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Alex_Xolod [135]
3 years ago
12

The length of a rectangle is 2 foot less than 3 times its width. Find the the dimensions of this rectangle if the area is 96 squ

are feet.
Mathematics
1 answer:
Xelga [282]3 years ago
6 0
For example,area = a, length = l, width = w
First we write two equations. The easier equation is the area equation, which we know to be
a = l x w
So that the first equation is : 
<span>96 = l x w </span>

we make the second equation of the following statements :
<em>The length of a rectangle is 2 foot less than 3 times its width.</em>
<span>so it becomes :
l = 3w - 2
</span>
<span>To solve, we can use the substitution method. 
</span>
96 = l \times w\\96=(3w-2) \times w\\96=3w^{2}-2w\\3w^{2}-2w-96=0~~~~~~[now\ factor\ the\ equation]\\ (3w+16)(w-6)=0

3w+16=0\\3w=-16\\w= -\frac{16}{3}~~~~\Rightarrow~~~answer\ doesnt\ make\ sense\ , negative\ width.&#10;

w-6=0\\\boxed{w=6~~~~~~~\Rightarrow~~~~positive\ answer\ for\ width\ makes\ sense }&#10;

<span><em>So if our width is 6, Now substitute the value of w = 6 into equation 2 </em></span>

l=3w-2\\l=3(6)-2\\l=18-2\\l=16

So "w" = 6 and "l" = 16, and if we multiply them together, we get the correct area, 96. So our dimensions are 6 by 16.
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kathy uses a 1/2 cup of milk with every bowl of her favorite cereal if there are only 3 3/5 cups of milk left, then how many bow
Murrr4er [49]

Taking a quotient, we will see that she can make 7 bowls of cereal (and some leftover milk).

<h3>How many bowls of cereal would kathy have?</h3>

We know that for each bowl, she needs 1/2 cups of milk.

And we also know that she has a total of (3 + 3/5) cups of milk.

To know how many bowls she can make, we need to take the quotient between the total that she has and the amount that she needs for each bowl:

(3 + 3/5)/(1/2)

We can rewrite the total as:

3 + 3/5 = 15/5 + 3/5 = 18/5

Then the quotient becomes:

(18/5)/(1/2) = (18/5)*2 = 36/5 = 35/5 + 1/5 = 7 + 1/5

So she can make 7 bowls of cereal (and some leftover milk).

If you want to learn more about quotients:

brainly.com/question/629998

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6 0
2 years ago
The product of a number and -7 is 63
Oduvanchick [21]
-7n=63
n=-9 is your final answer. Hope it help!
3 0
3 years ago
NEED YOUR HELP ASAP!!!!
Akimi4 [234]

Answer:

Angel: 5 min; Jayden: 4 1/6 min or 4 minutes and 10 seconds

Step-by-step explanation:

4 0
3 years ago
What two numbers multiply to 54 and add up to 7
k0ka [10]
Xy = 54
x + y = 7

xy = 54
\frac{xy}{x} = \frac{54}{x}
y = \frac{54}{x}

x + y = 7
x + \frac{54}{x} = 7
\frac{x^{2}}{x} + \frac{54}{x} = 7
\frac{x^{2} + 54}{x} = 7
x^{2} + 54 = 7x
x^{2} - 7x + 54 = 0
x = \frac{-(-7) \± \sqrt{(-7)^{2} - 4(1)(54)}}{2(1)}
x = \frac{7 \± \sqrt{49 - 216}}{2}
x = \frac{7 \± \sqrt{-167}}{2}
x = \frac{7 \± i\sqrt{167}}{2}
x = \frac{7 \± 12.9i}{2}
x = 3.5 \± 6.45i
x = 3.5 + 6.45i    or    3.5 - 6.45i

                  x + y = 7
   3.5 + 6.45i + y = 7
- (3.5 + 6.45i)       - (3.5 + 6.45i)
                        y = 3.5 - 6.45i
                  (x, y) = (3.5 + 6.45i, (3.5 - 6.45i)

                          or

                  x + y = 7
   3.5 - 6.45i + y = 7
- (3.5 - 6.45i)     - (3.5 - 6.45i)
                       y = 3.5 + 6.45i
                 (x, y) = (3.5 - 6.45i, 3.5 + 6.45i)

The two numbers that add up to 7 and can multiply to 54 is 3.5 ± 6.45i.
5 0
3 years ago
Challenge in a company, 95% of the workers are men. If 270people work for the company who
Alexeev081 [22]

Answer:

5,400

Step-by-step explanation:

5% = 270

270 ÷ 5 = 54

54 × 100 = 5400

6 0
3 years ago
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