I need this one done too! Really need help, big brain fart.

i will give brainliest A person who weighs 240 pounds burns 180 calories per mile of running.A person who weighs______pounds, bu

Vedmedyk [2.9K]

Set up a ratio:

240/180 = X/36

Cross multiply:

240 * 36 = 180x

8640 = 180x

Divide both sides by 180:

X = 8640 / 180 = 48

The person would weigh 48 pounds.

7 0

3 years ago

Read 2 more answers

Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

SpyIntel [72]

$\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}$
$\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)$

When $x=3$ , you're left with

$147=49a_1\implies a_1=\dfrac{147}{49}=3$

When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

Adding the two equations together gives $-10=2a_5$ , or $a_5=-5$ . Subtracting them gives $2\sqrt2=2\sqrt2a_4$ , $a_4=1$ .

Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
$5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)$
$2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)$

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that $a_2x^4=2x^4$ and $a_3(-3)(-2)=6a_3=-6$ . These alone tell you that you must have $a_2=2$ and $a_3=-1$ .

So the partial fraction decomposition is

$\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}$

7 0

3 years ago

A rectangle has a perimeter of 60 units and one side of length 18 units. If it can be determined, what are the lengths, in units

ladessa [460]

Answer:

option B. 18,12,12

Step-by-step explanation:

perimeter= 60 units

(consider a rectangle with sides a,b,c & d in order)

a= 18 units (given)

c=18 units (since opp. sides of a rectangle are equal)

now the remaining length= 60-(18+18)

= 60 - 36

= 24

so the sum of the remaining sides, ie, b+d= 24

since b and d are equal (opp.sides of a rect.)

b=d=24/2=12

therefore, b=12; c=18; d=12

i really hope i'm clear...but if i'm not then please do ask...

8 0

3 years ago

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Students were surveyed about their favorite colors 1/4 preferred red, 1/8 preferred blue, 3/5 preferred green. If 15 students pr

const2013 [10]

Answer:

Let us assume the total number of students surveyed = x

Then

Number of students preferring red = x/4

Number of students preferring blue = x/8

Then

Number of students remaining = x - [(x/4) + (x/8)]

=x - [(2x + x)/8)

= x - (3x/8)

= (8x - 3x)/8

= 5x/8

Number of students preferring the color green = (3/5) * (5x/8)

= 3x/8

We also know that the total number of students preferring the color green is 15

So

3x/8 = 15

3x = 15 * 8

x = (15 * 8)/3

= 5 * 8

= 40

So in total 40 students were surveyed. I hope the procedure is clear to you.

Step-by-step explanation:

6 0

3 years ago

X + 1.5x - 0.75 = 73<br><br> what is the value of x?

Natasha_Volkova [10]

X + 1.5x - 0.75 = 73
2.5x - 0.75 = 73
2.5x = 73 + 0.75
2.5x = 73.75
x = 29.5

The answer is: x = 29.5.

5 0

4 years ago