Answer:
Let's talk through this a one step at a time.
*Since f(x) is concave-up with its vertex on the x-axis, we know f(x) ≥ 0.
*We also know that when we shift a function's domain by a positive number, we shift the function left and when we shift a function's domain by a negative number, we shift the function right. So f(x-5) is f(x) shifted to the right by 5.
*At this point, f(x-5) has its vertex at (5,0).
*When we negate f(x-5), the parabola becomes concave down yet the vertex remains at (5,0). Now we're at -f(x-5). At this point we have -f(x-5)≤0 with a range (-∞,0]
*If we add 2 to create g(x)=2-f(x-5), then we have a concave down parabola with its vertex shifted up by 2, at (5,2). So, g(x) is concave down with its vertex at (5,2). Hence
The option D) x + x+2 + x+4 = 53 represents the exact equation of sum of three consecutive odd integers which is equal to 53.
<u>Step-by-step explanation:</u>
The sum of the three consecutive odd integers = 53
<u>To frame the equation :</u>
- Let us consider any of the three consecutive odd integers.
- Let us take 1,3,5 as the three consecutive odd integers.
Assume the first odd integer as 'x'. In this case, (x=1)
- The second consecutive odd integer is 3.
- The difference between 1 and 3 is 2.
Therefore, the second consecutive odd integer is x+2.
- The third consecutive odd integer is 5.
- The difference between 1 and 5 is 4.
Therefore, the third consecutive odd integer is x+4.
This means that, the sum of any three consecutive odd integers are given as x + x+2 + x+4.
Given that,
Sum of the three consecutive odd integers is 53.
The first odd integer + second odd integer + third odd integer = 53
x + x+2 + x+4 = 53.
The option D) x + x+2 + x+4 = 53 represents the exact equation of sum of three consecutive odd integers which is equal to 53.
Answer:
f(x) = -8/3(x+3)+8
a = -8/3
b = technically equals -3 but when we plug it in it gets turned into 3 *double negative
k = 8
Step-by-step explanation:
Vertex: (h,k)
Use the points (0,0) and (-3,8) to find the slope
y2-y1/x2- x1
1feet = 12 incches so 12times by 9=108 inches
We have the following functions:
log2x=5
log10x=3
log4x=2
log3x=1
log5x=4
Let's rewrite each function to solve for x:
x=2^5=32
x=10^3=1000
x=4^2=16
x=3^1=3
x=5^4=625
Answer:
Matching each function with the solution we have:
log2x=5 ----------->32
log10x=3---------->1000
log4x=2------------>16
log5x=4------------>625
