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USPshnik [31]
3 years ago
9

Find the distance of the line segment joining the two points (-4 /2 - /12) and (/32, 2/3)

Mathematics
1 answer:
astraxan [27]3 years ago
3 0

Answer: 4\sqrt{3} .

Step-by-step explanation:

Distance formula : Distance between points (a,b) and (c,d) is given by :-

D=\sqrt{(d-b)^2+(b-a)^2}

Distance between points (-4\sqrt{2},\sqrt{12}) \text{ and }(-\sqrt{32}, 2\sqrt{3}).

D=\sqrt{(2\sqrt{3}-(-\sqrt{12}))^2+(-\sqrt{32}-(-4\sqrt{2}))}\\\\=\sqrt{(2\sqrt{3}+\sqrt{2\times2\times3})^2+(-\sqrt{4\times4\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}-\sqrt{2^2\times3})^2+(-\sqrt{4^2\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}+2\sqrt{3})^2+(-4\sqrt{2}+4\sqrt{2})^2}\\\\=\sqrt{(4\sqrt{3})^2+0}\\\\=4\sqrt{3}\text{ units}

Hence, the correct option is 4\sqrt{3} .

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A rectangular bedroom has an area of 117 ft. the length of the bedroom is 4ft more than the width. find the length and the width
MrMuchimi

Answer: Length = 13 ft. , Width = 9 ft.

Step-by-step explanation:

Rectangle area = Length x width

Area = 117 ft.

Length = x + 4

Width = x

To solve

(x)(x + 4) = 117

x^2 + 4x = 117

x^2 + 4x - 117 = 0

(x - 9)(x + 13)

x = 9, -13

x = 9 <em>(measurement cannot be negative)</em>

Length

x + 4

9 + 4 = 13

5 0
2 years ago
A heating pad takes 8,827 Watts during each time it is turned on. If you only use it for 43 minutes, how much CO2 was created? R
devlian [24]

Answer:

6.3 Kwhr

Step-by-step explanation:

Given :

Power = 8827 watts

Time in minutes = 43 minutes

To obtain the amount of CO2 that was created :, which is the energy :

Recall

Energy = power * time

Energy in kw/hr = (8827/100) * (43/60)

Energy = 8.827 * 0.7166666

Energy = 6.326 Kwhr

3 0
2 years ago
The vertex of the parabola below is at the point (1,3), and the point (2,6) is
Inessa05 [86]

Answer:

B. y=3(x-1)2 + 3

Step-by-step explanation:

Given that

vertex of the parabola is at the point (1,3)

let's verify, if the option B is the correct equation of the parabola.

y=3(x-1)^2 + 3\\ \\y=3(x^2+1-2x) + 3\\\\y=3x^2+3-6x + 3\\\\y=3x^2-6x + 6....Eq1

comparing to standard equationof parabola (standard quadratic equation), we get

a=3, b=-6 and c=6

to find the vertex we use formula for x- coordinate as x=-b/2a

x=-(-6)/2(3)\\\\x=6/6\\x=1

to find y put x=1 in the Eq1, we get

y=3(1)^2-6(1)+6\\\\y=3-6+6\\\\y=3

vertex =(x,y) = (1, 3)

thus vertex of the parabola from the equation y=3(x-1)2 + 3 is (1,3), thus verified

7 0
2 years ago
Write the interval notation<br>the domain of the INVERSE<br>of the function shown​
alukav5142 [94]

Answer:

insta

Step-by-step explanation:

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6 0
2 years ago
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A bakery sells pie slices that are 1/6 of a pie. If they made 18 pies today.How many slices of pie will they have?
Lera25 [3.4K]

Answer:

108 slices

Step-by-step explanation:

One pie is 6 slices so 6*18 is equal to 108

4 0
2 years ago
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