.7 = (100% + 11%) × 10.7

111% × 10.7 = 111 ÷ 100 × 10.7

111 × 10.7 ÷ 100 = 1,187.7 ÷ 100

11.877 ≈ 11.88

Answer:

1. >

2. <

Step-by-step explanation:

When a > 0, the graph opens upwards, or positively, because the way the line curves is determined by a.

When a < 0, the graph opens downwards, or negatively, for the same reason.

Final answer:

The graph of a quadratic function opens upwards when the coefficient of the squared term is positive (a > 0), and opens downwards when this coefficient is negative (a < 0).

Explanation:

The graph of a quadratic function opens up or down based on the sign of the coefficient of the squared term (usually represented as 'a' in the quadratic equation ax2 + bx + c). When this coefficient a is positive (a > 0), the parabola opens upwards. Conversely, if the coefficient a is negative (a < 0), the parabola opens downwards. The orientation of the parabola reflects whether the quadratic function has a minimum value (opening upwards) or a maximum value (opening downwards).

the answers are:

Caspian Sea

Fedchenko Glacier

and Tian Shan Mountains

Step-by-step explanation:

i got it right in my quiz

Answer:

rdgvvsssddas

Step-by-step explanation:

42423412

Answer:

8

Step-by-step explanation:

Step-by-step explanation: -3x - 2

-3 x 3 = -9

-9 -2 = -11

-11 is the answer.

Answer:

n = 3

Step-by-step explanation:

Ratio from Triangle A to Triangle B is 2:1.

n+2 = 5

n = 3

Answer: The functions are v1(t)=10000*(1.04)^5  and v2(t)=8000(1.06)^5

v1(5)=12166$

v2(5)=10705 $

Step-by-step explanation:

Given:

Investment cost for 1st=10,000$  ,at 4%rate.

Investment cost for 2nd=8000$ ,at 6% rate.

To Find:

Exponential growth functions ,

that could be used to find v1(t) and v2(t),

the value of each investment after 5 years

And difference between their values.

Solution:

Consider for 1st investment function be v1(t) and for 2nd be v2(t)

and t be time period

Exponential growth is given by, as time function,

v(t)=initial cost*(1+rate)^time period.

for 1st investment its cost is 10000$  at 4 % rate.

[tex]v1(t)=10000(1+0.04)^t[/tex]

[tex]v1(t)=10000(1.04)^t[/tex]

for 2nd investment its cost is 8000$  at 6% rate.

[tex]v2(t)=8000(1+0.06)^t[/tex]

[tex]v2(t)=8000(1.06)^t[/tex]

For t=5 calculating for both investment,

[tex]v1(5)=10000(1.04)^5[/tex]

[tex]=10000*1.2166[/tex]

v1(5)=12166 $

For 2nd investment,

[tex]v2(5)=8000(1.06)^5[/tex]

[tex]=8000*1.3382[/tex]

v2(t)=10705.8 $

Now after 5 years the difference is =v1(t)-v2(t)

Which is about 1460 $ only.

This because of the both functions depends upon time,initial investment and rate of interest .

Here time period being same.But the rate of interest are different and initial values are different.

Answer:

Step-by-step explanation:

Looking at the information given, the population mean and population standard deviation are known. We would apply the formula

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

From the information given,

µ = 70

σ = 10

1) x = 60

The probability that the heart rate if an individual is less than 60 is expressed as

P(x < 60)

z = (60 - 70)/10 = - 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.16

The percentage rates of heart rates less than 60 is 0.16 × 100 = 16%

2) x = 80

The probability that the heart rate if an individual is less than 80 is expressed as

P(x < 80)

z = (80 - 70)/10 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

The percentage rates of heart rates less than 80 is 0.84 × 100 = 84%

3) x = 50

The probability that the heart rate if an individual is greater than 50 is expressed as

P(x > 50) = 1 - P(x ≤ 50)

z = (50 - 70)/10 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.23

P(x > 50) = 1 - 0.23 = 0.77

The percentage rates of heart rates greater than 50 is 0.77 × 100 = 77%

Look at the attached picture⤴

Hope it will help you.

