a patio is shaped like a golden rectangle. it's length ( the longer side) is 16ft. what is the patios width? write your answer in simplified radical form.

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Answer 1

Answer: $a\ golden\ rectangle:\ \ \ (a+b)/(a)= (a)/(b) \n----------------\na+b=16\ [ft]\ \ \ \ \Rightarrow \ \ \ b=16-a\n\n (16)/(a) = (a)/(16-a) \ \ \ \ \Leftrightarrow\ \ \ 16(16-a)=a^2\n\na^2+16a-256=0\n\n\ \ \ \Rightarrow\ \ \ \Delta=16^2-4\cdot(-256)=256\cdot5\ \ \ \Rightarrow\ \ \ √(\Delta) =16 √(5) \n\na_1= (-16-16 √(5) )/(2) =-8-8 √(5) <0\n\na_2= (-16+16 √(5) )/(2) =-8+8 √(5)=8( √(5) -1)>0\n\n$

$a=8( √(5) -1)\ \ \Rightarrow\ \ b=16-8( √(5) -1)=16-8√(5) +8=8(3- √(5) )\n\nAns.\ This\ golden\ ractangle\ has\ sides:\n.\ \ \ \ \ \ \ 8( √(5) -1)\ [ft]\ \ and\ \ 8(3- √(5) )\ [ft]$

-6

Step-by-step explanation:

$Use\n\n(a^n)^m=a^(nm)\n\n(a^n)/(a^m)=a^(n-m)\n------------------\n\n((x^(25))^(-6))/((x^(-3))^(48))=(x^((25)(-6)))/(x^((-3)(48)))=(x^(-150))/(x^(-144))=x^(-150-(-144))=x^(-150+144)=x^(-6)$

A bathtub is being filled with water. After 3 minutes 4/5 of the tub is full. Assuming the rate is constant, how much longer will it take to fill the tub?

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$3\ min\ ----->\frac45\nx\ min\ ----->1\nx\ \cdot\ \frac45=1\cdot3\n\frac45x=3\ /\ : \frac45\nx=3\ :\ \frac45\nx=\frac31\ \cdot\ \frac54\nx=(15)/(4)\nx=3\frac34\ [min]\nx=3\ min\ 45\ sec$

answer: 3 min 45 sec

$3\ min - \frac45\n x\ min - 1\n \n 3=\frac45 x\ /:\frac45\n (3)/(\frac45)=x\n x=3\cdot \frac54=\frac{15}4=3\frac34\ min=3\ min\ 45\ s$

Consider that 2 points are given on a scatter plot that models a negative correlation.Which situation is possible?

I. The first point has a larger x-value and a smaller y-value than the second point.

II. The first point has a larger x-value and a larger y-value than the second point.

III. The first point has a smaller x-value and a larger y-value than the second point.

Answers

Answer:

The answer would actually be D) I,II, and III

Step-by-step explanation:

i just did it on usa test prep

Answer:

The answer would be III. Hope I'm helpful.

In the last basketball game, the panthers scored 63 points. This was seven times the number of points that Reilly scored. Write and solve an equation to find the number of points Reilly scored

Answers

9
In this question all you have to do is divide 63 by 7.

you would first have to do the opposite of seven times which would be division, this would lead to being 63÷7, with this your answer would be 9, you can also check your work by doing 7×9 and getting 63.

Find the GCF of each number.

75 ¢, 25¢, $1.50, $3.00

Answers

So,

To find the G.C.F. of $0.75, $0.25, $1.50, and $300,

Think of them as 75, 25, 150, and 300.

Find the prime factored form (P.F.F.) of each number.

P.F.F. of 75: 3*5*5

P.F.F. of 25: 5*5

P.F.F. of 150: 2*3*5*5

P.F.F. of 300: 2*2*3*5*5

Find common groups.

5*5 is in all of them.

5(5) = 25

25 is the G.C.F. of 75, 25, 150, and 300 ($.75, $.25, $1.50, and $3.00).

the gcf of 75 cents, 25 cents ,$1.50 and $3.00 is 25 cents

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a patio is shaped like a golden rectangle. it's length ( the longer side) is 16ft. what is the patios width? write your answer in simplified radical form.

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