Answer:
The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)
Step-by-step explanation:
The standard form of the equation of a parabola is (y - k)² = 4p (x - h), where
- The vertex of the parabola is (h , k)
- The focus is (h + p, k)
∵ The vertex of the parabola is (3 , -2)
∴ h = 3 and k = -2
∵ The focus is (5 , -2)
∴ h + p = 5
- Substitute h by 3 to find p
∵ 3 + p = 5
- Subtract 3 from both sides
∴ p = 2
∵ The standard form of the equation of the parabola is (y - k)² = 4p (x - h)
- Substitute the values of h , k , and p in the equation
∴ (y - -2)² = 4(2) (x - 3)
∴ (y + 2)² = 8 (x - 3)
The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)
==> 225 is 75% of 300 .
==> 225 is 25% smaller than 300 .
==> 225 is 3/4 of 300 .
==> 300 is 4/3 the size of 225 .
==> 300 is (33 and 1/3)% bigger than 225 .
==> 225 is 75 less than 300 .
==> 225 has 10 fewer factors than 300 has.
==> 300 has 2.25 times as many factors as 225 has.
==> 225 and 300 have 5 common factors.
==> The greatest common factor of 225 and 300 is 75 .
Answer:
x=13
Step-by-step explanation:
1. divide both sides by 3
2. simplify: 4x-7=45
3. add 7 to both sides
4. 4x=52
5. divide both sides by 4
6. x=13
Answer:D
Step-by-step explanation:
-9+9=0
Answer:
896
Step-by-step explanation:
Let's talk first about how many 3 digit numbers there are. The first 3 digit number is 100 and the last is 999. So there are 999-100+1 numbers that are 3 digits long. That simplifies to 900.
Now let's find how many of those have a sum for the digits being 1, then 2 ? Then take that sum away from the 900 to see how many 3 digit numbers have the sum of their digits being more than 2.
3 digit numbers with sum of 1:
The first and only number is 100 since 1+0+0=1.
We can't include 010 or 001 because these aren't really three digits long.
3 digit numbers with sum of 2:
The first number is 101 since 1+0+1=2.
The second number is 110 since 1+1+0=2.
The third number is 200 since 2+0+0=2.
That's the last of those. We could only use 0,1, and 2 here.... Anything with a 3 in it would give us something larger than or equal to 3.
So there are 900-1-3 numbers who are 3 digits long and whose sum of digits is greater than 2.
This answer simplifies to 896.
