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2 years ago

Determine the unknown angle measures, to the nearest degree, in the diagram provided.

Mathematics

1 answer:

serg [7]2 years ago

7 0

Answer:

a is 53.8°, and b is 36.2°

Step-by-step explanation:

Using sine trig rule:

${ \boxed{ \bf{ \sin(b) = \frac{opposite}{hypotenuse} }}}$

${ \tt{ \sin(b) = \frac{78}{132} }} \\ \\ { \tt{b = { \sin }^{ - 1}( \frac{78}{132} ) }} \\ \\ { \tt{b = 36.2 \degree}}$

Summation of angles of triangle:

${ \tt{a + b + 90 \degree = 180 \degree}} \\ { \tt{a + 36.2 \degree + 90 \degree = 180 \degree}} \\ { \tt{a = (180 - 36.2 - 90) \degree}} \\ { \tt{a = 53.8 \degree}}$

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which expressions represents a 20% discount off the price of an item that originally cost D dollars

Charra [1.4K]

Answer:

D - (D/5)

Step-by-step explanation:

Let's imagine that D equals 100 dollars -

Well, we know that to get 20% of an amount, we need to divide the amount by five. So let's do that -

100 / 5 = 20

We now know that 20% of 100 dollars is equal to 20 dollars. We have now finished the first part. On to the second part.

We now need to take away 20% of 100 dollars off of 100 dollars - this is the price of the item after the discount.

100 - 20 = 80 dollars.

We now fit in D instead of 100 dollars -

D - (D/5)

6 0

2 years ago

Read 2 more answers

Work out the time taken, in minutes, for a 68km journey at an average speed of 85km/h

vovikov84 [41]

Answer:

48 minutes

Step-by-step explanation: Time taken is distance divided by speed, so 68/85 is 0.8. 0.8 is equal to 4/5. 4/5 of an hour is 48 minutes.

4 0

2 years ago

Please help me!

dybincka [34]

Answer:

They are only equal on day 0, both having 10 population.

Step-by-step explanation:

Given the bacteria on the counter is initially measured at 5 and doubles every 3 days we can generate the following geometric equation:

$f(x)=10*2^{\frac{x}{3} }$

Given the bacteria on the stove is measured at 10 and doubles every 4 days we can create another equation:

$f(x)=10*2^{\frac{x}{4} }$

To find how many days it will take for the bacteria population to equal the same lets set both equations equal to eachother:

$10*2^{x/3}=10*2^{x/4}$

Divide both sides by 10

$2^{x/3}=2^{x/4}$

Since both exponents have the same base we can set the exponents equal to eachother and solve for x:

$\frac{x}{3}=\frac{x}{4}$

Multiply both sides by 3 to isolate x on the left side

$x=\frac{3x}{4}$

Multiply both sides by 4 to remove fraction

$4x=3x$

Subtract 3x to isolate x on the left side

$x=0$

Plug x into one of our original equations

$f(0)=10*2^{0/3}$

Solve

$f(0)=10$

6 0

1 year ago

I need help with this answer

Llana [10]

Answer:

Im not sure but lets play warzone

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

PLEASE HURRY AND HELP ...

Nonamiya [84]

Answer:

Volume= 35.257

Step-by-step explanation:

∙ x V cylinder = π r 2 h

here diameter = 3.25 ⇒ radius = 1.625 ⇒ volume = π × ( 1.625 ) 2 × 4.25× × × × ≈ 35.257 cubic inches

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2 years ago