Given :f(x)=∑ n=1 ∞ ​ (x+2) Determine: the values of x for which f(x) converges . the value of (x) if x = 1/ 1/2 ​

Answer:

  (3, 6)

Step-by-step explanation:

You want the coordinates of the orthocenter of triangle WXY with vertices W(2,7), X(3, 4), and Y(6, 7).

The orthocenter is the point where the altitudes of the triangle meet. An altitude is the line through a vertex that is perpendicular to the opposite side.

This is an acute triangle, so the orthocenter is within the boundaries of the triangle.

We note that side WY of the triangle is a horizontal line, so the orthocenter will lie on the vertical line through point X. The x-coordinate of point X is 3, so that vertical line has equation x=3.

Side XY can be seen on the graph to have a slope of 1. Or, you can compute it from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (7 -4)/(6 -3) = 3/3 = 1

Then the point-slope equation of the altitude to that line will have the opposite reciprocal slope, and will go through point W(2, 7):

  y -7 = -1(x -2)

The y-value of the point of intersection of the altitude through W with the altitude through X will be the solution to ...

Substituting for x in the second equation, we have ...

  y -7 = -3 +2

  y = 6 . . . . . . . . . . add 7

The orthocenter is (x, y) = (3, 6).

__

Additional comment

The orthocenter of a right triangle is the vertex where the right angle is located. The orthocenter of an obtuse triangle is outside the triangle.

keeping in mind that a line with an undefined slope is always a vertical line, check the picture below.

now, we could use those two points from that line and check its slope

\((\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{6}}} \implies \cfrac{4 +2}{0}\implies \cfrac{6}{0}\implies und efined\)

Answer:

43.3in²

Step-by-step explanation:

The area of the equilateral triangle in the simplest radical form is 43.3 (inches)².

A simple polygon having 3 sides and three interior angles make up triangles. One of the fundamental geometric forms, it is represented by the symbol and comprises three connected vertices. Triangles can be categorized into the number of different varieties according to their sides and angles.

According to the information provided in the question,

Side of the equilateral triangle, a = 10 inches.

Area, a = (√3)/4 × a²

a = (√3)/4 × 10²

a = 43.3 (inches)²

Therefore, the area is 43.3 (inches)².

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68% of the stores will sell a gallon of milk for between $3.57 and $3.93 with one standard deviation of the mean.

Mean =  $3.75

Standard deviation = $0.09.

Selling variations = $3.57 to $3.93.

Chebyshev's theorem states that if k is a positive number, then, in any data at least \((1 - 1/k^2)\) of the data will fall in K standard deviations from the mean data.

For normal distributions, 68% of the values will fall within one standard deviation of the mean.

For non-normal deviations, 75% of values will fall within 2 standard deviations of the mean.

Here we need to find the Upper limit and lower limit of the data.

$3.75 - $0.09 = $3.66

$3.75 + $0.09 = $3.84

The price range will be between $3.66 and $3.84.

To calculate the minimum percentage of stores using Chebyshev's theorem

minimum percentage = \(1 - 1/k^2\)

minimum percentage = \(1 - 1/(1^2)\)

minimum percentage = 0

Here, 0% of stores will fall with only one standard deviation from the Mean.

Therefore, we can conclude that 68% of the stores will sell a gallon of milk for between $3.57 and $3.93.

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Answer:

1.875

Step-by-step explanation:

1. You can divide 7 by 8 to get the decimal awnser and add one.

The answer to the question is:

1.875

Answer:

Step-by-step explanation:

ima a braintlest

Fatma's account needs to earn a rate of return of approximately 0.2957% per month to stretch her money out for 17 years.

To determine the required rate of return for Fatma's account, we can use the future value formula:

FV = PV * (1 + r)^n

Where:

FV = Future value (amount needed for 17 years of expenses)

PV = Present value (initial amount Fatma has)

r = Rate of return

n = Number of compounding periods (monthly withdrawals over 17 years)

Given:

PV = $182,000.00

Monthly expenses = $1,350.00

Number of years = 17

Number of compounding periods = 17 years * 12 months = 204 months

We can rearrange the formula to solve for the required rate of return (r):

r = (FV / PV)^(1/n) - 1

Substituting the given values:

FV = $1,350.00 * 204 = $275,400.00

r = ($275,400.00 / $182,000.00)^(1/204) - 1

Calculating this expression:

r ≈ 0.002957 (approximately 0.2957%)

Therefore, Fatma's account needs to earn a rate of return of approximately 0.2957% per month to stretch her money out for 17 years.

