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charle [14.2K]
3 years ago
12

When is a sum of a geometric sequence finit and when is it infinite?

Mathematics
1 answer:
Olin [163]3 years ago
3 0
Hopefully this will help you

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What is the quotation of 7^-1/7^2
Temka [501]

Answer:

  • 7^-3

Step-by-step explanation:

<u>Solving in steps</u>

  • 7^-1/7^2 =
  • 7^-1 × 7^-2 =
  • 7^(-1 - 2) =
  • 7^-3
3 0
3 years ago
At 107°F, a certain insect chirps at a rate of 92 times per minute, and at 113°F, they chirp 116 times per minute. Write an equa
dsp73

Answer:

The equation in slope-intercept form that represents the situation is y=0.25*x + 84 where y represents the temperature in ° F and x the number of chirps per minute.

Step-by-step explanation:

A linear equation can be expressed in the form y=m*x + b. In this equation, x and y are coordinates of a point, m is the slope and b is the y coordinate of the y-intercept. Since this equation describes a line in terms of its slope and its y-intercept, this equation is said to be in its slope-intercept form.

When there are two points of a line (x1, y1) and (x2, y2), the slope is determined by the quotient between the difference of the ordinate of these two points and the difference of the abscissa of the same points. This is:

m=\frac{y2-y1}{x2-x1}

Having a point on the line, you can substitute the values ​​of m, x and y in the equation y = mx + b and thus find b.

In this case:

  • (x1, y1): (92, 107)
  • (x2, y2): (116, 113)

So:

m=\frac{113-107}{116-92}

m= 0.25

substituting the values ​​of m, x1 and y1 in the equation y = mx + b you have:

107= 0.25*92 + b

107 - 0.25*92= b

84=b

<u><em>The equation in slope-intercept form that represents the situation is y=0.25*x + 84 where y represents the temperature in ° F and x the number of chirps per minute.</em></u>

3 0
3 years ago
Solve (16×^3-3×^2+43×-5)÷(×^2-2)
Oksana_A [137]

Answer:

3872/(x^2 - 2)

Step-by-step explanation:

Simplify the following:

(16^3 - 3^2 - 5×43)/(x^2 - 2)

3^2 = 9:

(16^3 - 9 - 5×43)/(x^2 - 2)

16^3 = 16×16^2:

(16×16^2 - 9 - 5×43)/(x^2 - 2)

| 1 | 6

× | 1 | 6

| 9 | 6

1 | 6 | 0

2 | 5 | 6:

(16×256 - 9 - 5×43)/(x^2 - 2)

16×256 = 4096:

(4096 - 9 - 5×43)/(x^2 - 2)

43 (-5) = -215:

(4096 - 9 + -215)/(x^2 - 2)

4096 - 9 - 215 = 3872:

Answer: 3872/(x^2 - 2)

7 0
3 years ago
How to solve 2m - 3 = 13
Virty [35]

Answer:

m=8

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Wendy wants to put a wallpaper border around her bedroom. The room has two walls that each measure 10 feet 5
cestrela7 [59]

Answer:

11 yards

Step-by-step explanation:

The room has two sides both measuring 10 feet 5 inches. This gives a total of 20 feet 10 inches. It also has the other two sides both measuring 6 feet 1 inch and that too gives a total of 12 feet 2 inches. Adding them all together results in 32 feet 12 inches. Better still, the perimeter of the room is derived as;

Perimeter = 2 (L + W)

Perimeter = 2 (10'5" + 6'1")

Perimeter = 2(16'6")

Perimeter = 32'12"

Having in mind our conversion rate of 12 inches equals 1 foot, the results can be properly expressed as 32 feet plus 1 foot which gives us 33 feet.

If the perimeter of Wendy's room is now given as 33 feet, the conversion rate between feet and yards can now be applied. Having been given that

3 feet = 1 yard

Then 1 yard = 3 feet/3, that is

y = 3/3

Hence,

y = 33/3

y = 11

The results show that Wendy would needs to buy a total of 11 yards of wallpaper border.

3 0
3 years ago
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