What is the 11th term of the geometric sequence 178, 106.8, 64.08, ...?

A

0.39

B

0.65

С

1.08

D

1.79

3y + 20 = 3 + 2y

1y + 20 = 3

y = -17

Answer:

\(y=-17\)

Step-by-step explanation:

\(3y+20=3+2y\)

Start by subtracting 20 from each side...

\(3y+20-20=3+2y-20\\3y=2y-17\)

Now, subtract "2y" from each side...

\(3y-2y=2y-2y-17\\y=-17\)

Next, let's substitute -17 for y in the original equation to check our answer...

\(3(-17)+20=3+2(-17)\\-51+20=3+(-34)\\-31=3-34\\-31=-31\rightarrow Correct!\)

Therefore the answer is:

\(y=-17\)

Acceleration,a = Δv / ta = -5 / 8a = -0.625 m/s²Hence, the acceleration of the cycle in the last 8 seconds is -0.625 m/s².

The given velocity-time graph of a cycle is shown below:Velocity-Time graph of a cycleIt can be observed that the velocity of the cycle is constant during the first 12 seconds and it is equal to 5 m/s. Therefore, the acceleration of the cycle during this interval is zero.From the graph, it can be seen that the velocity of the cycle starts to decrease linearly after 12 seconds and it reaches zero at 20 seconds.

Therefore, the time taken by the cycle to come to rest is:Time taken by the cycle to come to rest = 20 - 12 = 8 secondsFrom the graph, it can be observed that the change in velocity during these 8 seconds is given by:Δv = 0 - 5 = -5 m/sTherefore, the acceleration of the cycle during these 8 seconds is given by:a = Δv / tWhere Δv is the change in velocity and t is the time taken.Change in velocity = -5 m/sTime taken = 8 seconds

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Answer:

A) 130 m

b) -1.25

Step-by-step explanation:

Can't show working out as it's in my maths book. Sorry but hope this helps

Answer:

1. Sometimes

1. Sometimes2. Always

1. Sometimes2. Always3. Never

1. Sometimes2. Always3. Never 4. Always

1. Sometimes2. Always3. Never 4. Always5. Never

Are the answers

1. The stretching technique emphasized in the scenario of a tennis player running up to the net and shuffling back to the baseline is dynamic stretching.

2. The stretching technique emphasized in the scenario of a runner performing various stretches for 30 seconds on each side after a run is static stretching.

1. The stretching technique emphasized in the scenario of a tennis player running up to the net and shuffling back to the baseline five times is dynamic stretching. Dynamic stretching involves performing controlled movements that mimic the motions of the activity or sport being performed. In this case, the tennis player is incorporating dynamic movements to warm up and prepare their muscles for the specific demands of playing tennis.

2. The stretching technique emphasized in the scenario of a runner performing a quadriceps stretch, gastrocnemius stretch, and a runner's stretch for 30 seconds on each side of the body after a run is static stretching. Static stretching involves holding a stretch in a stationary position for a certain period of time. In this case, the runner is holding each stretch for 30 seconds, which is a characteristic of static stretching. Static stretching is commonly used to improve flexibility and promote muscle relaxation after exercise.

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In the given scenario, the type of stretching technique being emphasized is Dynamic Stretching.

Dynamic stretching is a type of stretching technique that involves active movements to improve flexibility and range of motion. It is typically performed as part of a warm-up routine before engaging in physical activity. Unlike static stretching, which involves holding a stretch for an extended period, dynamic stretching incorporates dynamic movements that mimic the actions performed during the activity. This helps to warm up the muscles, increase blood flow, and prepare the body for the upcoming exercise or sports activity.

In the given scenario, the type of stretching technique being emphasized is Static Stretching.

Static stretching, on the other hand, is a stretching method where a stretch is held in a fixed position for a prolonged period of time, typically ranging from 15 to 60 seconds. This technique is often used to improve flexibility and increase the length of muscles and tendons. Static stretching is commonly performed during the cooldown phase after exercise or physical activity. It helps to relax the muscles, reduce muscle soreness, and improve overall flexibility and joint mobility.

Both dynamic stretching and static stretching have their benefits and serve different purposes in a fitness or sports routine. Dynamic stretching is effective for warming up the body and preparing it for physical activity, while static stretching is useful for improving flexibility and promoting relaxation in the muscles. It's important to choose the appropriate stretching technique based on your specific goals and the context of your exercise or sports regimen.

