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What is the 72nd term of -27, -11, 5

FinnZ [79.3K]

Answer:

1109

Step-by-step explanation:

The first term is -27, and the common difference is 16.

The nth term is:

a = a₁ + d (n − 1)

a = -27 + 16 (n − 1)

a = -27 + 16n − 16

a = 16n − 43

The 72nd term is:

a = 16(72) − 43

a = 1109

5 0

2 years ago

The sum of the ages of Berma, her mother Rinna and her father Erwin is 80. Two years from now, Rinna’s age will be 13 less than

jekas [21]

Answer: Berma is 5 years old

Rinna is 38 years old

Erwin is 37 years old

Step-by-step explanation:

Let x represent Berma's age

Let y represent Rinna's age

Let z represent Erwin's age

Since the sum of their ages is 80,

x + y + z = 80 - - - - - - -1

Two years from now, Rinna’s age will be 13 less than the sum of Erwin’s age and twice Berma’s age. This means that

y +2 = [ (z+2) + 2(x+2) ] - 13

y +2 = z + 2 + 2x + 4 - 13

2x - y + z = 13 + 2 - 4 -2

2x - y + z = 9 - - - - - - -2

Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. It means that

15(x - 3) = (y - 3) - 5

15x - 45 = y - 3 - 5

15x - y = - 8 + 45

15x - y = 37 - - - - - - - -3

From equation 3, y = 15x - 37

Substituting y = 15x - 37 into equation 1 and equation 2, it becomes

x + 15x - 37 + z = 80

16x + z = 80 + 37 = 117 - - - - - - 4

2x - 15x + 37 + z = 9

-13x + 2 = -28 - - - - - - - - -5

subtracting equation 5 from equation 4,

29x = 145

x = 145/29 = 5

y = 15x - 37

y = 15×5 -37

y = 38

Substituting x= 5 and y = 38 into equation 1, it becomes

5 + 38 + z = 80

z = 80 - 43

z = 37

6 0

2 years ago

Find the value of x by using the exterior angle theorem

murzikaleks [220]

Sorry just coming for the points

5 0

3 years ago

A. A line through P parallel to line L

m_a_m_a [10]

Answer:

b.a line through p intersecting line l

5 0

2 years ago

Read 2 more answers

alex wong basketball after making a half court shot. the display box for his new basketball is in the shape of a cube. alex meas

suter [353]

408.454 cubic inches of air is surrounding the ball in the box

Step-by-step explanation:

When a sphere is inscribed in a cube and touching all of its faces, then

The diameter of the sphere = the side of the cube
The empty volume of the cube is the difference between the volume of the cube and the volume of the sphere

∵ The basketball is shaped a sphere

∵ The box is shaped a cube

∵ The ball touching every wall of the box

∴ The diameter of the ball = the side of the box

∵ The length of one side of the cube = 9.5 inches

∴ The diameter of the ball = 9.5 inches

∵ The diameter of the ball = 2 r, where r is the radius of the ball

∴ 9.5 = 2 r

- Divide both sides by 2

∴ r = 4.75 inches

∵ The volume of the air that surrounded the ball in the box =

volume of the box - volume of the ball

∵ Volume box (cube) = s³

∵ s = 9.5 inches

∴ Volume of the box = (9.5)³

∴ Volume of the box = 857.375 inches³

∵ Volume the ball (sphere) = $\frac{4}{3}$ π r³

∵ r = 4.75

∴ Volume the ball = $\frac{4}{3}$ (π)(4.75)³

∴ Volume the ball = 448.921 inches³

Substitute the values of the volumes of the box and the ball in the rule above

∴ The volume of the air = 857.375 - 448.921

∴ The volume of the air = 408.454 inches³

408.454 cubic inches of air is surrounding the ball in the box

Learn more:

You can learn more about volume of solids in brainly.com/question/12497249

#LearnwithBrainly

6 0

3 years ago