All categories

2 years ago

If m(x) = x2 + 3 and n(x) = 5x + 9, which expression is equivalent to (mn)(x)?

Mathematics

2 answers:

ololo11 [35]2 years ago

8 0

Answer:

5x3+9x2+15x+27

Step-by-step explanation:

lisabon 2012 [21]2 years ago

8 0

Answer:

Step-by-step explanation:

You might be interested in

What is the answer to the equation: 8+10

alina1380 [7]

Answer:

18, the answer to 8+10 is 18, like you learn in 1st grade

3 0

3 years ago

Read 2 more answers

Need help finding out what 3x=y and x-2y = 10

sweet-ann [11.9K]

Answer:

x=-2, y=-6

Step-by-step explanation:

Simple substitution.

Since y is isolated in one of the equations already, you can plug it into the second equation.

x - 2(3x) = 10

x - 6x = 10

-5x = 10

x = -2

Sub. x = -2 into 3x = y:

3(-2) = y

y = -6

4 0

3 years ago

Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

3 0

3 years ago

A group of friends wants to go to the amusement park. They have no more than $320 to spend on parking and admission. Parking is

Hunter-Best [27]

A group of friends wants to go to the amusement park. They have no more than $320 to spend on parking and admission. Parking is $9.25, and tickets cost $28.25 per person, including tax. Write and solve an inequality which can be used to determine p, the number of people who can go to the amusement park.

___________________________________________

Please, give me some minutes to take over your question

________________________

They have no more than $320 to spend on parking and admission

320 ≥ 9.25 + 28.25*p

9.25 + 28.25*p ≤ 320

320- 9.25 ≥ 28.25*p

310.75/28.25 ≥ p

p ≤ 11

__________________________

Answer

The number of people who can go to the amusement park can be a maximum of 11 people (less than or equal to 11).

8 0

1 year ago

What is the y coordinate of point T write a decimal coordinate

Vikentia [17]

The y-coordinate of point T would be -4.5 the whole ordered paid would be (-3,-4.5).

5 0

3 years ago

Read 2 more answers