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Answer: 53

Step-by-step explanation:

Answer:

5 ,6,8,8,9,18

Step-by-step explanation:

5 ,6,8,8,9,18

Range:

18-5=13

Median:

8

Mean:

5+6+8+8+9+18=54

54÷6=9

Answer:

3 with the 6 on top

Step-by-step explanation:

Answer:

5 + 10\(\sqrt{3}\)

= 22.3205080757

Step-by-step explanation:

Answer:

≈ 13,7 inches

Step-by-step explanation:

Just use trigonometry (sin or cos) from the right triangles ∆ABC and ∆ADC

Answer:

slope m = - 8

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 3 = - 8(x - 4) ← is in point- slope form

with slope m = - 8

The slope is :

Solution:

Given: \(\bf{y+3=-8(x-4)}\)

To determine the slope, it's important to know the form of the equation first.

There are 3 forms that you should be familiar with.

The three forms of equations of a straight line are:

This equation matches point slope perfectly.

The question becomes, how do you work with point slope to find slope?

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

Answer:

The answer is D Hope this helps

Both Priya's equation and Han's equation are wrong . So , I don't agree with either of them

Slope-intercept form of equation of line is y =mx + b

where m is a slope of line

b is y-intercept

According to the question,

Slope of line is given as 1/2

m = 1/2

Putting the value of m in equation of line

y = 1/2 x + b --------(1)

It is given that line(1) passes through (1,2)

so, x = 1 and y = 2

Substituing the value of x and y in equation (1)

2 = 1/2 +b

Multiplying by 2 both sides

4 = 1 + 2b

=> 2b = 3

=> b = 3/2

substituting the value of b

Equation of line is y = 1/2 x + 3/2

=> 2y = x + 3

Therefore, Both Priya's equation and Han's equation are wrong

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To find the area of a rectangle with given length and width, you simply multiply the length and width together. In this case, the length is given by the difference between a and b (i.e., b - a), and the width is given by the value of the function f(x) at the midpoint of a and b. Here's how to calculate the area step-by-step:

1. Calculate the length of the rectangle: b - a = 0.9 - 0.5 = 0.4
2. Find the midpoint of a and b: (a + b) / 2 = (0.5 + 0.9) / 2 = 0.7
3. Calculate the value of f(x) at the midpoint: f(0.7) = (0.7)^2 - 4(0.7) + 19 = 0.49 - 2.8 + 19 = 16.69
4. Calculate the area of the rectangle: length × width = 0.4 × 16.69 = 6.676

Therefore, the area of the rectangle is approximately 6.676 square units.

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The curved line in the graph below is the function function f(x) = x^2 - 4x + 19 and the values a = 0.5 and b = 0.9. The area the area of the rectangle is approximately 153.81 square units.

To find the area of the rectangle, we first need to determine the coordinates of the two points where the line intersects the x-axis. We can do this by setting the function f(x) equal to zero and solving for x:
0 = x^2 - 4x + 19

Using the quadratic formula, we can solve for x:
x = [4 ± sqrt(16 - 4(1)(19))] / 2
x = [4 ± sqrt(-60)] / 2
x = 2 ± 3i√5

Since the graph is not drawn to scale, we cannot accurately determine the imaginary values of x. However, we can see that the two x-intercepts are symmetrical about the y-axis, so their distance from the y-axis is equal. Therefore, the midpoint of the line segment connecting the two x-intercepts must lie on the y-axis.

Using the midpoint formula, we can find the y-coordinate of the midpoint:
y = [f(2 + 3i√5) + f(2 - 3i√5)] / 2
y = [(2 + 3i√5)^2 - 4(2 + 3i√5) + 19 + (2 - 3i√5)^2 - 4(2 - 3i√5) + 19] / 2
y = [4 - 12i√5 - 45 - 4 + 12i√5 - 45] / 2
y = -40

Therefore, the midpoint of the line segment connecting the two x-intercepts is (0, -40). Since the x-intercepts are at x = 2 + 3i√5 and x = 2 - 3i√5, the width of the rectangle is the distance between these two points, which is:
w = |(2 + 3i√5) - (2 - 3i√5)|
w = 6√5

To find the height of the rectangle, we need to find the maximum value of the function f(x) between x = 0.5 and x = 0.9. We can do this by finding the x-coordinate of the vertex of the parabola:
x = -b / 2a
x = -(-4) / 2(1)
x = 2

Therefore, the vertex of the parabola is at (2, f(2)):
f(2) = 2^2 - 4(2) + 19
f(2) = 15

Since the parabola opens upwards, the maximum value of the function between x = 0.5 and x = 0.9 occurs at either x = 0.5 or x = 0.9, whichever gives the greater value. We can find the value of the function at these two points:
f(0.5) = 0.5^2 - 4(0.5) + 19
f(0.5) = 17.25
f(0.9) = 0.9^2 - 4(0.9) + 19
f(0.9) = 17.21

Therefore, the maximum value of the function between x = 0.5 and x = 0.9 is f(0.5) = 17.25. This is the height of the rectangle.

