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2 years ago

What is the expanded form of 8,069,960,699

Mathematics

2 answers:

Ymorist [56]2 years ago

8 0

Answer:

Expanded Notation Form:

8,000,000,000

+ 0

+ 60,000,000

+ 9,000,000

+ 900,000

+ 60,000

+ 0

+ 600

+ 90

+ 9

Expanded Factors Form:

8 × 1,000,000,000

+ 0 × 100,000,000

+ 6 × 10,000,000

+ 9 × 1,000,000

+ 9 × 100,000

+ 6 × 10,000

+ 0 × 1,000

+ 6 × 100

+ 9 × 10

+ 9 × 1

Expanded Exponential Form:

8 × 10^9

+ 0 × 10^8

+ 6 × 10^7

+ 9 × 10^6

+ 9 × 10^5

+ 6 × 10^4

+ 0 × 10^3

+ 6 × 10^2

+ 9 × 10^1

+ 9 × 10^0

Word Form:

eight billion sixty-nine million nine hundred sixty thousand six hundred ninety-nine

Step-by-step explanation:

juin [17]2 years ago

5 0

Answer:

8,000,000,000

+ 60,000,000

+9 ,000,000

+ 900,000

+ 60,000

+ 600

+ 90

+ 9

Step-by-step explanation:

split up each number into the decimal value place it falls into. hope this helped! :)

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A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that angle AD

Valentin [98]

Refer to the diagram shown below.

Let x = m∠ADB.

Because m∠BDC is 32° greater than m∠ADB, therefore
m∠BDC = x + 32°

Each angle of a rectangle is 90°, therefore
x + (x+32) = 90
2x + 32 = 90
2x = 58
x = 29°
x+32 = 61°

Answer:
m∠BDC = 61°
m∠ADB = 29°

8 0

2 years ago

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess

statuscvo [17]

Let's start by visualising this concept.

Number of grains on square:
1 2 4 8 16 ...

We can see that it starts to form a geometric sequence, with the common ratio being 2.

For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
$T_n = ar^{n - 1}$
$T_{15} = 2^{14} = 16384$

Thus, there are 16, 384 grains on the fifteenth square.

The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
$S_n = \frac{a(r^{n} - 1)}{r - 1}$
$S_{15} = \frac{2^{15} - 1}{2 - 1}$
$S_{15} = 2^{15} - 1 = 32767$

Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.

6 0

2 years ago

Read 2 more answers

Triangle XYZ is rotated to create the image triangle X'Y'Z'.

Solnce55 [7]

Answer:

The correct option is;

R0, 180°

Step-by-step explanation:

The coordinates of ΔXYZ are given as follows;

X(-2, 2), Y(1, 2), Z(0, 4)

The coordinates of ΔX'Y'Z' are given as follows;

X'(2, -2), Y'(-1, -1), Z'(0, -4)

Whereby, the coordinates of the point Y' is (-1, -2), we have the rule that describe the transformation of ΔXYZ to ΔX'Y'Z', given as follows

Coordinates of the preimage = (x, y)

Coordinates of the image = (-x, -y)

Which is in accordance with the transformation by rotation 180° about the origin.

7 0

2 years ago

General solution of equation sin x + sin 5x = sin 2x + sin 4x is

zaharov [31]

Answer:

x=nπ3, n∈I

Step-by-step explanation:

sin x + sin 5x = sin 2x + sin 4x

⇒⇒ 2 sin 3x cos 2x = 2 sin 3x cos x

⇒⇒ 2 sin 3x(cos 2x - cos x) = 0

⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3 , n∈I, n∈I

or cos 2x−cos x=0 ⇒ cos 2x=cos xcos 2x-cos x=0 ⇒ cos 2x=cos x

⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3 , n∈I, n∈I

But solutions obtained by x=2nπx=2nπ , n∈I, n∈I or x=2nπ3x=2nπ3 , n∈I, n∈I are all involved in x=nπ3x=nπ3 , n∈I

7 0

2 years ago

Daisy measured the heights of 20 plants.

sergiy2304 [10]

Answer:

30.5 cm

Step-by-step explanation:

<em>Refer to attached</em>

Height of plants (h) >> Frequency >> Midpoint >> Frequency x midpoint
0 <h < 10 >> 1 >> 5 >> 5
10 <h < 20 >> 4 >> 15 >> 60
20 <h < 30 >> 7 >> 25 >> 175
30 <h < 40 >> 2 >> 35 >> 70
40 <h < 50 >> 3 >> 45 >> 135
50 <h < 60 >> 3 >> 55 >> 165

Sum of frequencies = 20

Sum of frequency x midpoint product = 610

<u>Mean height </u>

610/20 = 30.5 cm

5 0

2 years ago