Determine whether the geometric series is convergent or divergent. 10 ? 4 + 1.6 - 0.64 + ... convergent divergen

The equivalent of the expressions are as follows;

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Two expressions are equivalent if:

Hence, let's simplify the expression to find it equivalent.

Therefore,

3(3t - 4) - (2t + 10)

open the bracket

9t - 12 - 2t - 10

7t - 22

5(2t + 1) + (-7t + 28)

10t + 5 - 7t + 28

3t + 33

[tex](4t -\frac{8}{5} ) - (3-\frac{4}{3}t ) = 4t+\frac{4}{3}t - \frac{8}{5}- 3 = \frac{12t+4t}{3} +\frac{-8-15}{5} = \frac{16}{3}t - \frac{23}{5}[/tex]

[tex](-\frac{9}{2}t+4 )+(\frac{7}{4}t+33 ) = -\frac{9}{2}t+ \frac{7}{4}t + 4 + 33 = \frac{-18t+7t}{4} + 37 = \frac{25}{4}t+ 37[/tex]

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Answer: 9 weeks

Step-by-step explanation:

Let x be the number of weeks

So the equation will be

1497 - 83x < 750

Subtract 1497 on both sides

-83x < -747

x < 9

So the answer is 9 weeks

The missing value after solving is 280 seconds .

Given :

james rode his bike 7 yards in 3 seconds. set up the table with the information you know. yards seconds 7 3 you got it!

Seconds :

The second ( s or sec ) is the International System of Units ( SI ) unit of time measurement.

Table :

yards           seconds

7                     3

120                 x

we need to find x :

1 yard = 7/3 seconds

120 yards = 7 / 3 * 120 seconds

= 7 / 1 * 40 seconds

= 7 * 40 seconds

= 280 seconds.

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Answer: 13,900

Step-by-step explanation:

To round numbers to the nearest hundred, you always look at the place one down which is the tens place. The tens place is 5.

The options for 856 to round to is either 800 or 900.

The rule is that 0-4 rounds down, 5-9 rounds up. Since the tens place is 5, it will round up to 900.

Therefore, the answer would be 13,900.

No, the line passing through  (-4, 26) and (-2, 0) is  not parallel to line passing through (10, 18) and (5, 3) because slopes of both lines are different.

Line is possible in 2-d forms so, it has only x and y-co-ordinates. Z-co-ordinates is not possible.

We know very well that to prove any two lines are parallel to each other we need to prove only whether their slopes are equal or not.

Now, talking about the slopes we know that if any line is passing from point(x₁,y₁) and again passing from other point(x₂,y₂) then slope(m) of that line is given by the formula=(y₂-y₁) / (x₂-x₁)

So, for first line we have (x₁, y₁)=(-4,26)

and (x₂, y₂)=(-2,0)

So, slope(m₁) of first line is =(0-26)/(-2 - (-4))

                  =>m₁ = -26/2

                   =>m₁ = -13     ----(eq1)

Similarly, for second line, we have (x₁, y₁)=(10,18)

and (x₂, y₂)=(5,3)

So, slope(m₂) of second line is =(3-18) / (5-10)

                =>m₂ = -15/-5

                 =>m₂=     3   -------(eq2)

On comparing eq1 and eq2,we get

 =>m₁≠m₂.

Hence, the given lines are not parallel.

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(Complete question) is:

Is the line through (-4, 26) and (-2, 0) parallel to the line through (10, 18) and (5, 3)?

Therefore ,The marked point will now have the updated coordinates P' (2, 7).

When a figure is transferred from one area to another without altering its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

Here,

On an X-Y coordinate plane, a figure is plotted.

When translating a figure 7 units to the down, we must provide the coordinates of the indicated point in the original figure

"(x, y)" = "(x + m, y + n)"

In response to the query, we have

The specified point's coordinates are: P (5,4).

The new coordinates of the indicated spot after this figure is translated 6 units to the right will be -

P'( 5,4- 7) = P'(5, -3) (5, -3)

As a result, the designated point's new coordinates are P' (5, -3)

The new coordinates of the marked point will be - P'(5, -3)

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Using the square formula, the value of (1+i)^4 is -4.

The square formula is the algebraic identity which is used to find the square or difference of the sum of two terms. The square of sum of the two terms and can be calculated by multiplying the binomial by itself. The general form of square formula to find the square of the sum of two terms is given by: (a + b)^2 = a^2 + 2ab + b^2 where a and b are variables.

The given expression can be rewritten as binomial with exponent:

((1 + i)^2)^2

Using the square formula to find the square of the sum of two terms to the (1 + i)^2. Hence,

(1 + i)^2 = 1 + 2i + i^2

As 'i' iota is the square root of negative 1, i^2 = -1

1 + 2i -1 = 2i

Therefore,

(2i)^2 = 4i^2 = 4*-1 = -4

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Answer:

The answer should be 5

Step-by-step explanation:

Hope it helps

Answer:

a b over c = c √ab

25 1/2 = 2√25 to the power of 1 → A number to the power of 1 is itself

√25

5

Step-by-step explanation:

The distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The time, t = π / 2 sec,

Calculate the distance by using the formula given below,

[tex]Distance = r\times time[/tex]

So, for distance, a = 1 × π / 2 =  π / 2

for distance, b = 1 × π =  π

for distance, c = 1 × 3 π / 2 =  3 π / 2

Therefore, the distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

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The surface area of the pyramid is [tex]3060mm^{2}[/tex].

If “P” is the base perimeter, “l” is the slant height, and “B” is the base area, then the total surface area of the regular pyramid formula is given by [tex]\frac{1}{2} PI+B[/tex]  Square units.

Given that the base is a square, therefore the area of the base is 30×30mm= 900mm².

So, B=900.

The perimeter of the base is equal to 4×30mm=120mm.

So, P=120.

The slant height is equal to 36mm.

So, I=36.

Now we will substitute the values in the surface area formula of the pyramid.

The surface area of the pyramid is equal to

[tex]\frac{1}{2}*120*36+900=3060mm^{2}[/tex]

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Answer: x=1

Step-by-step explanation:

Assume that "log" is the base-10 logarithm

log (2x)+log (5)=1

log 10{10}(2x)+log (5)=1

Assume that "log" is the base-10 logarithm

\log 10{10}(2x)+\log (5)=1

\log 10{10}(2x)+\log10{10}(5)=1

Apply the logarithm product identity

\log 10{10}(2x)+\log 10{10}(5)=1

log 10{10}(2x x 5)}=1

Answer:

log_20(35)= 1.5372435736805

Step-by-step explanation:

Therefore the part of expression of 48 represent the price per scarfs .

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. (Mathematical Operator, Number or Variable, Expression) is the structure of an expression.

Here,

In the given the expression 483, represents the number 0f scarves and 48 represents the price per scarf Buyers are charged shipping fee of $4.75 for each scarf order:

Therefore, from the given we can see the 48 represents the price per scarf.

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By using graphical method, it can be seen that-

(-4, 8) satisfies the system of inequality

So third option is correct

What is linear inequation?

Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by  >, <, ≥, ≤.

A one degree inequation is known as linear inequation.

The system of linear inequation is to be solved graphically

For y  ≥ -3x-4

The line passes through (0, -4) and ([tex]-\frac{4}{3}, 0[/tex])

Since (0, 0) satisfies the line, shaded region is towards the origin

Now, as equality is maintained, line is a solid line

The above line is plotted by a red line

For [tex]y \geq \frac{1}{2}x-6[/tex]

The line passes through (0, -6) and (12, 0)

Since (0, 0) satisfies the line, shaded region is towards the origin

Now, as equality is not maintained, line is a dotted line

The above line is plotted by a blue line

From the intersection of two shaded regions, it can be seen that (-4, 8) satisfies the system of inequality

