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3 years ago

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An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 340 feet of antique

picket fencing are used to enclosed the garden find the dimensions of the garden

1 answer:

NNADVOKAT [17]3 years ago

7 0

Answer:

l=102 feet, w=68 feet

Step-by-step explanation:

Let w=width and l=length

P=2l + 2w

And we know that w=2/3l

So, using substitution...

340=2l + 2(2/3l)

340=2l + 4/3l

340=6/3l + 4/3l

340=10/3l (now multiply both sides by 3 to get rid of fraction)

1020=10l

So l=102

Now plug in to get w

2(102)+2w=340

204+2w=340

2w=136

w=68

Now check:

2(102)+2(68)=

204+136=

340 It works!

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Honestly, I'm trying my best to solve this but my Math XL is being so rude.

Valentin [98]

<h3>Answer: 19</h3>

==============================================================

Explanation:

T is the midpoint of PQ, which means T splits PQ into two equal parts. Those parts being PT and TQ.

Set them equal to each other and solve for x.

PT = TQ

3x+7 = 7x-9

3x-7x = -9-7

-4x = -16

x = -16/(-4)

x = 4

So,

PT = 3x+7 = 3*4+7 = 19

TQ = 7x-9 = 7*4-9 = 19

Both PT and TQ are 19 units long to help confirm the answer.

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2 years ago

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What is the greatest common factor of 19x7 and 3x5?

Olenka [21]

The greatest common factor of 19x7 AND 3x5 is: X5

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3 years ago

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DiKsa [7]

Answer:

See Below.

Step-by-step explanation:

Problem 1)

We want to simplify:

$\displaystyle \frac{a+2}{a^2+a-2}+\frac{3}{a^2-1}$

First, let's factor the denominators of each term. For the second term, we can use the difference of two squares. Hence:

$\displaystyle =\frac{a+2}{(a+2)(a-1)}+\frac{3}{(a+1)(a-1)}$

Now, create a common denominator. To do this, we can multiply the first term by (<em>a</em> + 1) and the second term by (<em>a</em> + 2). Hence:

$\displaystyle =\frac{(a+2)(a+1)}{(a+2)(a-1)(a+1)}+\frac{3(a+2)}{(a+2)(a-1)(a+1)}$

Add the fractions:

$\displaystyle =\frac{(a+2)(a+1)+3(a+2)}{(a+2)(a-1)(a+1)}$

Factor:

$\displaystyle =\frac{(a+2)((a+1)+3)}{(a+2)(a-1)(a+1)}$

Simplify:

$\displaystyle =\frac{a+4}{(a-1)(a+1)}$

We can expand. Therefore:

$\displaystyle =\frac{a+4}{a^2-1}$

Problem 2)

We want to simplify:

$\displaystyle \frac{1}{(a-b)(b-c)}+\frac{1}{(c-b)(a-c)}$

Again, let's create a common denominator. First, let's factor out a negative from the second term:

$\displaystyle \begin{aligned} \displaystyle &= \frac{1}{(a-b)(b-c)}+\frac{1}{(-(b-c))(a-c)}\\\\&=\displaystyle \frac{1}{(a-b)(b-c)}-\frac{1}{(b-c)(a-c)}\\\end{aligned}$

Now to create a common denominator, we can multiply the first term by (<em>a</em> - <em>c</em>) and the second term by (<em>a</em> - <em>b</em>). Hence:

$\displaystyle =\frac{(a-c)}{(a-b)(b-c)(a-c)}-\frac{(a-b)}{(a-b)(b-c)(a-c)}$

Subtract the fractions:

$\displaystyle =\frac{(a-c)-(a-b)}{(a-b)(b-c)(a-c)}$

Distribute and simplify:

$\displaystyle =\frac{a-c-a+b}{(a-b)(b-c)(a-c)}=\frac{b-c}{(a-b)(b-c)(a-c)}$

Cancel. Hence:

$\displaystyle =\frac{1}{(a-b)(a-c)}$

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3 years ago

I wonder if I did #9 right and I’m having trouble with #10

yaroslaw [1]

Let's see....

QUESTION: Add. Write your answer as a mixed number in simplest form.

$6 \frac{7}{9} + 9 \frac{8}{9}$

1. Rewriting our equation with parts separated

<span><span> $=6+ \frac{7}{9} +9+ \frac{8}{9}$

</span></span>2. Solving the whole number parts

<span> $6+9=15$

</span>3. Solving the fraction parts

<span><span> $\frac{7}{9} + \frac{8}{9} = \frac{15}{9}$

</span></span>4. Reducing the fraction part, 15/9,

<span><span> $\frac{15}{9} = \frac{5}{3}$

</span></span>5. Simplifying the fraction part, 5/3,

<span><span> $\frac{5}{3} = 1\frac{2}{3}$

</span></span>6. Combining the whole and fraction parts

<span><span><span> $15+1+ \frac{2}{3} =16 \frac{2}{3}$

ANSWER: $16\frac{2}{3}$

Hope that helps!
</span></span></span>

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