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3241004551 [841]
3 years ago
8

Edmond doubled the width of the crate. How do the perimeter and the area of the floor of the new crate compare to those of the o

riginal crate? Original:length = 1.2 metres width = 0.8 metres
Mathematics
1 answer:
Mariana [72]3 years ago
7 0

Answer:

The area would be doubled also

The perimeter will be increased in a factor of 1.4

Step-by-step explanation:

Originally the area of new crate = L * B = 1.2 * 0.8 = 0.96 m^2

perimeter is 2(L+ B) = 2(1.2 + 0.8) = 4 m

Now let’s double the width , it becomes 0.8 * 2 = 1.6 m

Area would be 1.6 * 1.2 = 1.92 m^2 which is two times the previous area

The increased perimeter will be 2(1.6 + 1.2) = 5.6 m

This is an increase in factor of 1.4

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Using a graphing utility, find the exact solutions of the system. Round to the nearest hundredth and choose a solution to the sy
Margaret [11]

Answer:

Part 1) The exact solutions are

(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})   and  (\frac{-1-\sqrt{21}} {2},4-\sqrt{21})

Part 2) (1.79, 8.58)

Step-by-step explanation:

we have

y=x^{2} +3x ----> equation A

y=2x+5 ----> equation B

we know that

When solving the system of equations by graphing, the solution of the system is the intersection points both graphs

<em>Find the exact solutions of the system</em>

equate equation A and equation B

x^{2} +3x=2x+5\\x^{2} +3x-2x-5=0\\x^{2} +x-5=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

x^{2} +x-5=0  

so

a=1\\b=1\\c=-5

substitute in the formula

x=\frac{-1\pm\sqrt{1^{2}-4(1)(-5)}} {2(1)}

x=\frac{-1\pm\sqrt{21}} {2}

so

The solutions are

x_1=\frac{-1+\sqrt{21}} {2}

x_2=\frac{-1-\sqrt{21}} {2}

<em>Find the values of y</em>

<em>First solution</em>

For x_1=\frac{-1+\sqrt{21}} {2}

y=2(\frac{-1+\sqrt{21}} {2})+5

y=-1+\sqrt{21}+5\\\\y=4+\sqrt{21}

The first solution is the point (\frac{-1+\sqrt{21}} {2},4+\sqrt{21})

<em>Second solution</em>

For x_2=\frac{-1-\sqrt{21}} {2}

y=2(\frac{-1-\sqrt{21}} {2})+5

y=-1-\sqrt{21}+5\\\\y=4-\sqrt{21}

The second solution is the point (\frac{-1-\sqrt{21}} {2},4-\sqrt{21})

Round to the nearest hundredth

<em>First solution </em>

(\frac{-1+\sqrt{21}} {2},4+\sqrt{21}) -----> (1.79,8.58)

(\frac{-1-\sqrt{21}} {2},4-\sqrt{21}) -----> (-2.79,-0.58)

see the attached figure to better understand the problem

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