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Answer:

x < -3 or 2 < x < 7

Step-by-step explanation:

Let A be an mxn matrix, and let v and w be A(cv + dw) = Acv + Adw = c(Av) + d(Aw) = c(0) + d(0) = 0 + 0 = 0. In IRn with the property that Av = 0 and Aw = 0. We are to explain why A(v + w) must be the zero vector.

The sum of the vectors v and w is (v + w). The matrix-vector product between A and (v + w) can be found using matrix distribution properties.\(Av + Aw = 0 + 0 = 0, so A(v + w) = 0.\)

This is true because v and w were both mapped to the zero vector by A. Then explain why \(A(cv + dw) = 0\) for each pair of scalars c and d.

Now let’s consider the second part of the question. Let c and d be scalars. Then cv and dw are vectors in IRn.

The sum of these vectors is (cv + dw). The matrix-vector product between A and (cv + dw) can be found using matrix distribution properties. \(A(cv + dw) = Acv + Adw = c(Av) + d(Aw) = c(0) + d(0) = 0 + 0 = 0.\)

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Answer:

C

Step-by-step explanation:

It can, because any two sides of this triangle are longer than the other side.

Answer:

220mL

780mL

600mL

480mL

Step-by-step explanation:

500-280=220

500+280=780

280/8=35, so 35 mL is in one L, 35x5=175

875-175=600

750-280=480

Answer:

Step-by-step explanation:

Answer:

4 cups

Step-by-step explanation:

1 1/5 x 3 1/3 = 4

Answer:

4 dozen oranges cost $4.

Step-by-step explanation:

1 dozen = 12 units

4 dozen = 12 x 4 = 48 units

12 oranges cost $1. 48 units will cost $4 because 48 is 4 dozen.

I hope this helped you! If it did, please consider rating my answer, pressing thanks, and marking as Brainliest. Have a great day!

Answer:

x-intercept: (9,0)

y-intercept: (0,-9)  

Step-by-step explanation:

The x-intercept and y-intercept is the point at which a line intersects the x-axis and y-axis, respectively. All points on the x-axis have a y-value of 0, while all points on the y-axis have an x-value of 0. Thus, to find the x and y intercepts, substitute 0 for one of the variables in the equation, then solve for the other.

1) To find the x-intercept, substitute 0 for y. Then, isolate x.

\(4x-4(0)=36\\4x-0=36\\4x = 36\\x = 9\)

So, the x-intercept must be (9,0).

2) To find the y-intercept, substitute 0 for x. Then, isolate y.

\(4(0)-4y = 36\\0-4y = 36\\-4y = 36\\y = -9\)

So, the y-intercept must be (0,-9).

The miles Kathy can travel if she wants to spend exactly $20.00 on a cab ride is 37 miles.

The equation that can be used to represent the information in the question is:

20 = 1.50 + 0.5m

In order to determine the number of miles Kathy can ride, take the following steps :

Combine similar terms

20 - 1.50 = 0.5m

Add similar terms

18.50 = 0.5m

Divide both sides of the equation by 0.5

m = 18.50 / 0.5

m = 37 miles

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Answer:

fraction strips would just be;

1 box split into 12 parts because 12 is the common denominator, and 1/4 is equal to 3/12, so you would shade in 3 of the parts, and then 1/6 = 2/12, so you would shade in 2 parts. In the end, you should have a box (or rectangle) with 12 parts, and only 5 of those parts should be shaded in.

The equation would be as follows:

1/4+1/6 = 3/12+2/12 = 5/12

Hope this helped!! :)

Answer:

for 50 pulls, 12.5 blue socks, but you cant have half of a sock so we say 12

for 1000 pulls, 250 blue socks

for 10,000 pulls, 2500 blue socks

Step-by-step explanation:

First we add 5, 7 and 8 to find the total number of socks, 5+7=12 and 12+8 = 20

5 is the amount of blue socks, so

5/20 * how many pulls are conducted is the probability for blue socks

7 is the amount of pink socks, so

7/20 * how many pulls are conducted is the probability for pink socks

and

8 is the amount of yellow socks, so

8/20 * how many pulls are conducted is the probability for yellow socks

Answer:

4/5 x 2 1/2 < 2 1/2

Step-by-step explanation:

1/5 x 2 1/5 is 1/2 of 2 1/2 so 2 1/2 would be greater.

Answer:

60°

Step-by-step explanation:

ST = SW, since both are radii of the circle.

SW = WT, given.

STW is an equilateral triangle.

RED is an equilateral triangle.