Answer:

1/13

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

There are 2 numbers less than 3. (1 and 2) and one 6 on a dice. Therefore there is a 3 out of 6 chance of rolling one of these 3 numbers (1, 2, and 6). This can be represented as 3/6 which would simplify to 1/2 or 50%.

It can also be found this way...

Probability = Number of desired outcomes ÷ number of possible outcomes. Therefore 3 ÷ 6 = 0.5 which is equal to 50% or 1/2.

I hope you choose my answer so you do well on your assignment! I've gotten an A in math every year :)

Answer:

1/2

Step-by-step explanation:

Answer:

1.circle

2.triangle

3.trapezoid

4.parallelogram

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

B - Skewed right.

Step-by-step explanation:

Trust me!!!!

Answer:

(assuming the height is 13 and the width is 10 or vice versa) 65

Step-by-step explanation:

a = 1/2 base × height

1/2 13 × 10 or 10×13

130 ÷ 2

65

Area of isosceles triangle = [tex]\( \frac{13\sqrt{231}}{4} \)[/tex] square centimeters, approximately 43.03 square centimeters.

To find the area of an isosceles triangle, you can use the formula:

[tex]\[ Area = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Since it's an isosceles triangle, the height divides the triangle into two right-angled triangles of equal size.

Given:

Base = 13 cm

Height = ?

To find the height, we can use the Pythagorean theorem.

Let's denote the height as  [tex]\( h \),[/tex] and half of the base (since the triangle is isosceles, and the height splits the base into two equal parts) as  [tex]\( \frac{13}{2} \).[/tex]

Then, using the Pythagorean theorem:

[tex]\[ (\text{height})^2 + \left(\frac{13}{2}\right)^2 = 10^2 \]\[ (\text{height})^2 + \left(\frac{13}{2}\right)^2 = 100 \]\[ (\text{height})^2 + \frac{13^2}{2^2} = 100 \]\[ (\text{height})^2 + \frac{169}{4} = 100 \]\[ (\text{height})^2 = 100 - \frac{169}{4} \]\[ (\text{height})^2 = \frac{400}{4} - \frac{169}{4} \]\[ (\text{height})^2 = \frac{231}{4} \][/tex]

Now, let's solve for the height:

[tex]\[ \text{height} = \sqrt{\frac{231}{4}} \]\[ \text{height} = \frac{\sqrt{231}}{\sqrt{4}} \]\[ \text{height} = \frac{\sqrt{231}}{2} \][/tex]

Now that we have the height, we can calculate the area using the formula:

[tex]\[ Area = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Substituting the values:

[tex]\[ Area = \frac{1}{2} \times 13 \times \frac{\sqrt{231}}{2} \]\[ Area = \frac{13 \sqrt{231}}{4} \][/tex]

So, the area of the isosceles triangle is  [tex]\( \frac{13 \sqrt{231}}{4} \)[/tex]  square centimeters.

The complete question is here.

Find the area of the isosceles triangle with a base of 13 cm and a height of 10 cm.

Answer:

20

Step-by-step explanation:

The point of contact of the tangent and the diameter of the circle is a right angle.

Thus the triangle with legs 12 and 2 × 8 = 16 is right

Using Pythagoras' identity.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

?² = 12² + 16² = 144 + 256 = 400 ( take the square root of both sides )

? = [tex]\sqrt{400}[/tex] = 20

Final answer:

The question deals with mathematics, specifically the slope of tangent lines, use of the Pythagorean theorem, and solving scale ratios and proportions. Students need to find specific lengths using provided endpoints, hypotenuse calculations, and scale conversions.

Explanation:

The student appears to be asking about finding the length of a line segment in a geometric context, possibly related to tangents to curves and the Pythagorean theorem. The student is likely working with a diagram or curve not provided here, so it is important to make use of available data points or diagrams in the course material. Furthermore, when working with scales and ratios for determining lengths, the process involves setting up a proportion, solving for the unknown value by cross-multiplying and dividing.

For the slope of the tangent line to a curve:

Identify the endpoints of the tangent line that corresponds to given positions and times.

Find the slope of the tangent line, denoted as 'v', by using the change in position over the change in time.