Finally, we can find the area of the rectangle:
area = w * h
area = 6√5 * 17.25
area ≈ 153.81

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Answer:

5:2

6

Step-by-step explanation:

I simplest form it is 5:2

You need 6 more triangles

Hello

P(6) = 1/6 ≈ 16,7%

P(1) = 1/6

P(2) = 1/6

P(3) = 1/6

P(4) = 1/6

P(5) = 1/6

P(6) = 1/6

There are 6 faces, and one 6 on the die, so the probability of getting a 6 is 1/6.

Answer:

k=-1/2

Step-by-step explanation:

u have to change line 4x + ky=11 to this form:

y=11/k-4x/k

then, if 2 lines are parallel, their slopes have to equal

so: 8=-4/k -> k=-1/2

Answer:

3 (2+3×2-5×)

you see the two but it at the button

Therefore, the formula for the nth term, an, of the sequence is: -1742n² + 3489n + 266

The given sequence is 13, -47, 911, -1615. To find a formula for the nth term, an, let's first identify the pattern in the sequence.

The differences between consecutive terms are:
-47 - 13 = -60
911 - (-47) = 958
-1615 - 911 = -2526

The differences between these differences are:
958 - (-60) = 1018
-2526 - 958 = -3484

Since the second differences are constant (-3484), the sequence is quadratic. A quadratic sequence has a formula in the form of an = A×n² + B×n + C.

Let's find the coefficients A, B, and C using the first three terms of the sequence.

1. For n=1, a1 = 13:
A×(1²) + B×1 + C = 13

2. For n=2, a2 = -47:
A×(2²) + B×2 + C = -47

3. For n=3, a3 = 911:
A×(3²) + B×3 + C = 911

Solving this system of equations, we find that A = -1742, B = 3489, and C = 266.

Therefore, the formula for the nth term, an, of the sequence is: an = -1742n² + 3489n + 266

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Answer:

Step-by-step explanation:

hello,

As A and B are two independent events we can say that P(A∩B)=P(A)P(B)

P(A)=P(A∩B)/P(B)=16/13

thanks

Answer:

y - 10 = 5(x - 16)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = 5 and (a, b ) = (16, 10 ) , then

y - 10 = 5(x - 16) ← equation of line

Answer:

2.2

best of luck :D

Answer:

2.15443469003

Step-by-step explanation:

Step 1:

w³ = 10       Equation

Step 2:

\(\sqrt[3]{10}\)         Find the cube root

Answer:

w = 2.15443469003

Hope This Helps :)

Given:

novel: 3/4

dictionary: 4 1/2

Let's first convert the two given height into similar fractions (with the sa

Answer:

A third of 9 is 3.

Step-by-step explanation:

9 / 3 = 3.

3 * 3 = 9

The equation is f ( - x ) = 2x⁴ + x² + 5 and f ( x ) = f ( - x )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = 2x⁴ + x² + 5   be equation (1)

On simplifying the equation , we get

When the value of x = -x

Substitute the value of x = -x in the equation , we get

f ( - x ) = 2 ( -x )⁴ + ( - x )² + 5

On further simplification , we get

f ( - x ) = 2 ( x )⁴ + ( x )² + 5

So ,

f ( - x ) = 2x⁴ + x² + 5 = f ( x )

Therefore , the value of f ( - x ) = 2x⁴ + x² + 5

Hence , the equation is f ( -x ) = 2x⁴ + x² + 5

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Answer:

I could be wrong but I'm pretty sure it's not a function

Step-by-step explanation:

The reason is because there are 2 x values that are the same equal different things

Find how much money was spent:

25 - 18.70 = 6.30

Divide the amount spent by cost per yard:

6.30 / 0.14 = 45

She bought 45 yards

Answer: She bought 52 feet of ribbon. Hope this helps have a great day.

Step-by-step explanation:

Answer:

it's 42

Step-by-step explanation:

6 7's

6 12 28 24 30 36 42

Answer: 149.12

Step-by-step explanation:

to find out the extended warranty we do,

466*(32/100)=149.12

The extended warranty cost is $149.12.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, a set of floor speakers costs $466.

If the extended warranty on the speakers costs 32% of the price of the speakers.

Now, extended price =32% of 466

32/100 ×466

= 0.32×466

= $149.12

Therefore, the extended warranty cost is $149.12.

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