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2 years ago

Solve the following equation. Then place the correct number in the box provided.

Mathematics

1 answer:

Alex Ar [27]2 years ago

3 0

Answer:

x ≤ 6

Step-by-step explanation:

2x-1 ≤ x+5

Subtract x from each side

2x-x-1 ≤ x-x+5

x-1 ≤ 5

Add 1 to each side

x-1+1 ≤ 5+1

x ≤ 6

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3 x 5 x 8 =15 x 8 = 120

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At 3pm, the length of the shadow of a thin vertical pole standing on level ground is the same as the height of the pole. A while

aliya0001 [1]

Answer: The height of the pole is 175.97 ( approx )

Step-by-step explanation:

Let the height of the pole is x cm,

Also, let the angle of elevation of the sun to the pole at 3 pm is $\theta$

Thus, by the question,

$tan\theta = \frac{\text{ The height of the pole}}{\text{ The height of the shadow}}$

$\implies tan\theta = \frac{x}{x}$ ( at 3pm the height of shadow = height of the pole)

$\implies tan\theta = 1$

$\implies \theta = 45^{\circ}$

Again, according to the question,

When the angle of elevation is $(\theta - 12^{\circ})$ ,

The height of shadow = x + 95,

$\implies tan(45-12)^{\circ}=\frac{x}{x+95}$

$\implies tan 33^{\circ}=\frac{x}{x+95}$

$\implies tan 33^{\circ}x + 95\times tan33^{\circ}=x$

$\implies tan 33^{\circ}x - x = - 95\times tan33^{\circ}$

$\implies -0.3505924068 x = - 61.6937213538$

$x=175.969930202\approx 175.97\text{ cm}$

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2 years ago

Scientist A dissolved 1.0 kilogram of salt in 3.0 liters of water. Scientist B dissolved 20 pounds of salt in 7.0 pints of water

Lilit [14]

scientist A dissolved 1 kg of salt in 3 litres.

scientist B dissolved 20 pounds of slat in 7 pint of water.

we know that 1 pound =0.543 g

20 pounds=9.07 kg.

1 pint=0.5 litres

so 7 pints =3.5 litres

so dissoving 1 kg of salt in 3 litres of water and 9.07 kg in 3.5 litres of water

we know that for concentration kg/l units is used .

for A= 1/3=0.33kg/l

and B=9.07/3.5=2.59 kg/l.

so scientist A has prepared more concentrated solution .

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