Describe a situation with an output of area in square feet that can be modeled using the function f(x) = (x)(2x + 5).

2 answers:

4 0

The area of a rectangular garden can be represented by the function
f(x) = x(2x + 5)
Find the area if the length, x, is 3 feet.

BARSIC [14]3 years ago

4 0

The area is length times width
width=x and length is z

if the length is 5 more than twice the width, express the area in terms of the width

so then
f(x)=xz
z=5+2x or 2x+5
f(x)=(x)(2x+5)

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What add's up to 5 and multiplies to -36

Masteriza [31]

X, y - the numbers

The numbers add up to 5 and multiply to -36.
$x+y=5 \\
xy=-36 \\ \\
y=5-x \\
xy=-36 \\ \\
\hbox{substitute 5-x for y in the second equation:} \\
x(5-x)=-36 \\
5x-x^2=-36 \\
-x^2+5x+36=0 \\
-x^2-4x+9x+36=0 \\
-x(x+4)+9(x+4)=0 \\
(-x+9)(x+4)=0 \\
-x+9=0 \ \lor \ x+4=0 \\
x=9 \ \lor \ x=-4 \\ \\
y=5-x \\
y=5-9 \ \lor \ y=5-(-4) \\
y=-4 \ \lor \ y=9 \\ \\
(x,y)=(9,-4) \hbox{ or } (x,y)=(-4,9)$

The numbers are -4 and 9.

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3 years ago

Given cosα = −3/5, 180 < α < 270, and sinβ = 12/13, 90 < β < 180

torisob [31]

I got

$- \frac{6 3}{65}$

What we know

cos a=-3/5.

sin b=12/13

Angle A interval are between 180 and 270 or third quadrant

Angle B quadrant is between 90 and 180 or second quadrant.

What we need to find

Cos(b)

Cos(a)

What we are going to apply

Sum and Difference Formulas

Basics Sine and Cosines Identies.

1. Let write out the cos(a-b) formula.

$\cos(a - b) = \cos(a) \cos(b) + \sin(a) \sin(b)$

2. Use the interval it gave us.

According to the given, Angle B must between in second quadrant.

Since sin is opposite/hypotenuse and we are given a sin b=12/13. We. are going to set up an equation using the pythagorean theorem.

${12}^{2} + {y}^{2} = {13}^{2}$

$144 + {y}^{2} = 169$

$25 = {y}^{2}$

$y = 5$

so our adjacent side is 5.

Cosine is adjacent/hypotenuse so our cos b=5/13.

Using the interval it gave us, Angle a must be in the third quadrant. Since cos is adjacent/hypotenuse and we are given cos a=-3/5. We are going to set up an equation using pythagorean theorem,

$( - 3) {}^{2} + {x}^{2} = {5}^{2}$