Determine the vertex of the quadratic function represented by f(x)=(x+3)2−4f(x)=(x+3)

-x+5y=5 in function notation

Aliun [14]

Answer:

$y = f(x) = \frac{1}{5}x + 1$

Step-by-step explanation:

The function notation of a linear function is given by y = f(x) = ax + b.

Now, the given equation is - x + 5y = 5

So, we have to arrange it for the function notation.

Now, - x + 5y = 5

⇒ 5y = x + 5

⇒ $y = \frac{1}{5}(x + 5)$

⇒ $y = \frac{1}{5}x + 1$

Therefore, the function notation of the given equation will be

$y = f(x) = \frac{1}{5}x + 1$ (Answer)

7 0

3 years ago

Ben is 12 years older than Ishaan.Ben and Ishaan first met two years ago.Three years ago,Ben was 4 times as old as Ishaan.

djyliett [7]

Ben is 19 and Ishaan is 7.

If 3 years ago Ben was 4 times the age of Ishann, their ages could have been any of the following:

1. Ben is 4 and Ishaan is 1

2. Ben is 8 and Ishaan is 2

3. Ben is 12 and Ishaan is 3

4. Ben is 16 and Ishaan is 4

And so on.

Next add 3 to both ages, to show current age.

1. Ben is 7 and Ishaan is 4

2. Ben is 11 and Ishaan is 5

3. Ben is 15 and Ishaan is 6

4. Ben is 19 and Ishaan is 7

Ben is currently 12 years older than Ishaan. To find the difference, take Ben's age and subtract Ishaan's age.

1. 7 - 4 = 3

2. 11 - 5 = 6

3. 15 - 6 = 9

4. 19 - 7 = 12

Thus meaning Ben is 19 and Ishaan is 7.

I hope this helps!

4 0

3 years ago

Which expression is equivalent to (p^10r^−5)^1/5 ?

meriva

Answer:

p^2/r

Step-by-step explanation:

An equivalent expression is the expression in simplest form. Here apply exponent rules by multiplying the exponents of each term by 1/5.

$(p^{10}r^{-5})^{\frac{1}{5}}\\\\(p^{\frac{10}{5}}r^{\frac{-5}{5}})\\\\p^2r^{-1}\\\\\frac{p^2}{r}$

3 0

3 years ago

Please help me with this

dalvyx [7]

Answer:

Step-by-step explanation:

12/C-8d²

The numerator, which is 12 do not need any simplifying. some we center more on the denominator, c-8d².

C-8d² = 1 /C^8 × d²

=D²/C^8

Therefore,

12÷D²/C^8= 12 × C^8/D²

=12C^8/D²

4 0

3 years ago

Classify each of the power functions based on their end behavior (increasing or decreasing) as x = ∞

Svetlanka [38]

Answer: right side behavior:

f(x) is Decreasing

g(x) is Increasing

h(x) is Increasing

j(x) is Decreasing

Step-by-step explanation:

The rules for end behavior are based on 2 criteria: Sign of leading coefficient and Degree of polynomial

Sign of leading coefficient (term with greatest exponent):

If sign is positive, then right side is increasing
If sign is negative, then right side is decreasing

Degree of polynomial (greatest exponent of polynomial:

If even, then end behavior is the same from the left and right
If odd, then end behavior is opposite from the left and right

f(x) = -2x²

Sign is negative so right side is decreasing
Degree is even so left side is the same as the right side (decreasing)

as x → +∞, f(x) → +∞ Decreasing

as x → -∞, f(x) → -∞ Decreasing

g(x) = (x + 2)³

Sign is positive so right side is increasing
Degree is odd so left side is opposite of the right side (decreasing)

as x → +∞, f(x) → +∞ Increasing

as x → -∞, f(x) → -∞ Decreasing

$h(x)=-1+x^{\frac{1}{2}}\implies h(x)=x^{\frac{1}{2}}-1$

Sign is positive so right side is increasing
Degree is an even fraction so left side is opposite of the right side as it approaches the y-intercept (-1)

as x → +∞, f(x) → +∞ Increasing

as x → -∞, f(x) → -1 Decreasing to -1

$j(x)=\dfrac{1}{2}(-x)^5\implies j(x)=\dfrac{1}{2}(-1)^5(x)^5\implies j(x)=-\dfrac{1}{2}x^5$

Sign is negative so right side is decreasing
Degree is odd so left side is opposite of the right side (increasing)

as x → +∞, f(x) → +∞ Decreasing

as x → -∞, f(x) → -∞ Increasing

6 0

4 years ago