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3 years ago

In a right triangle, Sin (30 + x) º = Cos (3x) º. What is the value of x?

Mathematics

1 answer:

pogonyaev3 years ago

5 0

Answer:

$x=15^\circ$

Step-by-step explanation:

In a right triangle:

$\sin \theta =cos(90^\circ-\theta) $ (Complementary angles)$

Therefore, given:

$Sin (30 + x) \º = Cos (3x) \º\\30+x+3x=90^\circ\\30+4x=90^\circ\\4x=90^\circ-30^\circ\\4x=60^\circ\\$Divide both sides by 4\\x=15^\circ$

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Xsquared+11x+28+xsquared+13x+40

UNO [17]

X² + 11x + 28 + x² + 13x + 40

combine like terms

x² + x² = 2x²
11x + 13x = 24x
28 + 40 = 68

2x² + 24x + 68 is your answer

if you want it simplified:

2(x² + 12x + 34)

hope this helps

5 0

3 years ago

The accompanying table shows the value of a car over time that was purchased for 14000 dollars, where x is years and y is the va

dimaraw [331]

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3 years ago

Ken paid for $12 for two magazines. The cost of each magazine was a multiple of 3. What is Mare the possible prices of the magaz

Artist 52 [7]

Answer:

So the possibilities are

$12 and $ 0 , $9 and $ 3 , $6 and $6

Step-by-step explanation:

Given:

Total Magazines = 2

Price = $ 12

To Find:

Possible Prices of magazines = ?

Solution:

As it is given that Prices of magazines is multiples of 3

Multiples of 3 up till 12 are

0, 3 , 6 , 9 , 12

Now

Total Price of magazine is $12

Now The possible prices of the magazines are

First Possibility:

If price of first magazine is $12 then second would be $0 (free)

First possible price $12 and $0

Second Possibility:

If price of first magazine is $9 then second would be $3

Second possible price $3 and $9

Third Possibility:

If price of first magazine is $6 then second would be $6

Third possible price $6 and $6

So the possibilities are

$12 and $ 0 , $9 and $ 3 , $6 and $6

8 0

3 years ago

Verify the identity. 4 csc 2x = 2 csc2x tan x

vlada-n [284]

Step-by-step explanation:

$4csc(2x) = 2csc^2(x) tan(x)$

We start with Left hand side

We know that csc(x) = 1/ sin(x)

So csc(2x) is replaced by 1/sin(2x)

$4 \frac{1}{sin(2x)}$

Also we use identity

sin(2x) = 2 sin(x) cos(x)

$4 \frac{1}{2sin(x)cos(x)}$

4 divide by 2 is 2

Now we multiply top and bottom by sin(x) because we need tan(x) in our answer

$2\frac{1*sin(x)}{sin(x)cos(x)*sin(x)}$

$2\frac{sin(x)}{sin^2(x)cos(x)}$

$2\frac{1}{sin^2(x)} \frac{sin(x)}{cos(x)}$

We know that sinx/ cosx = tan(x)

Also 1/ sin(x)= csc(x)

so it becomes 2csc^2(x) tan(x) , Right hand side

Hence verified

6 0

3 years ago

The graph of the piecewise function f(x) is shown.

NeTakaya

Answer:

{f(x) | -∞ < f(x) ≤ 4 }

Step-by-step explanation:

The range is made up of the y values. Remember f(x) = y

In this graph the least value of y is -∞ and the greatest value of y is 4

So, the range is {f(x) | -∞ < f(x) ≤ 4 } which is the 2nd choice

4 0

3 years ago