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marysya [2.9K]
3 years ago
6

What is the 20th term of the arithmetic sequence?

Mathematics
2 answers:
podryga [215]3 years ago
8 0
You just need to substitute 20 for x and then solve.

a(20) = -5 +(20-1)3

Simplify: a(20) = -5 + (60-3)

Simplify: a(20) = -5 + 57

Result: a(20) = 52

So, 52 is the 20th term of the arithmetic sequence.
Mandarinka [93]3 years ago
8 0
In the equation
a(n) =  - 5 + (n - 1)3
Let n=20 and evaluate it as:

a(20) =  - 5 + (20 - 1)3 \\  \\ a(20) =  - 5 + (19)3 \\  \\ a(20) =  - 5 + 57 \\  \\ a(20) = 52
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1/4 times X -1+ 3X equals 2
iris [78.8K]

Answer:

41

Step-by-step explanation:

4 0
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The glass container is shown filled to a height of 2.25 inches. How much sand is currently in the container.
JulijaS [17]
2.25 inches of sand.
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Find the equation of line b described below, in slope-intercept form
Serjik [45]

Given:

Line a is perpendicular to line b .

Line a passes through the points (1,-8) and (9,-12) .

Line b passes through the point (-8, -16).

To find:

The equation of b.

Solution:

Line a passes through the points (1,-8) and (9,-12) . So, slope of line a is

m=\dfrac{y_2-y_1}{x_2-x_1}

m_a=\dfrac{-12-(-8)}{9-1}

m_a=\dfrac{-12+8}{8}

m_a=\dfrac{-4}{8}

m_a=-\dfrac{1}{2}

Product of slopes of two perpendicular lines is -1.

m_a\times a_b=-1

-\dfrac{1}{2}\times a_b=-1

b=2

Slope of line b is 2.

If a line passing through a point (x_1,y_1) with slope m, then equation of line is

y-y_1=m(x-x_1)

Line b passing through (-8,-16) with slope 2. So, equation of line b is

y-(-16)=2(x-(-8))

y+16=2(x+8)

y+16=2x+16

Subtract 16  from both sides.

y=2x

Therefore, the equation of line b is y=2x.

7 0
3 years ago
Find the two points on segment AB that divide the segment into 3 congruent Parts if A has coordinates (0 0) and point B has coor
Elena L [17]

Answer:

  (3, 2), (6, 4)

Step-by-step explanation:

Since one end (A) of the segment AB is at the origin, the required points will be 1/3 and 2/3 of the coordinates of B:

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  (2/3)(9, 6) = (6, 4)

8 0
3 years ago
For your friend's birthday, you have 3 presents to wrap. Find the combined surface area of these 3 gifts so you know how much wr
omeli [17]

The answer is: 5,614 square inches.

The explanation is shown below:

1. The gift on the bottom is a rectangular prism. To calculate its surface area, you must apply the following formula:

 SA=2[(l)(w)+(l)(h)+(h)(w)]

Where l is the length (20 inches), w is the width (42 inches) and h is the heigth (16 inches).

2. Substitute values:

SA1=2[(20in)(42in)+(20in)(16in)+(16in)(42in)]=3,664in^{2

3. The surface area of the other gifts can be calculated with the formula for calculate the surface area of a cube:

SA=6s^{2}

Where s is the side.

4. The surface area of the bigger cube is:

SA2=6(15in^{2})=1,350in^{2}

5. The surface area of the smaller cube is:

SA3=6(10in^{2})=600in^{2}

6. The total surface area (the combined surface area of the three gifts) is:

SAt=SA1+SA2+SA3\\SAt=3,664in^{2}+1,350in^{2}+600in^{2}\\SAt=5,614in^{2}

7 0
3 years ago
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