Answer:
d = 5t + 20
Step-by-step explanation:
d represents the distance and t represents the time, in hours
Let he equation which model this situation ⇒ d = a t + b
Where a and b are constant.
Let the gas station is the starting point
So, at gas station t = 0 , d = 20
∴ 20 = 0 * a + b ⇒ b = 20
When he reaches home 2 hours later notes that he has traveled 30 miles.
and with substituting with b = 20
∴ 30 = 2 * a + 20
2a = 30 - 20 = 10 ⇒ a = 10/2 = 5
∴ d = 5t + 20
The equations that can be used to model this situation <u>d = 5t + 20</u>
<span>f(x)=<span>x2</span>−1</span>That means to find the value of the function at any value of x, we square x and subtract 1. If <span>x=2a</span>, we square <span>2a</span> and subtract 1:<span>f(2a)=(2a<span>)2</span>−1=4<span>a2</span>−1</span>Now, we know that <span>f(2a)=35</span>so we can find the value of a:<span>f(2a)=(2a<span>)2</span>−1=4<span>a2</span>−1=35</span><span>4<span>a2</span>−1+1=35+1</span><span>4<span>a2</span>=36</span><span><span>a2</span>=9</span><span><span>a=±3</span></span>
Answer:
(x - 5)² + (y + 3)² = 16
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (5, - 3) and r = 4, so
(x - 5)² + (y - (- 3))² = 4², that is
(x - 5)² + (y + 3)² = 16
If you need clarification just reply back so I can help
The solution is when they intersect. So to find the answer, set each equation equal to each and solve:
-2x + 3 = x^2 -6x + 3
3 = x^2 -4x + 3
0 = x^2 -4x
0 = x(x-4)
So the solutions are x = 0 and x = 4
Plug in these values into the easier equation to solve for the y's
x = 0 into -2x + 3 gives y = 3
So one solution is (0, 3)
x = 4 into -2x + 3 gives y = -5
So the second solution is (4, -5)
