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3 years ago

A triangle has sides with lengths of 72 millimeters, 90 millimeters, and 54 millimeters. Is it a right triangle?

Mathematics

1 answer:

Travka [436]3 years ago

7 0

Answer:

Yes, it is a right triangle.

Step-by-step explanation:

a^2+b^2=c^2

The longest side is the hypotenuse so c^2 would be 90.

72^2+54^2=90^2

72 and 54 can be either a or b.

Solve for all exponents: 5184+2916=8100.

That equation is true, so the triangle is a right triangle.

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Please help me. The original blueprint of the Moreno’s’ living room has a scale of 2 inches= 5 feet. The family wants to use a n

Svetradugi [14.3K]

Answer:

Part a) The scale of the new blueprint is $\frac{5}{8} \frac{in}{ft}$

Part b) The width of the living room in the new blueprint is $9.4\ in$

Step-by-step explanation:

we know that

The scale of the original blueprint is

$\frac{2}{5}\frac{in}{ft}$

and

the width of the living room on the original blueprint is 6 inches

<em>Find the actual width of the living room, using proportion</em>

$\frac{2}{5}\frac{in}{ft}=\frac{6}{x}\frac{in}{ft}\\ \\x=5*6/2\\ \\x=15\ ft$

<em>Find the actual length of the living room, using proportion</em>

$\frac{2}{5}\frac{in}{ft}=\frac{9.6}{x}\frac{in}{ft}\\ \\x=5*9.6/2\\ \\x=24\ ft$

<em>Find the scale of the new blueprint</em>, divide the length of the living room on the new blueprint by the actual length of the living room

$\frac{15}{24} \frac{in}{ft}$

simplify

$\frac{5}{8} \frac{in}{ft}$

<em>Find the width of the living room in the new blueprint, using proportion</em>

$\frac{5}{8}\frac{in}{ft}=\frac{x}{15}\frac{in}{ft}\\ \\x=15*5/8\\ \\x=9.4\ in$

3 0

3 years ago

a dock is 5 feet above water. suppose you stand on the edge of the dock and pull a rope to a boat at a constant rate of 2 ft/s.

Firdavs [7]

Answer:

The boat is approaching the dock at a speed of 3.20 ft/s when it is 4 feet from the dock.

Step-by-step explanation:

The diagram of the situation described is shown in the attached image.

The distance of the boat to the dock along the water level at any time is x

The distance from the person on the dock to the boat at any time is y

The height of the dock is 5 ft.

These 3 dimensions form a right angle triangle at any time with y being the hypotenuse side.

According to Pythagoras' theorem

y² = x² + 5²

y² = x² + 25

(d/dt) y² = (d/dt) (x² + 5²)

2y (dy/dt) = 2x (dx/dt) + 0

2y (dy/dt) = 2x (dx/dt)

When the boat is 4 ft from dock, that is x = 4 ft,

The boat is being pulled at a speed of 2 ft/s, that is, (dy/dt) = 2 ft/s

The speed with which the boat is approaching the dock = (dx/dt)

Since we are asked to find the speed with which the boat is approaching the dock when the boat is 4 ft from the dock

When the boat is 4 ft from the dock, x = 4 ft.

And we can obtain y at that point.

y² = x² + 5²

y² = 4² + 5² = 16 + 25 = 41

y = 6.40 ft.

So, to the differential equation relation

2y (dy/dt) = 2x (dx/dt)

when x = 4 ft,

y = 6.40 ft

(dy/dt) = 2 ft/s

(dx/dt) = ?

2 × 6.40 × 2 = 2 × 4 × (dx/dt)

25.6 = 8 (dx/dt)

(dx/dt) = (25.6/8) = 3.20 ft/s.

Hope this Helps!!!

4 0

3 years ago

store A offers successive discounts of 10% one week and 20% the second week. store B offers a one-time discount of 25% the secon

11111nata11111 [884]

The store which offers the greater discount is store B.

<h3>Discount</h3>

Store A:

First week = 10%

= 10/100

= 0.1

Second week = 20%

= 20/100

= 0.2

Total discount = (0.1 + 0.2) / 2

= 0.15

Store B:

25%

= 25/100

= 0.25

Therefore, the store which offers the greater discount is store B.

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7 0

2 years ago

A triangle has the dimensions shown. The perimeter of

exis [7]

Answer:

A. linear expression

Step-by-step explanation:

Just got it right on the test.

4 0

3 years ago

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Which of these sequences is a geometric sequence?

podryga [215]

3, 9, 27, 81, 343, 729, … is a geometric sequence because each term is obtained by multiplying 3 to the preceding term.

7 0

3 years ago

Read 2 more answers