So third option is correct

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Answer:

To prove the given identity, we can start by multiplying both sides of the equation by (cosθ - sinθ) to obtain:

(cosθ/1 - tanθ) (cosθ - sinθ) - sin^2θ/(cosθ - sinθ) = (cosθ + sinθ)(cosθ - sinθ)

Expanding both sides of the equation gives us:

cos^2θ - tanθcosθ - sin^2θ = -sin^2θ + cos^2θ

We can simplify this equation to:

-tanθcosθ = -sin^2θ + cos^2θ

We can simplify this further by using the identity cos^2θ + sin^2θ = 1:

-tanθcosθ = 1 - 2sin^2θ

We can rearrange this equation to solve for sin^2θ:

sin^2θ = (1 + tanθcosθ)/2

This is the desired result, so we have successfully proved the given identity.

I hope this helps! Let me know if you have any questions.

Step-by-step explanation:

SELF EXPLANATORY

Answer:

slope = -9/7 or (negative fraction 9 over 7)

Step-by-step explanation:

what is the slope of the line that passes through (−2, 3) and (5, −6)?

slope = change in y / change in x

slope = (3 - (-6) / (-2 - 5)

slope = 9/-7

slope = -9/7

from your options:

negative fraction 9 over 7

The temperature of the mixture when it cools is; -10.7°C

A change in temperature is defined as the difference in the initial and final temperatures.

Now, we are told that the chemist has a mixture with a temperature of 3.5°C.

We are also told that the temperature changes by -14.2 °C

Let the initial temperature be T₁ and the final temperature be T₂ and as such,  the change in temperature will be;

ΔT = T₂ - T₁

Plugging in the relevant values gives;

-14.2 = T₂  - 3.5

T₂  = -14.2 + 3.5

T₂ = - 10.7°C

This is the temperature of the mixture after it cools.

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Three identically sized sectors make up a spinner. Two sectors are colored blue, while one sector is labeled red. Kathryn turns the spinning while recording the outcomes. Kathryn comes to the conclusion that there is a problem with her experiment after running several trials for it.

The object's sample space affects theoretical probability. For instance, the likelihood of rolling a 3 when using a fair die is 1/6. This is so because, when a fair die is rolled, the number 3 indicates one of the six possible results.

Divide the total number of trials by the number of times the desired result has occurred to determine the experimental probability.Every time, one fourth of the time, the spinner will land on a different color. The likelihood of rolling each number on the die in Experiment 2 is always one sixth. The results are equally likely to occur in both of these tests. Let's examine a test in which the results are not equally likely.

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Answer:

7.20cm I think

........

The value of area under the normal curve at a z-score of 0.33 with respect to the mean is 0.63 (2 dp).

It is a value that describes the deviation of a value from the standard deviation. Z-score is the number of standard deviations a given data point lies above or below mean.

To find the area under the normal curve at a specific value of z we look into the normal distribution table.

At 0.33 we can see that the value is 0.6293. This value is given from the center, which is the mean of the data.

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Answer:

a.  Area of rectangle: Length x Width or Base x height

b. The length of the base is 6

c. The height is 3

d. Area of the rectangle is 18

Step-by-step explanation:

a. Area of the rectangle formula is: L x W

b. We find the Length, which means we find the distance of the x; we see that to get from point A to point B the x change is 6, so the base is 6

c. We find the height, which means we find the distance of the y; we see that get from point B to point C, the y change by 3, so the height is 3

d. To find the area we take 6 times 3 = 18

fog(x) =4x²+44x+12,

f(x) is quadratic function  whose value is x²+6x -4 at x.

so , we have asked the value of f(x) at x=g(x) , which another function whose value is 2x-8 .

so, by the concept of composition of functions we have to put the value 2x-8 in place of x in the f(x) function to get fog(x).

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Answer:

7x

Step-by-step explanation:

The expressions have, the first expression has degree 5, end behavior to ± infinite terms , zeros are h = 0, -1/2 , -1/2, 11 , 11 and 2 multiplicity -1/2 and 11 and sketch is drawn in image 1. And second expression has degree 4, end behavior to + infinite terms , zeros are x = 0,0, 3,-3. , 2 multiplicity of 0 and sketch is drawn in image 2.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given that the expression ;

T(h) = h (2h + 1)²(h - 11)² and D(x) = 3x⁴ - 27x²

Now for the first expression T(h) = h (2h + 1)²(h - 11)²

Simplifying, the expression;

T(h) = h (2h + 1)²(h - 11)²

Degree of the highest polynomial of above expression is 5.

To find end behavior, we will find the factors of expression;

T(h) = h (2h + 1)²(h - 11)²

Here, h = 0,  (2h + 1)² = 0 , (h - 11)²= 0

h= 0 , h = -1/2 , -1/2 and h = 11 , 11

Multiplicity of -1/2 is 2 and 11 is 2.

End behavior, given expression has 2 pair of repeated roots.

And  (2h + 1)² ≥ 0 , (h - 11)²≥ 0

So the expression behavior depends on the term h alone.

And also it is an even polynomial.

So the graph of expression varies to infinity term for both positive and negative.

Zeros of the polynomial are  h = 0, -1/2 , -1/2, 11 , 11.

Sketch 1,

Now for the second expression D(x) = 3x⁴ - 27x²

Simplifying, the expression;

D(x) = 3x⁴ - 27x²

Degree of the highest polynomial of above expression is 4.

To find end behavior, we will find the factors of expression;

D(x) =3x²(x+3)(x−3)

Here, x = 0,0, 3,-3.

Multiplicity of 0 is 2.

End behavior, it is an odd polynomial. So the graph of expression varies to positive infinity.

Sketch 2,

Therefore, the first expression has degree 5, end behavior to ± infinite terms , zeros are h = 0, -1/2 , -1/2, 11 , 11 and 2 multiplicity -1/2 and 11 and sketch is drawn in image 1. And second expression has degree 4, end behavior to + infinite terms , zeros are x = 0,0, 3,-3. , 2 multiplicity of 0 and sketch is drawn in image 2.

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Answer:x=-5

Step-by-step explanation:

x2+10=0

0-10=-10

x2=-10

-10/2=-5

x=-5

Answer:

Step-by-step explanation:

52%

Answer: The slope is Negative

Step-by-step explanation:

The slope is rising over run

Let's pick 2 points (-3,0) (0,-2)

The slope is -2/3

As per the given probability, the two action that the base station would takes are, 1) increasing the transmission power, and 2) reducing the transmission rate.

Probability:

In statistics, probability refers the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Given,

Here we need to find the two actions that a base station could take to ensure that the loss probability of a transmitted frame does not increase.

Here we have given that, a mobile node gets farther and farther away from a base station,

And the two actions that a base station could take to ensure that the loss probability of a transmitted frame does not increase will be solve by  increased transmission power and then reduce the rate.

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Fitness related to endurance and fitness related to skill are the two basic types of physical fitness. Running is most likely the simplest solo sport for fostering both physical and mental fitness.

Jogging, riding, swimming, and brisk walking are among examples. Exercises that build muscle strength are known as resistance training. Using a resistance band and lifting weights are two examples. Walking on uneven ground can be made simpler with balance exercises, which can also assist prevent falls.

Fitness related to endurance and fitness related to skill are the two basic types of physical fitness. Running is most likely the simplest solo sport for fostering both physical and mental fitness.

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The value of angle x in the triangle is 130 degrees

From the question, we have the following parameters that can be used in our computation:

Lines = parallel lines

Shapes = Triangles

By the alternate interior angle, the third angle in the bottom triangle has the  same measure as 60 degrees

This means that

x = 70 + 60 -- by the alternate exterior angle throrem

Evaluate the sum

x = 130

Hence, the value of x is 130

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