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3 years ago

In the following equilateral triangle, each angle has a measure of 10x + 20. X=[? ]

Mathematics

2 answers:

maria [59]3 years ago

8 0

Answer:

4°

Step-by-step explanation:

All the angles in a triangle add together to equal 180°. We know there are three angles of 20° so let's subtract this.

20° × 3 = 60°

180° - 60° = 120°

Now well divide 120° up among the three angles.

120° ÷ 3 = 40°

Now we know the angles are 40° + 20°, but we need to find the value of x, so divide 40° by 10

40° ÷ 10 = 4°

x = 4°

Dafna1 [17]3 years ago

5 0

Answer:4

Step-by-step explanation: Since you know this triangle is an equilateral, you know all angles are the same, so you should automatically multiply 10x+20 by 3. You would then get 30x+60. Since all triangle's total angle sum is 180, you know to set 30x+60 to 180.

At this point this might seem new, but this is where you isolate x. First you move the 60, but subtracting it from both sides. This gets you 30x=120. You divide 30 on both sides and you finally get your answer: 4.

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For which function is f(x) equal to f^1(x) ( answer choices in picture )

Sonja [21]

Answer:

C. $f(x)=\frac{x+1}{x-1}$

Step-by-step explanation:

Let's find the inverse of each of the given options.

Option A:

$f(x)=\frac{x+6}{x-6}\\y=\frac{x+6}{x-6}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+6}{y-6}$

Rewrite in terms of 'y'. This gives,

$x(y-6)=y+6\\xy-6x=y+6\\xy-y=6x+6\\y=\frac{6x+6}{x-1}$

The given function $y=\frac{6x+6}{x-1}\ne y=\frac{x+6}{x-6}$

So, option A is incorrect.

Option B:

$f(x)=\frac{x+2}{x-2}\\y=\frac{x+2}{x-2}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+2}{y-2}$

Rewrite in terms of 'y'. This gives,

$x(y-2)=y+2\\xy-2x=y+2\\xy-y=2x+2\\y=\frac{2x+2}{x-1}$

The given function $y=\frac{2x+2}{x-1}\ne y=\frac{x+2}{x-2}$

So, option B is incorrect.

Option C:

$f(x)=\frac{x+1}{x-1}\\y=\frac{x+1}{x-1}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+1}{y-1}$

Rewrite in terms of 'y'. This gives,

$x(y-1)=y+1\\xy-x=y+1\\xy-y=x+1\\y=\frac{x+1}{x-1}$

The given function $y=\frac{x+1}{x-1}\ equals\ y=\frac{x+1}{x-1}$

So, option C is correct.

Option D:

$f(x)=\frac{x+5}{x-5}\\y=\frac{x+5}{x-5}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+5}{y-5}$

Rewrite in terms of 'y'. This gives,

$x(y-5)=y+5\\xy-5x=y+5\\xy-y=5x+5\\y=\frac{5x+5}{x-1}$

The given function $y=\frac{5x+5}{x-1}\ne y=\frac{x+6}{x-6}$

So, option D is incorrect.

Therefore, only option C is correct.

7 0

3 years ago

Solve for x: 3x+7 = 22 *

Lorico [155]

3x+7=22
Subtract 7 to both sides
3x=15
Divide by 3
x=5

4 0

3 years ago

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A child standing on a river bank ten feet above the river throws a toward the river at a speed of 12 feet per second . How long

Anastasy [175]

sure just give me head

8 0

2 years ago

24 inches is 250% of what length

Alinara [238K]

The answer is: " 9.6 inches " .
________________________________________________________
Explanation:
________________________________________________________

24 = 250/100 * x ;

24 = 2.5 x ;

↔ 2.5 x = 24 ;

2.5 x / 2.5 = 24/ 2.5 ;

x = 9.6 ;

The answer is: " 9.6 inches <span>" .
</span>_________________________________________________________

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tigry1 [53]

Answer:

The answer would be 20.05 hours per day.

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