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Katyanochek1 [597]

3 years ago

6

It is worked out that 4 ladles full of soup each will feed 160 people. The customers have complained in the past that the portio

ns are too small. The cook decides to give 5 ladles full of soup to each person. How many people can now be fed soup?

1 answer:

polet [3.4K]3 years ago

7 0

160 people x 4 ladle/1 person = 640 ladles full
640 ladles x 1 person/5 ladles = 128 people fed

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2 tan 30°<br>II<br>1 + tan- 300

shusha [124]

Question:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$

Answer:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= sin(60^{\circ})$

Step-by-step explanation:

Given

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$

Required

Simplify

In trigonometry:

$tan(30^{\circ}) = \frac{1}{\sqrt{3}}$

So, the expression becomes:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2 * \frac{1}{\sqrt{3}}}{1 + (\frac{1}{\sqrt{3}})^2}$

Simplify the denominator

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2 * \frac{1}{\sqrt{3}}}{1 + \frac{1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{1 + \frac{1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{ \frac{3+1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{ \frac{4}{3}}$

Express the fraction as:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2}{\sqrt 3} / \frac{4}{3}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2}{\sqrt 3} * \frac{3}{4}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{1}{\sqrt 3} * \frac{3}{2}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3}{2\sqrt 3}$

Rationalize

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3}{2\sqrt 3} * \frac{\sqrt{3}}{\sqrt{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3\sqrt{3}}{2* 3}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\sqrt{3}}{2}$

In trigonometry:

$sin(60^{\circ}) = \frac{\sqrt{3}}{2}$

Hence:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= sin(60^{\circ})$

3 0

3 years ago

Hello please help help

irinina [24]

9514 1404 393

Answer:

48°

Step-by-step explanation:

ΔACB is isosceles, so angles A and B have the same measure. The measure of angle C in that triangle is ...

∠C = 180° -2(69°) = 42°

Angle C in ΔCDE has the same measure. Angle D is the complement of that:

∠D = 90° -42° = 48°

_____

The relations we used are ...

the sum of angles in a triangle is 180°
base angles of an isosceles triangle are congruent
vertical angles are congruent
acute angles in a right triangle are complementary

5 0

3 years ago

Please help I don’t know this and I’m sick

Tems11 [23]

Answer:

3xy=96 2y2-z2=12

Step-by-step explanation:

4 0

3 years ago

Find <br> 1. 7.75 ÷ 0.25<br> 2. 25.5 ÷ 3

oksano4ka [1.4K]

Answer:

31,

8.5

Step-by-step explanation:

1) 7.75/0.25 = (7.75×100)/(0.25×100)

= 775 ÷ 25

= 31

2) 25.5/3 = (25.5×10)/ (3×10) = 255÷30

= 8.5

I hope this was helpful, please mark as brainliest

8 0

3 years ago

Sophia paid $3,360 00 in taxes in 2010. Her taxes rose to $4,848.60 in 2011. What was the percentage increase (to the nearest wh

denis-greek [22]

Answer:

31%

Step-by-step explanation:

4848.60 - 3360.00=1488.00

6 0

3 years ago