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3 years ago

X=The measure of the exterior angle of the triangle is:

Mathematics

2 answers:

Mrac [35]3 years ago

6 0

Step-by-step explanation:

We know that

$\sf \hookrightarrow \: \boxed{ \sf \: sum \: of \: two \: interior \: angles = exterior \: angle} \\ \sf \hookrightarrow \: 50 + x = 3x - 54 \\ \sf \hookrightarrow \: x - 3x = - 54 - 50 \\ \sf \hookrightarrow \: - 2x = - 104 \\ \sf \hookrightarrow \: 2x = 104 \\ \sf \hookrightarrow \: x = \frac{104}{2} \\ \sf \hookrightarrow \: x = 52$

aniked [119]3 years ago

6 0

Answer:

x= 52

exterior =102

Step-by-step explanation:

50+x=3x-54

50+54=3x-×

104=2x

52=x

3(52)-54

156-54=102

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Step-by-step explanation:

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3 years ago

find the values of the six trigonometric functions for angle theta in standard position if a point with the coordinates (1, -8)

frutty [35]

Answer:

cosФ = $\frac{1}{\sqrt{65}}$ , sinФ = $-\frac{8}{\sqrt{65}}$ , tanФ = -8, secФ = $\sqrt{65}$ , cscФ = $-\frac{\sqrt{65}}{8}$ , cotФ = $-\frac{1}{8}$

Step-by-step explanation:

If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:

cosФ = $\frac{x}{r}$
sinФ = $\frac{y}{r}$
tanФ = $\frac{y}{x}$
secФ = $\frac{r}{x}$
cscФ = $\frac{r}{y}$
cotФ = $\frac{x}{y}$

Where r = $\sqrt{x^{2}+y^{2} }$ (the length of the terminal side from the origin to point (x, y)

You should find the quadrant of (x, y) to adjust the sign of each function

∵ Point (1, -8) lies on the terminal side of angle Ф in standard position

∵ x is positive and y is negative

→ That means the point lies on the 4th quadrant

∴ Angle Ф is on the 4th quadrant

∵ In the 4th quadrant cosФ and secФ only have positive values

∴ sinФ, secФ, tanФ, and cotФ have negative values

→ let us find r

∵ r = $\sqrt{x^{2}+y^{2} }$

∵ x = 1 and y = -8

∴ r = $\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}$

→ Use the rules above to find the six trigonometric functions of Ф

∵ cosФ = $\frac{x}{r}$

∴ cosФ = $\frac{1}{\sqrt{65}}$

∵ sinФ = $\frac{y}{r}$

∴ sinФ = $-\frac{8}{\sqrt{65}}$

∵ tanФ = $\frac{y}{x}$

∴ tanФ = $-\frac{8}{1}$ = -8

∵ secФ = $\frac{r}{x}$

∴ secФ = $\frac{\sqrt{65}}{1}$ = $\sqrt{65}$

∵ cscФ = $\frac{r}{y}$

∴ cscФ = $-\frac{\sqrt{65}}{8}$

∵ cotФ = $\frac{x}{y}$

∴ cotФ = $-\frac{1}{8}$

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2 years ago

Jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. The area of the smalle

bulgar [2K]

Answer:

20 x 20 feet

Step-by-step explanation:

First I just drew out two squares, one was the first un-cut square and the second is the cut one. Since we know that the area of the smaller square is 144, and Area is just side^2 , we know that all the sides of the smaller square are 12. Now, all we have to do is add 8 to 12 to get the original lawn. The original lawn was a 20 x 20 ft lawn.

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2 years ago

In a list of numbers, the pattern increases by 0.001 as you move to the right. If the third number in the list is 0.064, what is

avanturin [10]

The <em>correct answer</em> is:

The first number is 0.062.

Explanation:

Let x represent the first number in the list.

We add 0.001 to each number to find the next number; this gives us:

x + 0.001 + 0.001 = 0.064

Combining like terms, we have:

x + 0.002 = 0.064

Subtract 0.002 from each side:

x + 0.002 - 0.002 = 0.064 - 0.002

x = 0.062

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2 years ago

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Which of following not a way to represent the solution of inequality 5(x + 2) GREATER THAN OR EQUAL TO 7x + 2(x − 1)?

mixer [17]

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3 years ago

Read 2 more answers

X=The measure of the exterior angle of the triangle is:​

X=The measure of the exterior angle of the triangle is: