Find the sum of the first seven terms of the geometric sequence series having the following information: 2-8+32- … +a n

Answer:

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

The distance is 710000 km and the first spaceship has travelled 110000 km in the first hour.

The remainder of the distance is reducing by:

Time to travel before they meet:

Add the first hour to this to get total travel time of 4 hours.

Answer:

390

Step-by-step explanation:

The pattern here is inversing between multiplying and adding

6 to 12 = ×2

12 to 15 = +3

15 to 60 = ×4

60 to 65 = +5

This means that to get the next number you must do ×6 since the next pattern has to be × and the number must be 6!

65 × 6 = 390

Have a lovely day :)

The value of the expression - 9(18 - 9 + 12) + 12(- 9 + 18 + 18) is 135.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Let, The rectangle be x, the triangle by y, and the star be z.

Therefore,The three linear equations are,

x + 3y + z = 57...(i)

12x + 5y = 234...(ii)

8x - 6x + 3x = 60...(iii)

5x = 60.

x = 12.

Putting the value of x in eqn(ii) we have,

12(12) + 5y = 234.

144 + 5y = 234.

5y = 90.

y = 18.

Now, Putting the value of x and y in eqn(i) we have,

12 + 3(18) + z = 57.

12 + 54 + z = 57.

z = - 9.

So, The value of the expression z(y + z + x) + x(z + y + y) is,

= - 9(18 - 9 + 12) + 12(- 9 + 18 + 18).

= - 9(21) + 12(27).

= - 189 + 324.

= 135.

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Answer:

Step-by-step explanation:

Answer:

The Graph is Below

Step-by-step explanation:

The volume of the rectangular prism is  10a⁵ - 30a⁴ + 10a³. Option A

The formula for determining the volume of a rectangular prism is expressed as;

Volume = l × w × h

Given that the parameters are;

We also have their values as;

Length, l = 5a

Width = 2a

h = (a³- 3a² + a)

Substitute the values, we get;

Volume = (5a . 2a. a³- 3a² + a)

Volume = 10a⁵ - 30a⁴ + 10a³)

Since they have different powers, it is impossible to add the like terms

Hence, the expression is  10a⁵ - 30a⁴ + 10a³

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The required Front view and a Side view of the given prism have been shown.

3D geometry is the study of shapes in 3D space using three coordinates: x-coordinate, y-coordinate, and z-coordinate. To discover the exact location of a point in 3D space, three criteria are required.

Here,
"Front view" and "side view" refer to two different perspectives of an object or a scene. "Front view" is a perspective of the object or scene as seen from the front, and "side view" is a perspective of the object or scene as seen from the side.

Thus, the required Front view and Side view of the given prism has been shown.

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11x = 99z

x = 9z

3y = 99z

y = 33z

1x + 1y + 1z = 9z + 33z + 1z = 43z

The area of the triangular side of the pyramid is given as follows:

21,852 m².

We consider that the side of the pyramid is triangular, hence we must consider that the area of a triangle is obtained as half the multiplication of the base by the height, that is:

Area = base x height / 2.

Considering b = 233, and dividing by the square root of 2, the coordinates of the endpoints of the base are given as follows:

(164.76, 0, 0) and (0, 164.76, 0).

Hence the length of the base is obtained using the distance between two points as follows:

Base = [tex]\sqrt{164.76^2 + 164.76^2}[/tex]

Base = 233.

The midpoint of the base has the coordinates given as follows:

(82.38, 82.38, 0).

The height is the distance between (0,0,147) and (82.38, 82.38, 0), hence it is given as follows:

Height = [tex]\sqrt{82.38^2 + 82.38^2 + 147^2}[/tex]

Height = 187.57.

Hence the area is of:

Area = 0.5 x 233 x 187.57

Area = 21,852 m².

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Answer:

Ryan

Step-by-step explanation:

Let's calculate the probabilities of John and Ryan hitting the target center

Let P(J) and P(R) be the respective probability representations

For John

John hits the center 1 time for every 3 tries(arrows)
Therefore

[tex]P(J) = \dfrac{1}{3}[/tex]

Out of 30 arrows (and therefore 30 attempts)  the expected number of times that John can hit the center is given by

[tex]30\cdot \dfrac{1}{3} = 10\\[/tex]

Since you need to hit the center more than 10 times, John is not expected to win the merit badge

For Ryan

Ryan Hits the center 2 times for every 5 arrows (attempts)

[tex]P(R) = \dfrac{2}{5}[/tex]

With 30 arrows the expected number of times that Ryan hits the target is:
[tex]30\cdot \dfrac{2}{5} = 18\\\\[/tex]

So Ryan is expected to win the Archery Merit Badge.

Important Note

Here you have to be careful of the words you use and interpret the results with some reality checks.

Probabilities after all are based on previous trials and represent only an estimate of guarantees of future events. That's why I have repeatedly used the word expected.

After all, John maybe able to hit the center a 11th time and thus he too will earn a merit badge.

In my opinion a poorly worded question

The value of the expression is (x∧2m-15)Yy∧5n +1). Option B

You should understand that simplification involves making an expression more simpler to understand. Also, the expression is in index form that involves the division law of indices.

the given expression to be simplified is

(x∧3m-8)/x∧m-7) (y∧7n +1)/(y∧2n)

This can be simplifies as follows

(x∧3m-8-(m-7)(y∧7n+1(2n)

Simplify further to have the value

(x∧3n-8-m-7)(y∧7m-2n+1)

This implies that the value is

(∧2m-15)(y2n+1)

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Answer: the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)

Step-by-step explanation:

To obtain the regression equation for costs related to age of cars, we can use the method of least squares. This method involves finding the line of best fit that minimizes the sum of the squared differences between the predicted values and the actual values.

The equation for a linear regression line is:

y = a + bx

where a is the y-intercept and b is the slope of the line.

To find the slope of the line (b), we can use the formula:

b = (n(∑xy) - (∑x)(∑y)) / (n(∑x^2) - (∑x)^2)

To find the y-intercept (a), we can use the formula:

a = (∑y - b(∑x)) / n

Given the data provided, we can calculate the following values:

∑x = 142

∑y = 150

∑xy = 2430

∑x^2 = 10304

n = 8

By substituting these values into the formulas for b and a, we can find the slope and y-intercept of the line:

b = (8(2430) - 142(150)) / (8(10304) - 142^2) = 0.5

a = (150 - 0.5(142)) / 8 = 13.5

Therefore, the regression equation for the costs related to age of cars is:

y = 13.5 + 0.5x

To estimate the maintenance cost of cars when the age of cars is 12 years, we can substitute x = 12 into the equation and solve for y:

y = 13.5 + 0.5(12) = 16.5

So the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)

Answer:

103

Step-by-step explanation:

because its the actual answer

Answer:

Step-by-step explanation:

Since we are given two points in the graph, we can use the slope equation shown below:

(y2-y1)/(x2-x1)

reading the graph left from right (1,11) will be the first point and (3,1) the second. plug in and solve!

(1-11)/(3-1) = -10/2 = -5

The slope is -5

a negative slope makes sense since the graph is leaving the first quadrant.

hope this helps!

Answer: A) -5. Graph slope.

Step-by-step explanation:

The formula to calculate the slope of the line is:

[tex]\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff m=\dfrac{x_2-x_1}{y_2-y_1} }}[/tex]

We have that the points are:

We substitute these points in the previous formula and solve:

     [tex]\boldsymbol{\sf{m=\dfrac{x_2-x_1}{y_2-y_1} }}\\ \\ \\ \boldsymbol{\sf{m=\dfrac{1-11 }{3-1} }}\\ \\ \\ \boldsymbol{\sf{m=\dfrac{-10}{5} }}\\ \\ \\ \boxed{\boldsymbol{\sf{m=-5}}}[/tex]

Explanation:

The TI-84 calculator is fairly powerful and can handle things like this, but it's not needed to be honest. Any calculator will do.

"csc" is shorthand for "cosecant". It's the reciprocal of sine.

csc = 1/sin

Recall that

sin = opposite/hypotenuse

which means

csc = 1/sin = hypotenuse/opposite

What we'll need are the hypotenuse and opposite sides. Plot the points (0,0) and (-20,21). Draw a segment between them. This forms the hypotenuse of the right triangle shown below. This triangle is in the quadrant Q2 in the upper left corner. The hypotenuse 29 is found using the pythagorean theorem a^2+b^2 = c^2.

Use a = 20 and b = 21 to find c = 29.

According to that diagram, we can then say:

csc = hypotenuse/opposite = 29/21

The equation y = 0.60x. The 0.60 represents the 0.60 feet in each second rise. The table is completed below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Every 10 seconds in the escalator step rise is 6 feet.

Let 'y' be the number of feet and 'x' be the number of seconds. Then the equation is given as,

y = 0.60x

Then the table is given as,

Time (x)           Distance escalator rises (feet)

     10                                   6

    20                                  12

    30                                  18

    40                                  24

The 0.60 represents the 0.60 feet in each second rise.

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The exponential equation that models the function of Maureen's car is 26,525 (0.92)

a = 26,525 and b = 0.92

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting value

b = the base function

x = the exponents

Considering the problem,

the starting = $26,525

the base = depreciation

the exponents = x

A year ago hence x = 1

$24,403 = $26,525(b)¹

b = 24,403 / 26,525

b = 0.92

hence we can say that a = 26,525 and b = 0.92

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Answer:

The minimum length and width of the tarp would be the diagonal length of the café's piece of ground. To find this length, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In this case, the café's piece of ground forms a right triangle, with one side measuring 6.0 m and the other side measuring 5.0 m. So, to find the length of the hypotenuse, we can use the formula: c = √(a^2 + b^2) where c is the length of the hypotenuse and a and b are the lengths of the other two sides. Plugging in the numbers, we get: c = √(6.0^2 + 5.0^2) = √(36 + 25) = √(61) = 7.81 m

So, the minimum length and width of the tarp would be 7.81 m.

The integers that -3.425 lie between are -3 and -4.

The rational numbers  that -3.425 lie between to the nearest tenth are -3.4 and -3.5.

The rational numbers  that -3.425 lie between to the nearest hundredth are -3.42 and -3.43.

Integers are numbers without decimals and fractions. They are whole numbers. Integers can either be positive, negative or zero. Examples of integers are -5 and 10.

A rational number is a number that can be expressed as a fraction of two integers. Examples of rational numbers are 1/4, -2/3  

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Answer:

There should be 8 of them

- 2 - 3i

- 2 + 3i

2 - 3i

2 + 3i

- 3 - 2i

- 3 + 2i

3 - 2i

3 + 2i

Thanks

absolute value is the real part squared + the complex part squared and the root of the things you get.

|a + ib|

= √(a²+b²)

so the sign doesn't matter

Answer:

C, E and F

Step-by-step explanation:

Answer:

any number added to 0 is equal to itself.

Step-by-step explanation:

Answer:

... 2?

Step-by-step explanation:

1+1+0 = 2

In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> [tex]\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}[/tex]  

=> [tex]\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}[/tex]  

From the above calculations given fractions are 31/36 and 32/36

Difference = [tex]\frac{32}{36} - \frac{31}{36} = \frac{1}{36}[/tex]  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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Answer:

see full calculations in below

Step-by-step explanation:

Answer:

don't know my dear friend

Answer:

m∠ABC = 180.

Step-by-step explanation:

In a triangle, the median to the side opposite the largest angle bisects that angle.

Since BM is a median, it bisects ∠C, the angle opposite side AB.

Let's call the angle opposite side AB angle x, so x/2 = 40.

Therefore, x = 80

Since a triangle has 180 degree, then if we add all the angles in the triangle we get:

m∠ABC = m∠BAC + m∠BCA + m∠CAB = x + (180-x) + (180-x) =180

So m∠ABC = 180

Answer:

-1 ≤ x ≤ 5

Step-by-step explanation:

-1 ≤ x ≤ 5 is the answer

Answer:

The compound interest formula is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = 2750, r = 0.035, n = 4 (because interest is compounded quarterly) and t = 7 (because we are trying to find the balance after 7 years).

So the formula becomes:

A = 2750(1 + 0.035/4)^(4*7)

By plugging the number into the formula we can find the final amount after 7 years

A = $3,974.23

So the amount of money in the account at the end of 7 years is $3,974.23, rounded to the nearest hundredth.

Answer:

In order to find the values of k and m in a parallelogram, you would need to have additional information such as the coordinates of the points that make up the parallelogram and the formulas or equations that relate k and m to these points.

Here is one way to find the values of k and m in a parallelogram:

Label the four vertices of the parallelogram as A, B, C, and D with the opposite sides parallel to each other.

Find the slope of the line segment AB by using the formula (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Let the slope of AB be represented by k.

Find the slope of the line segment AD by using the same formula and let it be represented by m.

The values of k and m are now found.

Please note that, this method is only applicable if the Parallelogram is not degenerate i.e, it is not a rectangle or a line.

It is also important to keep in mind that different formulas or equations may be used depending on the specific context of the problem. It is also important to check that the slopes of opposite sides are equal.

Step-by-step explanation:

Step-by-step explanation:

a/b is invalid, when b = 0.

so, F(x) is invalid, if (1 + sin(2x)) = 0.

(1 + sin(2x)) can only be 0, if sin(2x) = -1

sin(angle) = -1

angle = 2x = 270° or 3pi/2

x = 135° or 3pi/4

so,

x <> 135° or 3pi/4