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3 years ago

Is it possible to construct a triangle with the given lengths? 17, 37, 53

Mathematics

1 answer:

kvv77 [185]3 years ago

7 0

Answer:

Yes

Step-by-step explanation:

In any triangle, the sum of any two sides must be larger than the third side. To test this, we only actually need to pick the two shorter sides. In this case, the following inequality is true:

$17+37>53,\\54>53,\\\text{True}\:\checkmark$

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Find the dimensions of the rectangular corral producing the greatest enclosed area given 320 feet of fencing. (Assume that the l

jenyasd209 [6]

Answer:

The dimensions of the rectangular corral producing the greatest enclosed area is a square of 80 ft x 80 ft

Step-by-step explanation:

Let

x -----> the length of the rectangular corral in feet

y -----> the width of the rectangular corral in feet

we know that

The area of the rectangular corral is equal to

$A=xy$ -----> equation A

The perimeter of the rectangular corral is equal to

$P=2(x+y)$

$P=320\ ft$

$320=2(x+y)$

Simplify

$160=(x+y)$

$y=160-x$ -----> equation B

substitute equation B in equation A

$A=x(160-x)$

$A=-x^2+160x$

This is a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex represent the length for the maximum area

The y-coordinate of the vertex represent the maximum area

Convert the quadratic equation in vertex form

$A=-x^2+160x$

Factor -1

$A=-(x^2-160x)$

Complete the square

$A=-(x^2-160x+80^2)+80^2$

$A=-(x^2-160x+80^2)+6,400$

Rewrite as perfect squares

$A=-(x-80)^2+6,400$

The vertex is the point (80,6,400)

$x=80\ ft$

The maximum area is 6,400 ft^2

Find the value of y

$y=160-x$ ----> $y=160-80=80\ ft$

therefore

The dimensions of the rectangular corral producing the greatest enclosed area is a square of 80 ft x 80 ft

4 0

3 years ago

Jenny bought a wok for £9.60 in a 20% off sale. What was the price of the wok before the sale?

emmasim [6.3K]

Answer:

£12

Step-by-step explanation:

9.60 = 80% times y.

9.60 = 0.8y

Then, divide each side by 0.8 to get the equation in shape to solve for y.

y = 9.60/0.8

y=12

4 0

4 years ago

The Ratio of two numbers is 3/5, and their sum is 104. What are the 2 numbers?

Rom4ik [11]

Answer:

39 and 65

Step-by-step explanation:

the ratio of the two numbers is 3 : 5

sum the parts of the ratio, 3 + 5 = 8 parts

divide the sum by 8 to find the value of one part of the ratio

104 ÷ 8 = 13 ← value of 1 part of the ratio , then

3 parts = 3 × 13 = 39

5 parts = 5 × 13 = 65

the two numbers are 39 and 65

4 0

2 years ago

A trader needs $300000 to improve her business, she deposits $110000 in her savings account at 5% per annum compound interest. s

katrin [286]

interpret it that there are three payments of 50,000 aside from the current deposit of 110,000

amount after 3 years

= 110,000(1.05)^3 + 50,000( 1.05^3 - 1)/.05

4 0

3 years ago

Direction: Transform each pair of equations into slope-interaction form (y=mx + b) and identify slope (m) and y-intercept (b). W

Lunna [17]

Answer:

will I write the answer in the copy and show you

7 0

3 years ago

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