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dexar [7]
3 years ago
6

HELPP!!!! 30 POINTS!!! Points A and B are on the different sides on line l, the distance between point A and the line l is 10 in

, the distance between point B and line l is 4in. What is the distance between the midpoint O of the segment AB and the line l?

Mathematics
1 answer:
Rom4ik [11]3 years ago
5 0

OC = 3 in

Refer to the attachment for complete explaination

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There is a L-shaped sidewalk that is 158 meters long. By cutting across the lawn, the
NikAS [45]

Answer:

Each side of the L-shaped sidewalk is 126 m and 32m respectively.

Step-by-step explanation:

Given:

Total length of the sidewalk = 158 meters

Cutting across the lawn the distance = 130 meters

The L-shaped lawn will be treated as a right angled triangle.

So the 130 m distance is the hypotenuse here.

Let one side of the L-shaped lawn be 'x' meter so the another side will be (158-x) meters.

Applying Pythagoras formula.

(Hypotenuse)^2=(height)^2+(base)^2

So,

⇒ (130)^2=x^2 +(158-x)^2

⇒ (130)^2=x^2+(158-x)(158-x)

⇒ 16900=x^2+24964-158x-158x+x^2

⇒ 16900 =2x^2-316x+24964

⇒ 2x^2+316x+24964-16900=0

⇒ 2x^2-316x+8064=0

⇒ x^2-158x+4032=0

Applying quadratic formula;

Quadratic formula : \frac{\pm b \sqrt{b^2-4ac} }{2a} where a=1 and b=-158 and c=4032

So the value of x= 126 and 32.

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4 years ago
Find the area and perimeter of a rectangle that has a length of (x + 24) and (x + 16). Show all work for full credit.
klio [65]

Answer:

Perimeter of rectangle = 4x + 80

Area = x² + 40x + 384

Step-by-step explanation:

Perimeter of rectangle = 2*(length + width)

                                      = 2* (x + 24 + x + 16)

                                      = 2*( x +x + 24 + 16)    {Combine like terms}

                                      = 2* (2x + 40)

Use Distributive property : a*(b +c) = a *b + a*c

                                     = 2*2x + 2*40

                                     = 4x + 80

Area of rectangle = length * width

                             = (x + 24) (x + 16) {use FOIL method}

                            = x*x + x*16 + 24*x + 24*16

                             = x² + 16x + 24x + 384  {Combine like terms}

                             = x² + 40x + 384

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