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2 years ago

What is the inverse of the function f(x) = 2x + 1?|

Mathematics

1 answer:

padilas [110]2 years ago

6 0

Answer:

1st option

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2x ( divide both sides by 2 )

$\frac{y-1}{2}$ = x

Change y back into terms of x with x being the inverse h(x)

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

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It takes Dariya 35 seconds to download 5 songs from the Internet. How can the number of seconds it would take Dariya to download

netineya [11]

Answer:

Step-by-step explanation:

35/5=7

7x7=49 seconds

6 0

3 years ago

Read 2 more answers

Solve for b:<br><br> 6b+14 = -7-b

vladimir2022 [97]

Answer:

b = -3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

6b+14=−7−b

6b+14=−7+−b

6b+14=−b−7

Step 2: Add b to both sides.

6b+14+b=−b−7+b

7b+14=−7

Step 3: Subtract 14 from both sides.

7b+14−14=−7−14

7b=−21

Step 4: Divide both sides by 7.

$\frac{7b}{7} = \frac{-21}{7}$

b= -3

3 0

3 years ago

Read 2 more answers

Please Help ASAP! Will name Brainliest! Question: Minimize the objective function P = 5x + 8y for the given constraints. x ≥ 0 y

maksim [4K]

Answer:

Option D.

Step-by-step explanation:

Minimize the objective function P = 5x + 8y for the given constraints.

$x\geq 0,y\geq 0$

$2x+3y\geq 15$

$3x+2y\geq 15$

The related equations of above inequalities are

$2x+3y=15$

$3x+2y=15$

For $2x+3y=15$ ,

x y

0 5

7.5 0

Plot (0,5) and (7.5,0) and join them by straight line.

For $3x+2y=15$ ,

x y

0 7.5

5 0

Plot (0,7.5) and (5,0) and join them by straight line.

Check the inequalities for (0,0).

$2(0)+3(0)\geq 15\Rightarrow 0\geq 15$ False

$3(0)+2(0)\geq 15\Rightarrow 0\geq 15$ False

It means both lines are solid lines and shaded region for each lies opposite side of (0,0).

From the below graph it is clear that the vertices of feasible region are (0,7.5), (3,3), (7.5,0).

Point P = 5x + 8y

(0,7.5) P=5(0)+8(7.5)=60

(3,3) P=5(3)+8(3)=15+24=39

(7.5,0) P=5(7.5)+8(0)=37.5 (Minimum)

So, minimum value is 37.5.

Therefore, the correct option is D.

3 0

3 years ago

5. Solve using any method.<br> y = -x + 8<br> y=x+4

vlada-n [284]

Answer:

Step-by-step explanation:

$\bold{ELIMINATION\ METHOD}\\\\\left\{\begin{array}{ccc}y=-x+8\\y=x+4&\TEXT{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}y=-x+8\\-y=-x-4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad0=-2x+4\qquad\text{add}\ 2x\ \text{to both sides}\\.\qquad2x=4\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=2}\\\\\text{Put it to the second equation}\\y=2+4\\\boxed{y=6}$

$\bold{SUBSTITUTION\ METHOD}\\\\\left\{\begin{array}{ccc}y=-x+8&(1)\\y=x+4&(2)\end{array}\right\\\\\text{Substitute (1) to (2)}\\\\-x+8=x+4\qquad\text{subtract 8 from both sides}\\-x=x-4\qquad\text{subtract}\ x\ \text{from both sides}\\-x-x=-4\\-2x=-4\qquad\text{divide both sides by (-2)}\\\boxed{x=2}\\\\\text{Put it to the second equation}\\y=2+4\\\boxed{y=6}$

7 0

3 years ago

A person standing on a moving walkway travels 75 feet in 25 seconds. What equation represents this relationship? How many feet w

Goryan [66]

Answer: B

Step-by-step explanation: divide 75 by 25 to find how many feet you travel in 1 second (75/25=3) then you take 3 times 10 to see how many feet you travel in 10 seconds (3x10=30).

3 0

3 years ago