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3 years ago

Please show your work with each expression. Simplify.

Mathematics

1 answer:

Alina [70]3 years ago

6 0

(replace the variables) 6(9)-2(5)^2
(simplified) 54-10^2.... 54-100=-46

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Find the standard deviation of 36,18,12,10 and 9

babunello [35]

The standard deviation of 36,18,12,10 and 9 is 10

6 0

3 years ago

arlik [135]

Given:

In a right angle triangle θ is an acute angle and $\tan\theta =\dfrac{3}{5}$ .

To find:

The value of $\cos \theta$ .

Solution:

In a right angle triangle,

$\tan \theta=\dfrac{Perpendicular}{Base}$

We have,

$\tan\theta =\dfrac{3}{5}$

It means the ratio of perpendicular to base is 3:5. Let 3x be the perpendicular and 5x be the base.

By using Pythagoras theorem,

$Hypotenuse=\sqrt{Perpendicular^2+base^2}$

$Hypotenuse=\sqrt{(3x)^2+(5x)^2}$

$Hypotenuse=\sqrt{9x^2+25x^2}$

$Hypotenuse=\sqrt{34x^2}$

$Hypotenuse=x\sqrt{34}$

In a right angle triangle,

$\cos \theta=\dfrac{Base}{Hypotenuse}$

$\cos \theta=\dfrac{5x}{x\sqrt{34}}$

$\cos \theta=\dfrac{5}{\sqrt{34}}$

Therefore, the value of $\cos \theta$ is $\dfrac{5}{\sqrt{34}}$ .

8 0

2 years ago

Two gift shops sell postcards. Each gift shop charges a fixed amount per postcard. The prices, in cents, for different numbers o

Snowcat [4.5K]

1st gift shop:

120/4 = 30 cents each

180/6 = 30 cents each

390/13 = 30 cents each

2nd gift shop:

204/7 = 29.14 cents each

192/8 = 24 cents each

270 /9 = 30 cents each

360/10 = 36 cents each

so if both gift shops have a fixed price then the 9 post cards would be the answer since it matches 30 each like the 1st gift store

5 0

3 years ago

The diagram shows a square.

frosja888 [35]

Answer:

3.5 cm

Step-by-step explanation:

6x -1 = 4x + 6

2x = 7

x = 3.5

6 0

3 years ago

Gary earns $12 an hour plus $16 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week

hoa [83]

Part A.

Amount of money earned = Regular rate per hour * Number of working hours

M = 12 x

Part B.

Amount of wages earned = Regular rate per hour * Maximum number of regular working hours + Overtime rate per hour * Excess working hours

T = 12 * 30 + 16 * y

T = 360 + 16 y

T = 16 y + 360

Part C.

Given T = 408, find y:

408 = 16 y + 360

y = 3 hrs

Therefore the total hours Gary worked that week is,

<span>(x = 30 since that is the maximum limit for regular working hours)</span>

7 0

3 years ago