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2 years ago

Combine like terms: 80 + 50m + 65 + 40m

Mathematics

1 answer:

Nuetrik [128]2 years ago

3 0

Answer:

90m+145

Step-by-step explanation:

80 + 50m + 65 + 40m

90m+145

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At a price of $p the demand x per month (in multiples of 100) for a new piece of software is given by x 2 + 2xp + 4p 2 = 5200. B

WINSTONCH [101]

Answer:

The rate of decrease in demand for the software when the software costs $10 is -100

Step-by-step explanation:

Given the function of price $p the demand x per month as,

$x^{2}+2xp+4p^{2}=5200$

Also given that, the price is increasing at the rate of 70 dollar per month.

$\therefore \dfrac{dp}{dt}=70$ .

To find rate of decrease in demand, differentiate the given function with respect to t as follows,

$\dfrac{d}{dt}\left(x^2+2xp+4p^2\right)=\dfrac{d}{dt}\left(5200\right)$

Applying sum rule and constant rule of derivative,

$\dfrac{d}{dt}\left(x^2\right)+\dfrac{d}{dt}\left(2xp\right)+\dfrac{d}{dt}\left(4p^2\right)=0$

Applying constant multiple rule of derivative,

$\dfrac{d}{dt}\left(x^2\right)+2\dfrac{d}{dt}\left(xp\right)+4\dfrac{d}{dt}\left(p^2\right)=0$

Applying power rule and product rule of derivative,

$2x^{2-1}\dfrac{dx}{dt}+2\left(x\dfrac{dp}{dt}+p\dfrac{dx}{dt}\right)+4\left(2p^{2-1}\right)\dfrac{dp}{dt}=0$

Simplifying,

$2x\dfrac{dx}{dt}+2\left(x\dfrac{dp}{dt}+p\dfrac{dx}{dt}\right)+8p\dfrac{dp}{dt}=0$

Now to find the value of x, substitute the value of p=$10 in given equation.

$x^{2}+2x\left(10\right)+4\left(10\right)^{2}=5200$

$x^{2}+20x+400=5200$

Subtracting 5200 from both sides,

$x^{2}+20x+400-5200=0$

$x^{2}+20x-4800=0$

To find the value of x, split the middle terms such that product of two number is 4800 and whose difference is 20.

Therefore the numbers are 80 and -60.

$x^{2}+80x-60x-4800=0$

Now factor out x from $x^{2}+80x$ and 60 from $60x-4800$

$x\left(x+80\right)-60\left(x+80\right)=0$

Factor out common term x+80,

$\left(x+80\right)\left(x-60\right)=0$

By using zero factor principle,

$\left(x+80\right)=0$ and $\left(x-60\right)=0$

$x=-80$ and $x=60$

Since demand x can never be negative, so x = 60.

Now,

$2x\dfrac{dx}{dt}+2\left(x\dfrac{dp}{dt}+p\dfrac{dx}{dt}\right)+8p\dfrac{dp}{dt}=0$

Substituting the value.

$2\left(60\right)\dfrac{dx}{dt}+2\left(60\left(70\right)+10\dfrac{dx}{dt}\right)+8\left(10\right)\left(70\right)=0$

Simplifying,

$120\dfrac{dx}{dt}+2\left(4200+10\dfrac{dx}{dt}\right)+5600=0$

$120\dfrac{dx}{dt}+8400+20\dfrac{dx}{dt}+5600=0$

Combining common term,

$140\dfrac{dx}{dt}+14000=0$

Subtracting 14000 from both sides,

$140\dfrac{dx}{dt}=-14000$

Dividing 140 from both sides,

$\dfrac{dx}{dt}=-\dfrac{14000}{140}$

$\dfrac{dx}{dt}=-100$

Negative sign indicates that rate is decreasing.

Therefore, the rate of decrease in demand of software is -100

6 0

3 years ago

If matrix A has dimensions 3 x 2 and matrix B has dimensions 3 x 2, can matrix A and matrix B be multiplied?

Charra [1.4K]

Matrix A has 3 rows, 2 columns
Matrix B has 3 rows, 2 columns

The number of columns in matrix A (which is 2) does not match up with the number of rows in matrix B (which is 3).

So the matrix multiplication A*B is undefined. We cannot multiply the matrices.

8 0

3 years ago

Read 2 more answers

The length of the base of a rectangle is 6 less than 3 times the width. The perimeter of the rectangle is 52 inches. What is the

vivado [14]

Answer:

The rectangle has a width of 18 inches and a height length of 8 inches.

Step-by-step explanation:

The perimeter of a rectangle is described by the equation:

$p = 2w + 2l$

where <em>l</em> is width, <em>h</em> is height, and <em>p</em> is perimeter.

We're also told that the total perimeter is 52 inches.

We're also told that the length is six inches less than three times the width. We can express that as $w = 3l - 6$ .

We can plug that definition of w into the perimeter equation to find the length:

$p = 2w + 2l\\52 = 2(3l - 6) + 2 * l\\52 = 6l - 12 + 2l\\52 + 12 = 8l\\8l = 64\\l = 64/8\\l = 8$

Now we can take that and the given perimeter, and substitute those into the perimeter equation to find the width:

$p = 2w + 2l\\52 = 2w + 2(8)\\52 = 2w + 16\\36 = 2w\\w = 36 / 2\\w = 18$

So the width is 18

7 0

3 years ago

Given f of x is equal to the quantity x minus 4 end quantity divided by the quantity x squared plus 13x plus 36 end quantity, wh

gavmur [86]

The simplified expression of the function $f(x) =\dfrac{x-4}{x^2+13x+36}$ is

$f(x) = \dfrac{x-4}{(x+9)(x+4)}$ . f(x) is increasing for all x > –4.The correct answer is option C.

<h3>What is a function?</h3>

A function is defined as a relation between the set of inputs having exactly one output each.

The function expression is given as:

$f(x) =\dfrac{x-4}{x^2+13x+36}$

Expand the denominator

$f(x) =\dfrac{x-4}{x^2+4x +9x+36}$

Factorize the denominator

$f(x) =\dfrac{x-4}{x(x+4)+9(x+4)}$

Factor out x + 9

$f(x) = \dfrac{x-4}{(x+9)(x+4)}$

The simplified expression of the function $f(x) =\dfrac{x-4}{x^2+13x+36}$ is

$f(x) = \dfrac{x-4}{(x+9)(x+4)}$ . f(x) is increasing for all x > –4

Combine like terms: 80 + 50m + 65 + 40m​

Combine like terms: 80 + 50m + 65 + 40m