For the Pythagorean theorem:

Calculate the length of the hypotenuse as the square root of the sum of the squares of the other two sides.

Use significant figures appropriately to represent the precision of your result.

For solving ratios and proportions:

Set up the proportion based on given scale lengths and distances.

Solve for the unknown by cross-multiplying and dividing.

Answer:

How will Adam’s income change with the added expense?: it will decrease

Total expenses: $1,340

New net income:$1,760

Step-by-step explanation:

Answer:

it will decrease

Total expenses: $1,340

New net income:$1,760

Step-by-step explanation:

Tn = n + 7

The first three terms of the sequence is

T1 = 1 + 7 = 8

T2 = 2 +7 = 9

T3 = 3 + 7 = 10

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

The first three terms of the sequence is 8 , 9 and 10

Now

The tenth term of the sequence is

T10 = 10 + 7 = 17

Hope it will help you. :)

a) The first three terms of the sequence is given by 8 , 9 , 10 respectively

b) The tenth term of the sequence is a₁₀ = 17

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the arithmetic progression be represented as A

Now , the equation will be

A = n + 7   be equation (1)

a)

when n = 1

Substitute the value of n = 1 in the equation , we get

The value of a₁ = 1 + 7 = 8

when n = 2

Substitute the value of n = 2 in the equation , we get

The value of a₂ = 2 + 7 = 9

when n = 3

Substitute the value of n = 3 in the equation , we get

The value of a₃ = 3 + 7 = 10

b)

The tenth term of the arithmetic sequence is when n = 10

Substitute the value of n = 10 in the equation , we get

The value of a₁₀ = 10 + 7 = 17

Hence , the tenth term of the AP is  a₁₀ = 17

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Answer:

I THINK all but C apply for the second one. Just suggesting, but I hope it helps.

a) The function that represent this situation is y = 90 + 8x.

b)  His weight be after 8 weeks is 154 lbs.

Step-by-step explanation:

It is given that,

a) Write a function to represent this situation. Use x and y as your variables.

Hence the equation can be framed as,

Total weight = starting weight + weight gained in x weeks.

We know that, each week he gains 8 lbs. Therefore, for 8 weeks he gained 8x lbs of weight.

⇒ y = 90 + 8x.

∴ The function that represent this situation is y = 90 + 8x.

b) What would his weight be after 8 weeks?

To find his week after 8 weeks, substitute x=8 in the function y = 90 + 8x.

⇒ 90 + 8(8)

⇒ 90 + 64

⇒ 154 lbs.

∴ His weight be after 8 weeks is 154 lbs.

Answer:

88.2 squared

Step-by-step explanation:

The formula to find the area of a circle is a = pi * r ^2

Let's replace the values that we know.

a = 3.14 x 5.3 ^2

First, we should do 5.3 ^2, which is 28.09.

a = 3.14 x 28.09

Now we are able to do 3.14 x 28.09 which is 88.2026

But that isn't it! We need to round to the nearest tenth, which is this digit:

88.2026

Since next to the 2 there is a 0, you take out all the numbers after that 2. Which leaves you with:

88.2

Final answer:

The area of the round mirror with a radius of 5.3 inches, when calculated using the formula A = πr^2 and rounded to the nearest tenth, is 88.2 square inches.

To find the area of the round mirror with a radius of 5.3 inches, we will use the formula for the area of a circle, which is A = πr^2, where A is the area, π is approximately 3.14, and r is the radius of the circle.

Given that the radius of the mirror is 5.3 inches, we can substitute this value into the formula to find the area:

A = π(5.3)^2 ≈ 88.2 square inches.

Let's plug in the radius:

When rounded to the nearest tenth, the area of the mirror is 88.2 square inches.

Answer:9

Step-by-step explanation:

12-9=3 12-3=9 3+9=12

So C=9

Hey there!

[tex]\large\boxed{c=9}[/tex]

12 - 9 + c = 12

Combine like terms.

3 + c = 12

Subtract 3 from each side of the equation.

3 - 3 + c = 12 - 3

c = 9

Check:

12 - 9 + c = 12

12 - 9 + 9 = 12

3 + 9 = 12

12 = 12

Hope this helps!