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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.

The length of each side of the sidewalk is 'x'= 126 m and '(158-x)'='(158-126)'=32 m

7 0

3 years ago

Eden has a part time job. She gets paid £7. 20 per hourthis week she worked for 18 1/2 hourswork out Eden's total pay for this w

Dafna1 [17]

Answer:

$133.20

Step-by-step explanation:

Since the amount of hours she worked isn't a whole number, we can first separate 18 and 1/2 and work the problem out one at a time.

1. Multiply 7.20 by 18 to get 129.60

2. Multiply 0.50 by 7.20 to get 3.60.

3. Add 129.60 and 3.60 together to get the answer, 133.20.

5 0

2 years ago

Jada was using square stickers that were 3/4in long to decorate the spine of a photo album. The spine is 10 and 1/2in long. If s

nevsk [136]

Answer:

13

Step-by-step explanation:

Given:

Square stickers that were 3/4 in long
The spine is 10 and 1/2 in long

If she laid the stickers side by side without gaps or overlaps so the number of sticker to cover the length of the spine:

$\frac{The length of the spine}{the length of the sticker}$

10 : $\frac{3}{4}$ ≈13

She needs 13 stickers cover the length of the spine

7 0

3 years ago

Read 2 more answers

if the first and third of three consecutive odd integers are added, the result is 63 less than five times the second integer. fi

ollegr [7]

The value of third consecutive odd is 23

• In Mathematics, algebra is a branch which only deals with symbols and the rule for the manipulation of these symbols. Algebra is divided into different sub branches such as advanced algebra, linear algebra, elementary algebra, abstract algebra etc.

• The basics of algebra contains numbers, variables, constants, expressions and equations. The basic four operations of algebra are addition, subtraction, multiplication, division.

Let the first consecutive odd integer be x

Second consecutive integer = x+2

Third consecutive integer = x+4

We are given that

First + third = 5(Second) – 63

x + x + 4 = 5 (x+2) -63

2x + 4 = 5x +10 -63

-3x = -57

3x = 57

x = 19

First Consecutive odd = 19

Second Consecutive odd = 21

Third Consecutive odd = 23

Learn more about algebra here

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5 0

2 years ago

Helppp plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Lynna [10]

Answer:

Jacob served 16 quarts of juice.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers