Mathematics, 24.07.2019 18:00 michaelgibsonsto

Stacy wants to build a patio with a small, circular pond in her backyard. the pond will have a 6-foot radius. she also wants to install tiles in the remaining area of the patio. the length of the patio is 13 feet longer than the width. if the cost of installing tiles is $1 per square foot, and the cost of installing the pond is $0.62 per square foot, then which of the following inequalities can be used to solve for the width, x, of the patio, if stacy can spend no more than $536 on this project?

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Answer from: shakkahdbwjsjs3068

First we are going to find the Area of the pond using the area of a circle formula: $A= \pi r^2$
where

is the area of the circle

is the radius of the circle
We know for our problem that the pond will have a 6-foot radius, so r=6

. Lets replace that value on our area formula:
$A= \pi r^2$
$A= \pi (6)^2$
$A=113.1ft^{2}$
We know that the cost of installing the pond is $0.62 per square foot, so lets multiply the area we just found by the cost:
Total cost of pund= (0.62)(113.1)=70.12

dollars

Now, let

be the width the rectangle, so its length will be x+13

. Remember that the area of a rectangle is width times length, so:
A=x(x+13)

Since the cost of installing ties is $1, the cost of installing ties in our rectangle will be x^2+13x dollars.

Stacy can spend no more than $536 on this project, so we can setup an inequality relating the cost of the pound and the cost of installing ties:
$70.12+x^2+13x \leq 536$
$x^2+13x \leq 465.88$

We can conclude that the inequality that can be used to fin the width,

, of the patio is $x^2+13x \leq 465.88$

Answer from: Quest

answer: i guess 105 degrees?

step-by-step explanation:

Answer from: Quest

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab in the y coordinate

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

x coordinate

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

y coordinate

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

x coordinate

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

y coordinate

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

x coordinate

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

y coordinate

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

x coordinate

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

y coordinate

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

x coordinate

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

y coordinate

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

x coordinate

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

y coordinate

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

x coordinate

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

y coordinate

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕

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