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Brums [2.3K]
3 years ago
12

The Gilbert's are designing a rectangular patio. The patio has an area of 432 square feet. The width of the patio is 3/4 it's le

ngth. What is the length of the patio
Mathematics
1 answer:
ankoles [38]3 years ago
4 0
Represent the unknowns. 
<span>Let x = length </span>
<span>since the width is 3/4 of the length, </span>
<span>Let (3/4)x = width </span>

<span>Recall that the area of rectangle is just width multiplied by the length, </span>
<span>A = w * l </span>
<span>Substituting, </span>
<span>432 = (3/4)x * x </span>
<span>432 = (3/4)x^2 </span>
<span>432 * 4/3 = x^2 </span>
<span>576 = x^2 </span>
<span>Get the square root of both sides, </span>
<span>x = 24 feet (length) </span>
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Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4
Alik [6]

Answer:

\alpha=3

Step-by-step explanation:

<u>Equation of a Circle</u>

A circle of radius r and centered on the point (h,k) can be expressed by the equation

(x-h)^2+(y-k)^2=r^2

We are given the equation of a circle as

3x^2+3y^2-6\alpha x+12y-3\alpha=0

Note we have corrected it by adding the square to the y. Simplify by 3

x^2+y^2-2\alpha x+4y-\alpha=0

Complete squares and rearrange:

x^2-2\alpha x+y^2+4y=\alpha

x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4

(x-\alpha)^2+(y+2)^2=r^2

We can see that, if r=4, then

\alpha+\alpha^2+4=16

Or, equivalently

\alpha^2+\alpha-12=0

There are two solutions for \alpha:

\alpha=-4,\ \alpha=3

Keeping the positive solution, as required:

\boxed{\alpha=3}

8 0
3 years ago
How many different 4-digit numbers can be formed using the digits 2, 4, 5, 6, and 7 such that no digits repeat and the number is
quester [9]
If the last 2 digits of a number is divisble by 4, then the number is divisble by 4
see what combos are with ending with 2 digits divisible by 4
24
64
52
72



see their combos for the first  2 numbers
24 three other numbers to pick from so 3*2*1=6
64 three other numbers to pick from so 3*2*1=6
52 three other numbers to pick from so 3*2*1=6
72 three other numbers to pick from so 3*2*1=6

6*4=24

answer is 24 ways





7 0
3 years ago
Please help me with this question thank you
Fantom [35]
If the answer is an equation then it is:
x=(4y+15)/(5-3y)
8 0
3 years ago
Read 2 more answers
I need help with 1 and 2
oee [108]
1) -149, -1; -148, -2; -147, -3
2) No, according to the commutative property of addition, it does not matter the order they are put in.

Hope this helps!
6 0
3 years ago
Read 2 more answers
PLEASE HELP!! IM STUCK
lawyer [7]

Answer:

D) 1.9 meters

Step-by-step explanation:

a= -1.6, b=3.3, c=0.2

vertex is (1, 1.9)

6 0
3 years ago
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