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2 years ago

What is the length of YZ in XYZ

Mathematics

1 answer:

Studentka2010 [4]2 years ago

3 0

AZ=12 - is hypotenuse

∠XZY=30° ⇒

$XY=\dfrac{1}{2} \times12=6$

$\text{By the Pythagorean theorem}\\YZ=\sqrt{12^2-6^2} =\sqrt{(12-6)(12+6)} =\sqrt{6\times18} =\sqrt{108} =6\sqrt{3}$

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How to solve the problem

Mice21 [21]

Answer:

Step-by-step explanation:

PEMDAS

6 + (3^3) ÷ 9

6 + [(27) ÷ 9]

6 + [ 3 ]

= 9

5 0

2 years ago

£440 is divided between David, Mark & Henry so that David gets twice as much as Mark, and Mark gets three times as much as H

Lesechka [4]

Mark received £ 132

Solution:

Given that £440 is divided between David, Mark & Henry

Let "d" be the share of david

Let "m" be the share of mark

Let "h" be the share of henry

Total amount is 440

Therefore,

share of david + share of mark + share of henry = 440

d + m + h = 440 ------- eqn 1

David gets twice as much as Mark

d = 2m ----- eqn 2

Mark gets three times as much as Henry

m = 3h

$h = \frac{m}{3}$ ------ eqn 3

Substitute eqn 2 and eqn 3 in eqn 1

$2m + m + \frac{m}{3} = 440\\\\\frac{6m + 3m + m}{3} = 440\\\\10m = 1320\\\\m = 132$

Thus Mark received £ 132

8 0

3 years ago

A private airplane leaves an airport and flies due east at 192 km/hr. Two hours later, a jet leaves the same airport and flies d

elixir [45]

The answer is 0.5 hours.

A velocity (v) of an object is a distance (d) divided by time (t):
v = d ÷ t ⇒ t = d ÷ v

It is given:
v1 = 192 km/h
v2 = 960 km/h
t1 - t2 = 2h
We need to calculate t2.

Since they will travel the same distance before the jet overtakes the plane, we can say that d1 = d2 = d

Now, let's express t1 and t2:
t1 = d/192
t2 = d/960

Therefore: d/192 - d/960 = 2
The least common denominator is 960, so:
5d/960 - d/960 = 2
4d/960 = 2
4d = 2 · 960
4d = 1920
d = 1920 ÷ 4 = 480 km

Now t2 = d/960 = 480/960 = 0.5 hours.

5 0

3 years ago

Hola me podrían ayudar por favor. Convertir las fracciones a decimales y ubicar a los decimales en la recta numérica. a. 2/3 b.

NISA [10]

Answer:

Step-by-step explanation:

a decimal

2/3 = 0.7

8/5 = 1.6

-5/2 = -2.5

7/4 = 1.8

9/2 = 4.5

-11/3 = -3.7

13/5 = 2.6

-7/4 = -1.8

Esto es solo un bosquejo del número, usando un gráfico, use 0.1 para una unidad en la recta numérica.

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-5 -4 -3.7 -3 -2.5 -2 -1.8 -1 0 0.7 1 1.6 1.8 2 2.6 3 4 4.5 5

8 0

2 years ago

Select all the equations that have the same solution as the equation 3x−12=24

evablogger [386]

Answer:

3x=36, so x=12

Step-by-step explanation:

5 0

2 years ago