Let's take the 2 numbers are a and b.
a + b =14
if a > b
a - 3b = -2
Subtract both numbers
4b = 16
b = 4
lesser number is 4.
False
because
r=2
so
an=a1r^(n-1)
a4=(-1)(2^(4-1))
=(-1)(2^3)
=(-1)(8)
=-8
so a4 equals -8 not -6
Answer:
y = 1/12 (x − 5)²
Step-by-step explanation:
We can solve this graphically without doing calculations.
The y component of the focus is y = 3. Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient. That narrows the possible answers to A and C.
The x component of the focus is x = 5. Since this is above the vertex, we know the x component of the vertex is also x = 5.
So the answer is A. y = 1/12 (x−5)².
But let's say this wasn't a multiple choice question and we needed to do calculations. The equation of a parabola is:
y = 1/(4p) (x − h)² + k
where (h, k) is the vertex and p is the distance from the vertex to the focus.
The vertex is halfway between the focus and the directrix. So p is half the difference of the y components:
p = (3 − (-3)) / 2
p = 3
k, the y component of the vertex, is the average:
k = (3 + (-3)) / 2
k = 0
And h, the x component of the vertex, is the same as the focus:
h = 5
So:
y = 1/(4×3) (x − 5)² + 0
y = 1/12 (x − 5)²
Answer: B and D
Step-by-step explanation:
First, solve the terms inside of the parenthesis. As a general rule, whenever you multiply two terms that have the same base, you can add their exponents.
Applying this rule, the base in the problem is 6, and the exponents are 3 and -4. The sum of 3 and -4 leaves -1. Therefore, this is one of our solutions:
When you have an exponential term raised to another exponent, you can simply multiply the exponents. In the previous solution given above, multiply -1 and -3 to get 3. Therefore our second solution is:
Answer:
9x + 5y = 29 ........... (1) and
3x + y = 7 ........... (2)
Each game of ping pong requires 1 number of token and each game of pinball requires 4 number of tokens.
Step-by-step explanation:
Let, each game of ping pong requires x number of tokens and each game of pinball requires y number of tokens.
So, from the given conditions we can write
9x + 5y = 29 ........... (1) and
3x + y = 7 ........... (2)
Now, solving equations (1) and (2) we get,
9x + 5(7 - 3x) = 29
⇒ 35 - 6x = 29
⇒ 6x = 6
⇒ x = 1 token.
Now, putting x = 1 in equation (2) we get,
3 + y = 7
⇒ y = 4 tokens.
So, each game of ping pong requires 1 number of token and each game of pinball requires 4 number of tokens. (Answer)
