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3 years ago

The product of two consecutive odd numbers is 10 more than the square of the smaller number. Find the smaller number

Mathematics

1 answer:

True [87]3 years ago

8 0

Answer:

Step-by-step explanation:

let the consecutive odd numbers be n and n + 2 , then

n(n + 2) = n² + 10 , that is

n² + 2n = n² + 10 ( subtract n² from both sides )

2n = 10 ( divide both sides by 2 )

n = 5

That is the smaller number is 5

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A circular pool with a diameter of 18 ft will have a uniform 4 ft concrete walkway poured around it. If the concrete cost $4.25

zysi [14]

A circular pool with a diameter of 18 ft will have a uniform 4 ft concrete walkway poured around it. If the concrete cost $4.25 a square foot, how much will it cost for the concrete?

This can be solve be solving the area of walkway

Area of walkway is equal to = (pi)( 9 ft +4) ^2– (pi)(9ft)^2

= 276.46 sq ft

Cost = 276.46 sq ft * ($4.25 a square foot) = $1174.70

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3 years ago

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Select all the situations that can be represented by the tape diagram. 99 W W W W W 4 Clare buys 4 bouquets, each with the same

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Answer:

Third one 33333333333333333

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Urgent - Please help me with these questions!

Schach [20]

Answer:

1 thousand i think hope this helps!

Step-by-step explanation:

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3 years ago

Reggie has a rectangular piece of paper that is 12 inches long and 7 inches wide. He is going to cut the paper from corner to co

neonofarm [45]

A property from geometry states that rectangles have congruent opposite sides. Thus, no matter which diagonal Reggie cuts, it still has the same lengths. Since it's a rectangle and we cut from corner to corner, we create a right triangle. See the picture below:

___________12 inches_______

7 |

i |

n |

Because it's a rectangle, it won't matter which corner we cut. But if we fold at the cut lines, we would make an in the rectangle's center.

The cut line and two sides make a right triangle. One leg is 12, one leg is 7, and we need to find the third side. The Pythagorean Theorem - sum of the squares of the legs equals the square of the hypotenuse - is applied.

Let S = the length of the side from corner to corner

S² = 12² + 7²

S² = 144 + 49

S² = 193

S = √193 or -√193

Because we are dealing with lengths, we only want positive numbers. -√193 is not used. Thus S = √193

S = √193 = 13.8924439894

S = 18.92 (rounded to two places)

Thus, Reggie will cut 18.92 inches of paper.

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3 years ago

Which of these four sets of side lengths will form a right triangle? Set 1 4 cm, 5 cm, 6 cm Set 2 8 in., 12 in., 20 in. Set 3 10

Alenkasestr [34]

Answer: The correct option is (D) SET 4.

Step-by-step explanation: We are to select the correct set of side lengths that will form a right-angled triangle.

To form a right-angled triangle, we must have the following relation:

Perpendicular² + Base² = Hypotenuse².

Hypotenuse is the length of the largest side; perpendicular and base are the two legs of the triangle.

SET 1 : 14 cm, 5 cm, 6 cm.

We have

$5^2+6^2=25+36=61,\\\\14^2=196.$

Therefore,

Perpendicular² + Base² ≠ Hypotenuse².

So, this set will not form a right-angled triangle.

SET 2 : 8 in., 12 in., 20 in.

We have

$8^2+12^2=64+144=208,\\\\20^2=400.$

Therefore,

Perpendicular² + Base² ≠ Hypotenuse².

So, this set will not form a right-angled triangle.

SET 3 : 10 mm, 20 mm, 30 mm.

We have

$10^2+20^2=100+400=500,\\\\30^2=900.$

Therefore,

Perpendicular² + Base² ≠ Hypotenuse².

So, this set will not form a right-angled triangle.

SET 4 : 12 ft, 16 ft, 20 ft.

We have

$12^2+16^2=144+256=400,\\\\20^2=400.$

Therefore,

Perpendicular² + Base² = Hypotenuse².

So, this set will form a right-angled triangle.

Thus, the SET 4 will form a right-angles triangle.

Option (D) is correct.

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