Therefore, the measure of DE is 60°.

a. The equation representing the cost of buying and operating the Super Cool X1400 is: C = 800 + 60m. b. The equation representing the cost of buying and operating the Efficient Energy X2000 is: C = 1200 + 40m. c. Your family would have to use the Efficient Energy model for 10 months to compensate for the additional cost of the original purchase. d. Figuring your family will only use the air conditioner for four months each year, you would have to wait 5 years to start saving money overall.

a. The cost of buying the Super Cool X1400 is a one-time expense of $800. Additionally, the cost of operating it is $60 per month. Therefore, the equation representing the cost C as a function of months m is C = 800 + 60m.

b. The cost of buying the Efficient Energy X2000 is a one-time expense of $1200. The operating cost is $40 per month. Hence, the equation representing the cost C as a function of months m is C = 1200 + 40m.

c. To compensate for the additional cost of the original purchase (which is $400), we equate the two cost equations and solve for m:

800 + 60m = 1200 + 40m

20m = 400

m = 20

Therefore, your family would have to use the Efficient Energy model for 20 months (or 10 months more than the Super Cool X1400) to compensate for the additional cost.

d. Considering your family only uses the air conditioner for four months each year, we divide the total number of months (20) by four to find the number of years needed to start saving money overall:

20 months / 4 months/year = 5 years

Hence, you would have to wait 5 years to start saving money overall by choosing the Efficient Energy X2000.

a. The cost of buying and operating the Super Cool X1400 is represented by the equation C = 800 + 60m.

b. The cost of buying and operating the Efficient Energy X2000 is represented by the equation C = 1200 + 40m.

c. Your family would have to use the Efficient Energy model for 10 months to compensate for the additional cost of the original purchase.

d. Assuming your family uses the air conditioner for four months each year, you would have to wait 5 years to start saving money overall by choosing the Efficient Energy X2000.

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complete question- Your family plans to buy a new air conditioner. They can buy the Super Cool X1400 for $800, or they can buy the Efficient Energy X2000 for $1200. Both models will cool your home equally well, but the Efficient Energy model is less expensive to operate. The Super Cool X1400 will cost $60 per month to operate, while the Efficient Energy X2000 costs only $40 per month to operate. a. Write an equation to represent the cost of buying and operating the Super Cool X1400 where C= cost and m= months. b. Write an equation to represent the cost of buying and operating the Efficient Energy X2000. c. How many months would your family have to use the Efficient Energy model to compensate for the additional cost of the original purchase? d. Figuring your family will only use the air conditioner for four months each year, how many years ill you have to wait to start saving money overall?

Answer:

This picture kind of sums it up

Step-by-step explanation:

Answer:

\(y=\frac{3}{2} x - 2\)

Answer:

45° and 12

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

(8)

The polygon has n = 8, that is 8 exterior angles, thus

exterior angle = 360° ÷ 8 = 45°

(9)

The number of sides n is

n = 360 ÷ 30 = 12

Answer:

45° 12 sides

Step-by-step explanation:

1) Every polygons interior angles is equal to 180 times two less than the amount of sides it has (i.e 180•(4-2)=360:quadrilateral) So applying that here we have eight sides so 180(8-2)=1080. Now divide that by 8 to get the measure of one angle and subtract it from 180 to get the exterior angle 45°

2) if the exterior angle is 30° then the interior angle is 150°. For this part i guess and checked but you can refer to the equation above. (180(x-2)=y/150)

Answer:

-1

Step-by-step explanation:

Answer:

1 My dearest friend :D :)

Step-by-step explanation:

Answer:

WX = 8 mm

Step-by-step explanation:

To be able to solve for WX, we need to first find the size of angle \(\angle z\).

We use the law of sines in the blue triangle to do such:

\(\frac{sin(z)}{11} =\frac{sin(133)}{20} \\sin(z)=\frac{11\,sin(133)}{20} \\sin(z)=0.4022\)

Now we can use this value in the larger right angle triangle where WX is the opposite side to angle  \(\angle z\), and the 20 mm side is the hypotenuse:

\(sin(z)=\frac{opposite}{hypotenuse} \\sin(z)=\frac{WX}{20}\\0.4022=\frac{WX}{20}\\WX=20\,(0.4022)\\WX=8.044\,\,mm\)

which rounded to the nearest integer gives

WX = 8 mm

1) angle RQP

2) angle PQR

Answer:

x=-13/2=-6 1/2

Step-by-step explanation:

13 3/4 +x-7 1/4=

6 2/4+x

x= -6 1/2

Answer:

x=-13/2=-6 1/2

Step-by-step explanation: