Which of the following terminating decimals is equivalent to -1 3/4

The mass of the Earth is 5.972x10^24 kg. the mass of the moon is 7.3 x 10^22kg. find the total mass, in kg, of the Earth and the

torisob [31]

Answer:

6045000000000000000000000 kg.

Step-by-step explanation:

We have been given that the mass of Earth is $5.972\times10^{24}$ kg. The mass of the Moon is $7.3\times10^{22}$ kg.

To find the total mass we will add mass of Earth and Moon.

First of all let us convert the given masses in standard form.

$5.972\times10^{24}=5972000000000000000000000$

$7.3\times10^{22}=73000000000000000000000$

$5.972\times10^{24}+7.3\times10^{22}$

$5972000000000000000000000+73000000000000000000000$

$6045000000000000000000000$

Therefore, the mass of Earth and Moon is 6045000000000000000000000 kg.

8 0

3 years ago

Decrease 18 tonnes by 30%

Leviafan [203]

10% of 18 tonnes = 1.8 tonnes
30% of 18 tonnes = 5.4 tonnes
18 - 5.4 tonnes = 12.6 tonnes

5 0

3 years ago

What trigonometric ratio is defined as the length of the opposite leg divided by the length of the hypotenuse?

aleksley [76]

SOH CAH TOA

Sine is opposite over hypotenuse so you're answer is C.

:)))

8 0

3 years ago

A Gardner is planting two types of trees

Nina [5.8K]

It will take 6 years for the trees to have same height.

Step-by-step explanation:

Type A tree;

Initial height = 9 feet

We will convert feet into inches because growth is in inches.

1 feet = 12 inches

9 feet = 12*9 = 108 inches

Growth rate = 6 inches per year

Let,

x be the number of years.

A(x) = 108 + 6x

Type B;

Initial height = 4 feet = 4*12 = 48 inches

Growth rate = 16 inches per year

B(x) = 48 + 16x

The height will be same, when functions are equal

A(x) = B(x)

$108+6x=48+16x\\108-48=16x-6x\\60=10x\\10x=60$

Dividing both sides by 6

$\frac{10x}{10}=\frac{60}{10}\\x=6$

It will take 6 years for the trees to have same height.

Keywords: function, division

Learn more about division at:

#LearnwithBrainly

4 0

4 years ago

Classify each conic section and write its equations in standard form. Show work.

svp [43]

Answer:

The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1

Step-by-step explanation:

* Lets revise how to identify the type of the conic

- Rewrite the equation in the general form,

Ax² + Bxy + Cy² + Dx + Ey + F = 0

- Identify the values of A and C from the general form.

- If A and C are nonzero, have the same sign, and are not equal

to each other, then the graph is an ellipse.

- If A and C are equal and nonzero and have the same sign, then

the graph is a circle

- If A and C are nonzero and have opposite signs, and are not equal

then the graph is a hyperbola.

- If either A or C is zero, then the graph is a parabola

* Now lets solve the problem

The equation is 4x² + 2y² - 8x + 16y - 52 = 0

∴ A = 4 and C = 2 ⇒ same sign and different values

∴ The equation is ellipse

* The standard form of the ellipse is

(x - h)²/a² + (y - k)²/b² = 1

- Lets try to make this form from the general form

- Group terms that contain the same variable, and move the

constant to the opposite side of the equation

∴ (4x² - 8x) + (2y² + 16y) = 52

- Factorize the coefficients of the squared terms

∴ 4(x² - 2x) + 2(y² + 8y) = 52

- Complete the square for x and y

# To make completing square

- Divide the coefficient of x (or y) by 2 and then square the answer

- Add and subtract this square number and form the bracket of

the completing the square

# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1

∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4

- Rewrite as perfect squares ⇒ 4(x -1)² - 4

# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16

∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32

- Rewrite as perfect squares ⇒ 2(y + 4)² - 32

∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52

∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52

∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88

∴ (x - 1)²/22 + (y + 4)²/44 = 1

8 0

3 years ago