Complete both equations to represent the cubes and the vectors on the number line.
Part A
++
-10
1
1+
-5
+1
1+
+1
14
++++++
1
0
5
+
10

To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.

First, let's rewrite the expression for the nth term of the sequence:

an = 5n / (4n + 1)

As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:

an ≈ n / (4n + 1)

Now, we can consider the limit of the sequence as n approaches infinity:

lim(n→∞) n / (4n + 1)

To evaluate this limit, we can divide both the numerator and denominator by n:

lim(n→∞) (1 / 4 + 1/n)

As n approaches infinity, the term 1/n approaches zero, leaving us with:

lim(n→∞) 1 / 4 = 1/4

Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.

In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.

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Answer:

The answer option is C 45

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

x+6=±5

Step-by-step explanation:

Answer:

Step-by-step explanation:

fuge  this site i only get 1 answer a day!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

Answer:(24+12\3)m

Step-by-step explanation:

Answer:

a = 4

b = 5

Step-by-step explanation:

In parallelogram, opposite sides are equal and parallel.

therefore 2b + 15 = 5a + b

=> b + 15 = 5a

b = 5a - 15

and 4a + b = 5b - a

=> 5a = 4b

Substitute b = 5a - 15

5a = 4(5a - 15)

5a = 20a - 60

15a = 60

a = 4

b = 5a - 15

b = 5(4) - 15 = 20 - 15 = 5

If over 25.5 days a ponds water level changed by a average of -0.32 centimeter each day the total change in the water level will be:  C:8.16

Centimeter each day=-0.32

Days of changed in water level=25.5 days

Now let determine total change in the water level

Total change=25.5 days × (-0.32)

Total change=8.16 centimeter

Inconclusion if over 25.5 days a ponds water level changed by a average of -0.32 centimeter each day the total change in the water level will be:  C:8.16

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Answer:

3

Step-by-step explanation:

Any number and variable combined is a term.

So 8 (#1 - Constant), + 19y (#2 -Coefficient + Variable), - 4z (#3 -Coefficient + Variable)

3 terms - B

Answer: x=6-3y

Step-by-step explanation:

Answer:

1. (6-2)

2.40/4

3. 10-4

Step-by-step explanation:

Dont trust me but I think it

To the nearest whole foot, the car travels (b) 252 miles at 55 miles per hour during 5blink cycles.

The frequency of the turn signal is given as 1.6 hertz, which means that the signal completes 1.6 cycles every second. In other words, the time period of the signal is 1/1.6 = 0.625 seconds per cycle.

During one blink cycle, the car travels a distance equal to the product of its speed and the time period of the signal. Converting the car's speed from miles per hour to feet per second, we get:

55 miles/hour = 80.67 feet/second (approx)

Therefore, during one blink cycle, the car travels a distance of:

distance = speed × time period of signal

distance = 80.67 × 0.625

distance = 50.42 feet (approx)

Since we are interested in the distance traveled during 5 blink cycles, we multiply the distance for one cycle by 5:

total distance = 5 × 50.42

total distance = 252.1 feet (approx)

Therefore, to the nearest whole foot, the car travels 252 feet during 5 blink cycles. The answer is option B) 252.

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Answer:

4,746

Step-by-step explanation:

\(6 \times 789 = 4734\)

\(4734 + 12 = 4746\)

Answer:

It's 4746.

Step-by-step explanation:

Answer:

191

Step-by-step explanation:

An = a1 + (n-1)d

An = 5 + (63-1)3 = 191

Answer:

191

Step-by-step explanation:

Since it's an A.P, the formular = a+(n-1)d

a = first term = 5

n = 63

d = common difference

After, putting the values, you'll have that:

T63= 5+(63-1)3

T63= 5+(62)3

T63= 5+ 186

T63= 191

The y-intercept of the graph is: C. "the temperature in degrees Fahrenheit when the temperature is zero degrees Celsius."

In mathematical terms, the y-intercept is the point where a line or curve intersects the y-axis on a coordinate plane.

In practical terms, the y-intercept of a situation often represents the starting point or initial value of a variable or function.

In the graph given above that shows the relationship between temperature in degrees Fahrenheit and degrees Celsius, the y-intercept is 32 degrees Fahrenheit, which means: C. "the temperature in degrees Fahrenheit when the temperature is zero degrees Celsius."

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The difference between the length and width of the garden is 2.55 yards.

Two or more expressions with an Equal sign is called as Equation.

Given that jan created a garden that was 8.5 yards long and 5.95 yards wide.

Length=8.5 yards

Width=5.95 yards.

We need to find the difference between the length and width of the garden.

8.5-5.95

Eight point five minus five point nine five

2.55

Hence,  the difference between the length and width of the garden is 2.55 yards.

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Therefore, the Laplace transform of t² sin(4t) is 8 / (s³ * (s² + 16)).

To find the Laplace transform of t² sin(4t), we can use the properties of the Laplace transform.

