<u>Answer:</u>
The distance from earth to sun is 387.5 times greater than distance from earth to moon.
<u>Solution:</u>
Given, the distance from Earth to the sun is about 
The distance from Earth to the Moon is about 
We have to find how many times greater is the distance from Earth to the Sun than Earth to the Moon?
For that, we just have to divide the distance between earth and sun with distance between earth to moon.
Let the factor by which distance is greater be d.
Hence, the distance from earth to sun is 387.5 times greater than distance from earth to moon.
The answer to this is 5a-7
Answer:
(4, -3)
Step-by-step explanation:
You just divide each coordinate by 3.
Answer: First half was 24 minutes
Step-by-step explanation:
Let the time taken to finish the second half be y.
Since the student used 2/3 of the second half time to finish the first half, first half = 2/3 × y = 2y/3
The entire exam is an hour which equals 60 minutes
First half + Second half = 60minutes
Note that first half is denoted as 2y/3 and second half is denoted by y.
2y/3 + y = 60
5y/3 = 60
Cross multiply
5y = 60 × 3
5y = 180
y = 180/5
y = 36
Second half took 36 minutes
Since first half is 2y/3, it will be:
(2×36) / 3
= 72/3
= 24minutes
First half took 24 minutes.
Answer:
We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
