Given that f(x) = 6x + 2 and g(x) = solve for g(f(1)).

The reciprocal parent function is translated 5 units right and 3 units up. Write an equation to represent the new function.

ladessa [460]

Answer:

The new function is $y=\frac{1}{x-5}+3$ , where x ≠ 5

Step-by-step explanation:

The reciprocal parent function is $f(x)=\frac{1}{x}$ , where x ≠ 0

The translation of f(x) to the right h units is f(x - h)

The translation of f(x) up k units is f(x) + k

The translation of f(x) to the right h units and up k units is f(x - h) + k

∵ The equation of the reciprocal parent function is $y=\frac{1}{x}$

∵ The function is translated 5 units right

∴ h = 5

- That means 5 is subtracted from x ⇒ (x - 5)

∵ The function is translated 3 units up

∴ k = 3

- That means y added by 3

∴ $y=\frac{1}{x-5}+3$

The new function is $y=\frac{1}{x-5}+3$ , where x ≠ 5

3 0

4 years ago

A group of people were asked if they had run a red light in the last year. 385 responded "yes", and 472 responded "no".

Dimas [21]

Answer:

44.9%

Step-by-step explanation:

you can find the probability by dividing the total number of people by the number of people who have run a red light:

385/857

simplify into a decimal:

0.449

convert into a percent to get your answer:

44.9%

3 0

3 years ago

Which of the following is an appropriate estimate of the distance, in miles, from the west coast to the east coast of the United

vlada-n [284]

D

10^-3 would make a decimal, so would 10^-1.
10^1 would be 30 miles, 10^3 would be 3 with 3 zeros ( 3000 miles) which would be most accurate

5 0

3 years ago

Pls help me if I cabbnnnnsbdhdhdjdjxjkxx

lakkis [162]

Answer:

33.49 mm³

Step-by-step explanation:

The formula of volume of sphere

$= \frac{4}{3} \pi {r}^{3}$

The volume of the sphere

$= \frac{4}{3} \times 3.14 \times {2}^{3}$

$= \frac{100.48}{3}$

$= 33.4933333...$

= 33.49 mm³ (rounded to the nearest hundredth)

3 0

3 years ago

An island is 1 mi due north of its closest point along a straight shoreline. A visitor is staying at a cabin on the shore that i

Elanso [62]

Answer:

The visitor should run approximately 14.96 mile to minimize the time it takes to reach the island

Step-by-step explanation:

From the question, we have;

The distance of the island from the shoreline = 1 mile

The distance the person is staying from the point on the shoreline = 15 mile

The rate at which the visitor runs = 6 mph

The rate at which the visitor swims = 2.5 mph

Let 'x' represent the distance the person runs, we have;

The distance to swim = $\sqrt{(15-x)^2+1^2}$

The total time, 't', is given as follows;

$t = \dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}$

The minimum value of 't' is found by differentiating with an online tool, as follows;

$\dfrac{dt}{dx} = \dfrac{d\left(\dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}\right)}{dx} = \dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} }$

At the maximum/minimum point, we have;

$\dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} } = 0$

Simplifying, with a graphing calculator, we get;

-4.72·x² + 142·x - 1,070 = 0

From which we also get x ≈ 15.04 and x ≈ 0.64956

x ≈ 15.04 mile

Therefore, given that 15.04 mi is 0.04 mi after the point, the distance he should run = 15 mi - 0.04 mi ≈ 14.96 mi

$t = \dfrac{14.96}{6} +\dfrac{\sqrt{(15-14.96)^2+1^2}}{2.5} \approx 2..89$

Therefore, the distance to run, x ≈ 14.96 mile

6 0

3 years ago