The Laplace transform of \(t^n\) is given by the formula:

L{\(t^n\)} = n! / \(s^{(n+1)\)

The Laplace transform of sin(at) is given by:

L{sin(at)} = a / (s² + a²)

Using these formulas, we can find the Laplace transform of t² sin(4t) as follows:

L{t² sin(4t)} = L{t²} * L{sin(4t)}

Applying the first formula, we have:

L{t²} = 2! / s^(2+1) = 2 / s³

Applying the second formula, we have:

L{sin(4t)} = 4 / (s²+ 4²) = 4 / (s² + 16)

Multiplying these two Laplace transforms together, we get:

L{t² sin(4t)} = (2 / s³) * (4 / (s² + 16))

Combining the terms, we simplify further:

L{t² sin(4t)} = (8 / (s³ * (s² + 16))

Therefore, the Laplace transform of t² sin(4t) is 8 / (s³ * (s² + 16)).

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The statements which are true among the answer choices are as follows;

Since, it follows from the task content that; A 5 1/2 ounce raw hamburger patty has 27 1/2 grams of protein, it follows that the protein content per ounce is;

P(hamburger) = 55/2 ÷ 11/2

= 5g per ounce.

Also, A 6 ounce piece of raw chicken breast has 48grams of protein, hence we have;

P(chicken breast) = 48/6 = 8 grams per ounce.

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To find the partial derivative of z with respect to x, we need to differentiate the equation f(x,y) with respect to x while treating y as a constant. Using the formal definition of the partial derivative, we have:

∂z/∂x = lim(h→0) [f(x+h,y) - f(x,y)]/h
= lim(h→0) [(12(x+h)² - 9(x+h)y + 16y²) - (12x² - 9xy + 16y²)]/h
= lim(h→0) [24xh + 12h² - 9yh]/h
= lim(h→0) (24x + 12h - 9y)
= 24x - 9y

Similarly, to find the partial derivative of z with respect to y, we differentiate the equation with respect to y while treating x as a constant:

∂z/∂y = lim(k→0) [f(x,y+k) - f(x,y)]/k
= lim(k→0) [12x² - 9x(y+k) + 16(y+k)² - (12x² - 9xy + 16y²)]/k
= lim(k→0) (32k - 9x)
= -9x

Therefore, the partial derivatives of z with respect to x and y are:

∂z/∂x = 24x - 9y
∂z/∂y = -9x

This is the explanation for finding the partial derivatives of z with respect to x and y using the formal definition of the partial derivative. The derivative is a measure of the rate at which a function changes with respect to its input variables, while an equation is a statement that two expressions are equal. In this case, we used an equation to represent a function of two variables and found its partial derivatives with respect to each variable using the formal definition of the partial derivative.

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By using the expanded form of a number, it can be concluded that

Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99

What is expanded form of a number?
Every number can be written as a sum of the place value of its digit. This is known as expanded form of a number

Let the three digit positive integer be n = abc where a, b and c are distinct positive integers

n can be written as 100a + 10b + c

Its reverse is n' = cba

n' can be written as 100c + 10b + a

Difference between the number and its reverse

= 100a + 10b + c - 100c - 10b -a

=  99a - 99c

= 99(a - c)

= Since a and c are distinct, a - c \(\neq\) 0

Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99

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Answer:

24x - 4

Step-by-step explanation:

Perimeter of a table = 2(length + width)

length of Christina's table is the product of 4 and X

Length = 4x

The width of her table is 2 less

than twice the length.

Width = 2(4x) - 2

= 8x - 2

Perimeter of a table = 2(length + width)

= 2{4x + (8x - 2)}

= 2(4x + 8x - 2)

= 2(12x - 2)

= 24x - 4

Perimeter of a table = 24x - 4

Answer:

24/25 = 0.96

Step-by-step explanation:

there ya go XD

Answer: 7,000

Step-by-step explanation: the hundred was greater than 5 so we round up any number after whatever you are doing if it’s 5 or greater you round up

Answer:

15 hegevwyegecceccr

Step-by-step explanation:

5+3+0+7=15

Answer:

The digital root of 5307 is 6

Step-by-step explanation:

Answer:

It is not a function because the output of 9 repeats.

(1,9) (4,9)

:D

Answer:

11ft

Step-by-step explanation:

The equation for circumference is 2pi x radius

2 x pi x radius = 22 pi

2 x 22/7 x radius = 22 pi

44/7 x radius = 22 pi

radius = 22 pi x 7/44

radius = 11ft

first one is easy money

right angle = 90, and we also have 42 so:

90+42=132

180-132=48

2nd one is weird, why is there a 150 down there? triangles add up to 180 nso right angle already gets 90 degrees.--oh wait I just got it, so that is the angle of the outer. we know a line is 180 degrees, so 180-150=30 so we found that degree

So now 90+30=120, 180-120=60

The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.

The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.

Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.

Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):

y - 1 = (-1/8)(x - 2)

Simplifying and putting the equation in slope-intercept form:

y = (-1/8)x + 9/8

Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

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